The present invention discloses a microgrid delay margin calculation method based on critical characteristic root tracking, and in particular to a calculation method for the delay margin of secondary voltage control in a microgrid, which belongs to the technical field of microgrid operation control.
With the gradual depletion of earth resources and the concern of people about environmental issues, the access of renewable energy is receiving more and more attention from all the countries in the world.
As an emerging energy transmission mode that increases the penetration of renewable energies and distributed energy resources in an energy supply system, a microgrid comprises different types of distributed energy resources (DER), such as microturbines, wind-driven generators, photovoltaics, fuel cells, energy storage equipments, and the user terminals of various electrical loads and/or thermal loads and related monitoring and protection devices.
The power in the microgrid mainly depends on power electronic devices to convert energy and to provide necessary control. Relative to the main grid, the microgrid appears as a single controlled unit, which can simultaneously meet the requirements of users on the quality of electrical energy, the safety of power supply, etc. The microgrid exchanges energy with the main grid via a point of common coupling, and the two parts are standbys for each other, thus increasing the stability of power supply. As a small-scale decentralized system with a short distance from loads, the microgrid reduces power loss while increasing the reliability of local power supplies, which greatly increases the efficiency of energy utilization, so that microgrid is a novel power supply mode that meets the development requirement of intelligent power grids in the future.
Droop control has drawn attention due to the capability of realizing power sharing without communication. However, as the steady-state deviation of the output voltage of each distributed generation may occur and due to the difference of output impedances of all the distributed generations, accurate reactive power sharing can hardly be satisfactory, so that the secondary voltage control of the microgrid needs to be adopted to improve the reactive power sharing effect and voltage performance. At present, designed coordinated voltage control is of a centralized control structure in which a centralized voltage controller of the microgrid generates and sends a control signal to the local controller of each distributed generation. The centralized control structure depends on the centralized communication technology, however, the communication process is usually affected by information delay and packet loss, and the influence of information delay, packet loss and so on lead to the poor dynamic performance of the microgrid and even endanger system stability. For the aforementioned reasons, it is necessary to research a calculation method for the secondary voltage control delay margin of microgrid to analyze a maximum communication delay time in a stable microgrid, it is necessary to analyze the relationship between the centralized controller parameters of the microgrid and delay margins, consequently, the design of control parameters can be guided, and the stability and dynamic performance of the microgrid can be effectively improved.
Aimed at the phenomenon that the influence of communication delays on dynamic performance is usually neglected in the reactive power sharing and voltage recovery control of a microgrid, the present invention is directed to provide a microgrid delay margin calculation method based on critical characteristic root tracking in full consideration of the actual situation that the influence of communication delays on the system stability cannot be neglected due to the small inertia of power electronic-interfaced microgrid. By the method, all possible pure virtual characteristic roots of the microgrid characteristic equation are obtained, then the maximum delay time in a stable microgrid is calculated, and by researching the relationship between controller parameters and delay margins for stability, a guidance is provided for the design of controller parameters, solving the technical problem that the stability of existing microgrid system is affected by the communication technology.
In order to achieve the foregoing objectives, the present invention uses the following technical solutions:
Provided is a microgrid delay margin calculation method based on critical characteristic root tracking, comprising: establishing an inverter closed-loop small-signal model and a distributed generation closed-loop small-signal model with voltage feedback control amount including communication delays according to the static feedback output method, establishing a microgrid small-signal model consisting of the connection network model, the dynamic equation of load impedance and the distributed generation closed-loop small-signal model, obtaining a characteristic equation with a transcendental term from the microgrid small-signal model, performing critical characteristic root locus tracking for the transcendental term, and then determining the delay margin for the system stability.
Further, in the microgrid delay margin calculation method based on critical characteristic root tracking, the inverter closed-loop small-signal model with voltage feedback control amount including communication delay established according to the static feedback output is:
Δxinv and Δ{dot over (x)}inv respectively represent the state variables and the change rate of the closed-loop small signal model of the inverter, Δxinv=[Δxinv1, Δxinv2, . . . , Δxinvi, . . . , Δxinvn, Δφ1, Δφ2, . . . , Δφi, . . . , Δφn, Δγ]T, Δxinv1, Δxinv2, Δxinvi and Δxinvn respectively represent small-signal state variables of the first, second, ith and nth distributed generations, Δφ1, Δφ2, Δφi and Δφn respectively represent small-signal state variables for reactive power ancillaries of the first, second, ith and nth distributed generations, the small-signal state variable for the reactive power ancillary Δφi of the ith distributed generation is determined by an expression:
φi represents the change rate of the small-signal state variable for the reactive power ancillary of the ith distributed generation, Qi represents the actually output reactive power of the ith distributed generation, nQi represents the voltage droop characteristic coefficient of the ith distributed generation, n represents the number of the distributed generations, Δγ represents the small-signal state variable for voltage ancillary of the distributed generations, the small-signal state variable Δγ for the voltage ancillaries of the distributed generations is determined by an expression:
{dot over (γ)} represents the change rate of the small-signal state variable for the voltage ancillary of the distributed generations, V*i represents an expected value of the average voltage of the ith distributed generation, Vodi represents the d-axis component of the output voltage of the ith distributed generation under its own reference coordinate system dq, Ainv represents the state matrix of the distributed generation, ΔVbDQ represents the small-signal state variables of bus voltages in the common reference coordinate system DQ, ΔVbDQ=[ΔVbDQ1, ΔVbDQ2, . . . , ΔVbDQ1, . . . , ΔVbDQm]T, ΔVbDQ1, ΔVbDQ2, ΔVbDQ1 and ΔVbDQm respectively represent the small-signal state variables of voltages of first, second, lth and mth buses in the common reference coordinate system DQ, m represents the number of the buses, Binv represents the input matrix of the distributed generations to the bus voltages, Δu represents the small-signal control amounts of the secondary voltages of the distributed generations, Δu=[Δu1, Δu2, . . . , Δui, . . . , Δun)]T, Δu1, Δu2, Δui and Δun respectively represent the small-signal control amounts of the secondary voltages of the first, second, ith and nth distributed generations, Bu represents the input matrix of the distributed generation to the small-signal control amount of the secondary voltage Δui=KQiΔyinvQi(t−τi)+KViΔyinvV(t−τi), t represents the current time, τi represents the communication delay between the local controller of the ith distributed generation and the centralized secondary voltage controller of microgrid, KQi and KVi respectively represent the control coefficients of the reactive power and voltage of the ith distributed generation, ΔyinvQi represents the small-signal state variable of reactive power of the ith distributed generation, ΔyinvQ and ΔyinvV respectively represent the small-signal state variables of the reactive power and voltages of the distributed generations, and CinvQ and CinvV respectively represent the output matrices of reactive power and voltage of the distributed generations.
Further, in the microgrid delay margin calculation method based on critical characteristic root tracking, the distributed generation closed-loop small-signal model with voltage feedback control amount including communication delay established according to the static feedback output is:
Ādi represents the delayed state matrix of the ith distributed generation, Ādi=[0 . . . BuiKQiCinvQi+BuiKViCinvV . . . 0], Bui represents the input matrix of the ith distributed generation to the small-signal control amount of the secondary voltage, CinvQi represents the output matrix of reactive power of the ith distributed generation, ΔioDQ represents the small-signal state variables of the output currents of the distributed generations in the common reference coordinate system, and Cinvc represents the output matrix of currents of the distributed generations.
Further, in the microgrid delay margin calculation method based on critical characteristic root tracking, the microgrid small-signal model is
x and {dot over (x)} respectively represent the small-signal state variables and the change rate of microgrid, x=[ΔxinvΔilineDQΔiloadDQ]T, ΔilineDQ represents the small-signal state variables of the currents of connection lines between buses connected to the distributed generations in the common reference coordinate system, the small-signal state variable of the current of the connection line between the bus connected to the ith distributed generation and the bus connected to the jth distributed generation in the common reference coordinate system DQ is:
ΔilineDij and Δ{dot over (i)}lineDij respectively represent the D-axis component of small-signal variable of the current of the connection line ij and its change rate in the common reference coordinate system, ΔilineQij and ΔilineQij respectively represent the Q-axis component of small-signal variable of the current of the connection line ij and its change rate in the common reference coordinate system DQ, rlineij and Llineij respectively represent the line resistance and the line inductance of the connection line, ω0 represents the rated angular frequency of the microgrid, ΔVbusDi and ΔVbusQi respectively represent the D-axis component and the Q-axis component of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, ΔVbusDj and ΔVbusQj respectively represent the D-axis component and Q-axis component of the voltage of the bus connected to the jth distributed generation in the common reference coordinate system, ΔiloadDQ represents the small-signal state variables of the currents of loads connected to the buses in the common reference coordinate system DQ, the small-signal state variable of the current of the load connected to the lth bus in the common reference coordinate system DQ is:
ΔiloadD1 and Δ{dot over (i)}loadD1 respectively represent the D-axis component of the current of load connected to the lth bus and the change rate of the current of the load in the common reference coordinate system DQ, ΔiloadQl and ΔiloadQl respectively represent the Q-axis component of the current of the load connected to the lth bus and its change rate in the common reference coordinate system DQ, Rloadl and Lloadl respectively represent the load resistance and the load inductance of the load connected to the lth bus, ΔVbusDl and ΔVbusQl respectively represent the D-axis component and Q-axis component of the voltage of the lth bus in the common reference coordinate system DQ, and Adi and τi respectively represent the delayed state matrix and delay of the ith distributed generation.
As a further optimized solution of the microgrid delay margin calculation method based on critical characteristic root tracking, the method for obtaining the characteristic equation with the transcendental term from the microgrid small-signal model is as follows: when the delays of the distributed generations are consistent, the characteristic equation of the microgrid small-signal model is obtained: CEτ(s,τ)=det(sI−A−Ade−τs), s represents the parameter of the time domain complex plane, T represents the consistent delay time of each distributed generation, CEτ(⋅) represents a characteristic equation of the microgrid small-signal model obtained according to the consistent delay T of each distributed generation, det(⋅) represents the matrix determinant, I represents a unit matrix, Ad represents the delayed state matrix of the distributed generations,
and e−τs represents the transcendent term.
As a more further optimized solution of the microgrid delay margin calculation method based on critical characteristic root tracking, critical characteristic root locus tracking is performed for the transcendent term, then a delay margin meeting the requirement of system stability is determined, and the specific method is as follows: with a delay time ancillary variable as the variable of the characteristic equation, all pure virtual characteristic roots of the characteristic equation within the change cycle of the delay time ancillary variable are solved, a minimum value is chosen as the delay margin meeting the requirement of system stability from the critical delays corresponding to all the pure virtual characteristic roots, and the delay time ancillary variable is the product of the delay of distributed generation and the amplitude of the virtual characteristic root.
The technical solutions used in the present invention have the following beneficial effects:
(1) According to the calculation method for the secondary voltage control delay margin of the microgrid provided by the present invention, a microgrid closed-loop small-signal model with voltage feedback control amount including communication delay is established based on static output feedback, thus obtaining a characteristic equation with a transcendental term, critical characteristic root locus tracking is performed for the transcendental term of the system characteristic equation, possible pure virtual characteristic roots are searched, then a maximum delay time for a stable microgrid is calculated; the method can effectively alleviate the influence of communication delay on the dynamic performance of the microgrid, effectively improving the stability and dynamic performance of the microgrid.
(2) By solving system stability margins under different controller parameters, and researching the relationship between the controller parameters and the delay margins, the design of the controller parameters can be guided, effectively improving the stability and dynamic performance of the microgrid.
The following describes the technical solutions of the present invention in detail with reference to accompanying drawings.
As shown in
Step (10): Establish the inverter closed-loop small-signal model with voltage feedback control amount including communication delay based on static output feedback Each distributed generation utilizes the droop control loop in the local controller to set the references of inverter output voltage and frequency, as shown in formula (1):
In formula (1), ωi represents the local angular frequency of the ith distributed generation; ωn represents the reference value of the local angular frequency of the distributed generation, unit: rad/s; mPi represents the frequency droop characteristic coefficient of the ith distributed generation, unit: rad/s·W; P represents the output active power of the ith distributed generation, unit: W; kVi represents the droop control gain of the ith distributed generation; {dot over (V)}o,magi represents the change rate of the output voltage of the ith distributed generation, unit: V/s; Vn represents the reference value of the output voltage of the distributed generation, unit: V; Vo,magi represents the output voltage of the ith distributed generation, unit: V; nQi represents the voltage droop characteristic coefficient of the ith distributed generation, unit: V/Var; and Qi represents the output reactive power of the ith distributed generation, unit: Var.
The output active power Pi and the output reactive power Qi of the ith distributed generation are obtained by a low-pass filter, as shown in formula (2):
In formula (2), {dot over (P)}i represents the change rate of the output active power of the ith distributed generation, unit: W/s; ωci represents the cutoff frequency of the low-pass filter of the ith distributed generation, unit: rad/s; Vodi represents the d-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V; Voqi represents the q-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V; iodi represents the d-axis component of the output current of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A; ioqi represents the q-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A; and {dot over (Q)}i represents the change rate of the output reactive power of the ith distributed generation, unit: Var/s.
The primary and secondary control block diagrams of the microgrid are shown as
In formula (3), {dot over (V)}odi represents the change rate of the d-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V/s; Vni represents the reference value of the output voltage of the ith distributed generation, and ui represents the secondary voltage control amount, unit: V.
A dynamic equation for the output current of the distributed generation is shown as formula (4):
In formula (4), iodi represents the change rate of the d-axis component of the output current of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A/s; Rci represents the connection resistance from the ith distributed generation to its connected bus, unit: Ω; Lci represents the connection inductance from the ith distributed generation to the connected bus, unit: H; Vbusdi represents the d-axis component of the voltage of the bus connected to the ith distributed generation in the reference coordinate system dq of the ith distributed generation; ioqi represents the change rate of the q-axis component of the output current of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A/s; and Vbusqi represents the q-axis component of the voltage of the bus connected to the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V.
A model is established for each distributed generation on the basis of the local reference coordinate system dq. In order to establish an integrated microgrid model including a plurality of distributed generations, the reference coordinate system dq of one distributed generation is set as the common reference coordinate system DQ, the output currents of the other distributed generations in their reference coordinate systems dq need to be transformed into the common reference coordinate system, and the transformation equation is shown as formula (5):
In formula (5), ioDi represents the D-axis component of the output current of the ith distributed generation in the common reference coordinate system DQ, and ioQi represents the Q-axis component of the output current of the ith distributed generation in the common reference coordinate system, unit: A; Ti represents the transformation matrix of the output current of the ith distributed generation from the reference coordinate system dq of the ith distributed generation to the common reference coordinate system DQ,
δi represents the difference between the rotation angle of the reference coordinate system dq of the ith distributed generation and the rotation angle of the common reference coordinate system DQ, unit: degree, and δi can be obtained by formula (6):
{dot over (δ)}i=ωi−ωcom Formula (6).
In formula (6), ωcom represents the angular frequency of the common reference coordinate system DQ; and {dot over (δ)}i represents the change rate of δi.
Formulas (1)-(6) are linearized to obtain an open-loop small-signal model of the ith distributed generation shown as formula (7):
In formula (7), Δ{dot over (x)}invi represents the change rate of the small-signal state variables of the ith distributed generation, Δ{dot over (x)}invi=[Δ{dot over (δ)}i, Δ{dot over (P)}i, Δ{dot over (Q)}i, Δ{dot over (V)}odi, Δ{dot over (i)}odi, Δ{dot over (i)}oqi]T; Δxinvi represents the small-signal state variables of the ith distributed generation, Δxinvi=[Δδi, ΔPi, ΔQi, ΔVodi, Δiodi, Δioqi]T; ΔVbDQi represents the small-signal state variables of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ; ΔVbDQi=[ΔVbDi, ΔVbQi]T, ΔVbDi represents the D-axis small-signal component of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, and ΔVbQi represents the Q-axis small-signal component of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, unit: V; Δωcom represents the small-signal state variable of the angular frequency of the common reference coordinate system DQ, unit: rad/s; Δui represents the small-signal control amount of the secondary voltage of the ith distributed generation, unit: V; Ainvi represents the state matrix of the ith distributed generation; Binvi represents the input matrix of the ith distributed generation to the voltage of the connected bus; Biwcom represents the input matrix of the ith distributed generation to the angular frequency of the common reference coordinate system; Bui represents the input matrix of the ith distributed generation to the small-signal control amount of the secondary voltage; ΔioDQi represents the small-signal state variables of the output current of the ith distributed generation in the common reference coordinate system DQ, ΔΔioDQi=[ΔioDi, ΔioQi]T, unit: A; and Cinvci represents the output current matrix of the ith distributed generation.
According to formula (7), ΔVbusDQi and Δωcom serve as disturbance variables of the ith distributed generation, where the reference coordinate system of the first distributed generation is generally selected as the common reference coordinate system DQ, then
Δωcom=[0−mP1 0 0 0 0]Δxinv1 Formula (8).
In formula (8), mP1 represents the frequency droop characteristic coefficient of the first distributed generation, unit: rad/s·W; Δxinv1 represents the small-signal state variables of the first distributed generation, Δxinv1=[Δδ1, ΔPi, ΔQ1, ΔVod1, Δiod1, Δioq1]T.
According to formula (7) and formula (8), the small-signal model of the system consisting of n distributed generations can be obtained:
In formula (9), Δ
Based on the control requirements of reactive power sharing and voltage recovery, the present invention realizes microgrid voltage control. Reactive power sharing refers to that the output reactive power of each distributed generation is allocated according to the power capacity, voltage recovery refers to that the average output voltage of all the distributed generations is recovered to a rated value, and the following dynamic equation is first defined:
In formula (10), {dot over (φ)}i represents the change rate of the small-signal state variable of reactive power ancillary of the ith distributed generation, unit: Var; Qi: represents the expected output reactive power of the ith distributed generation, unit: Var; nQi represents the voltage droop characteristic coefficient of the ith distributed generation, unit: V/Var;
Therefore, an inverter closed-loop small-signal model based on output feedback is:
In formula (11), Δxinv represents the closed-loop small-signal state variables of n inverters, Δxinv=[Δxinvi, Δxinv2, . . . , Δxinvi, . . . , Δxinvn, Δφ1, Δφ2, . . . , Δφi, . . . , Δφn, Δγ]T, Δφ1 small-signal state variable of a reactive power ancillary of the first distributed generation, Δφ2 represents the small-signal state variable of a reactive power ancillary of the second distributed Δφ2 generation, Δφi represents the small-signal state variable of the reactive power ancillary of the ith distributed generation, Δφn represents the small-signal state variable of the reactive power ancillary of the nth distributed generation, and Δγ represents the small-signal state variable for voltage ancillary of distributed generations; ΔyinvQ represents small-signal state variables of output reactive powers ΔyinvQ=[Δ{dot over (φ)}1 Δφ1 Δ{dot over (φ)}2 Δφ2 . . . Δφn Δφn], Δ{dot over (φ)}1 represents the change rate of the small-signal state variable of the reactive power ancillary of the first distributed generation, Δ{dot over (φ)}2 represents the change rate of small-signal state variable of the reactive power ancillary of the second distributed generation, and Δ{dot over (φ)}n represents the change rate of small-signal state variable of the reactive power ancillary of the nth distributed generation; ΔyinvV represents the small-signal state variables of the output voltage of the distributed generations, ΔyinvV=[Δ{dot over (γ)}, Δγ]T, and Δ{dot over (γ)} represents the change rate of small-signal state variable for the voltage ancillary of each distributed generation; CinvQ represents the output matrix of reactive power of distributed generations; and CinvV represents the output matrix of the voltages of distributed generations.
The control amount of the distributed generation is defined as:
In formula (12), δQi represents the reactive power control signal of the ith distributed generation; kPQ represents the proportional term coefficient in a reactive power proportional-integral controller; kIQ represents the integral term coefficient in the reactive power proportional-integral controller; δVi represents the average voltage recovery control signal of the ith distributed generation; kPV represents the proportional term coefficient in the average voltage proportional-integral controller; and kIV represents the integral term coefficient in the average voltage proportional-integral controller.
When a communication delay exists between a centralized voltage controller of the microgrid and each distributed generation, a voltage control amount is:
Δui=ΔδQi(t−τi)+ΔδVi(t−τi)=KQiΔyinvQi(t−τi)+KViΔyinvV(t−τi) Formula (13).
In formula (13), τi represents the communication delay between the local controller of the ith distributed generation and the centralized secondary voltage controller of the microgrid, unit: s; KQi represents the reactive power controller of the ith distributed generation, KQi=[kPQi kIQi]; and KVi represents the voltage controller of the ith distributed generation, KVi=[kPVi kIVi].
By reference to formulas (11)-(13), the close-loop small-signal model of n distributed generations are obtained:
In formula (14), Ādx represents the delayed state matrix of the ith distributed generation,
Ādi=[0 . . . BuiKQiCinvQi+BuiKViCinvV . . . 0], Bui represents the input matrix of the ith distributed generation to the small-signal control amount of the secondary voltage, CinvQi represents the output matrix of reactive power of the ith distributed generation, and Cinvc represents the output matrix of the current of the distributed generation.
Step (20) Establish a microgrid small-signal model according to a connection network and a dynamic equation of load impedance
A current small-signal dynamic equation of a connection line ij between the bus connected to the ith distributed generation and the bus connected to the jth distributed generation in the common reference coordinate system DQ is shown as formula (15):
In formula (15), ΔilineDij represents the change rate of a D-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, unit: A/s; rlineij represents the line resistance of the ijth connection line, unit: Ω; Llineij represents the line inductance of the ijth connection line, unit: H; ΔilineDij represents the D-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, and ΔilineQij represents the Q-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, unit: A; ω0 represents the rated angular frequency of the microgrid, unit: rad/s; ΔVbusDi represents the D-axis component of small-signal variable of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ; ΔVbusDj represents the D-axis component of small-signal variable of the voltage of the bus connected to the jth distributed generation in the common reference coordinate system DQ; ΔilineQij represents the change rate of the Q-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, unit: A/s; ΔVbusQi represents the Q-axis component of small-signal variable of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, and ΔVbusQj represents the Q-axis component of small-signal variable of the voltage of the bus connected to the jth distributed generation in the common reference coordinate system DQ, unit: V.
A current dynamic equation of a load connected to the lth bus in the common reference coordinate system DQ is shown as formula (16):
In formula (16), ΔiloadD1 represents the change rate of D-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, unit: A/s; Rload1 represents the load resistance of the load connected to the lth bus, unit: Ω; Lload1 represents the load inductance of the load connected to the lth bus, unit: H; ΔiloadDl represents the D-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, and ΔiloadQl represents the Q-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, unit: A; and ΔiloadQl represents the change rate of Q-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, unit: A/s.
A small-signal equation of the connection line between the bus connected to the ith distributed generation and the bus connected to the jth distributed generation is set as formula (17):
In formula (17), Rloadj and Lloadj respectively represent the resistance value and the inductance value of a load on the bus connected the jth distributed generation; and ΔioDj and ΔioQj respectively represent the D-axis component small-signal variable and Q-axis component of small-signal variable of the output current of the jth distributed generation in the common reference coordinate system DQ.
Formula (17) is substituted into formulas (14)-(16) to obtain the microgrid small-signal model comprising n distributed generations, s branches and p loads:
In formula (18), x represents the microgrid small-signal state variables, x=[Δxinv ΔilineDQ ΔiloadDQ]T, ΔilineDQ represent the small-signal state variables of the current of the connection lines between the buses connected to the distributed generations in the common reference coordinate system DQ, and ΔiloadDQ represent the small-signal state variables of the current of the loads connected to the buses in the common reference coordinate system DQ; {dot over (x)} represents the change rate of the microgrid small-signal state variables; A represents the microgrid state matrix; Adi represents the delayed state matrix of the ith distributed generation; and τi represents the delay of the ith distributed generation.
Step (30) Obtain a characteristic equation with a transcendental term of a microgrid closed-loop small-signal model
When the delays of all the distributed generations are consistent, a characteristic equation of formula (18) is formula (19):
CE
τ(s,τ)=det(sI−A−Ade−τs) Formula (19).
In formula (19), s represents the parameter of the time domain complex plane; r represents the consistent delay time of each distributed generation, τ1=τ2= . . . =τn, unit: s; det(⋅) represents the matrix determinant; I represents the unit matrix; Ad represents the delayed state matrix of the distributed generation, Ad=Σi=1nAdi; and e−τs represents the transcendental term.
Step (40) Carry out critical characteristic root locus tracking for the transcendental term of the system characteristic equation to calculate the system stability margin For formula (19), if all system characteristic roots are on the left half of a complex plane, the system is stable; if there are characteristic roots on the right half of the complex plane, the system is unstable; and if there are characteristic roots on the left half of the complex plane or the imaginary axis, the system is critically stable. Because the system characteristic roots continuously change along with the delay time τ, in order to determine the system stability margin Td, that is, the system is stable if r is less than Td, and is unstable if r is greater than Td, the possible pure virtual characteristic roots and the corresponding delay margin need to be determined.
ξ=τω is defined and substituted into formula (19), and then,
CE
ξ(s,ξ)=det(sI−A−Ade−iξ) Formula (20).
Where, ξ represents the delay time ancillary variable, and ω represents the virtual characteristic root amplitude; here, i represents the imaginary unit, and i2=−1. ξ changes within the cycle of [0, 2π], so that corresponding characteristic roots of formula (20) are obtained. If there are pure virtual characteristic roots corresponding to certain ξ then a critical delay time is:
τc=ξc/abs(ωC) Formula (21).
In the formula, ξc represents the delay time ancillary variable for the existence of pure virtual characteristic roots in the system, abs(ωc) represents the amplitude of the corresponding pure virtual characteristic root, and τc represents the critical delay time.
When ξ changes within the cycle of [0, 2π], there may be a plurality of critical delay times in the system, i.e. τc1, τc2 . . . τcL, and the minimum value τd is selected as the delay margin:
τd=min(τc1 τc2 . . . τcL) Formula (22).
In the aforementioned embodiment, the common reference coordinate system DQ refers to the reference coordinate system dq of the first distributed generation, and the state variables of the other distributed generations, branch currents and load currents are transformed into the common reference coordinate system DQ by the transformation of coordinates. In step (10), because the proportional term coefficients in the proportional-integral controller of reactive power and the proportional-integral controller of the voltage are small, in practice, the proportional-integral controller of reactive power and the proportional-integral controller of the voltage can be respectively simplified into an integral controller of reactive power and an integral controller of voltage. In step (20), the loads are impedance type loads.
In the present embodiment, by introducing the microgrid closed-loop small-signal model of signal communication delay time, a system characteristic equation with a transcendental term is established, and thereby the microgrid delay margin calculation method based on critical characteristic root tracking is implemented. Aimed at the conventional microgrid secondary control method which neglects the influence of the communication delay on the dynamic performance of the system, the present embodiment works out a maximum delay time for maintaining the system stable in full consideration of the actual situation that the influence of the communication delay on system stability cannot be neglected due to the low inertia of power electronic interfaced microgrid. By analyzing the relationship between different controller parameters and delay margins, the delay margin calculation method of the present embodiment guides the design of the controllers, thus improving the stability and dynamic performance of the system.
The block diagram of the microgrid control system in the embodiment of the present invention is shown as
The following exemplifies an embodiment.
A simulation system is shown as
The method of the embodiment of the present invention is a microgrid delay margin calculation method based on critical characteristic root tracking, by which the microgrid closed-loop small-signal model including communication delay is established based on the output feedback method, and the maximum delay time for a stable system, i.e. the delay margin is analyzed. Aimed at the conventional microgrid secondary control method which neglects the influence of communication delay on the dynamic performance of the system, the present embodiment takes the influence of communication delay on system stability into full consideration, and in addition, by studying the relationship between different controller parameters and delay margins, the design of the controllers is guided, thus improving the robust stability and dynamic performance of the microgrid.
Number | Date | Country | Kind |
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201710456420.4 | Jun 2017 | CN | national |
This application is the national phase entry of International Application No. PCT/CN2018/084937, filed on Apr. 27, 2018, which is based upon and claims priority to Chinese Patent Application No. 201710456420.4, filed on Jun. 16, 2017, the entire contents of which are incorporated herein by reference.
Filing Document | Filing Date | Country | Kind |
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PCT/CN2018/084937 | 4/27/2018 | WO | 00 |