POWER CONVERTER AND DETECTION METHOD

Abstract

A power converter including: a frequency feedback unit configured to apply a transfer function to a frequency, and apply restriction to obtain a processing result; an addition unit configured to add a first amplitude command value related to the voltage at the interconnection point and the processing result, to output a second amplitude command value; an interconnection point voltage amplitude control unit configured to generate an inverter output voltage amplitude command value, based on the second amplitude command value and the voltage at the interconnection point; a voltage output unit configured to generate a three-phase AC voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; and an islanding operation detection unit configured to detect an islanding operation state. The transfer function includes a second-order polynomial and a first-order monomial of a Laplace operator in a denominator and a numerator thereof.

Description

BACKGROUND

Technical Field

The present disclosure relates to a power converter that operates while interconnected with a power system. In particular, the present disclosure relates to the power converter including a function of detecting, in a case of transition to an islanding operation state in which the device is separated from the system during operation, the state.

Description of the Related Art

In recent years, the percentage of inverter power supplies has been increased by increasing renewable energy in power systems, but existing current control inverters are lack of inertia force, and thus there is concern that further increase of the percentage of the inverter power supplies causes a frequency to easily change, resulting in system instability.

As a solution for this issue, an inverter that performs virtual synchronous generator (VSG) control for a function as a synchronous generator is expected. (Japanese Patent No. 4846450, IEEE Journal, Vol. 141 No. 11, 2021, Yushi Miura “Virtual Synchronous Generator Control of Inverters for Lack of Inertia of Power System”, Toyokuni Kato, Chihiro Okado, Hitoshi Ito, Masafumi Kokenawa, Shigeo Nomiya “Development of Islanding Operation Detection Device for Synchronous Generator,” the transactions of the Institute of Electrical Engineers of Japan. B, No. 7/8, volume 94120 (2000), issues 8 to 9)

Not only an inverter power supply but also a power generation facility interconnected with a system is required to quickly detect, in a case of transition to an islanding operation state where the facility is separated from a system power supply, the state, and cut off power supply to a partial system.

An inverter that performs VSG control fails to detect islanding operation by using a frequency shift method assuming use of PLL used frequently in normal current control inverters, and the like.

A first aspect of the disclosure has been made in view of such a situation, and a first objective of the first aspect is to provide a power converter that can, when the power converter including virtual synchronous generator control has transitioned to an islanding operation state, detect the state.

Incidentally, when system disturbance occurs in a state where a power generation facility is interconnected with a power system, it may be erroneously detected that the power generation facility has transitioned to an islanding operation state.

However, the islanding operation detection method described in Toyokuni Kato, Chihiro Okado, Hitoshi Ito, Masafumi Kokenawa, Shigeo Nomiya “Development of Islanding Operation Detection Device for Synchronous Generator,” the transactions of the Institute of Electrical Engineers of Japan. B, No. 7/8, volume 94120 (2000), issues 8 to 9 does not consider countermeasures against such system disturbance.

A second aspect of the disclosure has been made in view of such a situation, and a second objective of the second aspect is to provide a power converter that can accurately detect, even in system disturbance, whether the power converter has transitioned to an islanding operation state.

SUMMARY

A first aspect of the disclosure is a power converter configured to be interconnected with a power system and to perform virtual synchronous generator function, the power converter comprising: a processor, and a non-transitory storage medium having program instructions stored thereon, execution of which by the processor causes the power converter to provide functions of a frequency feedback unit configured to apply a transfer function to one of a frequency in the virtual synchronous generator function, or a frequency of a voltage at an interconnection point of the power converter to the power system, and apply an upper and lower limit restriction to a result of the application of the transfer function, to thereby generate a processing result; an addition unit configured to output, by adding a first amplitude command value related to the voltage at the interconnection point and the processing result, a second amplitude command value; an interconnection point voltage amplitude control unit configured to generate an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point; a voltage output unit configured to generate a three-phase Alternating Current (AC) voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; and an islanding operation detection unit configured to detect, responsive to the processing result reaching the upper and lower limit restriction, an islanding operation state in which the power converter is separated from the power system, wherein

• • the transfer function has: a denominator that includes at least a second-order polynomial of a Laplace operator, and a numerator that includes a first-order monomial of the Laplace operator, the polynomial and the monomial being so configured that the denominator is a stable polynomial when the power converter is interconnected with the power system and is an unstable polynomial when the power converter is the in islanding operation state.

A first aspect of the disclosure is a detection method for detecting an islanding operation state of a power converter configured to be interconnected with a power system and to perform virtual synchronous generator function, the power converter being separated from the power system in the islanding operation state, the detection method comprising, performed by the power converter that includes a processor: applying a transfer function to one of a frequency in the virtual synchronous generator function, or a frequency of a voltage at an interconnection point of the power converter to the power system, and applying an upper and lower limit restriction to a result of the application of the transfer function, to thereby generate a processing result; outputting, by adding a first amplitude command value related to the voltage at the interconnection point and the processing result, a second amplitude command value; generating an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point; generating a three-phase Alternating Current (AC) voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; and detecting, responsive to the processing result reaching the upper and lower limit restriction, the islanding operation state, wherein the transfer function has: a denominator that includes at least a second-order polynomial of a Laplace operator, and a numerator that includes a first-order monomial of the Laplace operator, the polynomial and the monomial being so configured that the denominator is a stable polynomial when the power converter is interconnected with the power system and is an unstable polynomial when the power converter is in the islanding operation state.

A second aspect of the disclosure is a power converter configured to be interconnected with a power system and to perform virtual synchronous generator function, the power converter comprising: a processor, and a non-transitory storage medium having program instructions stored thereon, execution of which by the processor causes the power converter to provide functions of a frequency feedback unit configured to output a voltage depending on one of a frequency in the virtual synchronous generator function, and a frequency of a voltage at an interconnection point of the power converter to the power system; a reactive power control unit configured to output a first voltage depending on reactive power at the interconnection point;

• • an output unit configured to apply a first upper and lower limit restriction to a result of addition of a second voltage based on the output of the frequency feedback unit and the first voltage, to thereby output a third voltage;
  • a first addition unit configured to output, by adding a first amplitude command value related to the voltage at the interconnection point and the third voltage, a second amplitude command value; an interconnection point voltage amplitude control unit configured to generate an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point; a voltage output unit configured to generate a three-phase Alternating Current (AC) voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; and an islanding operation detection unit configured to detect, responsive to the third voltage reaching the first upper and lower limit restriction, an islanding operation state in which the power converter is separated from the power system.

Other features of the first and second aspects of the disclosure are made clear by the present description.

According to the first aspect of the disclosure, it is possible to provide a power converter that can, when the power converter including virtual synchronous generator control has transitioned to an islanding operation state, detect the state.

According to the second aspect of the disclosure, it is possible to provide a power converter that can accurately whether the power converter has transitioned to an islanding operation state.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram to describe an example of a power system 1 provided with a power converter 2 of a first embodiment.

FIG. 2 is a diagram to describe a functional block of a control device 20 of the first embodiment.

FIG. 3 is a diagram to describe an inverter output voltage phase generation unit 21 of the first embodiment.

FIG. 4 is a diagram to describe an interconnection point voltage amplitude control unit 22 of the first embodiment.

FIG. 5 is a diagram to describe an interconnection point voltage amplitude control unit 52 of Variation 1.

FIG. 6 is a diagram to describe an example of a power system 1 provided with a power converter 6 of a second embodiment.

FIG. 7 is a diagram to describe a functional block of a control device 60 of the second embodiment.

FIG. 8 is a diagram to describe an inverter output voltage phase generation unit 61 of the second embodiment.

FIG. 9 is a diagram to describe an interconnection point voltage amplitude control unit 22 of the second embodiment.

FIGS. 10A to 10C are diagrams to show a result of numerical simulation.

FIGS. 11A to 11D are diagrams to show a result of numerical simulation.

FIGS. 12A to 12D are diagrams to show a result of numerical simulation.

FIG. 13 is a diagram to describe processing executed by an islanding operation detection unit of Variation 2.

FIGS. 14A to 14E are diagrams to show results of numerical simulation.

FIGS. 15A to 15E are diagrams to show results of numerical simulation.

FIG. 16 is a diagram to describe processing executed by an islanding operation detection unit of Variation 3.

FIG. 17 is a diagram to describe an inverter output voltage phase generation unit t 91 of a third embodiment.

FIGS. 18A to 18E are diagrams to show results of numerical simulation.

FIGS. 19A to 19E are diagrams to show results of numerical simulation.

DESCRIPTION OF EMBODIMENTS

First Embodiment

<<Power Conversion Device 2>>

FIG. 1 is a diagram to describe a power converter 2 interconnected with a power system 1. In the interconnection, a load G is supplied with power from both of the power system 1 and the power converter 2 via a power transmission line 10 having an impedance (reactance) X1.

A circuit breaker 11 released due to an accident or the like causes the power converter 2 to be in an islanding operation state.

A measurement unit 4a is installed between the load G and the circuit breaker 3. The measurement unit 4a measures, in the point of the installation, active power P_out, a voltage V_out (instantaneous value), a frequency ω_out, a voltage amplitude V_out, and the like, which are outputs from the power converter 2, and inputs them into the power converter. Alternatively, the measurement unit 4a measures an instantaneous voltage V_out and current I_out and inputs them into the power converter 2 to compute ω_out, P_out, and an interconnection point voltage amplitude V.

The power converter 2 is a system interconnection device including a virtual synchronous generator function. Furthermore, the power converter 2 is a device capable of detecting, when the power converter 2 has transitioned to an islanding operation state, the state.

In the islanding operation state, no power is supplied to the load G from the power system 1, and power is supplied to the load G only from the power converter 2.

The point of installation of the circuit breaker 3 is referred to as a “point of interconnection between the power system 1 and the power converter 2” or simply as an “interconnection point.” The power converter 2 includes control device 20 and a power conversion unit 30. Assume that an impedance (reactance) X2 between the power converter 2 and the circuit breaker 3 is small, if any.

<Control Device 20>

Hereinafter, a hardware configuration of the control device 20 will be described first, and then a functional block of the control device 20 will be described.

Hardware Configuration of Control Device 20

The control device 20 includes a DSP (Digital Signal Processor) 200 and a storage device 201 (FIG. 1).

{DSP 200}

The DSP 200 implements various functions of the control device 20 by executing a certain program stored in the storage device 201.

{Storage Device 201}

The storage device 201 includes a non-temporary (for example, non-volatile) storage device that stores various data executed or processed by the DSP 200.

The storage device 201 further includes, for example, a RAM (Random-Access Memory) and the like (memory 36a described below), and is used as a temporary storage area for various programs, data, and the like.

Functional Block of Control Device 20

FIG. 2 is a diagram to describe the functional block of the control device 20. The control device 20 is a device that controls an active power output and an interconnection point voltage and generates a voltage command value output by the power conversion unit 30.

An inverter output voltage phase generation unit 21, an interconnection point voltage amplitude control unit 22, an instantaneous voltage command generation unit 23, and a PWM pulse generation unit 24 are mounted on the control device 20.

{Inverter Output Voltage Phase Generation Unit 21}

FIG. 3 is a diagram to describe the inverter output voltage phase generation unit 21. The inverter output voltage phase generation unit 21 generates a phase θ of an output voltage of the power conversion unit 30, based on virtual synchronous generator control.

Specifically, the inverter output voltage phase generation unit 21 updates a VSG frequency ω, based on a difference between target power P_ref output to the power system 1 by the power converter 2 and power P_out actually output to the power system 1, and the VSG frequency, and generates the phase θ as an integrated value thereof.

Here, the target power P_ref is a value set beforehand by a designer, an operator, or the like of the power converter 2. The power P_out is a value measured by the measurement unit 4a in FIGS. 1 and 2.

In the following description, an inertia constant and a braking constant of a virtual synchronous generator mounted on the inverter output voltage phase generation unit 21 are M and D, respectively.

As shown in FIG. 3, the inverter output voltage phase generation unit 21 includes adders 21a, 21b, 21d, multipliers 21e, 21f, and integrators 21c, 21g.

The adder 21a outputs, to the adder 21b, a value obtained by subtracting the power P_out from the power P_ref (P_ref−P_out).

The adder 21b outputs, to the integrator 21c, a value obtained by adding an input from the multiplier 21e (described below) to the input value (P_ref−P_out) from the adder 21a.

The integrator 21c multiplies the input from the adder 21b by 1/M (that is, divides the input by M) and outputs, to the multiplier 21f, a result of time integration of the resultant multiplication over a certain period.

The value obtained here by the integration operation is a value obtained by unitizing, by a nominal frequency ω_n, a frequency ω of a voltage output from the power converter 2.

For example, in Japan, the nominal frequency ω_n is a value obtained by multiplying 50 Hz by 2π in eastern Japan and is a value obtained by multiplying 60 Hz by 2π in western Japan.

The adder 21d outputs, to the multiplier 21e, a value obtained by subtracting the input from the integrator 21c from 1. Note that, here, the input to the adder 21d may be a value obtained by dividing, by the nominal frequency ω_n, an interconnection point frequency ω_out measured by the measurement unit 4a, in place of the input from the integrator 21c.

The multiplier 21e outputs, to the adder 21b, a value obtained by multiplying the input from the adder 21d by the braking constant D of the VSG.

The multiplier 21f outputs a value obtained by multiplying the input from the integrator 21c by the nominal frequency ω_n. The output value of the multiplier 21f is a frequency related to the output voltage of the power converter 2.

The integrator 21g computes time integration of the input from the multiplier 21f over a certain period. With this computation, the integrator 21g outputs a phase θ of the voltage output from the power converter 2.

{Interconnection Point Voltage Amplitude Control Unit 22}

FIG. 4 is a diagram to describe the interconnection point voltage amplitude unit control 22. The interconnection point voltage amplitude control unit 22 computes an inverter output voltage amplitude command value V_INV for controlling an amplitude of the voltage output from the power converter 2. The inverter output voltage amplitude command value V_INV corresponds to an amplitude of a voltage actually output from the power converter 2.

Specifically, the interconnection point voltage amplitude control unit 22 outputs the inverter output voltage amplitude command value V_INV, based on a certain amplitude command value V_ref** and ω or ω_out that is an output from the multiplier 21f of the inverter output voltage phase generation unit 21 (FIG. 3) and that is equal to the output voltage frequency.

The interconnection point voltage amplitude control unit 22 includes a frequency feedback unit 22a, an adder 22b, an amplitude control unit 22c, and an islanding operation detection unit 22d.

The frequency feedback unit 22a outputs, as a processing result, a signal for identifying whether the power converter 2 is interconnected with the power system 1 or is in islanding operation, based on the frequency ω or the like.

The power converter 2 includes the frequency feedback unit 22a and satisfies a condition described below, thereby allowing the power converter 2 to detect, when transitioning to an islanding operation state, the state.

The frequency feedback unit 22a outputs, after applying computation of a certain transfer function G_o to a frequency ω or ω_out in the virtual synchronous generator function, a processing result obtained by applying an upper and lower limit restriction to the resultant computation. Note that the “frequency ω in the virtual synchronous generator function” is the frequency of the voltage output from the power converter 2.

In the present embodiment, the following equation is used as a transfer function G_o.

$\begin{array}{cc}{G}_O=-\frac{\gamma \tau s}{{\left(1+\tau s\right)}^2}& \left[\mathrm{Math}.1\right]\end{array}$

As shown in Equation 1, in the present embodiment, the transfer function G_o includes a numerator being a first-order monomial of a Laplace operator s. The transfer function G_o includes a denominator expressed by a square of a first-order polynomial of a Laplace operator s. The parameters γ and τ are parameters set beforehand by a designer, an operator, or the like of the power converter 2 (described below).

The frequency feedback unit 22a includes a computation unit 22e and a restriction unit 22f. The computation unit 22e outputs, to the restriction unit 22f, a value obtained by applying computation of the transfer function G_o to the frequency ω or ω_out. The restriction unit 22f outputs, as an additional voltage V_add, a processing result obtained by applying an upper and lower limit restriction to the input from the computation unit 22e.

If the input from the computation unit 22e is a certain lower limit value V_L or greater and is a certain upper limit value V_U or less, the restriction unit 22f directly outputs the input from the computation unit 22e as the additional voltage V_add (following equation).

$\begin{array}{cc}{V}_{\mathrm{add}}=-\frac{\gamma \tau s}{{\left(1+\tau s\right)}^2}\omega & \left[\mathrm{Math}.2\right]\end{array}$

If the input from the computation unit 22e is greater than the upper limit value V_U, the restriction unit 22f outputs the upper limit value V_U as the additional voltage V_add (following equation).

$\begin{array}{cc}{V}_{\mathrm{add}}=V_U& \left[\mathrm{Math}.3\right]\end{array}$

If a value of an input from the adder 22b is less than the lower limit value V_L, the restriction unit 22f outputs the lower limit value V_L as the additional voltage V_add (following equation).

$\begin{array}{cc}{V}_{\mathrm{add}}=V_L& \left[\mathrm{Math}.4\right]\end{array}$

A condition for determination of the parameters γ and τ on the right-hand side of Equation 1 will be briefly described below. Note that details of the condition will be described below.

The parameters γ and τ are determined such that stability is maintained in system interconnection and instability occurs in an islanding operation state.

The parameters are determined such that instability occurs in an islanding operation state, and thus, in the islanding operation state, the output of 22e diverges to V_U or V_L.

The parameters γ and τ are determined in such a manner as that described above, thereby allowing the islanding operation detection unit 22d described below to detect an islanding operation state when an output from the restriction unit 22f reaches the upper limit value V_U or the lower limit value V_L.

Referring back to FIG. 4, the adder 22b (corresponding to an “addition unit”) outputs an interconnection point voltage amplitude command value V_ref* (corresponding to a “second amplitude command value”) obtained by adding a certain amplitude command value V_ref** (corresponding to a “first amplitude command value”) related to a voltage at an interconnection point to the processing result (that is, the additional voltage V_add) of the frequency feedback unit 22a.

In other words, the amplitude command value V_ref** an interconnection point voltage amplitude command value before the additional voltage V_add is added. The interconnection point voltage amplitude command value V_ref* is an interconnection point voltage amplitude command value after the additional voltage V_add is added to the amplitude command value V_ref**.

The amplitude control unit 22c generates an inverter output voltage amplitude command value V_INV, based on the interconnection point amplitude command value V_ref* and a voltage amplitude V_out at the interconnection point.

In this case, the amplitude control unit 22c generates the inverter voltage amplitude command value V_INV such that a measured value V_out of the voltage amplitude matches the interconnection point amplitude command value V_ref* at the point of the installation of the measurement unit 4a.

When the processing result of the frequency feedback unit 22a reaches the upper and lower limit restriction, the islanding operation detection unit 22d detects an islanding operation state in which the power converter 2 is separated from the power system 1.

When the islanding operation state is detected, the circuit breaker 3 is released or the power converter 2 is stopped, thereby releasing the power converter 2 from the islanding operation state.

Note that, in the interconnection point voltage amplitude control unit 22 of the present embodiment described above, the input to the frequency feedback unit 22a is ω, but the frequency ω_out of the voltage V_out measured by the measurement unit 4a may be used.

{Instantaneous Voltage Command Generation Unit 23}

Referring back to FIG. 2, the instantaneous voltage command generation unit 23 generates an instantaneous voltage command value V_INV for each of three phases for the voltage output from the power converter 2.

{PWM Pulse Generation Unit 24}

The PWM pulse generation 24 unit detects an intersection of a carrier wave realized by, for example, a triangular wave, and a sine wave as a fundamental wave. With this, the PWM pulse generation unit 24 determines a duty ratio of a PWM pulse and generates a PWM pulse signal V_PWM having the determined duty ratio.

The PWM pulse signal VPWM is output to the power conversion unit 30, and an inverter circuit of the power conversion unit 30 is driven.

<Power Conversion Unit 30>

The power conversion unit 30 includes a direct-current power supply and an inverter circuit (not shown) including a plurality of switching elements. The inverter circuit converts a DC voltage from the direct-current power supply into an AC voltage and outputs the AC voltage to the power system 1.

In this case, the inverter circuit outputs a voltage generated based on the PWM pulse signal V_PWM being an output from the PWM pulse generation unit 24.

When the voltage based on the PWM pulse signal V_PWM is output from the power conversion unit 30, voltage V_out corresponding to the instantaneous voltage command value V_INV being an output of the instantaneous voltage command generation unit 23 is measured by the measurement unit 4a.

Note that a combination of the PWM pulse generation unit 24 and the power conversion unit 30 corresponds to a “voltage output unit.” In other words, the voltage output unit generates a three-phase AC voltage, based on a phase and an output voltage amplitude in the virtual synchronous generator function.

<Setting of Parameters γ and τ>

The setting of the parameters γ and τ included in the transfer function G_o shown in Equation 1 is briefly described above, but will be described here in detail.

The parameters γ and τ are set based on a characteristic equation related to a closed-loop transfer function G_C in a case where a change in a phase θ being an output of the virtual synchronous generator using active power as an input, a voltage amplitude change being a result obtained by performing computation of a certain transfer function G_o using a frequency ω of the virtual synchronous generator or an interconnection point voltage frequency ω_out as an input, and an active power change caused by the phase change and the voltage amplitude change are collectively regarded as one closed-loop system.

The characteristic equation of the closed-loop transfer function G_C differs between a case where the power converter 2 is interconnected and a case where the power converter 2 is in islanding operation. The characteristic equation in each case will be derived below. Note that, in the derivation of the characteristic equation, assume that the impedance X2 (FIGS. 1 and 2) is sufficiently small and can be ignored. Also, assume that a system frequency is equal to the nominal frequency.

First, consider a case where a frequency ω for the voltage output from the power converter 2 changes by Δω from a rated frequency ω_n.

Accordingly, a change Δθ in a phase of the voltage output from the power converter 2 (equal to a change in a phase difference between the voltage and a voltage from the system) is expressed as the following equation.

$\begin{array}{cc}\Delta \theta =\frac{\Delta \omega }{s}& \left[\mathrm{Math}.5\right]\end{array}$

Here, the denominator on the right-hand side is a Laplace operator s.

A change ΔP₁ in active power P₁ flowing in the power system 1 caused by the change Δθ in the phase in Equation 5 is expressed as the following equation, if the phase difference is not large.

$\begin{array}{cc}\Delta P_1=\{\begin{array}{c}\frac{V_{\mathrm{out}}{V}_0}{X1}\sin \mathrm{\Delta \theta }\approx \frac{V_{\mathrm{out}}{V}_0}{X1}\mathrm{\Delta \theta }\\ 0\end{array}& \left[\mathrm{Math}.6\right]\end{array}$

Here, an upper part and a lower part of the right-hand side correspond to a case of interconnection and a case of an islanding operation state, respectively. In the islanding operation state, the active power P₁ flowing in the power system 1 is always 0, and thus the change ΔP₁ is also 0. V₀ is an amplitude of a voltage output from the power system 1.

Furthermore, a change ΔP₂ in power consumption P₂ in the load G caused by an interconnection point voltage change is expressed as the following equation.

$\begin{array}{cc}\Delta P_2=\Delta \left(G{V}_{out}^2\right)\approx 2G{V}_{out}\Delta V_{\mathrm{out}}& \left[\mathrm{Math}.7\right]\end{array}$

Thus, when a change (ΔP=ΔP₁+ΔP₂) in active power P_out output from the power converter 2 occurs, a frequency change Δω of the following equation occurs in the virtual synchronous generator function.

$\begin{array}{cc}\Delta \omega =-\frac{{\omega }_n}{Ms+D}\Delta P& \left[\mathrm{Math}.8\right]\end{array}$

Furthermore, when the change Aw in the frequency ω of Equation 8 occurs, a change AV in the amplitude V_out of the voltage is expressed as the following equation by using Equation 1.

$\begin{array}{cc}\Delta V=-\frac{\gamma \tau s}{{\left(1+\tau s\right)}^2}\Delta \omega & \left[\mathrm{Math}.9\right]\end{array}$

In consideration of Equations 5 to 9, the characteristic equation of the closed-loop transfer function G_C in a closed loop in each of the interconnection and the islanding operation can be derived as follows.

• • A characteristic polynomial in the interconnection.

$\begin{array}{cc}\left(Ms+D\right){s\left(1+\tau s\right)}^2+{\omega }_n\frac{V_{\mathrm{out}}{V}_0}{X1}{\left(1+\tau s\right)}^2-2G{V}_{out}{\omega }_n\gamma \tau s^2& \left[\mathrm{Math}.10\right]\end{array}$

• • A characteristic polynomial in the islanding operation.

$\begin{array}{cc}\left(Ms+D\right){\left(1+\tau s\right)}^2-2{\mathrm{GV}}_{\mathrm{out}}{\omega }_n\mathrm{\gamma \tau s}& \left[\mathrm{Math}.11\right]\end{array}$

A condition for the parameters y and t will be derived below by using Equations 10 and 11.

In the interconnection, the parameters are set such that stability is maintained even when the voltage amplitude is changed depending on frequency change.

Accordingly, Equation 10 is required to be a stable polynomial. This requires at least that signs of coefficients with respective orders of a Laplace operator in Equation 10 are all the same.

In Equation 10, the signs of the fourth, third, first, and zero-order coefficients of the Laplace operator s are all positive, but the sign of the second-order coefficient is indefinite.

Accordingly, the following condition is necessary for making the sign of the second-order coefficient of the Laplace operator s in Equation 10 positive.

$\begin{array}{cc}\gamma <\frac{V_0\tau }{2GX1}& \left[\mathrm{Math}.12\right]\end{array}$

Furthermore, in the islanding operation, the parameters are determined such that the system becomes unstable.

Accordingly, Equation 11 is required to be an unstable polynomial. This only requires that at least one of coefficients with respective orders of a Laplace operator s in Equation 11 has a sign different from a sign of another coefficient with an order.

In Equation 11, the signs of the third, second, and zero-order coefficients of the Laplace operator s are all positive, but the sign of the first-order coefficient is indefinite.

Accordingly, the following condition is given to make the sign of the first-order coefficient of the Laplace operator s in Equation 11 negative.

$\begin{array}{cc}\gamma <\frac{M+2D\tau }{2G{V}_{\mathrm{out}}{\omega }_n\tau }& \left[\mathrm{Math}.13\right]\end{array}$

To summarize the description above, the parameters y and t satisfying the conditions of Equations 12 and 13 are set, thereby maintaining stability in interconnection and leading to instability in an islanding operation state, and thus it is possible to detect islanding operation.

<<Transfer Function G_o>>

The present embodiment describes the transfer function G_o by using Math. 1 as an example thereof, but is not limited to this example. A condition to be satisfied by the transfer function G_o will be described in detail.

As shown in the following equation, the transfer function G_o is required to include at least a second-order polynomial of a Laplace operator s in the denominator and a first-order monomial of a Laplace operator s in the numerator.

$\begin{array}{cc}{G}_O=\frac{bs}{1+a_{1}s+a_2{s}^2+\dots +a_n{s}^n}& \left[\mathrm{Math}.14\right]\end{array}$

Here, n≥2 and b≠0.

Note that a case where the denominator of the transfer function G_o is a first or lower-order term of a Laplace operator s and a case where the numerator of the transfer function G_o is a zero-order term of a Laplace operator s cannot satisfy the conditions for the stable polynomial and the unstable polynomial described above, although description thereof is omitted.

Here, for example, the closed-loop transfer function G_C in a closed loop with an active power command as an input is formally expressed as the following equation.

$\begin{array}{cc}{G}_C=\frac{1+d_{1}s+d_2{s}^2+\dots +d_m{s}^m}{1+c_{1}s+c_2{s}^2+\dots +c_l{s}^l}& \left[\mathrm{Math}.15\right]\end{array}$

Here, l and m are integers. In other words, the denominator is an l-order polynomial of a Laplace operator s, and the numerator is an m-order polynomial of a Laplace operator s.

The transfer function G_o of Equation 14 is given coefficients (a₁, a₂, . . . , a_n, and b) in the polynomial and the monomial such that the denominator of the closed-loop transfer function G_C becomes a stable polynomial in interconnection and becomes an unstable polynomial in an islanding operation state.

In the following example, the transfer function G_o of Equation 14 is assumed to include a denominator being a second-order polynomial (n=2) of a Laplace operator.

In this case, the coefficients (a₁, a₂, and b) in the polynomial of the denominator and the monomial of the numerator of the transfer function G_o may be set so as to satisfy the following two conditions.

{Case Where Power Conversion Device 2 Is Interconnected With Power System 1}

The characteristic polynomial in this case is expressed as the following equation by defining the transfer function G_o in the description of the above-described embodiment as Equation 14 in place of Equation 1.

$\begin{array}{cc}\left(M{s}^2+Ds+{\omega }_n\frac{V_{\mathrm{out}}{V}_0}{X1}\right)\left(a_2{s}^2+a_{1}s+1\right)-2G{V}_{out}{\omega }_{n}b{s}^2& \left[\mathrm{Math}.16\right]\end{array}$

The plurality of coefficients (a₁, a₂, and b) in Equation 14 are set such that the coefficients of the terms included in the characteristic equation (Math. 16) of the closed-loop transfer function G_C have all the same sign.

This case requires a condition of the following equation in which a sign of the second-order coefficient of a Laplace operator s is positive.

$\begin{array}{cc}M+D{a}_1+{\omega }_n\frac{V_{\mathrm{out}}{V}_0}{X1}{a}_2-2G{V}_{out}{\omega }_{n}b>0& \left[\mathrm{Math}.17\right]\end{array}$

{Case Where Power Conversion Device 2 Is in Islanding Operation}

The characteristic polynomial in this case is also expressed as the following equation by defining the transfer function G_o in the description described above as Equation 14 in place of Equation 1.

$\begin{array}{cc}\left(Ms+D\right)\left(a_2{s}^2+a_{1}s+1\right)-2G{V}_{out}{\omega }_{n}b{s}^2& \left[\mathrm{Math}.18\right]\end{array}$

The plurality of coefficients (a₁, a₂, and b) in Equation 14 are further set such that in the characteristic equation (Equation 18) of the closed-loop transfer function G_C, a term with a sign different from a sign of a coefficient of another term occurs.

This case requires a condition of the following equation in which a sign of the first-order coefficient of a Laplace operator s is negative.

$\begin{array}{cc}M+D{a}_1-2{\mathrm{GV}}_{\mathrm{out}}{\omega }_{n}b<0& \left[\mathrm{Math}.19\right]\end{array}$

With the transfer function G_o satisfying the conditions (Equations 17 and 19) described above, the power converter 2 can easily detect, when being in an islanding operation state, the state.

{Variation 1}

A power converter according to the present variation will be described. FIG. 5 is a diagram to describe an interconnection point voltage amplitude control unit 52 of the power converter according to the present variation.

The power converter according to the present variation differs from the power converter 2 according to the embodiment in that the interconnection point voltage amplitude control unit 52 further includes an amplitude control unit 52a.

In the embodiment above, a certain value as the amplitude command value V_ref** is used as an input to the interconnection point voltage amplitude control unit 22.

In contrast, in the present variation, the amplitude control unit 52a outputs an amplitude command value V_ref**, based on a reactive power command value Q_ref output to the power system 1 and reactive power Q_out actually output to the power system 1.

Here, the reactive power command value Q_ref is a value set beforehand by a designer, an operator, or the like of the power converter 2, or is a value dynamically set so as to maintain a power factor. The reactive power Q_out is a value measured by the measurement unit 4a (FIGS. 1 and 2).

As in the present variation, the amplitude command value V_ref** may be computed. With this, it is possible to detect islanding operation even when performing reactive power control or constant power factor control.

Second Embodiment

<<Power Conversion Device 2>>

FIG. 6 is a diagram to describe a power converter 6 interconnected with a power system 1. In the interconnection, a load G is supplied with power from both of the power system 1 and the power converter 6 via a power transmission line 10 having an impedance (reactance) X1. The power transmission line 10 and the power converter 6 are connected with each other in a point of installation of a circuit breaker 3.

A measurement unit 4b is installed in front of the circuit breaker 3. The measurement unit 4b measures, in the point of the installation, active power P_out, a voltage V_out (instantaneous value), a frequency ω_out, a voltage amplitude V_out, and the like, which are outputs from the power converter 6, and inputs them into the power converter. Alternatively, the measurement unit 4b measures an instantaneous voltage V_out and current Tout and inputs them into the power converter 2 to compute ω_out, P_out, and an interconnection point voltage amplitude V.

Note that it is assumed that a section between an interconnection point N and the point of the installation of the measurement unit 4b is sufficiently short and that an impedance of this section can be ignored. It is assumed that a value measured by the measurement unit 4b is regarded as a measured value at the interconnection point N.

The power converter 6 is a device capable of being interconnected with the power system 1 and including a virtual synchronous generator function. Furthermore, the power converter 2 is a device capable of detecting, when the power converter 6 has transitioned to an islanding operation state, the state.

In the islanding operation state, no power is supplied to the load G from the power system 1, and power is supplied to the load G only from the power converter 6.

Assume that an impedance (reactance) X2 between the power converter 6 and the circuit breaker 3 is small, if any.

<Control Device 60>

A functional block of the control device 60 will be described below. Note that a hardware configuration of the control device 60 is the same as that of the power converter 2 of the first embodiment.

Functional Block of Control Device 60

FIG. 7 is a diagram to describe the functional block of the control device 60. The control device 60 is a device that controls a voltage output by a power conversion unit 30 described in detail below.

An inverter output voltage phase generation unit 61, an interconnection point voltage amplitude control unit 62, an instantaneous voltage command generation unit 63, and a PWM pulse generation unit 64 are implemented on the control device 60.

{Inverter Output Voltage Phase Generation Unit 61}

FIG. 8 is a diagram to describe the inverter output voltage phase generation unit 61. The inverter output voltage phase generation unit 61 generates a phase θ of an output voltage of the power conversion unit 30, based on virtual synchronous generator control.

Specifically, the inverter output voltage phase generation unit 61 updates a VSG frequency, based on a difference between target power P_ref output to the power system 1 by the power converter 6 and power P_out actually output to the power system 1, and the VSG frequency, and generates the phase θ as an integrated value thereof.

Here, the target power P_ref is a value set beforehand by a designer, an operator, or the like of the power converter 2. The power P_out is a value measured by the measurement unit 4b in FIGS. 6 and 7.

In the following description, an inertia constant and a braking constant of a virtual synchronous generator mounted on the inverter output voltage phase generation unit 61 are M and D, respectively.

As shown in FIG. 8, the inverter output voltage phase generation unit 61 includes adders 61a, 61b, 61d, multipliers 61e, 61f, and integrators 61c, 61g.

The adder 61a outputs, to the adder 61b, a value obtained by subtracting the power P_out from the power P_ref (P_ref−P_out).

The adder 61b outputs, to the integrator 61c, a value obtained by adding an input from the multiplier 61e (described below) to the input value (P_ref−P_out) from the adder 61a.

The integrator 61c multiplies the input from the adder 61b by 1/M (that is, divides the input by M) and outputs, to the multiplier 61f, a result of time integration of the resultant multiplication over a certain period.

The value obtained here by the integration operation is a value obtained by unitizing, by a nominal frequency ω_n of the power system 1, a frequency ω output from the power converter 6.

For example, in Japan, the nominal frequency ω_n of the power system 1 is a value obtained by multiplying 50 Hz by 21 in eastern Japan and is a value obtained by multiplying 60 Hz by 2π in western Japan.

The adder 61d outputs, to the multiplier 61e, a value obtained by subtracting the input from the integrator 61c from 1.

Note that, here, the input to the adder 61d may be a value obtained by dividing, by the nominal frequency ω_n, an interconnection point frequency ω_out measured by the measurement unit 4b, in place of the input from the integrator 61c.

The multiplier 61e outputs, to the adder 61b, a value obtained by multiplying the input from the adder 61d by the braking constant D of the VSG.

The multiplier 61f outputs a value obtained by multiplying the input from the integrator 61c by the nominal frequency ω_n of the power system 1. The output value of the multiplier 61f is a frequency related to the output voltage of the power converter 6 output to the power system 1.

The integrator 61g computes time integration of the input from the multiplier 61f over a certain period. With this computation, the integrator 61g outputs a phase θ of the voltage output from the power converter 6.

{Interconnection Point Voltage Amplitude Control Unit 62}

FIG. 9 is a diagram to describe the interconnection point voltage amplitude unit control 62. The interconnection point voltage amplitude control unit 62 computes an inverter output voltage amplitude command value V_INV for controlling an amplitude of the voltage output from the power conversion unit 30.

The interconnection point voltage amplitude control unit 62 includes a frequency feedback unit 62a, an upper and lower limit restriction unit 62b, a change rate restriction unit 62c, a reactive power control unit 62d, an output unit 62e, an adder 62h, an amplitude control unit 62i, and an islanding operation detection unit 62j.

Frequency Feedback Unit 62a

The frequency feedback unit 62a outputs a voltage ΔV₁** depending on a frequency ω in the virtual synchronous generator function.

The frequency feedback unit 62a outputs, when the power converter 6 is in an islanding operation state, a voltage with an increased width of change due to lack of stability.

In the present embodiment, the frequency feedback unit 62a outputs the voltage ΔV₁** (following equation) obtained by applying computation of a certain transfer function G_o to the frequency ω.

$\begin{array}{cc}\Delta V_1^{**}=G_O\omega & \left[\mathrm{Math}.20\right]\end{array}$

In the present embodiment, the following equation is used as a transfer function G_o.

$\begin{array}{cc}{G}_O=-\frac{\gamma \tau s}{{\left(1+\tau s\right)}^2}& \left[\mathrm{Math}.21\right]\end{array}$

Here, s is a Laplace operator. The parameters γ and τ are parameters set beforehand by a designer, an operator, or the like of the power converter 6.

The parameters γ and τ of Equation 21 are determined such that stability is maintained in system interconnection and instability occurs in an islanding operation state.

Specifically, the parameters γ and τ are set based on a characteristic equation related to a closed-loop transfer function G_C in a case where a change in a phase θ being an output of the virtual synchronous generator using active power as an input, a voltage amplitude change being a result obtained by performing computation of a certain transfer function G_o using a frequency ω of the virtual synchronous generator or an interconnection point voltage frequency ω_out as an input, and an active power change caused by the phase change and the voltage amplitude change are collectively regarded as one closed-loop system.

The characteristic equation of the closed-loop transfer function G_C differs between a case where the power converter 6 is interconnected and a case where the power converter 6 is in islanding operation. The characteristic equation in each case will be derived below. Note that, in the derivation of the characteristic equation, assume that the impedance X2 (FIGS. 6 and 7) is sufficiently small and can be ignored. Also, assume that a system frequency is equal to the nominal frequency.

First, consider a case where a frequency ω for the voltage output from the power converter 6 changes by Δω from a rated frequency ω_n.

Accordingly, a change Δθ in a phase of the voltage output from the power converter 6 (equal to a change in a phase difference between the voltage and a voltage from the system) is expressed as the following equation.

$\begin{array}{cc}\Delta \theta =\frac{\Delta \omega }{s}& \left[\mathrm{Math}.22\right]\end{array}$

Here, the denominator on the right-hand side is a Laplace operator s.

A change ΔP₁ in active power P₁ flowing in the power system 1 caused by the change Δθ in the phase in Equation 22 is expressed as the following equation, if the phase difference is not large.

$\begin{array}{cc}\Delta P_1=\{\begin{array}{c}\frac{V_{\mathrm{out}}{V}_0}{X1}\sin \mathrm{\Delta \theta }\approx \frac{V_{\mathrm{out}}{V}_0}{X1}\mathrm{\Delta \theta }\\ 0\end{array}& \left[\mathrm{Math}.23\right]\end{array}$

Here, an upper part and a lower part of the right-hand side correspond to a case of interconnection and a case of an islanding operation state, respectively. In the islanding operation state, the active power P₁ flowing in the power system 1 is always 0, and thus the change ΔP₁ is also 0. V₀ is an amplitude of a voltage output from the power system 1.

Furthermore, a change ΔP₂ in power consumption P₂ in the load G caused by an interconnection point voltage change is expressed as the following equation.

$\begin{array}{cc}\Delta P_2=\Delta \left({\mathrm{GV}}_{out}^2\right)\approx 2G{V}_{\mathrm{out}}\Delta V_{\mathrm{out}}& \left[\mathrm{Math}.24\right]\end{array}$

Thus, when a change (ΔP=ΔP₁+ΔP₂) in active power P_out output from the power converter 2 occurs, a frequency change Δω of the following equation occurs in the virtual synchronous generator function.

$\begin{array}{cc}\Delta \omega =-\frac{{\omega }_n}{Ms+D}\Delta P& \left[\mathrm{Math}.25\right]\end{array}$

Furthermore, when the change Δω in the frequency ω of Equation 25 occurs, a change ΔV in the amplitude V_out of the voltage is expressed as the following equation by using Equation 21.

$\begin{array}{cc}\Delta V=-\frac{\gamma \tau s}{{\left(1+\tau s\right)}^2}\Delta \omega & \left[\mathrm{Math}.26\right]\end{array}$

In consideration of Equations 22 to 26, the characteristic equation of the closed-loop transfer function G_C in a closed loop in each of the interconnection and the islanding operation can be derived as follows.

• • A characteristic polynomial in the interconnection.

$\begin{array}{cc}\left(Ms+D\right){s\left(1+\tau s\right)}^2+{\omega }_n\frac{V_{\mathrm{out}}{V}_0}{X1}{\left(1+\tau s\right)}^2-2G{V}_{out}{\omega }_n\gamma \tau s^2& \left[\mathrm{Math}.27\right]\end{array}$

• • A characteristic polynomial in the islanding operation.

$\begin{array}{cc}\left(Ms+D\right){\left(1+\tau s\right)}^2-2G{V}_{out}{\omega }_n\gamma \tau s& \left[\mathrm{Math}.28\right]\end{array}$

A condition for the parameters γ and τ will be derived below by using Equations 27 and 28.

In the interconnection, the parameters are set such that stability is maintained even when the voltage amplitude is changed depending on frequency change.

Accordingly, Equation 27 is required to be a stable polynomial. This requires at least that signs of coefficients with respective orders of a Laplace operator in Equation 27 are all the same.

In Equation 27, the signs of the fourth, third, first, and zero-order coefficients of the Laplace operator s are all positive, but the sign of the second-order coefficient is indefinite.

Accordingly, the following condition is necessary for making the sign of the second-order coefficient of the Laplace operator s in Equation 27 positive.

$\begin{array}{cc}\gamma <\frac{V_0\tau }{2GX1}& \left[\mathrm{Math}.29\right]\end{array}$

Furthermore, in the islanding operation, the parameters are determined such that the system becomes unstable.

Accordingly, Equation 28 is required to be an unstable polynomial. This only requires that at least one of coefficients with respective orders of a Laplace operator s in Equation 28 has a sign different from a sign of another coefficient with an order.

In Equation 28, the signs of the third, second, and zero-order coefficients of the Laplace operator s are all positive, but the sign of the first-order coefficient is indefinite.

Accordingly, the following condition is given to make the sign of the first-order coefficient of the Laplace operator s in Equation 28 negative.

$\begin{array}{cc}\gamma <\frac{M+2D\tau }{2G{V}_{out}{\omega }_n\tau }& \left[\mathrm{Math}.30\right]\end{array}$

To summarize the description above, the parameters γ and τ satisfying the conditions for Equations 29 and 30 are set, thereby maintaining stability in interconnection and leading to instability in an islanding operation state, and thus it is possible to detect islanding operation.

Note that the processing executed by the frequency feedback unit 62a is not limited to this example. The processing executed by the frequency feedback unit 62a is preferably computation with which stability is maintained in system interconnection and instability occurs in an islanding operation state.

The frequency feedback unit 62a may use a frequency ω_out of a voltage at the interconnection point to the power system 1, in place of the frequency ω of the VSG.

Upper and Lower Limit Restriction Unit 62b

The upper and lower limit restriction unit 62b outputs a voltage obtained by applying an upper and lower limit restriction (corresponding to a “second upper and lower limit restriction”) to the output of the frequency feedback unit 62a.

In other words, if an input from the frequency feedback unit 62a is a certain lower limit value or greater and is a certain upper limit value or less, the upper and lower limit restriction unit 62b directly outputs the input from the frequency feedback unit 62a as a voltage ΔV₁**.

If the input from the frequency feedback unit 62a is greater than the certain upper limit value, the upper and lower limit restriction unit 62b outputs the upper limit value as ΔV₁**. If the input from the frequency feedback unit 62a is less than the certain lower limit value, the upper and lower limit restriction unit 62b outputs the lower limit value as ΔV₁**. Note that the upper and lower limit restriction unit 62b is an optional configuration, and may not necessarily be provided.

Change Rate Restriction Unit 62c

The change rate restriction unit 62c outputs a voltage obtained by applying, to the output of the upper and lower limit restriction unit 62b, an upper limit restriction of a time change rate.

In other words, if a value (time change rate) obtained by differentiating, by time, the voltage ΔV₁** being an input from the upper and lower limit restriction unit 62b is a certain upper limit value or less, the change rate restriction unit 62c directly outputs the input from the upper and lower limit restriction unit 62b as a voltage ΔV₁*.

If the value obtained by differentiating, by time, the voltage ΔV₁** being an input from the upper and lower limit restriction unit 62b is greater than the certain upper limit value, the change rate restriction unit 62c outputs, as a voltage ΔV₁*, a voltage modulated so that the value obtained by differentiating the voltage ΔV₁** by time is the upper limit value. Note that the change rate restriction unit 62c is an optional configuration, and may not necessarily be provided.

Reactive Power Control Unit 62d

The reactive power control unit 62d outputs a voltage ΔV_q (corresponding to a “first voltage”) depending on reactive power Q_out at an interconnection point P.

Specifically, when the power converter 6 is interconnected with the power system 1, the reactive power control unit 62d outputs the voltage ΔV_q for suppressing change in the reactive power Q_out at the interconnection point P.

When the power converter 6 is interconnected with the power system 1, the reactive power Q_out also changes with change in the interconnection point voltage. Thus, ΔV_q is output so as to cancel the frequency feedback output, thereby suppressing change in the interconnection point voltage.

On the other hand, when the power converter 6 is in an islanding operation state, the reactive power is independent of the interconnection point voltage. Thus, the frequency feedback output cannot be canceled, and the interconnection point voltage changes in conjunction with the frequency feedback output.

The islanding operation detection unit 62j described below utilizes this to detect, when the power converter 6 has actually transitioned to an islanding operation state, the state.

Output Unit 62e

The output unit 62e outputs a voltage ΔV₂ (corresponding to a “third voltage”) obtained by applying an upper and lower limit restriction (corresponding to a “first upper and lower limit restriction”) to a result of addition of a voltage ΔV₁ (corresponding to a “second voltage”) based on the output of the frequency feedback unit 62a to the voltage ΔV_q (ΔV₁+ΔV_q).

In the present embodiment, the “voltage ΔV₁ based on the output of the frequency feedback unit 62a” is an output of the change rate restriction unit 62c.

Note that, as described above, the change rate restriction unit 62c is an optional configuration. When the interconnection point voltage amplitude control unit 62 includes the upper and lower limit restriction unit 62b and does not include the change rate restriction unit 62c, the voltage ΔV₁ is preferably a voltage based on the output of the upper and lower limit restriction unit 62b.

When the interconnection point voltage amplitude control unit 62 includes both of the upper and lower limit restriction unit 62b and the change rate restriction unit 62c, the voltage ΔV₁ is preferably a voltage based on the output of the change rate restriction unit 62c.

The output unit 62e includes an adder 62f and a restriction unit 62g. The adder 62f outputs a result of addition of the voltage ΔV₁ to the voltage ΔV_q (ΔV₁+ΔV_q).

The restriction unit 62g outputs a voltage ΔV₂ obtained by applying an upper and lower limit restriction to the input (ΔV₁+ΔV_q) from the adder 62f.

Adder 62h

The adder 62h (corresponding to a “first addition unit”) outputs an amplitude command value V_ref* (corresponding to a “second amplitude command value”) obtained by adding a certain amplitude command value V_ref** (corresponding to a “first amplitude command value”) related to a voltage V_out at the interconnection point P to the voltage ΔV₂.

Amplitude Control Unit 62i

The amplitude control unit 62i generates an inverter output voltage amplitude command value V_INV, based on the amplitude command value Vref* and a voltage amplitude V_out at the interconnection point.

In this case, the amplitude control unit 62i generates the inverter voltage amplitude command value V_INV such that a measured value V_out of the voltage amplitude at the point of the installation of the measurement unit 4b matches the amplitude command value V_ref*.

Islanding Operation Detection Unit 62j

The islanding operation detection unit 62j determines whether the power converter 6 is in an islanding operation state, and outputs, when judging that the power converter 6 is in the islanding operation state, the determination as a detection result.

Specifically, when the voltage ΔV₂ reaches the upper and lower limit restriction in the restriction unit 62g, the islanding operation detection unit 62j detects an islanding operation state in which the power converter 6 is separated from the power system 1.

In the present embodiment, the islanding operation detection unit 62j outputs “0” when not detecting an islanding operation state and outputs “1” when detecting the state.

Validity of detection based on such processing by the islanding operation detection unit 62j will be described by using results of numerical simulation described below.

Note that, in the interconnection point voltage amplitude control unit 62 of the present embodiment described above, the input to the frequency feedback unit 62a is the VSG frequency ω, but is not limited to this. As the input to the frequency feedback unit 62a, the frequency ω_out of the voltage V_out measured by the measurement unit 4b may be used.

{Instantaneous Voltage Command Generation Unit 23}

Referring back to FIG. 7, the instantaneous voltage command generation unit 23 generates an instantaneous voltage command value V_INV for each of three phases for the voltage output from the power converter 6.

Note that the PWM pulse generation unit 24 and the power conversion unit 30 are the same as those of the power converter 2 of the first embodiment.

Also, in the present embodiment, a combination of the PWM pulse generation unit 24 and the power conversion unit 30 corresponds to a “voltage output unit.” In other words, the voltage output unit generates a three-phase AC voltage, based on a phase and an inverter output voltage amplitude command value in the virtual synchronous generator function.

The “phase in the virtual synchronous generator function” is a command value 0 of the phase in FIG. 8, and the “inverter output voltage amplitude command value in the virtual synchronous generator function” is the voltage amplitude command value V_INV in FIG. 9.

<<Result of Numerical Simulation>>

FIG. 10 is a result of numerical simulation assuming a conventional power converter. In other words, this case does not include the reactive power control unit 62d of FIG. 9 in the power converter 6 of the present embodiment, and corresponds to a case where the voltage ΔV₁ is directly input to the output unit 62e.

FIGS. 11 and 12 are diagrams to show the results of the numerical simulation assuming the power converter 6 of the present embodiment.

Here, FIGS. 10 and 11 are numerical simulation results in a case assuming that a power converter is interconnected with the power system 1 without transitioning to an islanding operation state and that a frequency changes. FIG. 12 is a numerical simulation result in a case assuming that the power converter has transitioned to an islanding operation state.

In FIGS. 10, 11, and 12, (a), (b), (c), and (d) indicate transition of a frequency of the power system 1, transition of active power P_out and reactive power Q_out, transition of a voltage amplitude V_out, and transition of a value [PU] obtained by unitizing voltages ΔV₁ and ΔV₂, respectively ((d) is only for FIGS. 11 and 12). The horizontal axis corresponds to a time point [sec].

These numerical simulations assume that the inertia constant M is 5, the braking constant D is 25, and the parameters γ and τ of the transfer function D_o (Equation 21) are 2.0 and 1.0, respectively. Note that these are common to the numerical simulations described in the present description.

First, the result shown in FIG. 10 will be described. FIG. 10 assumes a power converter that changes a voltage amplitude by performing frequency feedback as an islanding operation detection means without performing reactive power feedback, and is a numerical simulation result in a case assuming that the power converter is interconnected with the power system 1 and that a frequency changes.

FIG. 10(a) shows transition of the frequency of the power system 1 assumed in this numerical simulation. As described above, FIG. 10(a) assumes a case where a system frequency increases by 0.2% at time points 10 [sec] to 20 [sec].

FIG. 10(b) shows transition of the active power P_out (solid line) and the reactive power Q_out (broken line). In FIG. 10(b), in particular, the transition of the reactive power Cout transitions at almost 0 (zero) until the time point 10 [sec] at which frequency change is assumed to start, but starts to drop at the time point 10 [sec].

The transition of the reactive power Q_out is saturated for about 2.0 [sec] from around a time point 11.5 [sec], and then rises toward 0 (zero).

Thereafter, the transition of the reactive power Q_out starts to rise at a time point 20 [sec] at which the frequency change is assumed to end, and then is saturated for about 2.0 [sec], and then drops toward 0 (zero).

FIG. 10(c) shows transition of the voltage amplitude V_out. The transition of the voltage amplitude V_out is similar to that of the reactive power Cout shown in FIG. 10(b).

As can be seen from the result shown in FIG. 10, in the conventional power converter, occurrence of change in the system frequency causes large change in a voltage amplitude, resulting in erroneous detection of islanding operation.

Next, the result shown in FIG. 11 will be described. FIG. 11 assumes the power converter 6 of the present embodiment, and is a numerical simulation result in a case assuming that the power converter is interconnected with the power system 1 and that a frequency changes.

FIG. 11(a) is the same as FIG. 10(a), and shows transition of the frequency of the power system 1 assumed in this numerical simulation. In other words, FIG. 11(a) assumes a case where the frequency of the power system increases by 0.2% at time points 10 [sec] to 20 [sec].

FIG. 11(b) shows transition of active power P_out (solid line) and reactive power Q_out (broken line). In FIG. 11(b), in particular, the transition of the reactive power Q_out is substantially constant over time points 0 [sec] to 30 [sec].

This is accompanied by the case that the reactive power control unit 62d of FIG. 9 outputs, to the adder 62f, the voltage ΔV_q for suppressing change in the reactive power Q_out.

FIG. 11(c) shows transition of the voltage amplitude V_out. The transition of the voltage amplitude V_out is similar to that of the reactive power Cout shown in FIG. 11(b), and is substantially constant.

FIG. 11(d) shows transition of the voltage ΔV₁ (solid line) and the voltage ΔV₂ (broken line) in FIG. 9. In FIG. 11(d), in particular, the voltage ΔV₂ transitions substantially constantly.

This numerical simulation assumes that the upper limit value and the lower limit value in the restriction unit 62g of FIG. 9 are 0.2 [PU] and −0.2 [PU], respectively. In other words, in FIG. 11(d), the voltage ΔV₂ transitions within a range of the upper and lower limits. In such a case, the islanding operation detection unit 22j does not determine that the power converter 6 has transitioned to an islanding operation state.

Therefore, according to the power converter 6 of the present embodiment, even if a system frequency changes for some reason when the power converter 6 is interconnected with the power system 1, it is possible to avoid detecting that the power converter 6 has transitioned to an islanding operation state.

Next, the result shown in FIG. 12 will be described. FIG. 12 assumes the power converter 6 of the present embodiment, and is a numerical simulation result in a case assuming that the power converter is interconnected with the power system 1 and has transitioned to an islanding operation state.

This example assumes that the power converter 2 is interconnected with the power system 1 until a time point 25 [sec] and that the power converter 2 transitions to an islanding operation state at the time point 25 [sec].

FIG. 12(a) shows transition of the frequency of the power system 1. FIG. 12(b) shows transition of the active power P_out (solid line) and the reactive power Q_out (broken line). In FIG. 12(b), in particular, the transition of the reactive power Q_out is constant at 0 (zero) over time points 0 [sec] to 30 [sec].

FIG. 12(c) shows transition of the voltage amplitude V_out. The transition of the voltage amplitude V_out starts to rise at the time point 25 [sec] at which the power converter 6 transitions to the islanding operation state. The transition of the voltage amplitude V_out is saturated at 1.2 [PU].

FIG. 12(d) shows transition of the voltage AV₁ (solid line) and the voltage ΔV₂ (broken line) in FIG. 9. The voltage ΔV₁ and the voltage ΔV₂ transition in the same manner. These transitions are saturated at 0.2 [PU].

As described above, this numerical simulation assumes that the upper limit value in the restriction unit 62g of FIG. 9 is 0.2 [PU]. In other words, in FIG. 12(d), the voltage ΔV₂ reaches the upper limit. In such a case, the islanding operation detection unit 62j determines that the power converter 6 has transitioned to an islanding operation state.

Therefore, according to the power converter 6 of the present embodiment, it is possible to detect, when the power converter 6 has actually transitioned to an islanding operation state, the state while avoiding erroneous detection of islanding operation when a system frequency changes in interconnection.

{Variation 2}

A power converter 7 according to the present variation differs from the second embodiment in the processing executed by the islanding operation detection unit 62j of FIG. 9. FIG. 13 is a diagram to describe processing executed by an islanding operation detection unit 72a in the present variation.

The smaller power consumed by the load G (FIG. 6) is, the smaller a width of change in the voltage ΔV₁ (FIG. 7) is. In such a case, in the processing executed by the islanding operation detection unit 62j of the second embodiment, there is a case where even when the power converter 7 is actually in an islanding operation state, the voltage ΔV₂ does not reach the upper and lower limit restriction in the restriction unit 62g, as change in the voltage ΔV₂ is insufficient.

Thus, the load being small makes a voltage and a frequency less divergent even in transition to an islanding operation state, and makes it difficult to detect islanding operation. According to the islanding operation detection unit 72a in the present variation, it is possible to detect an islanding operation state even in such a case.

The islanding operation detection unit 72a in the present variation detects that the power converter 7 is in an islanding operation state, based on the voltage ΔV₁ and the voltage ΔV₂.

Specifically, the islanding operation detection unit 72a in the present variation detects that the power converter 7 is in an islanding operation state, based on transition of the voltage ΔV₁ and transition of a ratio between the voltage ΔV₁ and the voltage ΔV₂.

The islanding operation detection unit 72a in the present variation includes a first block 72b, a second block 72c, and a determination unit 738.

The first block 72b is a block that determines whether there is a possibility that the power converter 7 has transitioned to an islanding operation state when both of the voltage ΔV₁ and the voltage ΔV₂ change in a positive direction. The first block 72b includes a multiplication unit 722, processing units 725 and 727, and determination units 724, 726, 728, 729, and 739.

The determination unit 724 determines whether the voltage ΔV₁ has exceeded a certain upper limit value Vth, and outputs the determination result to the determination unit 729. Here, as the upper limit value V_th, a value being a positive value is set, the value being smaller than the upper limit value in the restriction unit 62g of FIG. 9.

Note that whether the voltage ΔV₁ has exceeded the upper limit value V_th is referred to as “Condition 1.” A case that the voltage ΔV₁ has exceeded the upper limit value V_th is referred to as “Condition 1 has been satisfied.”

Here, a case that Condition 1 has been satisfied means that the voltage ΔV₁ starts rising. There is a possibility that the power converter 7 has transitioned to islanding operation when the voltage ΔV₁ starts to rise, but there is a case where the voltage ΔV₁ does not reach the upper limit value in the restriction unit 62g, depending on such a state of the load G as that described above.

The processing unit 725 outputs a time change rate of the voltage ΔV₁ (that is, a value of a first-order differential of the voltage ΔV₁ with respect to time t (dΔV₁/dt)).

In a case where the time change rate of the voltage ΔV₁ (dΔV₁/dt) being an input from the processing unit 725 is greater than 0, the determination unit 726 outputs, to the determination unit 729, a determination result indicating the case.

Note that whether the time change rate of the voltage ΔV₁ (dΔV₁/dt) is greater than 0 is referred to as “Condition 2.” The time change rate of the voltage ΔV₁ (dΔV₁/dt) being greater than 0 is referred to as “Condition 2 has been satisfied.”

Here, a case that Condition 2 has been satisfied means that the voltage ΔV₁ is rising monotonously. There is a possibility that the power converter 7 has transitioned to islanding operation when the voltage ΔV₁ is rising monotonously, but there is a case where the voltage ΔV₁ does not reach the upper limit value in the restriction unit 72g, depending on such a state of the load G as that described above.

The processing unit 727 outputs a value of a first-order differential of the voltage ΔV₂ with respect to time t (dΔV₂/dt).

The multiplication unit 722 outputs a value (αdΔV₁/dt) obtained by multiplying the output (dΔV₁/dt) of the processing unit 725 by a constant α. Here, the constant o is a positive value less than 1.0.

The determination unit 728 compares the output (dΔV₂/dt) of the processing unit 727 with the output (αdΔV₁/dt) of the multiplication unit 722, and outputs, in a case where the output of the multiplication unit 722 is greater, the case to the determination unit 729.

Note that whether the output of the multiplication unit 722 is greater than the output of the processing unit 727 is referred to as “condition 3.” A case that the output of the multiplication unit 722 being greater than the output of the processing unit 727 is referred to as “Condition 3 has been satisfied.”

Here, a case that Condition 3 has been satisfied means that the time change rates of the voltage ΔV₁ and the voltage ΔV₂ indicate transitions similar to each other. In such a case, there is a possibility that the voltage V_q in FIG. 7 is low and that the power converter 7 has transitioned to islanding operation.

The determination unit 729 determines whether there is a possibility that the power converter 7 has transitioned to an islanding operation state, based on respective inputs from the determination units 724, 726, and 728.

Specifically, when all of Conditions 1 to 3 described above are satisfied, the determination unit 729 determines that there is a possibility that the power converter 7 has transitioned to an islanding operation state.

The determination unit 730 further determines whether there is a possibility that the power converter 7 has transitioned to an islanding operation state, based on an input from the determination unit 729.

Specifically, when the unit determination 729 continues judging, over a certain period, that there is a possibility that the power converter 7 has transitioned to an islanding operation state, the determination unit 730 determines that there is a possibility that the power converter 7 has transitioned to the islanding operation state.

With the processing described above, the first block 72b determines whether there is a possibility that the power converter 7 has transitioned to an islanding operation state when both of the voltage ΔV₁ and the voltage ΔV₂ change in a positive direction.

The second block 72c determines whether there is a possibility that the power converter 7 has transitioned to an islanding operation state when both of the voltage ΔV₁ and the voltage ΔV₂ change in a negative direction.

The second block 72c differs from the first block 72b in that the second block 72c further includes multiplication units 720 and 721.

The multiplication unit 720 multiplies the voltage ΔV₁ by −1, and the multiplication unit 720 multiplies the voltage ΔV₂ by −1, thereby inverting signs of the voltage ΔV₁ and the voltage ΔV₂.

After inverting the signs, the second block 72c executes the same processing as that of the first block 72b. Therefore, detailed description of the second block 72c is omitted.

Note that the multiplication unit 723 and the determination units 731, 733, 735, 736, and 737 of the second block 72c execute the same processing as that of the multiplication unit 722 and the determination units 724, 726, 728, 729, and 739 of the first block 72b, respectively.

The determination unit 738 determines whether the power converter 7 has transitioned to an islanding operation state, based on inputs from the determination unit 730 and the determination unit 737.

Specifically, when both of the determination units 730 and 737 determine that there is a possibility that the power converter 7 has transitioned to an islanding operation state, the determination unit 738 determines that the power converter 7 has transitioned to the islanding operation state.

In the present variation, the islanding operation detection unit outputs “1” when judging that the power converter is in an islanding operation state, otherwise the islanding operation detection unit outputs “0.”

<<Numerical Simulation Result>>

FIGS. 14 and 15 assumes the power converter 5 of the present variation, and are numerical simulation results in a case assuming that the power converter has transitioned to an islanding operation state. The load G is assumed to be 0.25 [PU] in FIG. 9, and is assumed to be 0.1 [PU] in FIG. 15.

First, the result shown in FIG. 14 in a case where the load G is large (0.25 [PU]) will be described. In FIG. 14, (a), (b), (c), (d), and (e) correspond to the active power and reactive power, the voltage, the frequency, the voltage ΔV₁ and voltage ΔV₂, and a result of the determination by the determination unit 738, respectively. Note that the same also applies to FIG. 15 described below.

In each of these diagrams, the horizontal axis corresponds to a time point [sec] and shows 0 [sec] to 30 [sec]. Each of these diagrams assume that the power converter is interconnected with the power system 1 at 0 [sec] to 25 [sec] and that the power converter transitions to an islanding operation state at 25 [sec].

Here, focusing particularly on the voltage ΔV₂ in FIG. 14(d), the voltage ΔV₂ starts to rise at a time point 25 [sec] at which the power converter transitions to the islanding operation state, and is saturated at 0.2 [PU] assumed to be the upper limit in the restriction unit 62g (FIG. 7).

Accordingly, the determination result in FIG. 14(f) shows switching from 0 to 1 around a time point 26 [sec], which shows the transition to the islanding operation state.

Next, the result shown in FIG. 10 in a case where the load G is small (0.1 [PU]) will be described.

Focusing particularly on the voltage ΔV₂ in FIG. 15(d), the voltage ΔV₂ starts to rise at a time point 25 [sec] at which the power converter transitions to the islanding operation state, but does not reach 0.2 [PU] assumed to be the upper limit in the restriction unit 62g of FIG. 7. Note that, in such a case, the power converter 6 of the second embodiment fails to determine transition to an islanding operation state.

However, after the transition to the islanding operation state, both of the voltage ΔV₁ and the voltage ΔV₂ start to rise in a positive direction and transition in the same manner. This means that the voltage V_q in FIG. 7 is low.

The determination result in FIG. 15(f) shows switching from 0 to 1 around a time point 26 [sec], which shows the transition to the islanding operation state.

In other words, according to the power converter 7 of the present variation, it is possible to accurately perform the determination even when a width of change in the voltage ΔV₂ does not reach the upper limit value in the restriction unit 62g of FIG. 7 in a short time because of small power consumed by the load. In other words, when the power converter 7 has transitioned to an islanding operation state, the transition to the islanding operation state being missed is suppressed.

{Variation 3}

A power converter 8 according to the present variation differs from the second embodiment in the processing executed by the islanding operation detection unit 62j of FIG. 9. FIG. 16 is a diagram to describe processing executed by an islanding operation detection unit 82a in the present variation.

In the present variation, the islanding operation detection unit 82a detects that the power converter 8 is in an islanding operation state, based on transition of the voltage ΔV₁ and a degree of similarity between the transition of the voltage ΔV₁ and transition of the voltage ΔV₂.

The islanding operation detection unit 82a of the present variation differs from the islanding operation detection unit 72a of Variation 1 in that the islanding operation detection unit 82a further includes multiplication units 820 and 821 and determination units 822 and 823.

Furthermore, the islanding operation detection unit 82a of the present variation includes determination units 824 and 825 in place of the determination units 729 and 736 of Variation 2. The following description will focus on differences between Variation 2 and the present variation, and description of shared portions will be omitted.

First, the first block 82b further includes the multiplication unit 820 and the determination unit 822, as compared with the first block 72b of Variation 2.

The multiplication unit 820 outputs a value (α₂ΔV₁) obtained by multiplying the voltage ΔV₁ by a constant α₂. Here, the constant α₂ is a positive value less than 1.0.

The determination unit 822 compares the input (α₂ΔV₁) from the multiplication unit 820 with the voltage ΔV₂, and outputs, in a case where the output of the multiplication unit 722 is greater, the case to the determination unit 824.

Note that whether the voltage ΔV₂ is greater than the output of the multiplication unit 820 is referred to as “Condition 4.” A case that the voltage ΔV₂ is greater than the output of the multiplication unit 820 is referred to as “Condition 4 has been satisfied.”

Here, when Condition 4 has been satisfied, there is an increased possibility that the voltage V_q in FIG. 7 is low and that the power converter 8 has transitioned to islanding operation.

Note that, here, the ratio between the voltage ΔV₁ and the voltage ΔV₂ is an example of the “degree of the similarity” described above. The ratio between the voltage ΔV₁ and the voltage ΔV₂ means that the closer to 0 the ratio is, the lower the degree of the similarity is, and that the closer to 1 the ratio is, the higher the degree of the similarity is.

The determination unit 824 determines whether there is a possibility that the power converter 8 has transitioned to an islanding operation state, based on respective inputs from the determination units 724, 726, 728, and 822.

Specifically, when all of Conditions 1 to 4 described above are satisfied, the determination unit 824 determines that there is a possibility that the power converter 8 has transitioned to an islanding operation state.

With the processing described above, the first block 82b determines whether there is a possibility that the power converter 8 has transitioned to an islanding operation state when both of the voltage ΔV₁ and the voltage ΔV₂ change in a positive direction.

The second block 82c determines whether there is a possibility that the power converter 8 has transitioned to an islanding operation state when both of the voltage ΔV₁ and the voltage ΔV₂ change in a negative direction.

The multiplication unit 821 and the determination units 823 and 825 of the second block 82c execute the same processing as that of the multiplication unit 829 and the determination units 822 and 825 of the first block 82b, respectively, although description thereof is omitted.

Third Embodiment

A power converter 9 of the present embodiment differs from the second embodiment in the interconnection point voltage amplitude control unit 62 of FIG. 9. FIG. 17 is a diagram to describe an interconnection point voltage amplitude control unit 92 of the present embodiment.

As described above, the smaller power consumed by the load G is, the less the voltage diverges. In such a case, in the processing executed by the islanding operation detection unit 62j of the embodiment above, there is a case where even when the power converter is in an islanding operation state, the voltage ΔV₂ does not reach the upper and lower limit restriction in the restriction unit 62g.

According to the interconnection point voltage amplitude control unit 92 of the present variation, it is possible to detect an islanding operation state even in such a case.

The interconnection point voltage amplitude control unit 92 of the present embodiment further includes an adder 92a (corresponding to a “second addition unit”), as compared with the second embodiment.

The adder 92a outputs a voltage obtained by adding a certain modulation signal V_add to an output of the change rate restriction unit 62c, when power consumption of the load G supplied with power from the power converter 9 is a certain value or less. In the present embodiment, the voltage ΔV₁ input to the output unit 62e is the output of the adder 92a.

Here, the certain modulation signal V_add is preferably a signal that causes a voltage output from the change rate restriction unit 62c to be ΔV₂ having a sufficient amplitude for the processing executed by the islanding operation detection unit 62j. The modulation signal V_add may be, for example, a sine wave, a triangular wave, or the like having a certain amplitude.

The effect of including the adder 92a will be described below by using results of numerical simulation.

<<Numerical Simulation Result>>

FIGS. 18 and 19 are results of the numerical simulation assuming the power converter 6 of the second embodiment and the power converter 9 of the present variation. First, the result shown in FIG. 18 for the power converter 6 of the second embodiment will be described.

In FIG. 18, (a), (b), (c), (d), and (e) correspond to the active power and reactive power, the voltage amplitude, the frequency, the voltage ΔV₁ and voltage ΔV₂, and a result of the determination by the determination unit 738, respectively. FIG. 18 assumes that power consumed by the load G is 0 (zero). Note that the same also applies to FIG. 19 described below.

In each of these diagrams, the horizontal axis corresponds to a time point [sec] and shows 0 [sec] to 30 [sec]. Each of these diagrams assume that the power converter is interconnected with the power system 1 at 0 [sec] to 25 [sec] and that the power converter transitions to an islanding operation state at 25 [sec].

Here, focusing particularly on the voltage ΔV₂ in FIG. 18(d), the power converter 6 transitions to an islanding operation state, but the voltage ΔV₂ transitions at almost 0 (zero) because of the load G not being sufficiently large.

Accordingly, the voltage ΔV₂ does not reach the upper and lower limit restriction in the restriction unit 62g (FIG. 9). Thus, a result of the determination by the islanding operation detection unit 62j of FIG. 14(e) is always 0, and in spite of the transition to the islanding operation state, the islanding operation state is not detected.

Next, the result shown in FIG. 19 for the power converter 9 of the present embodiment will be described.

In particular, the voltage ΔV₁ (solid line) in FIG. 19(d) transitions in a waveform of a triangular wave. On the other hand, the voltage ΔV₂ (broken line) transitions at almost 0 (zero) until the transition to the islanding operation state at the time point 25 [sec], but transitions in a waveform of a triangular wave together with the voltage ΔV₁ from the time point 25 [sec].

The determination result in FIG. 19(e) shows switching from 0 to 1 around a time point 26 [sec], which shows detection of the transition to the islanding operation state. This is because the voltage ΔV₂ starts to transition in the waveform of the triangular wave together with the voltage ΔV₁ at the time point 25 [sec].

Therefore, according to the power converter 9 of the present embodiment, it is possible to accurately detect whether the power converter 9 has transitioned to an islanding operation state even when power consumed by the load G is not sufficiently large.

SUMMARY

The power converter 2 according to the first embodiment is a power converter 2 capable of being interconnected with a power system 1 and including a virtual synchronous generator function, the power converter including: a frequency feedback unit 22a that outputs, after applying computation of a certain transfer function G_o to frequency in the virtual synchronous generator function or a frequency of a voltage at an interconnection point to the power system 1, a processing result obtained by applying an upper and lower limit restriction to the resultant computation; an addition unit that outputs a second amplitude command value obtained by adding a certain first amplitude command value related to the voltage at the interconnection point to the processing result; an interconnection point voltage amplitude control unit 22 that generates an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point; a voltage output unit that generates a three-phase AC voltage, based on a phase and an output voltage amplitude in the virtual synchronous generator function; and an islanding operation detection unit 22d that detects, when the processing result reaches the upper and lower limit restriction, an islanding operation state in which the power converter 2 is separated from the power system 1, wherein the transfer function G_o includes at least a second-order polynomial of a Laplace operator in a denominator and a first-order monomial of a Laplace operator in a numerator, and is given coefficients in the polynomial and the monomial such that a denominator of a closed-loop transfer function G_C in a closed loop in a case where a change in a phase being an output of a virtual synchronous generator using active power as an input, a voltage amplitude change being a result obtained by performing computation of a certain transfer function using a frequency of the virtual synchronous generator or an interconnection point voltage frequency as an input, and an active power change caused by the phase change and the voltage amplitude change are collectively regarded as one closed-loop system becomes a stable polynomial when the power converter 2 is interconnected with the power system 1 and becomes an unstable polynomial when the power converter 2 is in islanding operation.

According to such a configuration, stability is maintained in the interconnection and instability occurs after transition to the islanding operation state, thereby allowing islanding operation to be detected.

In the power converter 2 according to the first embodiment, the coefficients in the polynomial and the monomial are set such that coefficients of terms included in a characteristic equation of the closed-loop transfer function G_C have all the same sign when the power converter 2 is interconnected with the power system 1 and that a term with a sign different from a sign of a coefficient of another term occurs in the characteristic equation of the closed-loop transfer function G_C when the power converter 2 is in the islanding operation. According to such a configuration, it is possible to easily achieve securing of stability in the interconnection and instability after transition to the islanding operation state.

In the power converter 2 according to the first embodiment, the transfer function G_o includes the denominator being a second-order polynomial of a Laplace operator. According to such a setting, the number of independent parameters to be set can be suppressed, thereby simplifying setting of the parameters.

In the power converter 2 according to the first embodiment, the transfer function G_o includes the denominator expressed by a square of a first-order polynomial of a Laplace operator. According to such a setting, the number of independent parameters to be set can be further suppressed, thereby further simplifying setting of the parameters.

The detection method according to the first embodiment is a detection method for detecting an islanding operation state in which a power converter 2 including virtual synchronous generator control and interconnected with a system is separated from a power system 1, wherein the power converter 2 includes: outputting, after applying computation of a certain transfer function G_o to a frequency in the virtual synchronous generator function or a frequency of a voltage at an interconnection point to the power system 1, a processing result obtained by applying an upper and lower limit restriction to the resultant computation; outputting, by adding a certain first amplitude command value related to the voltage at the interconnection point and the processing result, a second amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point; generating a three-phase AC voltage, based on a phase and an output voltage amplitude in the virtual synchronous generator function; and detecting, when the processing result reaches the upper and lower limit restriction, an islanding operation state in which the power converter 2 is separated from the power system 1, and wherein the transfer function G_o includes at least a second-order polynomial of a Laplace operator in a denominator and a first-order monomial of a Laplace operator in a numerator, and is given coefficients in the polynomial and the monomial such that a denominator of a closed-loop transfer function G_C in a closed loop in a case where a change in a phase being an output of a virtual synchronous generator using active power as an input, a voltage amplitude change being a result obtained by performing computation of a certain transfer function using a frequency of the virtual synchronous generator or an interconnection point voltage frequency as an input, and an active power change caused by the phase change and the voltage amplitude change are collectively regarded as one closed-loop system becomes a stable polynomial when the power converter 2 is interconnected with the power system 1 and becomes an unstable polynomial when the power converter 2 is in islanding operation.

According to such a method, stability is maintained in the interconnection and instability occurs after transition to the islanding operation state, thereby allowing islanding operation to be detected.

The power converters 6, 7, 8, and 9 according to the second and third embodiments and Variations 2 and 3 are each a power converter capable of being interconnected with a power system 1 and including a virtual synchronous generator function, the power converter including: a frequency feedback unit 62a that outputs a voltage depending on one frequency out of a frequency ω in the virtual synchronous generator function and a frequency ωout of a voltage at an interconnection point to the power system 1; a reactive power control unit 62d that outputs a voltage ΔV_q depending on reactive power at the interconnection point, an output unit 62e that outputs a voltage ΔV₂ obtained by applying a first upper and lower limit restriction to a result of addition of a voltage ΔV₁ based on the output of the frequency feedback unit 62a to the voltage ΔV_q; 62h an adder that outputs an interconnection point voltage amplitude command value V_ref* obtained by adding a certain amplitude command value V_ref** related to the voltage at the interconnection point to the voltage ΔV₂; an interconnection point voltage amplitude control unit 62 that generates an inverter output voltage amplitude command value V_INV, based on the interconnection point voltage amplitude command value V_ref* and an amplitude V_out of the voltage at the interconnection point; a voltage output unit that generates a three-phase AC voltage, based on a phase θ in the virtual synchronous generator function and the inverter output voltage amplitude command value V_INV; and an islanding operation detection unit 62j that detects, when the voltage ΔV₂ reaches the first upper and lower limit restriction, an islanding operation state in which the power converter is separated from the power system 1. The frequency feedback unit 62a outputs, when the power converter is in the islanding operation state, a voltage with an increased width of change caused by change in the one frequency, and the reactive power control unit 62d outputs, when the power converter is interconnected with the power system 1, the voltage ΔV_q for suppressing change in the reactive power at the interconnection point caused by change in the frequency.

According to such a configuration, in a state where the power converter is interconnected with the power system 1, it is possible to prevent occurrence of erroneous detection of transition to the islanding operation state in a case where the frequency changes for some reason. Thus, it is possible to accurately detect whether the power converter has transitioned to an islanding operation state.

In the power converter above, the frequency feedback unit 62a outputs, when the power converter is in the islanding operation state, a voltage with an increased width of change caused by change in the one frequency, and the reactive power control unit 62d outputs, when the power converter is interconnected with the power system 1, the voltage ΔV_q for suppressing change in the reactive power at the interconnection point caused by change in the frequency. According to such a configuration, it is possible to more accurately detect whether the power converter has transitioned to an islanding operation state.

The power converter above may further include an upper and lower limit restriction unit 62b that outputs a voltage obtained by applying a second upper and lower limit restriction to the output of the frequency feedback unit 62a, and the voltage ΔV₁ may be a voltage based on the output of the upper and lower limit restriction unit 62b. According to such a configuration, an amplitude of the voltage ΔV₁ is limited, thereby allowing the voltage ΔV_q to easily follow change in the voltage ΔV₁ (in other words, allowing the voltage ΔV_q to cancel the voltage ΔV₁ without difficulty). Thus, it is possible to more effectively prevent occurrence of erroneous detection of transition to the islanding operation state.

The power converter above may further include a change rate restriction unit 62c that outputs a voltage obtained by applying an upper limit restriction of a time change rate to the output of the upper and lower limit restriction unit 62b, and the voltage ΔV₁ may be a voltage based on the output of the change rate restriction unit 62c. According to such a configuration, a time change rate of the voltage ΔV₁ is limited, thereby allowing the voltage ΔV_q to more easily follow change in the voltage ΔV₁ (in other words, allowing the voltage ΔV₁ to be easily canceled). Thus, it is possible to more effectively prevent occurrence of erroneous detection of transition to the islanding operation state.

In the power converter above, the islanding operation detection unit 62j detects that the power converter is in the islanding operation state, based on the voltage ΔV₁ and the voltage ΔV₂. According to such a configuration, even when it is difficult to determine whether the power converter has transitioned to an islanding operation state due to lack of sufficient amplitudes of the voltage ΔV₁ and the voltage ΔV₂, it is possible to accurately determine the transition.

In the power converter above, the islanding operation detection unit 62j may detect that the power converter is in the islanding operation state, based on transition of the voltage ΔV₁ and transition of a ratio between the voltage ΔV₁ and the voltage ΔV₁. According to such a configuration, even when it is difficult to determine whether the power converter has transitioned to an islanding operation state due to lack of sufficient amplitudes of the voltage ΔV₁ and the voltage ΔV₂, it is possible to more accurately determine the transition.

In the power converter above, the islanding operation detection unit 62j may detect that the power converter is in the islanding operation state, based on transition of the second voltage and a degree of similarity between transition of the voltage ΔV₁ and transition of the voltage ΔV₂. According to such a configuration, even when it is difficult to determine whether the power converter has transitioned to an islanding operation state due to lack of sufficient amplitudes of the voltage ΔV₁ and the voltage ΔV₂, it is possible to more accurately determine the transition.

The power converter above may further include an adder 92a that outputs a voltage obtained by adding a certain modulation signal to the output of the change rate restriction unit 62c, when power consumption of a load supplied with power from the power converter is a certain value or less, and the second voltage may be the output of the second addition unit. According to such a configuration, even when it is difficult to determine whether the power converter has transitioned to an islanding operation state due to lack of sufficiently large power consumed by the load G, it is possible to more accurately determine the transition.

The embodiments above are presented as examples of the disclosure and are not intended to limit the scope of the disclosure. Various omissions, replacements, and changes can be made on the configurations above without departing from the scope of the disclosure. The embodiments above and variations thereof are included in the scope and gist of the disclosure, and are included in the disclosure described in the claims and the equivalents thereof.

Claims

1. A power converter configured to be interconnected with a power system and to perform virtual synchronous generator function, the power converter comprising: a processor, anda non-transitory storage medium having program instructions stored thereon, execution of which by the processor causes the power converter to provide functions of a frequency feedback unit configured to apply a transfer function to one of a frequency in the virtual synchronous generator function, ora frequency of a voltage at an interconnection point of the power converter to the power system, andapply an upper and lower limit restriction to a result of the application of the transfer function,to thereby generate a processing result;an addition unit configured to output, by adding a first amplitude command value related to the voltage at the interconnection point and the processing result, a second amplitude command value;an interconnection point voltage amplitude control unit configured to generate an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point;a voltage output unit configured to generate a three-phase Alternating Current (AC) voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; andan islanding operation detection unit configured to detect, responsive to the processing result reaching the upper and lower limit restriction, an islanding operation state in which the power converter is separated from the power system, whereinthe transfer function has: a denominator that includes at least a second-order polynomial of a Laplace operator, anda numerator that includes a first-order monomial of the Laplace operator,the polynomial and the monomial being so configured that the denominator is a stable polynomial when the power converter is interconnected with the power system and is an unstable polynomial when the power converter is the in islanding operation state.

2. The power converter according to claim 1, wherein the transfer function includes a characteristic equation that has a first term and a second term, andthe polynomial and the monomial are so configured that coefficients of the first and second terms have a same sign when the power converter is interconnected with the power system, and have different signs when the power converter is in the islanding operation state.

3. The power converter according to claim 1, wherein the denominator of the transfer function includes only the second-order polynomial of the Laplace operator.

4. The power converter according to claim 3, wherein the denominator of the transfer function is expressed by a square of the first-order polynomial of the Laplace operator.

5. A detection method for detecting an islanding operation state of a power converter configured to be interconnected with a power system and to perform virtual synchronous generator function, the power converter being separated from the power system in the islanding operation state, the detection method comprising, performed by the power converter that includes a processor: applying a transfer function to one of a frequency in the virtual synchronous generator function, ora frequency of a voltage at an interconnection point of the power converter to the power system, and applying an upper and lower limit restriction to a result of the application of the transfer function, to thereby generate a processing result;outputting, by adding a first amplitude command value related to the voltage at the interconnection point and the processing result, a second amplitude command value;generating an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point;generating a three-phase Alternating Current (AC) voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; anddetecting, responsive to the processing result reaching the upper and lower limit restriction, the islanding operation state, whereinthe transfer function has: a denominator that includes at least a second-order polynomial of a Laplace operator, anda numerator that includes a first-order monomial of the Laplace operator,the polynomial and the monomial being so configured that the denominator is a stable polynomial when the power converter is interconnected with the power system and is an unstable polynomial when the power converter is in the islanding operation state.

6. A power converter configured to be interconnected with a power system and to perform virtual synchronous generator function, the power converter comprising: a processor, anda non-transitory storage medium having program instructions stored thereon, execution of which by the processor causes the power converter to provide functions of a frequency feedback unit configured to output a voltage depending on one of a frequency in the virtual synchronous generator function, anda frequency of a voltage at an interconnection point of the power converter to the power system;a reactive power control unit configured to output a first voltage depending on reactive power at the interconnection point; an output unit configured to apply a first upper and lower limit restriction to a result of addition of a second voltage based on the output of the frequency feedback unit and the first voltage, to thereby output a third voltage;a first addition unit configured to output, by adding a first amplitude command value related to the voltage at the interconnection point and the third voltage, a second amplitude command value;an interconnection point voltage amplitude control unit configured to generate an inverter output voltage amplitude command value, based on the second amplitude command value and an amplitude of the voltage at the interconnection point;a voltage output unit configured to generate a three-phase Alternating Current (AC) voltage, based on a phase for the virtual synchronous generator function and the inverter output voltage amplitude command value; andan islanding operation detection unit configured to detect, responsive to the third voltage reaching the first upper and lower limit restriction, an islanding operation state in which the power converter is separated from the power system.

7. The power converter according to claim 6, wherein the frequency feedback unit outputs, when the power converter is in the islanding operation state, a voltage with an increased width of change caused by change in the one frequency, andthe reactive power control unit outputs, when the power converter is interconnected with the power system, the first voltage for suppressing change in the reactive power at the interconnection point.

8. The power converter according to claim 6, wherein the frequency feedback unit applies a transfer function to the one frequency, andthe transfer function is so determined such that stability of the power system is maintained when the power converter is interconnected with the power system and instability occurs in the islanding operation state.

9. The power converter according to claim 6, the execution of the program instructions by the processor causes the power converter to further provide functions of: an upper and lower limit restriction unit configured to output a voltage obtained by applying a second upper and lower limit restriction to the output of the frequency feedback unit, whereinthe second voltage is a voltage based on the output of the upper and lower limit restriction unit.

10. The power converter according to claim 9, the execution of the program instructions by the processor causes the power converter to further provide functions of: a change rate restriction unit configured to output a voltage obtained by applying an upper limit restriction of a time change rate to the output of the upper and lower limit restriction unit, wherein the second voltage is a voltage based on the output of the change rate restriction unit.

11. The power converter according to claim 6, wherein the islanding operation detection unit detects that the power converter is in the islanding operation state, based on the second voltage and the third voltage.

12. The power converter according to claim 11, wherein the islanding operation detection unit detects that the power converter is in the islanding operation state, based on transition of the second voltage and transition of a ratio between the second voltage and the third voltage.

13. The power converter according to claim 11, wherein the islanding operation detection unit detects that the power converter is in the islanding operation state, based on transition of the second voltage and a degree of similarity between transition of the second voltage and transition of the third voltage.

14. The power converter according to claim 10, the execution of the program instructions by the processor causes the power converter to further provide functions of: a second addition unit configured to output a voltage obtained by adding a modulation signal to the output of the change rate restriction unit, when power consumption of a load supplied with power from the power converter is a value or less, whereinthe second voltage is the output of the second addition unit.