WO2018228068A1 - 基于临界特征根跟踪的微电网延时裕度计算方法 - Google Patents

基于临界特征根跟踪的微电网延时裕度计算方法 Download PDF

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WO2018228068A1
WO2018228068A1 PCT/CN2018/084937 CN2018084937W WO2018228068A1 WO 2018228068 A1 WO2018228068 A1 WO 2018228068A1 CN 2018084937 W CN2018084937 W CN 2018084937W WO 2018228068 A1 WO2018228068 A1 WO 2018228068A1
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distributed power
power supply
small
voltage
delay
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French (fr)
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顾伟
楼冠男
曹戈
柳伟
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东南大学
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Energy or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P80/00—Climate change mitigation technologies for sector-wide applications
    • Y02P80/10—Efficient use of energy, e.g. using compressed air or pressurized fluid as energy carrier
    • Y02P80/14—District level solutions, i.e. local energy networks

Definitions

  • the invention discloses a method for calculating a delay margin of a micro grid based on critical eigen-root tracking, in particular to a method for calculating a delay margin of a secondary voltage control of a micro-grid, which belongs to the technical field of micro-grid operation control.
  • Microgrid is an emerging energy transmission mode that increases the renewable energy and distributed energy penetration rate in energy supply systems. Its components include different types of distribution such as micro gas turbines, wind turbines, photovoltaics, fuel cells, and energy storage equipment.
  • Distributed Energy Resources DER
  • user terminals for various electrical loads and/or heat loads, and associated monitoring and protection devices.
  • the power supply inside the microgrid is primarily converted by the power electronics and provides the necessary control.
  • the microgrid is a single controlled unit relative to the external large grid, which can meet the requirements of users for power quality and power supply security.
  • the micro-grid and the large power grid exchange energy through a common connection point, and the two sides spare each other, thereby improving the reliability of the power supply.
  • the microgrid is a small-scale distributed system with a relatively close load, which reduces the network loss while increasing the reliability of local power supply, which greatly increases the energy utilization efficiency. Therefore, the microgrid is a kind of future smart grid development requirement. New power supply mode.
  • the droop control is concerned because it can achieve power sharing without communication, but the distributed power supply output voltage will have a steady-state deviation.
  • the designed coordinated voltage control is a centralized control structure.
  • the microgrid centralized voltage controller generates control signals and sends them to the distributed power local controllers.
  • the centralized control structure relies on communication technology, but the communication process is usually subject to The effects of information delay, data packet loss, information delay, data packet loss, etc. lead to poor dynamic performance of the microgrid and even compromise system stability.
  • micro-grid secondary voltage control delay margin calculation method it is necessary to study a set of micro-grid secondary voltage control delay margin calculation method, analyze the maximum communication delay time to stabilize the micro-grid, and it is necessary to analyze the relationship between the micro-network centralized controller parameters and the delay margin. Analyze to guide the design of control parameters and effectively improve the stability and dynamic performance of the microgrid.
  • the object of the present invention is to ignore the influence of communication delay on the dynamic performance in the reactive power equalization and voltage recovery control of the micro grid, and fully considers that the power electronic interface type microgrid has small inertia and thus causes communication delay to the system.
  • the actual situation that stability can not be neglected provides a method for calculating the delay margin of microgrid based on critical eigen-root tracking. By calculating all possible pure virtual eigenvalues of the microgrid characteristic equation, the maximum delay time for stabilizing the microgrid is calculated. By studying the relationship between controller parameters and stability margin, it provides guidance for the design of control parameters, and solves the technical problems that the stability of existing microgrid systems is affected by communication technology.
  • the closed-loop small-signal model of the inverter including the communication delay voltage feedback control amount and the closed-loop small-signal model of the distributed power supply are established according to the static feedback output, combined with the connection network and the load.
  • the dynamic equation of impedance and the closed-loop small-signal model of distributed power supply establish a micro-signal small-signal model.
  • the characteristic equations with transcendental terms are obtained from the small-signal model of the micro-grid, and the critical eigen-trajectory tracking of the transcendental items is performed to determine the stability requirements of the system. Delay margin.
  • the closed-loop small-signal model of the inverter including the communication delay voltage feedback control amount established according to the static feedback output is: ⁇ x inv , They are the closed-loop small-signal state variables of the inverter and their rate of change, ⁇ x inv1 , ⁇ x inv2 , ⁇ x invi , and ⁇ x invn are small signal state variables of the first, second, ith, and nth distributed power sources, respectively.
  • Reactive power assisted small signal state variables for the first, second, ith, and nth distributed power supplies, and reactive power assisted small signal state variables for the ith distributed power supply By expression: determine, For the i-th distributed power source reactive power assisted small signal state variable rate of change, Q i is the reactive power actually output by the i-th distributed power source, and n Qi is the voltage droop characteristic coefficient of the i-th distributed power source, n is the number of distributed power sources, ⁇ is the voltage-assisted small-signal state variable of the distributed power source, and the voltage-assisted small-signal state variable ⁇ of the distributed power source is expressed by the expression: determine, For the rate of change of the voltage-assisted small-signal state variable of the distributed power supply, V i * is the expected value of the average voltage of the i-th distributed power supply, and V odi is the output voltage of the i-th distributed power supply under its own reference coordinate system dq
  • the d-axis component, A inv
  • ⁇ u 1 , ⁇ u 2 , ⁇ u i , ⁇ u n are the first, second, ith, and nth, respectively.
  • B u secondary voltage is distributed power control amount of small signal input matrix
  • ⁇ u i K Qi ⁇ y invQi (t- i) + K Vi ⁇ y invV (t- ⁇ i)
  • t is the current time
  • ⁇ i is the i-th communication delay between the local controller and the distributed power piconet secondary voltage centralized controller
  • K Qi, K Vi is the reactive power control coefficient and voltage control coefficient of the i-th distributed power supply
  • ⁇ y invQi is the reactive power output small signal state variable of the i-th distributed power supply
  • ⁇ y invQ and ⁇ y invV are respectively
  • the reactive power output of the distributed power supply is a small signal state variable
  • C invQ and C invV are respectively a reactive power output matrix and a voltage output matrix of the distributed power source.
  • the distributed power supply closed-loop small-signal model including the communication delay voltage feedback control amount established according to the static feedback output is: For the delay state matrix of the i-th distributed power supply, B ui i-th secondary voltage distributed power control amount of small signal input matrix, C invQi distributed to the i-th power of the reactive power output matrix, ⁇ i oDQ common reference coordinate system is a distributed power DQ
  • the small signal state variable of the output current, C invc is the current output matrix of the distributed power supply.
  • the small signal state variable, the small signal state variable of the current of the connection line ij between the bus connected to the i-th distributed power source and the bus connected to the jth distributed power source in the common reference coordinate system DQ is: ⁇ i lineDij , The D-axis small signal component of the current connecting the line ij in the common reference coordinate system DQ and its rate of change, ⁇ i lineQij , The Q-axis small signal component and its rate of change of the current connecting the line ij in the common reference coordinate system DQ, respectively, r lineij , L lineij are the line resistance and line inductance of the connection line ij, respectively, and ⁇ 0 is the rated angular frequency of the micro-grid , ⁇ V busDi and ⁇ V busQi are respectively the D-axis component and the Q-axis component of the voltage of the bus connected to the i-th distributed power source in the common reference coordinate system DQ, and ⁇ V busDj and ⁇ V bus
  • the method of obtaining the characteristic equation containing the transcendental term from the small-signal model of the micro-grid is as follows: when the delay of the distributed power supply is consistent, the micro-grid is small.
  • CE ⁇ (s, ⁇ ) det(sI-AA d e - ⁇ s ), s is the time domain complex plane parameter, ⁇ is the uniform delay time of each distributed power source, CE ⁇ ( ⁇ ) indicates the characteristic equation of the micro-grid small-signal model obtained when the distributed power supply has the same delay ⁇ , det( ⁇ ) is the matrix determinant, I is the unit matrix, and A d is the delay state matrix of the distributed power supply. e - ⁇ s is the transcendental term.
  • the critical eigen-track trajectory is tracked for the transcendental term to determine the delay margin that satisfies the system stability requirement.
  • the specific method is: delay
  • the time auxiliary variable is used as the variable of the characteristic equation to solve all pure virtual eigenvalues of the characteristic equation in the period of delay time auxiliary variable change.
  • the minimum value is selected from the critical delay time corresponding to all pure virtual eigen roots to meet the system stability requirements.
  • the delay margin is the product of the distributed power supply delay and the virtual eigen-root amplitude.
  • the present invention proposes a method for calculating the secondary voltage control delay margin of a microgrid, which is based on static output feedback to establish a closed loop small signal model of a microgrid including a communication delay voltage feedback control quantity, thereby obtaining a transcendental
  • the characteristic equation of the term the critical feature root trajectory tracking of the transcendental term of the system characteristic equation, searching for possible pure virtual feature roots and calculating the maximum delay time for making the microgrid stable.
  • This method can effectively reduce the communication delay to the microgrid dynamics.
  • the impact of performance effectively improve the stability and dynamic performance of the microgrid;
  • Figure 1 is a flow chart of an embodiment of the present invention
  • FIG. 2 is a block diagram of primary and secondary control of a microgrid according to an embodiment of the present invention
  • FIG. 3 is a schematic diagram of a microgrid simulation system used in an embodiment of the present invention.
  • the method for calculating a micro grid delay margin based on critical feature root tracking disclosed by the present invention comprises the following steps:
  • Step 10 Establish a closed-loop small-signal model of the inverter including the communication delay voltage feedback control amount based on the static output feedback
  • Each distributed power supply sets the inverter output voltage and frequency reference command through the droop control loop in the local controller, as shown in equation (1):
  • ⁇ i represents the local angular frequency of the ith distributed power source
  • ⁇ n represents the reference value of the local angular frequency of the distributed power source, in units of radians/second
  • m Pi represents the frequency of the ith distributed power source Droop characteristic coefficient, unit: radians/second ⁇ watt
  • P represents the active power of the actual output of the i-th distributed power source, unit: watt
  • k Vi represents the droop control gain of the i-th distributed power source; Indicates the rate of change of the output power of the i-th distributed power supply, in volts per second
  • V n represents the reference value of the distributed power supply output voltage, in volts
  • V o,magi represents the actual output voltage of the i-th distributed power supply , unit: volt
  • n Qi represents the voltage droop characteristic coefficient of the i-th distributed power supply, unit: volt/lack
  • Q i represents the reactive power of the actual output of the i-th distributed
  • the active power P i and the reactive power Q i actually output by the i-th distributed power source are obtained by a low-pass filter, as shown in the formula (2):
  • micro-grid primary and secondary control block diagram is shown in Figure 2.
  • Each distributed power supply is controlled once by the phase-locked loop control so that the output voltage q-axis component is 0.
  • equation (3) is obtained:
  • Equation (3) Indicates the rate of change of the d-axis component of the i-th distributed power supply output voltage in the dq reference coordinate system of the i-th distributed power supply, in volts per second;
  • V ni represents the reference of the i-th distributed power supply output voltage The value, u i represents the secondary voltage control amount, in volts.
  • Each distributed power source establishes a model based on the local dq reference coordinate system.
  • the dq reference coordinate system of one of the distributed power sources is set to the common reference coordinate system DQ, and other distributions are performed.
  • the output current of the reference power supply dq reference coordinate system needs to be converted to the common reference coordinate system DQ, and the conversion equation is as shown in equation (5):
  • i oDi represents the component of the i-th distributed power supply output current in the D-axis in the common reference coordinate system DQ
  • i oQi represents the i-th distributed power supply output current in the common reference coordinate system DQ
  • the component in the Q axis, unit: amp; T i represents the conversion matrix of the i-th distributed power supply output current from the i-th distributed power supply dq reference coordinate system to the common reference coordinate system DQ, ⁇ i represents the static difference between the rotation angle of the i-th distributed power supply dq reference coordinate system and the rotation angle of the common reference coordinate system DQ, and the unit: degree, ⁇ i can be obtained by the equation (6):
  • ⁇ com represents the angular frequency of the common reference coordinate system DQ; Indicates the rate of change of ⁇ i .
  • ⁇ x invi represents the small signal state variable of the i-th distributed power source
  • ⁇ x invi [ ⁇ i , ⁇ P i , ⁇ Q i , ⁇ V odi , ⁇ i odi , ⁇ i oqi ] T
  • ⁇ V bDQi is represented in the common reference coordinate system DQ
  • the small signal state variable of the voltage of the bus connected to the i-th distributed power source; ⁇ V sDQi [ ⁇ V bDi , ⁇ V bQi ] T
  • ⁇ V bDi represents the voltage of the bus connected to the i-th distributed power source in the common reference coordinate system DQ
  • ⁇ V bQi represents the small signal component of the voltage of the bus connected to the i-th distributed power source in the common reference coordinate system DQ
  • ⁇ V busDQi and ⁇ com are used as disturbance variables of the i-th distributed power source, wherein the reference coordinate system of the first distributed power source is generally selected as the common reference coordinate system DQ,
  • ⁇ com [0 -m P1 0 0 0 0] ⁇ x inv1 (8)
  • m P1 represents the frequency droop characteristic coefficient of the first distributed power source, unit: radians/second ⁇ watt;
  • ⁇ x inv1 represents the small signal state variable of the first distributed power source
  • ⁇ x inv2 represents the small signal state variable of the second distributed power source
  • ⁇ x invn represents the small signal state variable of the nth distributed power source
  • ⁇ V bDQ [ ⁇ V bDQ1 ⁇ V bDQ2 ...
  • ⁇ V busDQm [ ⁇ V bD1 ⁇ V bQ1 ] T
  • ⁇ V bD1 represents the small signal component of the voltage of the bus 1 in the common reference coordinate system DQ on the D axis
  • ⁇ V bQ1 is expressed in the common reference
  • ⁇ V bDQ2 [ ⁇ V bD2 ⁇ V bQ2 ] T
  • ⁇ V bD2 represents the small signal component of the voltage of the bus 2 in the common reference coordinate system DQ on the D axis
  • ⁇ V bQ2 represents the small signal component of the voltage of the busbar 2 in the common reference coordinate system DQ on the Q axis
  • ⁇ V bDQm [ ⁇ V bDm ⁇ V bQm ] T
  • ⁇ V bDm represents the voltage of the bus bar m in the common
  • ⁇ u 1 represents the distributed power source 1 a small amount of secondary voltage control signal
  • ⁇ u 2 represents the secondary voltage of the distributed power supply 2 Control amount signals
  • ⁇ u n represents the secondary voltage of the small signal distributed power control amount of n
  • ⁇ i oDQ [ ⁇ i oDQ1 ⁇ i oDQ2 ...
  • ⁇ i oDQn [ ⁇ i oD1, ⁇ i oQ1] T
  • ⁇ i oD1 [ ⁇ i oD1, ⁇ i oQ1] T
  • ⁇ i oD1 Representing the small signal component of the first distributed power supply output current in the D-axis in the common reference coordinate system DQ
  • ⁇ i oQ1 indicating the small signal component of the i-th distributed power supply output current in the Q-axis in the common reference coordinate system DQ
  • ⁇ i oDQ2 [ ⁇ i oD2 , ⁇ i oQ2 ] T
  • ⁇ i oD2 represents the small signal component of the second distributed power supply output current in the D-axis in the common reference coordinate system DQ
  • ⁇ i oQ2 represents the second in the common reference coordinate system DQ
  • the distributed signal output current is a small signal component of the Q axis
  • ⁇ i oDQn [ ⁇ i oDn , ⁇ i o
  • the invention realizes microgrid voltage control based on the control requirements of reactive power sharing and voltage recovery.
  • the reactive power equalization means that the distributed power output reactive power is distributed according to the power capacity.
  • the voltage recovery means that the average output voltage of each distributed power source is restored to the rated value.
  • Equation (10) The rate of change of the reactive power assisted small signal state variable for the i-th distributed power source, in units of: The reactive power expected to be output for the i-th distributed power supply, unit: lack; n Qi represents the voltage droop characteristic coefficient of the i-th distributed power supply, unit: volt/lack; The rate of change of the voltage-assisted small-signal state variable for the distributed power supply, in volts; For the average output voltage of each distributed power supply, V i * is the expected value of the average of the i-th distributed power supply, in volts.
  • ⁇ x inv represents the closed-loop small-signal state variable of n inverters, Reactive power assisted small signal state variable for the first distributed power source, Reactive power assisted small signal state variable for the second distributed power source, Reactive power assisted small signal state variable for the i-th distributed power supply
  • ⁇ is the voltage assisted small signal state variable of each distributed power source
  • ⁇ y invQ is the reactive power output small signal state variable The rate of change of the reactive power assisted small signal state variable for the first distributed power source, The rate of change of the reactive power assisted small signal state variable for the second distributed power source, The rate of change of the reactive power assisted small signal state variable for the nth distributed power source
  • ⁇ y invV is the voltage output small signal state variable of the distributed power source, The rate of change of the voltage-assisted small-signal state variable for each distributed power source
  • C invQ represents the reactive power output matrix of each distributed power source
  • C invV represents the voltage output
  • ⁇ Q i represents the reactive power control signal of the i-th distributed power source
  • k PQ represents the proportional term coefficient in the reactive power proportional-integral controller
  • k IQ represents the reactive power proportional-integral controller
  • ⁇ V i represents the average voltage recovery control signal of the i-th distributed power source
  • k PV represents the proportional term coefficient in the average voltage proportional-integral controller
  • k IV represents the integral term coefficient in the average voltage proportional-integral controller.
  • the voltage control amount is:
  • ⁇ i is the communication delay between the i-th distributed power local controller and the micro-network secondary voltage centralized controller, unit: second;
  • Equation (14) For the delay state matrix of the i-th distributed power supply, B ui is the input matrix of the i-th distributed power supply to the secondary voltage small signal control quantity, C invQi is the reactive power output matrix of the i-th distributed power source, and C invc is the current output matrix of the distributed power source.
  • Step 20 Combine the dynamic equations of the connected network and the load impedance to establish a small signal model of the microgrid
  • Equation (15) Indicates the rate of change of the small signal component of the D-axis of the ij connecting line current in the common reference coordinate system DQ, unit: ampere/second; r lineij represents the line resistance of the ij connecting line, unit: ohm; L lineij indicates Line inductance of ij connecting lines, unit: Henry; ⁇ i lineDij indicates that in the common reference coordinate system DQ, the ij line connects the line signal to the D-axis small signal component, and ⁇ i lineQij represents in the common reference coordinate system DQ,
  • the voltage of the connected busbar is a small signal component of the D axis; ⁇ V busDj represents a small signal component of the
  • Equation (16) Indicates the rate of change of the small signal component of the current connected to the load of the lth bus in the common reference coordinate system DQ, unit: ampere/second;
  • R loadl represents the load resistance of the load connected to the 1st bus, unit: Ohm;
  • L loadl represents the load inductance of the load connected to the 1st bus, unit: Henry;
  • ⁇ i loadDl is the small signal component of the current on the D axis of the load connected to the 1st bus in the common reference coordinate system DQ, ⁇ i loadQl is the small signal component of the Q-axis current of the load connected to the lth bus in the common reference coordinate system DQ, unit: amp;
  • R loadj and L loadj are respectively the resistance and inductance values of the load on the bus connected to the jth distributed power source; ⁇ i oDj and ⁇ i oQj are respectively the jth distributed power supply output current in the common The D-axis small signal component and the Q-axis small signal component in the reference coordinate system DQ.
  • the small signal state variable, ⁇ i loadDQ is a small signal state variable of the current of the load connected to the bus in the common reference coordinate system DQ;
  • the rate of change of the small signal state variable of the microgrid A is the microgrid state matrix;
  • a di is the delay state matrix of the ith distributed power source;
  • ⁇ i is the delay of the ith distributed power source.
  • Step 30 Acquire a characteristic equation of the micro-grid closed-loop small-signal model with transcendental terms
  • s is the time domain complex plane parameter
  • ⁇ is the uniform delay time of each distributed power source
  • det( ⁇ ) represents the matrix row and column I represents the identity matrix
  • a d represents the delay state matrix of the distributed power supply
  • e - ⁇ s is the transcendental term.
  • Step 40 Perform critical feature root trajectory tracking on the transcendental term of the system feature method to calculate the system stability margin
  • ⁇ is the delay time auxiliary variable
  • ⁇ is the virtual feature root amplitude
  • i is the imaginary unit
  • i 2 -1.
  • ⁇ c is the delay time auxiliary variable that causes the system to have a pure virtual eigenvalue
  • abs( ⁇ c ) represents the amplitude of the corresponding pure virtual eigenvalue
  • ⁇ c is the critical delay time
  • the system may have multiple critical delay times, namely ⁇ c1 , ⁇ c2 ... ⁇ cL , and the delay margin takes the minimum value ⁇ d :
  • the common reference coordinate system DQ refers to the dq reference coordinate system of the first distributed power source, and the state variables of the remaining distributed power source, branch current, and load current are converted to common reference coordinates by coordinate transformation.
  • the DQ In the reactive power proportional integral controller and the voltage proportional integral controller in step 10), since the proportional term coefficients are relatively small, in practice, they can be simplified into a reactive power integral controller and a voltage integral controller, respectively.
  • the load is an impedance type load.
  • a micro-grid closed-loop small-signal model with signal communication delay time is introduced to establish a system characteristic equation with transcendental term, so as to realize a micro-grid delay margin calculation method based on critical eigen-root tracking.
  • this embodiment fully considers the actual situation that the power electronic interface type micro-grid has small inertia and thus the communication delay can not be ignored.
  • the delay margin calculation method of the embodiment guides the controller design by analyzing the relationship between different controller parameters and the delay margin, thereby improving system stability and dynamic performance.
  • the block diagram of the microgrid control system in the embodiment of the present invention is as shown in FIG. 2, and the control block diagram mainly includes two layers: the first layer is a local controller of each distributed power source, and is composed of power calculation, droop control, and voltage and current double loop; The second layer is a secondary voltage control layer that achieves reactive power equalization and average voltage recovery.
  • the secondary voltage centralized controller collects the distributed power supply output voltage and outputs the reactive power, and after calculating the secondary voltage control amount, the control command is sent to the local controller of each distributed power source.
  • the communication delay exists between the secondary voltage centralized controller and each distributed power local controller, and the delay affects the dynamic performance of the system.
  • the simulation system is shown in Figure 3.
  • the microgrid consists of two distributed power sources, two connecting lines and three loads.
  • the load 1 is connected to the busbar 1
  • the load 2 is connected to the busbar 2
  • the load 3 is connected to the busbar 3.
  • the load in the system uses an impedance load.
  • the distributed power supply 1 and the distributed power supply 2 have a capacity ratio of 1:1
  • the corresponding frequency droop coefficient and voltage droop coefficient are designed so that each distributed power source expects to output active power and the reactive power ratio is 1:1.
  • the micro-grid theoretical delay margin under different controller parameters is studied, and the micro-grid simulation model is built based on MATLAB/Simulink platform to simulate the theoretical delay margin.
  • the communication delay auxiliary variable ⁇ changes in [0, 2 ⁇ ], and the two pairs of conjugate eigenvalues are closely related to system stability.
  • FIG. 5 is a diagram showing the relationship between the delay margin of the microgrid based on the critical characteristic root tracking and the controller parameters in the embodiment of the present invention, under controller parameters 0.005 ⁇ k IQ ⁇ 0.06, 5 ⁇ k IV ⁇ 60. It can be seen from the figure that as the reactive power controller integral coefficient k IQ or the voltage controller integral coefficient k IV increases, the system delay margin decreases, that is, the system robust stability decreases. Therefore, when the parameters of different combination controllers reach similar dynamic performance, the delay margin will be used as an additional robust stability indicator to guide the controller parameter design and provide system stability and dynamic performance.
  • each distributed power supply operates in the droop control mode, and the secondary voltage control is input at 0.5 s.
  • the simulation results are shown in Fig. 6.
  • Fig. 6(a) is a graph of the average voltage of the distributed power supply in the microgrid.
  • the abscissa indicates the time, the unit is seconds, and the ordinate indicates the average voltage in volts. watt.
  • Fig. 6(a) is a graph of the average voltage of the distributed power supply in the microgrid.
  • the abscissa indicates the time, the unit is seconds, and the ordinate indicates the average voltage in volts. watt.
  • Fig. 6(a) under the action of droop control, the average voltage of the distributed power supply has a steady-state deviation. After 0.5 s, the voltage amplitude increases under the secondary control. It can be seen from Fig. 6(a) that when there is no communication delay in the system, the average voltage is smoother and reaches the rated value. When the delay time is 53ms, the voltage curve is restored by the damped oscillation. When the delay time is 61ms, the curve increases. Oscillation, the system is unstable.
  • Fig. 6(b) is a graph of reactive power output of distributed power supply 1, unit: second, ordinate indicates reactive power, unit: lack. It can be seen from Fig.
  • FIG. 6(b) that the initial reactive power equalization effect under the drooping effect is not ideal (less than the expected reactive power output value of the distributed power source 1), and the reactive power is under the secondary control after 0.5 s. The output is increased. It can be seen from Fig. 6(b) that when there is no communication delay in the system, the reactive power is smoother and reaches the desired value. When the delay time is 53ms, the power curve is oscillated to reach the control target. When the delay time is 61ms, The curve increases and the system is unstable. Under the effect of secondary control, the effect of the reactive power equalization of the microgrid is significantly improved.
  • Figure 6 (c) is a graph of reactive power output of distributed power supply 2, unit: second, ordinate represents reactive power, unit: lack.
  • each distributed power supply operates in the droop control mode, and the secondary voltage control is input at 0.5 s.
  • the simulation results are shown in Fig. 7.
  • Fig. 7(a) is a graph of the average voltage of the distributed power supply in the microgrid. The abscissa indicates the time, the unit is seconds, and the ordinate indicates the average voltage in volts. watt. As shown in Fig.
  • FIG. 7(a) under the action of droop control, the average voltage of the distributed power supply has a steady-state deviation. After 0.5 s, the voltage amplitude increases under the secondary control. It can be seen from Fig. 7(a) that when there is no communication delay in the system, the average voltage is smoother and reaches the rated value. When the delay time is 25ms, the voltage curve is recovered by the damped oscillation. When the delay time is 33ms, the curve increases. Oscillation, the system is unstable.
  • Figure 7 (b) is a graph of reactive power output of distributed power supply 1, unit: second, ordinate represents reactive power, unit: lack. It can be seen from Fig.
  • Figure 7 (c) is a graph of reactive power output of distributed power supply 2, unit: second, ordinate represents reactive power, unit: lack. It can be seen from Fig. 7(c) that the initial reactive power equalization effect under the drooping effect is not ideal (higher than the expected reactive power output value of the distributed power supply 2), and the reactive power is under the secondary control after 0.5 s. The output is reduced. It can be seen from Fig. 7(c) that when there is no communication delay in the system, the reactive power is smoother and reaches the desired value. When the delay time is 25ms, the power curve is oscillated to reach the control target. When the delay time is 33ms, The curve increases and the system is unstable. It can be seen from Fig. 6 that the system delay margin under this controller parameter is between 25ms and 33ms, which is consistent with the theoretical calculation.
  • the method of the embodiment of the invention is based on the micro-grid delay margin calculation method based on the critical eigen-root tracking, and establishes a closed-loop small-signal model of the micro-grid with communication delay based on the output feedback, and analyzes the maximum delay time for the system to be stable, ie delay Time margin.
  • this embodiment fully considers the influence of communication delay on system stability, and also studies the relationship between different controller parameters and delay margin. Guide the controller design to improve the robust stability and dynamic performance of the microgrid.

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Abstract

一种基于临界特征根跟踪的微电网延时裕度计算方法，属于运行控制的技术领域。基于静态输出反馈建立包含通讯延时电压反馈控制量的微电网闭环小信号模型，从而获取含有超越项的特征方程，对系统特征方程的超越项进行临界特征根轨迹跟踪，搜寻可能的纯虚特征根，进而计算使微电网稳定的最大延时时间。该方法对控制器参数与延时裕度间的关系进行了研究，从而指导了控制参数的设计，有效地提高了微电网的稳定性及动态性能。

Description

基于临界特征根跟踪的微电网延时裕度计算方法 技术领域
本发明公开了基于临界特征根跟踪的微电网延时裕度计算方法，尤其涉及一种微电网二次电压控制延时裕度的计算方法，属于微电网运行控制的技术领域。
背景技术
随着地球资源的日渐衰竭以及人们对环境问题的关注，可再生能源的接入越来越受到世界各国的重视。微电网是一种在能量供应系统中增加可再生能源和分布式能源渗透率的新兴能量传输模式，其组成部分包括微型燃气轮机、风力发电机、光伏、燃料电池、储能设备等不同种类的分布式能源(Distributed Energy Resources，DER)、各种电负荷和/或热负荷的用户终端以及相关的监控保护装置。
微电网内部的电源主要由电力电子器件转换能量并提供必须的控制。微电网相对于外部大电网表现为单一的受控单元，可同时满足用户对电能质量和供电安全等要求。微电网与大电网之间通过公共连接点进行能量交换，双方互为备用，从而提高了供电的可靠性。微电网是规模较小的分散系统且负荷的距离较近，在增加本地供电可靠性的同时降低了网损，这大大增加了能源利用效率，因此微电网是一种符合未来智能电网发展要求的新型供电模式。
下垂控制因可以实现无通讯的功率均分而受到关注，但各分布式电源输出电压会出现稳态偏差，同时，由于各分布式电源输出阻抗不同，无功功率均分很难达到满意效果，因此，需要采用微电网二次电压控制以提高无功均分效果及电压性能。目前，设计的协同电压控制为集中式控制结构，微电网集中式电压控制器产生控制信号并下发至各分布式电源本地控制器，该集中式控制结构依赖于通讯技术，但是通讯过程通常受到信息延时、数据丢包的影响，信息延时、数据丢包等影响导致微电网动态性能不佳甚至危及系统稳定性。基于以上原因，有必要研究一套微电网二次电压控制延时裕度计算方法，分析使微电网稳定的最大通讯延时时间，有必要对微网集中控制器参数与延时裕度的关系进行分析，从而指导控制参数的设计，有效提高微网稳定性及动态性能。
发明内容
本发明的发明目的是针对在微电网无功功率均分和电压恢复控制中通常忽略通讯延时对动态性能影响的现象，充分考虑了电力电子接口型微电网惯性小从而导致通讯延时对系统稳定性不可忽视的实际情况，提供了基于临界特征根跟踪的微电网延时裕度计算方法，通过求取微电网特征方程的所有可能纯虚特征根进而计算使微电网稳定的最大延时时间，通过对控制器参数与稳定裕度间的关系进行研究为控制参数的设计提供指导意见，解决了现有微电网系统的稳定性受通讯技术影响的技术问题。
本发明为实现上述发明目的采用如下技术方案：
基于临界特征根跟踪的微电网延时裕度计算方法，根据静态反馈输出建立包含通讯延时电压反馈控制量的逆变器闭环小信号模型及分布式电源闭环小信号模型，结合连接网络、负载阻抗的动态方程及分布式电源闭环小信号模型建立微电网小信号模型，从微电网小信号模型获取含有超越项的特征方程，对超越项进行临界特征根轨迹跟踪进而确定满足系统稳定性要求的延时裕度。
进一步地，基于临界特征根跟踪的微电网延时裕度计算方法中，根据静态反 馈输出建立的包含通讯延时电压反馈控制量的逆变器闭环小信号模型为：
Figure PCTCN2018084937-appb-000001
△x inv、
Figure PCTCN2018084937-appb-000002
分别为逆变器的闭环小信号状态变量及其变化率，
Figure PCTCN2018084937-appb-000003
△x inv1、△x inv2、△x invi、△x invn分别为第1个、第2个、第i个、第n个分布式电源的小信号状态变量，
Figure PCTCN2018084937-appb-000004
分别为第1个、第2个、第i个、第n个分布式电源的无功功率辅助小信号状态变量，第i个分布式电源的无功功率辅助小信号状态变量
Figure PCTCN2018084937-appb-000005
由表达式：
Figure PCTCN2018084937-appb-000006
确定，
Figure PCTCN2018084937-appb-000007
为第i个分布式电源无功功率辅助小信号状态变量的变化率，Q i为第i个分布式电源实际输出的无功功率，n Qi为第i个分布式电源的电压下垂特性系数,n为分布式电源的数目，△γ为分布式电源的电压辅助小信号状态变量，分布式电源的电压辅助小信号状态变量△γ由表达式：
Figure PCTCN2018084937-appb-000008
确定，
Figure PCTCN2018084937-appb-000009
为分布式电源的电压辅助小信号状态变量的变化率，V i *为第i个分布式电源平均电压的期望值，V odi为在第i个分布式电源输出电压在其自身参考坐标系dq下的d轴分量，A inv为分布式电源的状态矩阵，△V bDQ为母线电压在公共参考坐标系DQ中的小信号状态变量，△V bDQ＝[△V bDQ1,△V bDQ2,…,△V bDQl,…,△V bDQm] T，△V bDQ1、△V bDQ2、△V bDQl、△V bDQm分别为第1根、第2根、第l根、第m根母线的电压在公共参考坐标系DQ中的小信号状态变量，m为母线的数目，B inv为分布式电源对母线电压的输入矩阵，△u为分布式电源的二次电压小信号控制量，△u＝[△u 1,△u 2,…,△u i,…,△u n] T，△u 1、△u 2、△u i、△u n分别为第1个、第2个、第i个、第n个分布式电源的二次电压小信号控制量，B u为分布式电源对二次电压小信号控制量的输入矩阵，△u i＝K Qi△y invQi(t-τ i)+K Vi△y invV(t-τ i)，t为当前时刻，τ i为第i个分布式电源本地控制器与微网二次电压集中控制器间的通讯时延，K Qi、K Vi分别为第i个分布式 电源的无功功率控制系数、电压控制系数，△y invQi为第i个分布式电源的无功功率输出小信号状态变量，△y invQ、△y invV分别为分布式电源的无功功率输出小信号状态变量、电压输出小信号状态变量，C invQ、C invV分别为分布式电源的无功功率输出矩阵、电压输出矩阵。
再进一步地，基于临界特征根跟踪的微电网延时裕度计算方法中，根据静态反馈输出建立的包含通讯延时电压反馈控制量的分布式电源闭环小信号模型为：
Figure PCTCN2018084937-appb-000010
Figure PCTCN2018084937-appb-000011
为第i个分布式电源的延时状态矩阵，
Figure PCTCN2018084937-appb-000012
B ui为第i个分布式电源对二次电压小信号控制量的输入矩阵，C invQi为第i个分布式电源的无功功率输出矩阵，△i oDQ为公共参考坐标系DQ中分布式电源输出电流的小信号状态变量，C invc为分布式电源的电流输出矩阵。
更进一步地，基于临界特征根跟踪的微电网延时裕度计算方法中，微电网小信号模型为
Figure PCTCN2018084937-appb-000013
x、
Figure PCTCN2018084937-appb-000014
分别为微电网小信号状态变量及其变化率，x＝[△x inv△i lineDQ△i loadDQ] T，△i lineDQ为公共参考坐标系DQ中分布式电源所连接母线间的连接线路的电流的小信号状态变量，公共参考坐标系DQ中第i个分布式电源所连接母线和第j个分布式电源所连接母线之间的连接线路ij的电流的小信号状态变量为：
Figure PCTCN2018084937-appb-000015
△i lineDij、
Figure PCTCN2018084937-appb-000016
分别为连接线路ij的电流在公共参考坐标系DQ下的D轴小信号分量及其变化率，△i lineQij、
Figure PCTCN2018084937-appb-000017
分别为连接线路ij的电流在公共参考坐标系DQ下的Q轴小信号分量及其变化率，r lineij、L lineij分别为连接线路ij的线路电阻和线路电感，ω 0为微电网额定角频率，△V busDi、△V busQi分别为第i个分布式电源所连接母线的电压在公共参考坐标系DQ下的D轴分量、Q轴分量，△V busDj、△V busQj分别为第j个分布 式电源所连接母线的电压在公共参考坐标系DQ下的D轴分量、Q轴分量，△i loadDQ为公共参考坐标系DQ中母线所连接负载的电流的小信号状态变量，公共参考坐标系DQ中第l根母所连接负载的电流的小信号状态变量为：
Figure PCTCN2018084937-appb-000018
△i loadDl、
Figure PCTCN2018084937-appb-000019
分别为第l根母线所连接负载的电流在公共参考坐标系DQ下的D轴分量及其变化率，△i loadQl、
Figure PCTCN2018084937-appb-000020
分别为第l根母线所连接负载的电流在公共参考坐标系DQ下的Q轴分量及其变化率，R loadl、L loadl分别为第l根母线所连接负载的负载电阻、负载电感，△V busDl、△V busQl分别为第l根母线的电压在公共参考坐标系DQ下的D轴分量、Q轴分量，A di、τ i分别为第i个分布式电源的延时状态矩阵和延时。
作为基于临界特征根跟踪的微电网延时裕度计算方法的进一步优化方案，从微电网小信号模型获取含有超越项的特征方程的方法为：在分布式电源的延时一致时得到微电网小信号模型的的特征方程：CE τ(s,τ)＝det(sI-A-A de -τs)，s为时域复平面参数，τ为各分布式电源的一致时延时间，CE τ(·)表示各分布式电源一致时延τ时得到的微电网小信号模型的特征方程，det(·)为矩阵行列式，I为单位矩阵，A d为分布式电源的延时状态矩阵，
Figure PCTCN2018084937-appb-000021
e -τs为超越项。
作为基于临界特征根跟踪的微电网延时裕度计算方法的再进一步优化方案，对超越项进行临界特征根轨迹跟踪进而确定满足系统稳定性要求的延时裕度，具体方法为：以延时时间辅助变量作为特征方程的变量，求解特征方程在延时时间辅助变量变化周期内的所有纯虚特征根，从所有纯虚特征根对应的临界延时时间中选取最小值作为满足系统稳定性要求的延时裕度，所述延时时间辅助变量为分布式电源延时和虚特征根幅值的乘积。
本发明采用上述技术方案，具有以下有益效果：
(1)本发明提出了一种微电网二次电压控制延时裕度的计算方法，该方法基于静态输出反馈建立包含通讯延时电压反馈控制量的微电网闭环小信号模型，从而获取含有超越项的特征方程，对系统特征方程的超越项进行临界特征根轨迹跟踪，搜寻可能的纯虚特征根进而计算使微电网稳定的最大延时时间，该方法能够有效降低通讯延时对微网动态性能的影响，有效提高微网稳定性及动态性能；
(2)通过对不同控制器参数下的系统稳定裕度进行求取，对控制器参数与延时裕度间的关系进行研究，从而指导控制参数的设计，有效提高微网稳定性及动态性能。
附图说明
图1是本发明实施例的流程图；
图2是本发明实施例中微电网一次、二次控制框图；
图3是本发明实施例中采用的微电网仿真系统图；
图4是在某一组控制参数k IQ＝0.02,k IV＝20下，临界特征根轨迹跟踪示意图；
图5是本发明实施例中控制器参数与系统延时裕度的关系；
图6(a)是本发明实例在某一组控制参数k IQ＝0.02,k IV＝20下，3种不同通讯延时对平均电压动态性能的影响；
图6(b)是本发明实例在某一组控制参数k IQ＝0.02,k IV＝20下，3种不同通讯延时对分布式电源1无功功率动态性能的影响；
图6(c)是本发明实例在某一组控制参数k IQ＝0.02,k IV＝20下，3种不同通讯延时对分布式电源2无功功率动态性能的影响；
图7(a)是本发明实例在某一组控制参数k IQ＝0.04,k IV＝40下，3种不同通讯延时对平均电压动态性能的影响；
图7(b)是本发明实例在某一组控制参数k IQ＝0.04,k IV＝40下，3种不同通讯延时对分布式电源1无功功率动态性能的影响；
图7(c)是本发明实例在某一组控制参数k IQ＝0.04,k IV＝40下，3种不同通讯延时对分布式电源2无功功率动态性能的影响。
具体实施方式
下面结合附图对发明的技术方案进行详细说明。
如图1所示，本发明公开的基于临界特征根跟踪的微电网延时裕度计算方法，包括下述步骤：
步骤10)基于静态输出反馈建立包含通讯时延电压反馈控制量的逆变器闭环小信号模型
各分布式电源通过本地控制器中的下垂控制环设置逆变器输出电压及频率参考指令，如式(1)所示：
Figure PCTCN2018084937-appb-000022
式(1)中，ω i表示第i个分布式电源的本地角频率；ω n表示分布式电源本地角频率的参考值，单位：弧度/秒；m Pi表示第i个分布式电源的频率下垂特性系数，单位：弧度/秒·瓦；P表示第i个分布式电源实际输出的有功功率,单位：瓦；k Vi表示第i个分布式电源的下垂控制增益；
Figure PCTCN2018084937-appb-000023
表示第i个分布式电源输出电压的变化率，单位：伏/秒；V n表示分布式电源输出电压的参考值，单位：伏；V o,magi表示第i个分布式电源实际输出的电压，单位：伏；n Qi表示第i个分布式电源的电压下垂特性系数，单位：伏/乏；Q i表示第i个分布式电源实际输出的无功功率，单位：乏。
第i个分布式电源实际输出的有功功率P i、无功功率Q i通过低通滤波器获得，如式(2)所示：
Figure PCTCN2018084937-appb-000024
式(2)中，
Figure PCTCN2018084937-appb-000025
表示第i个分布式电源实际输出有功功率的变化率，单位：瓦/秒；ω ci表示第i个分布式电源所连接低通滤波器的剪切频率，单位：弧度/秒；V odi表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源输出电压的d轴分量，单位：伏；V oqi表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源输出电压的q轴分量，单位：伏；i odi表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源输出电流的d轴分量，单位：安；i oqi表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源输出电压的q轴分量，单位：安；
Figure PCTCN2018084937-appb-000026
表示第i个分布式电源实际输出无功功率的变化率，单位：乏/秒。
微电网一次、二次控制框图如图2所示，各分布式电源一次控制通过锁相环控制使输出电压q轴分量为0，基于分布式电源电压的二次控制得到式(3)：
Figure PCTCN2018084937-appb-000027
式(3)中，
Figure PCTCN2018084937-appb-000028
表示在第i个分布式电源的dq参考坐标系下，第i个分布式电源输出电压的d轴分量的变化率，单位：伏/秒；V ni表示第i个分布式电源输出电压的参考值，u i表示二次电压控制量，单位：伏。
分布式电源输出电流的动态方程如式(4)所示：
Figure PCTCN2018084937-appb-000029
式(4)中，
Figure PCTCN2018084937-appb-000030
表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源输出电流的d轴分量的变化率，单位：安/秒；R ci表示第i个分布式电源至其所连接母线的连接电阻，单位：欧姆；L ci表示第i个分布式电源至其所连接母线的连接电感，单位：亨利；V busdi表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源所连接母线的电压d轴分量；
Figure PCTCN2018084937-appb-000031
表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源输出电流的q轴分量的变化率，单位：安/秒；V busqi表示在第i个分布式电源的dq参考坐标系中，第i个分布式电源所连接母线的电压q轴分量，单位： 伏。
各分布式电源基于本地的dq参考坐标系建立模型，为建立含多个分布式电源的微电网整体模型，设定其中一个分布式电源的dq参考坐标系为公共参考坐标系DQ，则其它分布式电源dq参考坐标系下的输出电流需要转换到公共参考坐标系DQ下，转换方程如式(5)所示：
Figure PCTCN2018084937-appb-000032
式(5)中，i oDi表示在公共参考坐标系DQ中，第i个分布式电源输出电流在D轴的分量，i oQi表示在公共参考坐标系DQ中，第i个分布式电源输出电流在Q轴的分量，单位：安；T i表示第i个分布式电源输出电流从第i个分布式电源dq参考坐标系到公共参考坐标系DQ的转换矩阵，
Figure PCTCN2018084937-appb-000033
δ i表示第i个分布式电源dq参考坐标系旋转角度与公共参考坐标系DQ旋转角度之间的静态差值，单位：度，δ i可以由式(6)求得：
Figure PCTCN2018084937-appb-000034
式(6)中，ω com表示公共参考坐标系DQ的角频率；
Figure PCTCN2018084937-appb-000035
表示δ i的变化率。
线性化式(1)～式(6)得到如式(7)所示的第i个分布式电源的开环小信号模型：
Figure PCTCN2018084937-appb-000036
式(7)中，
Figure PCTCN2018084937-appb-000037
表示第i个分布式电源的小信号状态变量的变化率，
Figure PCTCN2018084937-appb-000038
Figure PCTCN2018084937-appb-000039
Δx invi表示第i个分布式电源的小信号状态变量，Δx invi＝[Δδ i,ΔP i,ΔQ i,ΔV odi,Δi odi,Δi oqi] T；△V bDQi表示在公共参考坐标系DQ中第i个分布式电源所连接母线的电压的小信号状态变量；ΔV sDQi＝[ΔV bDi,ΔV bQi] T，ΔV bDi表示在公共参考坐标系DQ中第i个分布式电源所连接母线的电压在D轴的小信号分量，ΔV bQi表示在公共参考坐标系DQ中第i个分布式电源所连接母线的电压在Q轴的小信号分量，单位：伏；Δω com表示公共参考坐标系DQ角频率的小信号状态变量，单位：弧度/秒；Δu i表示第i个分布式电源二次电压的小信号控制量，单位：伏；A invi表示第i个分布式电源的状态矩阵；B invi表示第i个分布式电源对其所连接母线电压的输入矩阵；B iwcom表示第i个分布式电源对公共参考坐标系角频率的输入矩阵； B ui表示第i个分布式电源对其二次电压小信号控制量的输入矩阵；Δi oDQi表示在公共参考坐标系DQ中，第i个分布式电源输出电流的小信号状态变量，Δi oDQi＝[Δi oDi,Δi oQi] T，单位：安；C invci表示第i个分布式电源的电流输出矩阵。
根据式(7)，ΔV busDQi和Δω com作为第i个分布式电源的扰动变量，其中一般选取第1个分布式电源的参考坐标系作为公共参考坐标系DQ，则
△ω com＝[0 -m P1 0 0 0 0]△x inv1     式(8)，
式(8)中，m P1表示第1个分布式电源的频率下垂特性系数，单位：弧度/秒·瓦；Δx inv1表示第1个分布式电源的小信号状态变量，Δx inv1＝[Δδ 1,ΔP 1,ΔQ 1,ΔV od1,Δi od1,Δi oq1] T。
根据式(7)和式(8)，可以得到n个分布式电源所组成系统的小信号模型：
Figure PCTCN2018084937-appb-000040
式(9)中，
Figure PCTCN2018084937-appb-000041
Δx inv1表示第1个分布式电源的小信号状态变量，Δx inv2表示第2个分布式电源的小信号状态变量,Δx invn表示第n个分布式电源的小信号状态变量；ΔV bDQ＝[ΔV bDQ1ΔV bDQ2...ΔV busDQm] T，ΔV bDQ1＝[ΔV bD1ΔV bQ1] T,ΔV bD1表示在公共参考坐标系DQ中母线1的电压在D轴的小信号分量，ΔV bQ1表示在公共参考坐标系DQ中母线1的电压在Q轴的小信号分量，ΔV bDQ2＝[ΔV bD2ΔV bQ2] T，ΔV bD2表示在公共参考坐标系DQ中母线2的电压在D轴的小信号分量，ΔV bQ2表示在公共参考坐标系DQ中母线2的电压在Q轴的小信号分量，ΔV bDQm＝[ΔV bDmΔV bQm] T,ΔV bDm表示在公共参考坐标系DQ中母线m的电压在D轴的小信号分量，ΔV bQm表示在公共参考坐标系DQ中母线m的电压在Q轴的小信号分量；Δu＝[Δu 1Δu 2....Δu n] T，Δu 1表示分布式电源1的二次电压小信号控制量，Δu 2表示分布式电源2的二次电压小信号控制量，Δu n表示分布式电源n的二次电压小信号控制量；Δi oDQ＝[Δi oDQ1Δi oDQ2...Δi oDQn] T，Δi oDQ1＝[Δi oD1,Δi oQ1] T,Δi oD1表示在公共参考坐标系DQ中第1个分布式电源输出电流在D轴的小信号分量，Δi oQ1表示在公共参考坐标系DQ中第i个分布式电源输出电流在Q轴的小信号分量，Δi oDQ2＝[Δi oD2,Δi oQ2] T,Δi oD2表示在公共参考坐标系DQ中第2个分布式电源输出电流在D轴的小信号分量，Δi oQ2表示在公共参考坐标系DQ中第2个分布式电源输出电流在Q轴的小信号分量；Δi oDQn＝[Δi oDn,Δi oQn] T,Δi oDn表示在公共参考坐标系DQ中第n个分布式电源输出电流在D轴的小信号分量，Δi oQn表示在公共参考坐标系DQ中第n个分布式电源输出电流在Q轴的小信号分量，
Figure PCTCN2018084937-appb-000042
为n个分布式电源的状态矩阵；
Figure PCTCN2018084937-appb-000043
为n个分布式电源对母线电压的输入矩阵；
Figure PCTCN2018084937-appb-000044
为n个分布式电源对二次电压小信号控制量的输入矩阵；
Figure PCTCN2018084937-appb-000045
为n个分布式电源的电流输出矩阵。
本发明基于无功功率均分和电压恢复的控制要求实现微电网电压控制。无功功率均分是指各分布式电源输出无功功率按功率容量进行分配，电压恢复指各分 布式电源输出电压平均值恢复至额定值，首先定义如下动态方程：
Figure PCTCN2018084937-appb-000046
式(10)中，
Figure PCTCN2018084937-appb-000047
为第i个分布式电源的无功功率辅助小信号状态变量的变化率，单位：乏；
Figure PCTCN2018084937-appb-000048
为第i个分布式电源期望输出的无功功率，单位：乏；n Qi表示第i个分布式电源的电压下垂特性系数，单位：伏/乏；
Figure PCTCN2018084937-appb-000049
为分布式电源的电压辅助小信号状态变量的变化率，单位：伏；
Figure PCTCN2018084937-appb-000050
为各分布式电源的平均输出电压，V i *为第i个分布式电源平均电压的期望值，单位：伏。
因此，基于输出反馈的逆变器闭环小信号模型为：
Figure PCTCN2018084937-appb-000051
式(11)中，Δx inv表示n个逆变器的闭环小信号状态变量，
Figure PCTCN2018084937-appb-000052
Figure PCTCN2018084937-appb-000053
为第1个分布式电源的无功功率辅助小信号状态变量，
Figure PCTCN2018084937-appb-000054
为第2个分布式电源的无功功率辅助小信号状态变量，
Figure PCTCN2018084937-appb-000055
为第i个分布式电源的无功功率辅助小信号状态变量，
Figure PCTCN2018084937-appb-000056
为第n个分布式电源的无功功率辅助小信号状态变量,△γ为各分布式电源的电压辅助小信号状态变量；Δy invQ为无功功率输出小信号状态变量
Figure PCTCN2018084937-appb-000057
Figure PCTCN2018084937-appb-000058
为第1个分布式电源的无功功率辅助小信号状态变量的变化率，
Figure PCTCN2018084937-appb-000059
为第2个分布式电源的无功功率辅助小信号状态变量的变化率，
Figure PCTCN2018084937-appb-000060
为第n个分布式电源的无功功率辅助小信号状态变量的变化率；Δy invV为分布式电源的电压输出小信号状态变量，
Figure PCTCN2018084937-appb-000061
Figure PCTCN2018084937-appb-000062
为各分布式电源的电压辅助小信号状态变量的变化率；C invQ表示各分布式电源的无功功率输出矩阵；C invV表示各分布式电源的电压输出矩阵。
定义分布式电源控制量为：
Figure PCTCN2018084937-appb-000063
式(12)中，δQ i表示第i个分布式电源的无功功率控制信号；k PQ表示无功功 率比例积分控制器中的比例项系数；k IQ表示无功功率比例积分控制器中的积分项系数；δV i表示第i个分布式电源的平均电压恢复控制信号；k PV表示平均电压比例积分控制器中的比例项系数；k IV表示平均电压比例积分控制器中的积分项系数。
当微网电压集中控制器与各分布式电源间存在通讯延时时，电压控制量为：
△u i＝△δQ i(t-τ i)+△δV i(t-τ i)＝K Qi△y invQi(t-τ i)+K Vi△y invV(t-τ i)  式(13)，
式(13)中，τ i为第i个分布式电源本地控制器与微网二次电压集中控制器间的通讯时延，单位：秒；K Qi表示第i个分布式电源的无功功率控制器，K Qi＝[k PQi k IQi]；K Vi表示第i个分布式电源的电压控制器，K Vi＝[k PVi k IVi]。
结合式(11)～式(13)，得到n个分布式电源的闭环小信号模型为：
Figure PCTCN2018084937-appb-000064
式(14)中，
Figure PCTCN2018084937-appb-000065
为第i个分布式电源的延时状态矩阵，
Figure PCTCN2018084937-appb-000066
B ui为第i个分布式电源对二次电压小信号控制量的输入矩阵，C invQi为第i个分布式电源的无功功率输出矩阵，C invc为分布式电源的电流输出矩阵。
步骤20)结合连接网络、负载型阻抗的动态方程，建立微电网小信号模型
公共参考坐标系DQ中第i个分布式电源所连接母线和第j个分布式电源所连接母线之间的连接线路ij的电流小信号动态方程如式(15)所示：
Figure PCTCN2018084937-appb-000067
式(15)中，
Figure PCTCN2018084937-appb-000068
表示在公共参考坐标系DQ中，第ij条连接线路电流D轴小信号分量的变化率，单位：安/秒；r lineij表示第ij条连接线路的线路电阻，单位：欧姆；L lineij表示第ij条连接线路的线路电感，单位：亨利；△i lineDij表示在公共参考坐标系DQ中，第ij条连接线路电流的D轴小信号分量，△i lineQij表示在公共参考坐标系DQ中，第ij条连接线路的电流的Q轴小信号分量，单位：安；ω 0表示微网额定角频率，单位：弧度/秒；ΔV busDi表示在公共参考坐标系DQ中，第i个分布式电源所连接母线的电压在D轴的小信号分量；ΔV busDj表示在公共参考坐标系DQ中，第j个分布式电源所连接母线的电压在D轴的小信号分量；
Figure PCTCN2018084937-appb-000069
表示在公共参考坐标系 DQ中，第ij条连接线路电流的Q轴小信号分量的变化率，单位：安/秒；ΔV busQi表示在公共参考坐标系DQ中，第i个分布式电源所连接母线的电压在Q轴的小信号分量，ΔV busQj表示在公共参考坐标系DQ中，第j个分布式电源所连接母线的电压在Q轴的小信号分量，单位：伏。
公共参考坐标系DQ中第l根母所连接负载的电流动态方程，如式(16)所示：
Figure PCTCN2018084937-appb-000070
式(16)中，
Figure PCTCN2018084937-appb-000071
表示在公共参考坐标系DQ中，第l根母线所连接负载的电流在D轴的小信号分量变化率，单位：安/秒；R loadl表示第l根母线所连接负载的负载电阻，单位：欧姆；L loadl表示第l根母线所连接负载的负载电感，单位：亨利；△i loadDl为在公共参考坐标系DQ中，第l根母线所连接负载的电流在D轴的小信号分量，△i loadQl为在公共参考坐标系DQ中，第l根母线所连接负载的电流在Q轴的小信号分量，单位：安；
Figure PCTCN2018084937-appb-000072
表示在公共参考坐标系DQ中，第l根母线所连接负载的电流在Q轴的小信号分量变化率，单位：安/秒。
设定连接于第i个分布式电源所连接母线和第j个分布式电源所连接母线之间的连接线路的小信号方程如式(17)所示：
Figure PCTCN2018084937-appb-000073
式(17)中，R loadj、L loadj分别为第j个分布式电源所连接母线上负载的阻值和电感值；△i oDj、△i oQj分别为第j个分布式电源输出电流在公共参考坐标系DQ中的D轴小信号分量和Q轴小信号分量。
将式(17)代入式(14)～式(16)，可得包含n个分布式电源、s条支路、p个负载的微电网小信号模型为：
Figure PCTCN2018084937-appb-000074
式(18)中，x为微电网小信号状态变量，x＝[Δx invΔi lineDQΔi loadDQ] T，△i lineDQ为公共参考坐标系DQ中分布式电源所连接母线间的连接线路的电流的小信号状态变量，△i loadDQ为公共参考坐标系DQ中母线所连接负载的电流的小信号状态变量；
Figure PCTCN2018084937-appb-000075
为微电网小信号状态变量的变化率；A为微电网状态矩阵；A di为第i个分布式电源 的延时状态矩阵；τ i为第i个分布式电源的延时。
步骤30)获取微电网闭环小信号模型含有超越项的特征方程
在各分布式电源的延时一致时，式(18)的特征方程为式(19)：
CE τ(s,τ)＝det(sI-A-A de -τs)     式(19)，
式(19)中，s为时域复平面参数；τ为各分布式电源的一致时延时间，τ 1＝τ 2＝...＝τ n，单位：秒；det(·)表示矩阵行列式；I表示单位矩阵；A d表示分布式电源的延时状态矩阵，
Figure PCTCN2018084937-appb-000076
e -τs为超越项。
步骤40)对系统特征方法的超越项进行临界特征根轨迹跟踪以计算系统稳定裕度
对式(19)，当系统特征根都在复平面左半平面时，系统稳定；当存在特征根在复平面右半平面时，系统不稳定；当特征根在复平面左半平面或者虚轴上时，系统临界稳定。由于系统特征根随着时延时间τ连续变化，因此要确定系统稳定裕度τ d，即，τ<τ d时系统稳定，τ>τ d时系统不稳定，需要确定系统可能存在的纯虚特征根和对应的延时裕度。
定义ξ＝τω，代入式(19)，则，
CE ξ(s,ξ)＝det(sI-A-A de -iξ)     式(20)，
其中，ξ为时延时间辅助变量，ω为虚特征根幅值；这里i为虚数单位，i 2＝-1。
ξ在[0,2π]的周期内进行变化，获取式(20)的相应特征根。如果对应于某个ξ存在纯虚特征根，则临界延时时间为：
τ c＝ξ c/abs(ω c)    式(21)，
式中，ξ c为使系统存在纯虚特征根的延时时间辅助变量，abs(ω c)表示对应的纯虚特征根的幅值，τ c为临界延时时间。
当ξ在[0,2π]周期内变化时，系统可能存在多个临界延时时间，即τ c1,τ c2...τ cL，延时裕度取最小值τ d：
τ d＝min(τ c1 τ c2 … τ cL)    式(22)，
在上述实施例中，所述的公共参考坐标系DQ是指第1个分布式电源的dq参考坐标系，其余分布式电源、支路电流、负载电流的状态变量通过坐标变换转换到公共参考坐标系DQ中。在步骤10)中无功功率比例积分控制器和电压比例积分控制器中，由于比例项系数比较小，实际中可以分别简化为无功功率积分控制器和电压积分控制器。在步骤20)中，负载为阻抗型负载。
本实施例通过引入信号通讯延时时间的微电网闭环小信号模型，建立含有超越项的系统特征方程，从而实现基于临界特征根跟踪的微电网延时裕度计算方法。针对常规的忽略通讯时延对系统动态性能影响的微网二次控制方法，本实施例充 分考虑了电力电子接口型微电网惯性小从而导致通讯延时对系统稳定性不可忽视的实际情况，计算出系统维持稳定的最大延时时间。本实施例的延时裕度计算方法，通过对不同控制器参数与延时裕度间关系的分析，指导控制器设计，从而提升了系统稳定性和动态性能。
本发明实施例中的微电网控制系统框图如2所示，该控制框图主要包括两层：第一层为各分布式电源的本地控制器，由功率计算、下垂控制和电压电流双环组成；第二层为二次电压控制层，实现无功功率均分和平均电压恢复。二次电压集中控制器采集各分布式电源输出电压、输出无功功率，计算出各二次电压控制量后，将控制指令下发至各分布式电源的本地控制器中。在控制指令下发过程中，通讯时延存在于二次电压集中控制器与各分布式电源本地控制器间，该时延对系统动态性能产生影响。
下面例举一个实施例。
仿真系统如图3所示，微电网由2个分布式电源，2条连接线路和3个负载组成，负载1连接于母线1，负载2连接于母线2，负载3连接于母线3。系统中负载采用阻抗型负载。假设分布式电源1，分布式电源2容量比为1:1，则设计相应的频率下垂系数、电压下垂系数使各分布式电源期望输出有功功率、无功功率比值为1:1。研究在不同控制器参数下的微电网理论延时裕度，并基于MATLAB/Simulink平台搭建微电网仿真模型对理论延时裕度进行仿真验证。
图4为在控制器参数k IQ＝0.02,k IV＝20下，与系统稳定性相关的临界特征根轨迹跟踪示意图。通讯延时辅助变量ξ在[0,2π]变化，2对共轭特征根与系统稳定性密切相关，记录下4个经过复平面虚轴的临界特征根A(jω c1),A'(-jω c1),B(jω c2)and B'(-jω c2)及相应的ξ，根据式(21)和式(22)计算出延时裕度τ d＝0.0588s。
图5是本发明实施例中，在控制器参数0.005≤k IQ≤0.06，5≤k IV≤60下，基于临界特征根跟踪计算的微电网延时裕度与控制器参数的关系。由图可知，随着无功功率控制器积分系数k IQ或电压控制器积分系数k IV的增加，系统延时裕度减少，也就是系统鲁棒稳定性降低。因此当不同组合控制器参数达到相似的动态性能时，延时裕度将作为附加的鲁棒稳定性指标，指导控制器参数设计，提供系统稳定性及动态性能。
图6为微电网采用本发明实施例在某一组控制器参数k IQ＝0.02,k IV＝20下，3种不同通讯延时对系统动态性能的影响中的分散式控制方法的仿真结果。开始运行时，各分布式电源运行于下垂控制模式，0.5s时二次电压控制投入。仿真结果如图6所示，图6(a)为微电网中分布式电源平均电压曲线图，横坐标表示时间，单位：秒，纵坐标表示平均电压，单位：伏。瓦。如图6(a)所示，最初在下垂控制作用下，分布式电源平均电压存在稳态偏差，0.5s后在二次控制作用下，电压幅值提升。由图6(a)可知：系统不存在通讯延时时，平均电压较平滑得到达额定值，当延时时间为53ms时，电压曲线经过衰减振荡恢复，当延时时间为61ms时，曲线增幅振荡，系统不稳定。图6(b)为分布式电源1无功功率输出曲线图，单位：秒，纵坐标表示无功功率，单位：乏。由图6(b)可知，最初在下垂作用下无功功率均分效果并不理想(少于分布式电源1期望无功功率输出值)，0.5s后在二次控制作用下，无功功率输出增加。由图6(b)可知，系统不存在通讯延时时，无功功率较平滑得到达期望值，当延时时间为53ms时，功率曲线经过衰减振荡达到控制目标，当延时时间为61ms时，曲线增幅振荡，系统不稳定。在二次控制作用下，微电网无功功率均分的效果得到显著改善。图6(c)为分布式电源2无功功率输出曲线图，单位：秒，纵坐标表示无功功率，单位：乏。由图6(c)可知，最初在下垂作用下无功功率均分效果并不理想(高于分布式电源2期望无功功率输出值)，0.5s后在二次控制作用下，无 功功率输出减少。由图6(c)可知，系统不存在通讯延时时，无功功率较平滑得到达期望值，当延时时间为53ms时，功率曲线经过衰减振荡达到控制目标，当延时时间为61ms时，曲线增幅振荡，系统不稳定。由图6可知，在此控制器参数下的系统延时裕度介于53ms和61ms间，与理论计算值一致。
图7为微电网采用本发明实施例在某一组控制器参数k IQ＝0.04,k IV＝40下，3种不同通讯延时对系统动态性能的影响中的分散式控制方法的仿真结果。开始运行时，各分布式电源运行于下垂控制模式，0.5s时二次电压控制投入。仿真结果如图7所示，图7(a)为微电网中分布式电源平均电压曲线图，横坐标表示时间，单位：秒，纵坐标表示平均电压，单位：伏。瓦。如图7(a)所示，最初在下垂控制作用下，分布式电源平均电压存在稳态偏差，0.5s后在二次控制作用下，电压幅值提升。由图7(a)可知：系统不存在通讯延时时，平均电压较平滑得到达额定值，当延时时间为25ms时，电压曲线经过衰减振荡恢复，当延时时间为33ms时，曲线增幅振荡，系统不稳定。图7(b)为分布式电源1无功功率输出曲线图，单位：秒，纵坐标表示无功功率，单位：乏。由图7(b)可知，最初在下垂作用下无功功率均分效果并不理想(少于分布式电源1期望无功功率输出值)，0.5s后在二次控制作用下，无功功率输出增加。由图6(b)可知，系统不存在通讯延时时，无功功率较平滑得到达期望值，当延时时间为25ms时，功率曲线经过衰减振荡达到控制目标，当延时时间为33ms时，曲线增幅振荡，系统不稳定。在二次控制作用下，微电网无功功率均分的效果得到显著改善。图7(c)为分布式电源2无功功率输出曲线图，单位：秒，纵坐标表示无功功率，单位：乏。由图7(c)可知，最初在下垂作用下无功功率均分效果并不理想(高于分布式电源2期望无功功率输出值)，0.5s后在二次控制作用下，无功功率输出减少。由图7(c)可知，系统不存在通讯延时时，无功功率较平滑得到达期望值，当延时时间为25ms时，功率曲线经过衰减振荡达到控制目标，当延时时间为33ms时，曲线增幅振荡，系统不稳定。由图6可知，在此控制器参数下的系统延时裕度介于25ms和33ms间，与理论计算值一致。
本发明实施例的方法是基于临界特征根跟踪的微电网延时裕度计算方法，基于输出反馈建立含有通讯时延的微电网闭环小信号模型，分析使系统稳定的最大延时时间，即延时裕度。针对常规的忽略通讯时延对系统动态性能影响的微网二次控制方法，本实施例充分考虑了通讯延时对系统稳定性的影响，此外通过研究不同控制器参数与延时裕度间关系，指导控制器设计，从而提升了微电网的鲁棒稳定性和动态性能。

Claims (6)

  1. 基于临界特征根跟踪的微电网延时裕度计算方法，其特征在于，根据静态反馈输出建立包含通讯延时电压反馈控制量的逆变器闭环小信号模型及分布式电源闭环小信号模型，结合连接网络、负载阻抗的动态方程及分布式电源闭环小信号模型建立微电网小信号模型，从微电网小信号模型获取含有超越项的特征方程，对超越项进行临界特征根轨迹跟踪进而确定满足系统稳定性要求的延时裕度。
  2. 根据权利要求1所述基于临界特征根跟踪的微电网延时裕度计算方法，其特征在于，根据静态反馈输出建立的包含通讯延时电压反馈控制量的逆变器闭环小信号模型为：
    Figure PCTCN2018084937-appb-100001
    Δx inv、
    Figure PCTCN2018084937-appb-100002
    分别为逆变器的闭环小信号状态变量及其变化率，
    Figure PCTCN2018084937-appb-100003
    Δx inv1、Δx inv2、Δx invi、Δx invn分别为第1个、第2个、第i个、第n个分布式电源的小信号状态变量，
    Figure PCTCN2018084937-appb-100004
    分别为第1个、第2个、第i个、第n个分布式电源的无功功率辅助小信号状态变量，第i个分布式电源的无功功率辅助小信号状态变量
    Figure PCTCN2018084937-appb-100005
    由表达式：
    Figure PCTCN2018084937-appb-100006
    确定，
    Figure PCTCN2018084937-appb-100007
    为第i个分布式电源无功功率辅助小信号状态变量的变化率，Q i为第i个分布式电源实际输出的无功功率，n Qi为第i个分布式电源的电压下垂特性系数,n为分布式电源的数目，Δγ为分布式电源的电压辅助小信号状态变量，分布式电源的电压辅助小信号状态变量Δγ由表达式：
    Figure PCTCN2018084937-appb-100008
    确定，
    Figure PCTCN2018084937-appb-100009
    为分布式电源的电压辅助小信号状态变量的变化率，V i *为第i个分布式电源平均电压的期望值，V odi为在第i个分布式电源输出电压在其自身参考坐标系dq下的d轴分量，A inv为分布式电源的状态矩阵，ΔV bDQ为母线电压在公共参考坐标系DQ中的小信号状态变量， ΔV bDQ＝[ΔV bDQ1,ΔV bDQ2,…,ΔV bDQl,…,ΔV bDQm] T，ΔV bDQ1、ΔV bDQ2、ΔV bDQl、ΔV bDQm分别为第1根、第2根、第l根、第m根母线的电压在公共参考坐标系DQ中的小信号状态变量，m为母线的数目，B inv为分布式电源对母线电压的输入矩阵，Δu为分布式电源的二次电压小信号控制量，Δu＝[Δu 1,Δu 2,…,Δu i,…,Δu n] T，Δu 1、Δu 2、Δu i、Δu n分别为第1个、第2个、第i个、第n个分布式电源的二次电压小信号控制量，B u为分布式电源对二次电压小信号控制量的输入矩阵，Δu i＝K QiΔy invQi(t-τ i)+K ViΔy invV(t-τ i)，t为当前时刻，τ i为第i个分布式电源本地控制器与微网二次电压集中控制器间的通讯时延，K Qi、K Vi分别为第i个分布式电源的无功功率控制系数、电压控制系数，Δy invQi为第i个分布式电源的无功功率输出小信号状态变量，Δy invQ、Δy invV分别为分布式电源的无功功率输出小信号状态变量、电压输出小信号状态变量，C invQ、C invV分别为分布式电源的无功功率输出矩阵、电压输出矩阵。
  3. 根据权利要求2所述基于临界特征根跟踪的微电网延时裕度计算方法，其特征在于，根据静态反馈输出建立的包含通讯延时电压反馈控制量的分布式电源闭环小信号模型为：
    Figure PCTCN2018084937-appb-100010
    Figure PCTCN2018084937-appb-100011
    为第i个分布式电源的延时状态矩阵，
    Figure PCTCN2018084937-appb-100012
    B ui为第i个分布式电源对二次电压小信号控制量的输入矩阵，C invQi为第i个分布式电源的无功功率输出矩阵，Δi oDQ为公共参考坐标系DQ中分布式电源输出电流的小信号状态变量，C invc为分布式电源的电流输出矩阵。
  4. 根据权利要求3所述基于临界特征根跟踪的微电网延时裕度计算方法， 其特征在于，所述微电网小信号模型为
    Figure PCTCN2018084937-appb-100013
    x、
    Figure PCTCN2018084937-appb-100014
    分别为微电网小信号状态变量及其变化率，x＝[Δx invΔi lineDQΔi loadDQ] T，Δi lineDQ为公共参考坐标系DQ中分布式电源所连接母线间的连接线路的电流的小信号状态变量，公共参考坐标系DQ中第i个分布式电源所连接母线和第j个分布式电源所连接母线之间的连接线路ij的电流的小信号状态变量为：
    Figure PCTCN2018084937-appb-100015
    Δi lineDij、
    Figure PCTCN2018084937-appb-100016
    分别为连接线路ij的电流在公共参考坐标系DQ下的D轴小信号分量及其变化率，Δi lineQij、
    Figure PCTCN2018084937-appb-100017
    分别为连接线路ij的电流在公共参考坐标系DQ下的Q轴小信号分量及其变化率，r lineij、L lineij分别为连接线路ij的线路电阻和线路电感，ω 0为微电网额定角频率，ΔV busDi、ΔV busQi分别为第i个分布式电源所连接母线的电压在公共参考坐标系DQ下的D轴分量、Q轴分量，ΔV busDj、ΔV busQj分别为第j个分布式电源所连接母线的电压在公共参考坐标系DQ下的D轴分量、Q轴分量，Δi loadDQ为公共参考坐标系DQ中母线所连接负载的电流的小信号状态变量，公共参考坐标系DQ中第l根母所连接负载的电流的小信号状态变量为：
    Figure PCTCN2018084937-appb-100018
    Δi loadDl、
    Figure PCTCN2018084937-appb-100019
    分别为第l根母线所连接负载的电流在公共参考坐标系DQ下的D轴分量及其变化率，Δi loadQl、
    Figure PCTCN2018084937-appb-100020
    分别为第l根母线所连接负载的电流在公共参考坐标系DQ下的Q轴分量及其变化率，R loadl、L loadl分别为第l根母线所连接负载的负载电阻、负载电感，ΔV busDl、ΔV busQl分别为第l根母线的电压在公共参考坐标系DQ下的D轴分量、Q轴分量，A di、τ i分别为第i个分布式电源的延时状态矩阵和延时。
  5. 根据权利要求4所述基于临界特征根跟踪的微电网延时裕度计算方法，其特征在于，从微电网小信号模型获取含有超越项的特征方程的方法为：在分布式电源的延时一致时得到微电网小信号模型的的特征方程：CE τ(s,τ)＝det(sI-A-A de -τs)，s为时域复平面参数，τ为各分布式电源的一致时延时间，CE τ(·)表示各分布式电源一致时延τ时得到的微电网小信号模型的特征方程，det(·)为矩阵行列式，I为单位矩阵，A d为分布式电源的延时状态矩阵，
    Figure PCTCN2018084937-appb-100021
    e -τs为超越项。
  6. 根据权利要求5所述基于临界特征根跟踪的微电网延时裕度计算方法，其特征在于，对超越项进行临界特征根轨迹跟踪进而确定满足系统稳定性要求的延时裕度，具体方法为：以延时时间辅助变量作为特征方程的变量，求解特征方程在延时时间辅助变量变化周期内的所有纯虚特征根，从所有纯虚特征根对应的临界延时时间中选取最小值作为满足系统稳定性要求的延时裕度，所述延时时间辅助变量为分布式电源延时和虚特征根幅值的乘积。
PCT/CN2018/084937 2017-06-16 2018-04-27 基于临界特征根跟踪的微电网延时裕度计算方法 WO2018228068A1 (zh)

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CN107994564A (zh) * 2017-10-27 2018-05-04 东南大学 基于特征根聚类的多重时滞微电网电压稳定性分析方法
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