Pulse-width modulation method for a frequency converter

Abstract

A space-vector pulse-width modulation method for a frequency converter provided with a voltage intermediate circuit, said frequency converter comprising a mains bridge (10) to be connected to an alternating current source (UU, UV, UW), a direct-voltage intermediate circuit and a controlled load bridge (11) for supplying a variable-frequency alternating voltage (US, UR, UT) to a load (12), and in which method the modulator performing the modulation is given a reference. The load bridge modulator is given a reference consisting of the references for the flux linkage changes produced by the voltage vectors, the flux linkage change is calculated on the basis of measured intermediate-circuit voltage, and the currently active voltage vector is kept turned on until the reference value is reached.

Description

The present invention relates to a space-vector pulse-width modulation method for a use in a frequency converter. In particular, the invention relates to a space-vector pulse-width modulation method for a frequency converter provided with a voltage intermediate circuit. The invention also relates to a voltage-controlled frequency converter controllable by a space-vector pulse-width modulation method.

Space-vector pulse-width modulation (Space vector PWM, SVPWM) is a pulse-width modulation method for a frequency converter provided with a voltage intermediate circuit that is particularly well suited for digital implementation. In the modulation method, the on-time is generally calculated beforehand for two output voltage vectors of the frequency converter (i.e. for two software positions in the inverter bridge of the frequency converter) by software, from which the requested output voltage space vector is generated as an average. A control system containing a digital counter then takes care of changing the switch positions so that these two switch positions are on for the calculated times in question. The times are calculated by using the output voltage space vector as an input variable.

In the calculation of the on-times of the switch positions in question, the intermediate circuit voltage is assumed to be constant. This assumption holds good in the case of an intermediate circuit designed to so-called traditional ratings. If for some reason the intermediate circuit voltage undergoes a considerable change during a switching period, then the modulation method will be unable to implement the requested average output voltage space vector.

In the following, prior-art space-vector PWM, which is described e.g. in reference H. van der Broeck, H. Skudelny, and G. Stanke, “Analysis and realization of a pulse width modulator based on voltage space vectors”, in IEEE-IAS Conf. Records, pages 244-251, Denver, USA, 1986, will be referred to as traditional space vector PWM or SVPWM for short. The input variable in SVPWM is an output voltage reference, which can be divided into real and imaginary components U_s,ref=U_x+jU_y  (1)

The inverter output voltage can be expressed as a space vector $\begin{array}{cc}{U}_{s,\mathrm{out}}\left(\mathrm{sA},\mathrm{sB},\mathrm{sC}\right)=\frac{2}{3}{U}_{\mathrm{DC}}\left(\mathrm{sA}+\mathrm{sB}·e^{j·2·\pi /3}+\mathrm{sC}·e^{j·4·\pi /3}\right)& \left(2\right)\end{array}$

• • where s{A,B,C} is 1 if the phase {A,B,C} is connected to the upper arm of the inverter and 0 if the phase is connected to the lower arm. In different combinations, 6 active voltage vectors and two so-called zero vectors (all phases connected to the same arm) are obtained. The directions of the active voltage vectors in the complex plane are 0, 60, 120, 180, 240 and 300 degrees.

As shown in FIG. 1, the complex plane is divided into six equal sectors, with the first sector starting from the real axis. The direction of the real axis corresponds to the direction of the magnetic axis of the A phase of the stator of a three-phase motor connected to the inverter, direction 120 degrees corresponds to the direction of the magnetic axis of the B phase of the motor and 240 degrees to the direction of the C phase. The active voltage vectors form the borders between these sectors.

It is now possible in any sector m to produce any average voltage vector (of limited magnitude, however) by using the voltage vectors V_m and V_m+1 at the sector borders for time T_m and T_m+1. Space vector PWM implements such a voltage vector when the voltage reference is U_s,ref. $\begin{array}{cc}{U}_{s,\mathrm{ref}}=\frac{T_m}{T_s}{V}_m+\frac{T_{m+1}}{T_s}{V}_{m+1},& \left(3\right)\end{array}$

T_s is the sampling period, i.e. the update interval of the voltage reference. The voltage vectors V_m and V_m+1 at the borders of the sector m can be defined by equations $\begin{array}{cc}{V}_m=\frac{2}{3}{U}_{\mathrm{DC}}{e}^{j\frac{\pi }{3}\left(m-1\right)}{V}_{m+1}=\frac{2}{3}{U}_{\mathrm{DC}}{e}^{j\frac{\pi }{3}\left(m\right)}.& \left(4\right)\end{array}$

From equations (3) and (4), it is possible to calculate the times T_m and T_m+1 for the counter $\begin{array}{cc}\left[\begin{array}{c}{T}_m\\ T_{m+1}\end{array}\right]=\frac{\sqrt{3T_s}}{U_{\mathrm{DC}}}\left[\begin{array}{cc}\sin \left(\frac{\pi }{3}m\right)& -\cos \left(\frac{\pi }{3}m\right)\\ -\sin \left(\frac{\pi }{3}\left(m-1\right)\right)& \cos \left(\frac{\pi }{3}\left(m-1\right)\right)\end{array}\right]\left[\begin{array}{c}{U}_x\\ U_y\end{array}\right].& \left(5\right)\end{array}$

For the remaining time of the switching period T_s, the zero vector is used T₀=T_s−T_m−T_m+1

SVPWM can be implemented as a so-called symmetric method. In that case, the zero vector is used at the beginning, middle and end of the switching period, and the active voltage vectors V_m and V_m+1 are divided into two parts. Symmetric implementation provides the advantage of a lower harmonics content.

The object of the present invention is to create a new modulation method, so-called differential space-vector pulse-width modulation (DSVPWM), which takes a changing intermediate circuit voltage into account in such manner that the flux linkage change produced by the switch combinations is the same as would be produced by a constant intermediate circuit voltage with space vector PWM. In this way, the requested average output voltage space vector is achieved.

The new modulation method is based on converting a voltage reference into a flux linkage change reference. Instead of turn-on times of the voltage vectors, the modulator is given a reference for the flux linkage changes produced by the voltage vectors. The modulator then calculates the flux linkage change on the basis of the measured intermediate circuit voltage and keeps the currently active voltage vector turned on until the reference value is reached.

The details of the features characterizing the modulation method of the invention and the corresponding frequency converter are presented in the claims below.

In the following, the invention will be described in detail with reference to an example and the attached drawings, wherein

FIG. 1. Division of the complex plane into 60° sectors, with the voltage vectors forming the borders between sectors.

FIG. 2. Voltage vector V₁ produces flux linkage change Δψ₁ and voltage vector V₂ produces flux linkage change Δψ₂.

FIG. 3. DSVPWM implemented as a (quasi)symmetric method.

FIG. 4. Torque produced by a motor provided with a DSVPWM modulator.

FIG. 5. Torque produced by a motor provided with a SVPWM modulator.

FIG. 6. Frequency converter provided with a controlled mains bridge.

FIG. 6 presents a three-phase voltage-controlled frequency converter with an AC inductor L_AC for limiting mains current harmonics, a mains bridge 10 (rectifier) for rectifying the three-phase alternating voltage of a supply network having phase voltages U_U, U_V, U_W to produce the direct voltage U_DC of a DC intermediate circuit, and a load bridge (inverter) 11 for inverting the direct voltage of the DC intermediate circuit to produce a variable-frequency three-phase alternating voltage consisting of phase voltages U_R, U_S, U_T. The frequency converter feeds a three-phase motor (M) 12. The load bridge 11 is a full-wave bridge with a control unit 13 controlling the semiconductor switches V11-V16 of each phase and with zero diodes D11-D16 connected in inverse-parallel with the switches. The mains bridge 10 may be a controlled full-wave bridge according to the example in FIG. 6, having in each arm of the bridge controllable semiconductor switches V1-V6, such as IGBTs, and zero diodes 01-D6 connected in inverse-parallel with these, so that power can flow from the mains to the load and also from the load to the mains e.g. when the motor is braking. The mains bridge 10 may also be a non-controlled circuit with no controlled semiconductor switches, in which case power can only flow from the mains to the load.

If the intermediate circuit voltage U_DC remains constant during the turn-on times, then the flux linkage of the motor will change Δψ=T_mV_m+T_m+1V_m+1

The new modulation method DSVPWM is thus based on converting the voltage reference into a flux linkage change reference. Instead of turn-on times of the voltage vectors, the modulator is given references for the flux linkage changes produced by the voltage vectors. The modulator then calculates the flux linkage change on the basis of the measured intermediate circuit voltage and keeps the currently active voltage vector turned on until the reference value is reached.

The reference value of flux linkage change is obtained by partly multiplying equation (3) by the sampling period T_s: U_s,refT_s=T_mV_m+T_m+1V_m+1 Δψ_s,ref=Δψ_m+Δψ_m+1  (6)

Now, terms T_mV_m=Δψ_m and T_m+1V_m+1=Δψ_m+1 are the flux linkage changes that the voltage vectors V_m and V_m+1 should produce as they are acting on the machine. Thus, Δψ_m and Δψ_m+1 are the reference values for the flux linkage changes. Since the equation for T_m and T_m+1 was already solved above into equation (4), the equation for Δψ_m and Δψ_m+1 will be obtained by multiplying (4) with the matrix diag([V_m V_m+1]) from the right. After simplification, we obtain $\begin{array}{cc}\left[\begin{array}{c}{\mathrm{\Delta \psi }}_{m,\mathrm{ref}}\\ {\mathrm{\Delta \psi }}_{m+1,\mathrm{ref}}\end{array}\right]=\frac{2T_s}{\sqrt{3}}\left[\begin{array}{cc}\sin \left(\frac{\pi }{3}m\right)& -\cos \left(\frac{\pi }{3}m\right)\\ -\sin \left(\frac{\pi }{3}\left(m-1\right)\right)& \cos \left(\frac{\pi }{3}\right)m-1))\end{array}\right]\left[\begin{array}{c}{U}_x{e}^{\mathrm{j\pi }\left(m-1\right)/3}\\ U_y{e}^{\mathrm{j\pi m}/3}\end{array}\right].& \left(7\right)\end{array}$

The idea of the flux linkage change reference can be understood from the attached FIG. 2, which illustrates the way in which the flux linkage change is produced in sector m=1. In the figure, the flux linkage change reference is Δψ_ref. With voltage vector V_m=V₁, flux linkage change Δψ₁ has to be produced, and with voltage vector V_m+1=V₂, flux linkage change Δψ₂ has to be produced. The transition between voltage vectors takes place when the actual value reaches the reference.

The actual value of flux linkage change for comparison with the reference is obtained by calculating the time integral of the inverter output voltage during the turn-on period $\begin{array}{cc}{\mathrm{\Delta \psi }}_{m,\mathrm{cale}}=\int V_{m}dt=\int \frac{2}{3}{U}_{\mathrm{DC},\mathrm{meas}}{e}^{j\frac{\pi }{3}\left(m-1\right)}dt,\mathrm{kun}{V}_m\mathrm{on}\mathrm{aktiivinen}\text{}{\mathrm{\Delta \psi }}_{m+1,\mathrm{cale}}=\int V_{m+1}dt=\int \frac{2}{3}{U}_{\mathrm{DC},\mathrm{meas}}{e}^{j\frac{\pi }{3}\left(m\right)}dt,\mathrm{kun}{V}_{m+1}\mathrm{on}\mathrm{aktiivinen}& \left(8\right)\end{array}$

• • where U_Dc,meas is the measured intermediate circuit voltage.

The flux linkage change Δψ_m,calc, is only calculated when V_m is active. Although V_m+1 also produces a component in the direction of V_m, it is not taken into account in the calculation of b Neither is the component produced by V_m in the direction of V_m+1 taken into account in the calculation of Δψ_m+1,calc. The voltage vector is changed from V_m to V_m+1 (i.e. the position of the switches of the inverter is changed) when the actual value Δψ_m,calc reaches the reference Δψ_m,ref.

It is to be noted that the complex exponential function appearing in both the reference and the actual value has an absolute value of unity. Therefore, it is possible to consider only the absolute value in both the reference and the actual value and omit the multiplication by the complex exponential function in the implementation of both. A further advantageous observation is that if the equations for both the reference and the actual value are multiplied by 3/2, one multiplication operation will be left out from the calculation of the actual value and in the calculation of the reference value the coefficient will be T_s{square root}{square root over (3)}.

Like SVPWM, DSVPWM can also be implemented as a (quasi)symmetric method. In a symmetric implementation, the first voltage vector V_m is turned on at the beginning of the switching period. V_m is kept turned on until the flux linkage change equals half the reference Δψ_m,ref. After this, the second voltage vector V_m+1 is applied and it is kept turned on until the flux linkage change produced by it equals half the reference Δψ_m,ref. After this, the zero voltage vector V₇ is turned on until time T_s/2 has elapsed from the beginning of the switching period. Upon the lapse of T_s/2, V_m+1 is turned on until the remaining half of reference m for flux linkage change has been fulfilled. After that, V_m is turned on and applied until the remaining half of reference Δψ_m,ref for flux linkage change has been fulfilled. If there is still time left over before T_s, then the zero vector V₀ is additionally turned on. This sequence is illustrated in the attached FIG. 3.

Presented in the attachment is a comparison between the performances of SVPWM and the described DSVPWM. FIGS. 4 and 5 represent the torque produced by the motor. The results have been obtained by simulating the operation of a motor drive with both modulation methods so that in both cases the voltage references for both control methods are generated by current vector control. The simulations were performed using a low-capacitance intermediate circuit, so a constant intermediate circuit assumption can no longer be used with a good accuracy. In other respects, the same boundary conditions were applied in the simulations. Thus, the only difference between the two situations is the modulation method. A high value of the inertial mass of the rotor of the motor was used, so the rotational speed could not vary from its set value, which was 0.7 pu.

It can be seen from FIGS. 4 and 5 that the torque produced by SVPWM oscillates badly, whereas DSVPWM is able to produce a more even torque.

Although the example presented above describes the application of the disclosed new modulation method to the modulation of the voltage to be supplied to a motor, the method can also be applied to the modulation of the voltage of a controlled mains bridge. In this case, instead of being converted into a reference for the flux linkage change of the motor, the voltage reference is converted into an imaginary reference for the flux linkage change of the inductor (L_AC, FIG. 6) connected between the power supply mains and the bridge. The modulation method now produces at the mains bridge input voltage connection exactly the requested voltage regardless of variations of the intermediate circuit voltage

It is obvious to the person skilled in the art that different embodiments of the invention are not limited to the example described above, but that they may be varied within the scope of the claims presented below.

Claims

1. Space-vector pulse-width modulation method for a frequency converter provided with a voltage intermediate circuit, said frequency converter comprising a mains bridge (10) to be connected to an alternating current source (UU, UV, UW), a direct-voltage intermediate circuit and a controlled load bridge (11) for supplying a variable-frequency alternating voltage (US, UR, UT) to a load (12), characterized in that the references for the flux linkage changes produced by the voltage vectors are given as a reference to the modulator of the load bridge, the flux linkage change is calculated on the basis of measured intermediate-circuit voltage, and the currently active voltage vector is kept turned on until the reference value is reached.

2. Method according to claim 1, characterized in that, in the method, a first voltage vector (Vm) is turned on and kept in the turned-on state until the flux linkage change equals half the reference (Δψm,ref), whereupon a second voltage vector (Vm+1) is applied and kept turned on until the flux linkage change produced by it equals half the reference Δψm+1,ref, whereupon a zero voltage vector (V7) is turned on until a time (Ts/2) corresponding to half the duration of the switching period has elapsed from the beginning of the switching period, and after that the second voltage vector (Vm+1) is turned on until the remaining half of reference (Δψm+1,ref) for flux linkage change has been fulfilled, whereupon the first voltage vector (Vm) is again turned on and applied until the remaining half of reference (Δψm,ref) for flux linkage change has been fulfilled, and after that, if any time of the switching period still remains, the zero voltage vector (V0) is additionally turned on until the end of the switching period.

3. Method according to claim 1 and 2, wherein the frequency converter's mains bridge is also a controlled bridge, characterized in that the mains bridge is likewise controlled using a corresponding differential space-vector pulse-width modulation (DSVPWM) method, wherein the mains bridge modulator is given a reference value consisting of imaginary references for the flux linkage change of the inductor (LAC) connected between the power supply mains and the bridge.

4. Frequency converter, comprising a mains bridge (10) to be connected to an alternating current source (UU, UV, UW), a direct-voltage intermediate circuit and a controlled load bridge (11) for supplying a variable-frequency alternating voltage (US, UR, UT) to a load (12), said load bridge being controlled by space vector pulse-width modulation by means of a modulator provided in a control unit (13), characterized in that in the control unit (13) the reference for the mains bridge modulator consists of the references for the flux linkage changes produced by the voltage vectors, the modulator calculates the flux linkage change on the basis of measured intermediate-circuit voltage and keeps the currently active voltage vector turned on until the reference value is reached.

5. Frequency converter according to claim 4, characterized in that the modulator turns on a first voltage vector (Vm), which is kept turned-on until the flux linkage change equals half the reference (Δψm,ref) whereupon the modulator changes to a second voltage vector (Vm+1), which is kept turned-on until the flux linkage change produced by it equals half the reference Δψm+1,ref, whereupon the modulator turns on a zero voltage vector (V7) until a time (Ts/2) corresponding to half the duration of the switching period has elapsed from the beginning of the switching period, and after that the modulator turns on the second voltage vector (Vm+1) until the remaining half of reference (Δψm+1,ref) for flux linkage change has been fulfilled, whereupon the modulator again turns on the first voltage vector (Vm), which is applied until the remaining half of reference (Δψm,ref) for flux linkage change has been fulfilled, and after that, if any time of the switching period still remains, the modulator additionally turns on the zero voltage vector (V0) until the end of the switching period.

6. Frequency converter according to claim 4 and 5, in which frequency converter the mains bridge is also a controlled bridge, characterized in that the modulator of the mains bridge controls the mains bridge by a corresponding differential space-vector pulse-width modulation (DSVPWM) method, wherein the reference value for the mains bridge modulator consists of imaginary references for the flux linkage change of the inductor (LAC) connected between the power supply mains and the bridge.