CN113098053B - Reactive power optimization method containing transient voltage safety constraint based on cooperative game - Google Patents

Reactive power optimization method containing transient voltage safety constraint based on cooperative game Download PDF

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CN113098053B
CN113098053B CN202110294999.5A CN202110294999A CN113098053B CN 113098053 B CN113098053 B CN 113098053B CN 202110294999 A CN202110294999 A CN 202110294999A CN 113098053 B CN113098053 B CN 113098053B
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transient voltage
node
safety
representing
reactive power
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CN113098053A (en
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王彬
崔惟
郭庆来
张振安
孙宏斌
单瑞卿
葛怀畅
林银鸿
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Tsinghua University
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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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
    • H02J3/38—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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • 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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • 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
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention provides a reactive power optimization method containing transient voltage safety constraint based on cooperative game, and belongs to the field of transient voltage safety evaluation and control of a power system. Firstly, establishing a reactive optimal power flow model containing transient voltage safety constraint, which is composed of a target function and constraint conditions; converting the model into a cooperative game model between the security party and the economic party, and solving the model by a method of giving a decision by the game parties in turn to obtain an optimal operating point of reactive power output of each generator and an optimal set value of a tap joint of a transformer; simulating the time domain of the solution result, scanning an expected fault set, and calculating to obtain a transient voltage safety quantitative evaluation index of each node under each fault; and when the safety quantitative evaluation indexes of all the nodes under all the faults meet the transient voltage safety constraint, completing the reactive power optimization. The method has high solving efficiency, and the optimization result obtained by the method can reduce the operation cost and ensure the safe and reliable operation of the power grid.

Description

Reactive power optimization method containing transient voltage safety constraint based on cooperative game
Technical Field
The invention belongs to the field of transient voltage safety assessment and control of a power system, and particularly relates to a reactive power optimization method containing transient voltage safety constraint based on cooperative game.
Background
In recent years, with High Voltage Direct Current (HVDC) transmission and large-scale new energy access to a power grid, a large number of power electronic devices appear in a power system, and the devices are sensitive to voltage transient changes, so that the transient voltage problem of the system becomes more and more prominent. Once short circuit fault occurs in the system, serious accidents such as multi-circuit direct current continuous commutation failure, even locking, new energy interlocking off-line and the like can be caused, and the risk of large-area power failure exists. In order to improve the transient voltage safety level of the power system, the output of different reactive devices in the system can be optimized by establishing a reactive optimal power flow model containing transient voltage safety constraints. However, the problem is essentially a large-scale mixed integer nonlinear programming problem, direct solution is difficult, and the calculation time is difficult to meet the requirement of online application.
In consideration of the complexity of the reactive power optimal power flow model, the existing research mainly adopts an immune algorithm, a genetic algorithm, a particle swarm algorithm and other intelligent algorithms when solving the model. However, because relevant parameters in the algorithms do not have actual meanings, the problem of difficult parameter setting generally exists, and the defects of long time consumption and the like exist in solving the actual problem.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a reactive power optimization method containing transient voltage safety constraint based on cooperative game. The method comprises the steps of firstly defining a quantitative index for measuring the transient voltage safety level of a power system based on a transient voltage response curve of each node under the fault action, then establishing a reactive optimal power flow model containing transient voltage safety constraint based on the index, then converting the model into a cooperative game problem between two opposite players of a safety party and an economic party, and finally designing a method for solving the model by which two game parties give decisions in turn, thereby solving the equilibrium solution of the game problem. The method has high solving efficiency, and the optimization result obtained by the method can reduce the operation cost and ensure the safe and reliable operation of the power grid.
The invention provides a reactive power optimization method containing transient voltage safety constraint based on cooperative game, which is characterized in that the method is based on a transient voltage safety quantitative evaluation index, establishes a reactive power optimal power flow model containing the transient voltage safety constraint and consisting of a target function and a constraint condition, then converts the model into a cooperative game model between a safety party and an economic party, the cooperative game model comprises a safety square sub-model and an economic square sub-model, and the two sub-models are sequentially solved to obtain an optimal operating point of reactive power output of each generator and an optimal set value of a transformer tap; performing time domain simulation on the solution result, scanning an expected fault set, and calculating to obtain a transient voltage safety quantitative evaluation index of each node under each fault; and when the safety quantitative evaluation indexes of all the nodes under all the faults meet the transient voltage safety constraint, completing the reactive power optimization. The method comprises the following steps:
(1) defining a TVSI, which is a quantified evaluation index of transient voltage safety, as shown in the following formula:
Figure GDA0003536907320000021
in the formula, V0And V'minRespectively representing the initial value of the node voltage and the minimum value of the node voltage after fault removal; vth、TthSafe threshold value representing voltage and voltage lower than V after fault occurrencethA tolerable time of; t ismx_span、Tcut、
Figure GDA0003536907320000022
Respectively indicate that the node voltage is lower than V after the fault occursthMaximum duration, fault clearing time, and voltage average at the end of the simulation;
(2) based on the transient voltage safety quantitative evaluation index in the step (1), according to an expected fault set SFltEstablishing a reactive optimal power flow model containing transient voltage safety constraint, wherein the model consists of a target function and constraint conditions; the method comprises the following specific steps:
(2-1) determining an objective function of the model, wherein the expression is as follows:
Figure GDA0003536907320000023
wherein, PlossRepresenting the network loss, P, of the systemiRepresenting the active power injected into the network from node i, NbusRepresenting the number of nodes in the power system;
(2-2) determining constraints of the model; the method comprises the following specific steps:
(2-2-1) the power flow equation of the power system before the occurrence of the expected fault is constrained as follows:
Figure GDA0003536907320000024
Figure GDA0003536907320000025
wherein Q isiRepresenting the reactive power injected into the network from node i;
Figure GDA0003536907320000026
respectively representing active power and reactive power generated by a generator connected with the node i;
Figure GDA0003536907320000027
respectively representing the active power and the reactive power absorbed by the loads connected with the node i; vi、VjRespectively representing steady state voltage values, G, of nodes i, jij、BijRespectively representing the real part and the imaginary part, theta, of the ith row and jth column element in the nodal admittance matrixijRepresenting the phase angle difference between node i and node j;
(2-2-2) during steady-state operation of the power system, the voltage of each node, the reactive power output of the generator and inequality constraints met by the adjustable tap of the transformer are as follows:
Vmin＜Vi＜Vmax
Figure GDA0003536907320000031
Ts,min＜Ts＜Ts,max
wherein, Vmin、VmaxRespectively representing the lower and upper limits of the node voltage,
Figure GDA0003536907320000032
respectively representing the lower limit and the upper limit of the i output of the generator, TsIndicating an adjustable tap of the s-th transformer, Ts,min、Ts,maxRespectively representing the lower limit and the upper limit of the adjustable tap of the s-th transformer;
(2-2-3) the system constrains the differential algebraic equation system of the dynamic trajectory under the action of the kth fault as follows:
Figure GDA0003536907320000033
gk(xk,yk,uk)＝0
k＝1,2…NFlt
wherein x isk、yk、ukRespectively representing a state variable response curve, a node voltage response curve and a control variable response curve in the power system after the kth fault occurs; f. ofkDifferential equation, g, representing the dynamics of the elements of the system after the occurrence of the kth faultkAn algebraic equation representing the voltage-current relationship of each node in the network after the kth fault occurs;
(2-2-4) transient voltage safety constraints;
after the kth fault occurs in the power system, the response curves of all the node voltages meet the following transient voltage safety constraint:
TVSIk(yk)＜TVSIth
wherein, TVSIkThe method comprises the steps that a quantitative evaluation index of the transient voltage safety calculated according to a voltage response curve of each node after the kth fault occurs in the system is represented; TVSIthRepresenting a safety threshold value of the transient voltage safety quantitative evaluation index;
(3) converting a reactive optimal power flow model containing transient voltage safety constraint into a cooperation game model between a safety party and an economic party and solving, wherein the cooperation game model comprises a safety square model and an economic square model; the method comprises the following specific steps:
(3-1) establishing a safety square sub-model;
wherein the payment function of the security is as follows:
Figure GDA0003536907320000034
in the formula (I), the compound is shown in the specification,
Figure GDA0003536907320000035
respectively representing the lower limit and the upper limit of the reactive power output of the jth generator after the transient voltage safety constraint is considered, NGRepresenting the number of generators;
the constraint conditions met during the safety decision are as follows:
Figure GDA0003536907320000036
Figure GDA0003536907320000041
Figure GDA0003536907320000042
Figure GDA0003536907320000043
k＝1,2…NFlt
wherein the content of the first and second substances,
Figure GDA0003536907320000044
representing a transient voltage safety quantitative evaluation index of the node i when the kth fault occurs in an initial state;
Figure GDA0003536907320000045
the sensitivity of the transient voltage safety quantitative evaluation index of the node i to the reactive power output of the generator j is shown when the kth fault occurs in the initial state;
Figure GDA0003536907320000046
representing the initial reactive power output of generator j;
(3-2) the safety party obtains the safe operation range of each generator by solving the submodel in the step (3-1)
Figure GDA0003536907320000047
And communicates the range to the economic party;
(3-3) establishing an economic square model;
wherein the payment function of the economic party is as follows:
Figure GDA0003536907320000048
the constraint conditions met by the economic party during decision are as follows:
Figure GDA0003536907320000049
Figure GDA00035369073200000410
Vmin＜Vi＜Vmax
Figure GDA00035369073200000411
Ts,min＜Ts＜Ts,max
(3-4) the economic party obtains the current optimal solution of reactive power optimization by solving the submodels in the step (3-3) and comprises the following steps: optimal operating point of reactive power output of each generator
Figure GDA00035369073200000412
And optimal setting value of transformer tap
Figure GDA00035369073200000413
(4) Adjusting the reactive power output of the generator and the tap joint of the transformer to be corresponding values in the current optimal solution obtained in the step (3-4), then executing time domain simulation calculation, and completely scanning the expected fault set SFltObtaining the voltage response curve of each node under each fault, and calculating to obtain the transient voltage safety quantitative evaluation index of each node under each fault
Figure GDA00035369073200000414
(5) And (4) judging whether the transient voltage safety constraint is satisfied by using the result of the step (4):
Figure GDA00035369073200000415
i＝1,2…Nbus
k＝1,2…NFlt
if yes, finishing the optimization and outputting the current optimal solution
Figure GDA00035369073200000416
The final reactive power optimization result is obtained; if not, calculating by perturbation method to obtain updated
Figure GDA0003536907320000051
And order
Figure GDA0003536907320000052
And then returning to the step (3).
The invention has the characteristics and beneficial effects that:
1. the method provided by the invention provides a power system transient voltage safety quantitative evaluation index based on a voltage response curve, and can evaluate the transient voltage safety margin of the system in the current state.
2. According to the method, the transient voltage safety constraint which needs to be met by the system under the fault is represented by means of the transient voltage safety quantitative evaluation index, so that a reactive optimal power flow model containing the transient voltage safety constraint is constructed.
3. The method of the invention decomposes the reactive optimal power flow model into a cooperative game model between two competitors of the security party and the economic party, and designs a method for the two competitors to make alternative decisions to solve the model, thereby improving the solving efficiency of the model.
4. The optimization result obtained by the invention can reduce the operation cost and ensure the safe and reliable operation of the power grid.
Detailed Description
The invention provides a reactive power optimization method containing transient voltage safety constraint based on cooperative game, which comprises the following steps:
(1) according to the specification of the safety and stability guide rule of the power system in China, that the voltage of a load bus can be recovered to be above a specified operating voltage level in the transient and dynamic processes after the power system is disturbed, a transient voltage safety quantitative evaluation index TVSI based on a voltage response curve can be defined, and the following formula is shown:
Figure GDA0003536907320000053
in the formula: v0And V'minRespectively representing the initial value of the node voltage and the minimum value of the node voltage after fault removal; vth、TthSafety thresholds respectively representing voltagesValue and voltage after fault lower than VthThe typical value can be 0.8 and 0.4s respectively; t ismx_span、Tcut、
Figure GDA0003536907320000054
Respectively, that the node voltage is lower than V after the occurrence of the faultthMaximum duration of time, fault clearing time, and voltage average at the end of the simulation.
(2) Based on the transient voltage safety quantitative evaluation index in the step (1), giving an expected fault set S according to the actual power gridFltA reactive optimal power flow model containing transient voltage safety constraint can be established, and the model consists of a target function and constraint conditions; the method comprises the following specific steps:
(2-1) determining an objective function of the model, wherein the expression is as follows:
Figure GDA0003536907320000061
wherein, PlossRepresenting the network loss, P, of the systemiRepresenting the active power injected into the network from node i, NbusRepresenting the number of nodes in the power system.
(2-2) determining constraints of the model; the method comprises the following specific steps:
(2-2-1) the power flow equation of the power system before the occurrence of the expected fault is constrained as follows:
Figure GDA0003536907320000062
Figure GDA0003536907320000063
wherein Q isiRepresenting the reactive power injected into the network from node i.
Figure GDA0003536907320000064
Respectively representing connections of nodes iActive power and reactive power generated by the generator.
Figure GDA0003536907320000065
Respectively representing the active and reactive power absorbed by the load connected to node i. Vi、VjRepresenting steady state voltage values, G, of nodes i, j, respectivelyij、BijRespectively representing the real part and the imaginary part, theta, of the ith row and jth column element in the nodal admittance matrixijRepresenting the phase angle difference between node i and node j.
(2-2-2) during steady-state operation of the power system, the voltage of each node, the reactive power output of the generator and inequality constraints met by the adjustable tap of the transformer are as follows:
Vmin＜Vi＜Vmax
Figure GDA0003536907320000066
Ts,min＜Ts＜Ts,max
wherein, Vmin、VmaxRespectively representing the lower limit and the upper limit of the node voltage, given by the national grid standard.
Figure GDA0003536907320000067
The lower limit and the upper limit of the output of the generator i are respectively represented and are determined by the capacity parameter of the device. T issShowing the adjustable tap of the s-th transformer. T iss,min、Ts,maxRespectively representing the lower limit and the upper limit of the adjustable tap of the s-th transformer.
(2-2-3) the system constrains the differential algebraic equation system of the dynamic trajectory under the action of the kth fault as follows:
Figure GDA0003536907320000068
gk(xk,yk,uk)＝0
wherein x isk、yk、ukRespectively representing a state variable response curve, a node voltage response curve and a control variable response curve in the power system after the k-th fault occurs. f. ofkThe differential equations describing the dynamics of the various elements of the system after the occurrence of the kth fault are represented, including the dynamics of the generator and its excitation system, and the dynamics of the load. gkAn algebraic equation describing the voltage-current relationship of each node in the network after the occurrence of the kth fault is expressed. N is a radical ofFltRepresents the expected failure set SFltThe number of failures is envisioned.
(2-2-4) transient voltage safety constraints;
after the kth fault occurs in the power system, all node voltage response curves need to satisfy the following transient voltage safety constraints:
TVSIk(yk)＜TVSIth
wherein, TVSIkAnd the quantitative evaluation index of the transient voltage safety is calculated according to the voltage response curve of each node in the system after the kth fault occurs in the system. TVSIthThe safety threshold value of the transient voltage safety quantitative evaluation index is represented, and the value of the embodiment is 2.
(3) And converting the reactive optimal power flow model containing the transient voltage safety constraint into a cooperative game model between the safety party and the economic party and solving, wherein the cooperative game model comprises a safety square model and an economic square model. The safe side refers to a main body seeking safe and reliable operation of the power grid, and the economic side refers to a main body seeking minimum operation cost of the power grid. The method comprises the following specific steps:
(3-1) establishing a safety square sub-model;
wherein the payment function of the security is as follows:
Figure GDA0003536907320000071
in the formula (I), the compound is shown in the specification,
Figure GDA0003536907320000072
respectively representing the considered transient voltageLower limit and upper limit of reactive power output of jth generator after safety restriction, NGIndicating the number of generators.
The constraint conditions to be met in the safety decision are as follows:
Figure GDA0003536907320000073
Figure GDA0003536907320000074
Figure GDA0003536907320000075
Figure GDA0003536907320000076
k＝1,2…NFlt
wherein the content of the first and second substances,
Figure GDA0003536907320000077
and the quantitative evaluation index value of the transient voltage safety of the node i when the k-th fault occurs in the initial state (namely the state before optimization).
Figure GDA0003536907320000078
And the sensitivity of the transient voltage safety quantitative evaluation index of the node i to the reactive power output of the generator j when the kth fault occurs in the initial state is shown.
Figure GDA0003536907320000079
Representing the initial reactive power output of generator j.
(3-2) the safety party obtains the safe operation range of each generator by solving the submodel in the step (3-1)
Figure GDA00035369073200000710
And convey that range to economyThe method is used as a part of constraint conditions when the economic party makes a decision;
(3-3) establishing an economic square model;
wherein the payment function of the economic party is as follows:
Figure GDA0003536907320000081
the constraint conditions to be met when the economic party makes a decision are as follows:
Figure GDA0003536907320000082
Figure GDA0003536907320000083
Vmin＜Vi＜Vmax
Figure GDA0003536907320000084
Ts,min＜Ts＜Ts,max
(3-4) the economic party obtains the current optimal solution of reactive power optimization by solving the submodels in the step (3-3) and comprises the following steps: optimal operating point of reactive power output of each generator
Figure GDA0003536907320000085
And optimal setting value of transformer tap
Figure GDA0003536907320000086
(4) Adjusting the reactive power output of the generator and the tap joint of the transformer to be corresponding values in the current optimal solution obtained in the step (3-4), then executing time domain simulation calculation, and completely scanning the expected fault set SFltAnd obtaining the voltage response curve of each node under each fault. Calculating to obtain the transient voltage safety of each node under each fault based on the step (1)Quantitative evaluation index
Figure GDA0003536907320000087
(5) And (4) judging whether the transient voltage safety constraint is satisfied by using the result of the step (4):
Figure GDA0003536907320000088
i＝1,2…Nbus
k＝1,2…NFlt
if yes, finishing the optimization and outputting the current optimal solution
Figure GDA0003536907320000089
And the final reactive power optimization result is obtained. Otherwise, calculating by perturbation method to obtain new
Figure GDA00035369073200000810
And order
Figure GDA00035369073200000811
And then returning to the step (3) again to perform the next round of iterative computation.

Claims (1)

1. A reactive power optimization method based on a cooperative game and containing transient voltage safety constraint is characterized in that the method is based on a transient voltage safety quantitative evaluation index, a reactive power optimal power flow model containing the transient voltage safety constraint and formed by a target function and constraint conditions is established, then the model is converted into a cooperative game model between a safety party and an economic party, the cooperative game model comprises a safety square sub-model and an economic square sub-model, the two sub-models are sequentially solved, and an optimal running point of reactive power output of each generator and an optimal set value of a transformer tap are obtained; performing time domain simulation on the solution result, scanning an expected fault set, and calculating to obtain a transient voltage safety quantitative evaluation index of each node under each fault; when the safety quantitative evaluation indexes of all nodes under all faults meet the transient voltage safety constraint, completing reactive power optimization;
the method comprises the following steps:
(1) defining a TVSI, which is a quantified evaluation index of transient voltage safety, as shown in the following formula:
Figure FDA0003536907310000011
in the formula, V0And V'minRespectively representing the initial value of the node voltage and the minimum value of the node voltage after fault removal; vth、TthSafe threshold value representing voltage and voltage lower than V after fault occurrencethA tolerable time of; t ismx_span、Tcut、
Figure FDA0003536907310000012
Respectively indicate that the node voltage is lower than V after the fault occursthMaximum duration, fault clearing time, and voltage average at the end of the simulation;
(2) based on the transient voltage safety quantitative evaluation index in the step (1), according to an expected fault set SFltEstablishing a reactive optimal power flow model containing transient voltage safety constraint, wherein the model consists of a target function and constraint conditions; the method comprises the following specific steps:
(2-1) determining an objective function of the model, wherein the expression is as follows:
Figure FDA0003536907310000013
wherein, PlossRepresenting the network loss, P, of the systemiRepresenting the active power injected into the network from node i, NbusRepresenting the number of nodes in the power system;
(2-2) determining constraints of the model; the method comprises the following specific steps:
(2-2-1) the power flow equation of the power system before the occurrence of the expected fault is constrained as follows:
Figure FDA0003536907310000021
Figure FDA0003536907310000022
wherein Q isiRepresenting the reactive power injected into the network from node i;
Figure FDA0003536907310000023
respectively representing active power and reactive power generated by a generator connected with the node i;
Figure FDA0003536907310000024
respectively representing the active power and the reactive power absorbed by the loads connected with the node i; vi、VjRespectively representing steady state voltage values, G, of nodes i, jij、BijRespectively representing the real part and the imaginary part, theta, of the ith row and jth column element in the nodal admittance matrixijRepresenting the phase angle difference between node i and node j;
(2-2-2) during steady-state operation of the power system, the voltage of each node, the reactive power output of the generator and inequality constraints met by the adjustable tap of the transformer are as follows:
Vmin＜Vi＜Vmax
Figure FDA0003536907310000025
Ts,min＜Ts＜Ts,max
wherein, Vmin、VmaxRespectively representing the lower and upper limits of the node voltage,
Figure FDA0003536907310000026
respectively representing the lower limit and the upper limit of the i output of the generator, TsAdjustable tap for representing the s-th transformer，Ts,min、Ts,maxRespectively representing the lower limit and the upper limit of the adjustable tap of the s-th transformer;
(2-2-3) the system constrains the differential algebraic equation system of the dynamic trajectory under the action of the kth fault as follows:
Figure FDA0003536907310000027
gk(xk,yk,uk)＝0
k＝1,2…NFlt
wherein x isk、yk、ukRespectively representing a state variable response curve, a node voltage response curve and a control variable response curve in the power system after the kth fault occurs; f. ofkDifferential equation, g, representing the dynamics of the elements of the system after the occurrence of the kth faultkAn algebraic equation representing the voltage-current relationship of each node in the network after the kth fault occurs;
(2-2-4) transient voltage safety constraints;
after the kth fault occurs in the power system, the response curves of all the node voltages meet the following transient voltage safety constraint:
TVSIk(yk)＜TVSIth
wherein, TVSIkThe method comprises the steps that a quantitative evaluation index of the transient voltage safety calculated according to a voltage response curve of each node after the kth fault occurs in the system is represented; TVSIthRepresenting a safety threshold value of the transient voltage safety quantitative evaluation index;
(3) converting a reactive optimal power flow model containing transient voltage safety constraint into a cooperation game model between a safety party and an economic party and solving, wherein the cooperation game model comprises a safety square model and an economic square model; the method comprises the following specific steps:
(3-1) establishing a safety square sub-model;
wherein the payment function of the security is as follows:
Figure FDA0003536907310000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003536907310000032
respectively representing the lower limit and the upper limit of the reactive power output of the jth generator after the transient voltage safety constraint is considered, NGRepresenting the number of generators;
the constraint conditions met during the safety decision are as follows:
Figure FDA0003536907310000033
Figure FDA0003536907310000034
Figure FDA0003536907310000035
Figure FDA0003536907310000036
k＝1,2…NFlt
wherein the content of the first and second substances,
Figure FDA0003536907310000037
representing a transient voltage safety quantitative evaluation index of the node i when the kth fault occurs in an initial state;
Figure FDA0003536907310000038
the sensitivity of the transient voltage safety quantitative evaluation index of the node i to the reactive power output of the generator j is shown when the kth fault occurs in the initial state;
Figure FDA0003536907310000039
representing the initial reactive power output of generator j;
(3-2) the safety party obtains the safe operation range of each generator by solving the submodel in the step (3-1)
Figure FDA00035369073100000310
And communicates the range to the economic party;
(3-3) establishing an economic square model;
wherein the payment function of the economic party is as follows:
Figure FDA00035369073100000311
the constraint conditions met by the economic party during decision are as follows:
Figure FDA00035369073100000312
Figure FDA00035369073100000313
Vmin＜Vi＜Vmax
Figure FDA00035369073100000314
Ts,min＜Ts＜Ts,max
(3-4) the economic side obtains the current optimal solution of reactive power optimization by solving the submodels in the step (3-3) and comprises the following steps: optimal operating point of reactive power output of each generator
Figure FDA00035369073100000315
And optimal setting value of transformer tap
Figure FDA00035369073100000316
(4) Adjusting the reactive power output of the generator and the tap joint of the transformer to be corresponding values in the current optimal solution obtained in the step (3-4), then executing time domain simulation calculation, and completely scanning the expected fault set SFltObtaining the voltage response curve of each node under each fault, and calculating to obtain the transient voltage safety quantitative evaluation index of each node under each fault
Figure FDA0003536907310000041
(5) And (5) judging whether the transient voltage safety constraint is established or not by using the result of the step (4):
Figure FDA0003536907310000042
i＝1,2…Nbus
k＝1,2…NFlt
if yes, finishing the optimization and outputting the current optimal solution
Figure FDA0003536907310000043
The final reactive power optimization result is obtained; if not, calculating by perturbation method to obtain updated
Figure FDA0003536907310000044
And order
Figure FDA0003536907310000045
And then returning to the step (3).
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