CN110416983B - Cooperative optimization configuration method for current-limiting reactor and fault current limiter in flexible direct-current power grid - Google Patents
Cooperative optimization configuration method for current-limiting reactor and fault current limiter in flexible direct-current power grid Download PDFInfo
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Abstract
The invention relates to the technical field of flexible direct-current power grids, in particular to a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in a flexible direct-current power grid. The method comprises the steps of comprehensively considering system performance and current limiting equipment cost, establishing a multi-target optimal configuration mathematical model by taking a current limiting effect, a total inductance value of a current limiting reactor and the number of fault current limiters as objective functions and taking the on-off current of a direct current breaker, the overcurrent protection of a converter valve and the current limiting reactor as constraint conditions, solving by adopting a multi-target mixed leapfrogging algorithm to obtain an optimal solution set, and selecting a proper configuration scheme in the optimal solution set by combining with actual conditions. According to the method, the current-limiting reactors and the fault current limiters in the flexible direct-current power grid are optimally configured, the global optimization target of the best current-limiting effect, the minimum total inductance value of the current-limiting reactors and the minimum installation number of the fault current limiters is achieved, and continuous and stable operation of the healthy part of the flexible direct-current power grid can be guaranteed when a fault occurs.
Description
Technical Field
The invention relates to the technical field of flexible direct-current power grids, in particular to a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in a flexible direct-current power grid.
Background
The flexible direct current power grid is an important direction for the development of modern power grids, wherein the modular multilevel converter MMC is widely applied to flexible direct current engineering by virtue of the advantages of low harmonic content, low switching frequency, high reliability and the like. Because the flexible direct-current power grid has a low damping characteristic, the direct-current fault is fast in development speed and wide in spread range, and the safe and reliable operation of the system is seriously threatened. Ensuring the viability of the flexible direct current power grid under the fault is a current key technical difficulty.
The scheme that the direct current circuit breakers are arranged at two ends of the line is adopted to quickly isolate faults, the stable operation of a non-fault area is recovered, and the reliability of the system can be guaranteed to the greatest extent. However, this solution currently faces two problems: 1) along with the development of a direct current system towards high voltage and high capacity, the development of a corresponding high voltage and high capacity direct current breaker is limited by the current technical background and the investment cost. 2) An Insulated Gate Bipolar Transistor (IGBT) in the converter valve is weak in current endurance, once the bridge arm fault current of the MMC exceeds the overcurrent protection threshold value of the converter valve, the MMC can be locked to protect the IGBT, the fault coverage is expanded, and the method is contrary to the original intention that a direct current breaker is adopted by a flexible direct current power grid to quickly isolate faults. Therefore, the research on the method for reasonably configuring the current limiting equipment can inhibit the fault current before the MMC is locked, and the method has important significance for ensuring the safe and reliable operation of the flexible direct-current power grid.
Current limiting devices that are relatively common include Current Limiting Reactors (CLRs) and Fault Current Limiters (FCLs). The CLR is configured at two ends of the direct current line, fault current can be passively inhibited, and the boundary of a direct current line protection area can be formed by means of the CLR, but the current limiting effect of the current limiting reactor is limited, and meanwhile, the parameter selection of the current limiting reactor has a reasonable value range. Compared with the CLR, the FCL has the characteristic of inhibiting fault current actively put into a line during fault, and has no influence on the dynamic characteristic of a system. At present, an effective and reliable theoretical method is still lacked for the cooperative configuration of the CLR and the FCL in the flexible direct-current power grid, and although a configuration scheme meeting conditions can be found by adopting simulation, global optimal configuration cannot be realized.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in a flexible direct current power grid, which takes the best current-limiting effect, the minimum total inductance value of the current-limiting reactor and the minimum installation number of the fault current limiters as global optimization targets to ensure the continuous and stable operation of a healthy part of the flexible direct current power grid when a fault occurs.
In order to solve the technical problems, the invention provides the following technical scheme:
the invention provides a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in a flexible direct current power grid, which comprises the following steps:
and constructing a target function of the cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid based on the system performance and the current-limiting equipment cost of the flexible direct current power grid. The objective function includes: a current limiting effect objective function, a total inductance value objective function of the current limiting reactor, and an installation number objective function of the fault current limiters.
And constructing a constraint condition of a cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid. The constraint conditions include: the current limiting device comprises a direct current breaker breaking current constraint condition, a converter valve overcurrent protection constraint condition and a current limiting reactor constraint condition.
And obtaining a multi-objective optimization configuration mathematical model of the cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid by combining the objective function and the constraint condition.
And obtaining an optimal solution set by adopting a multi-objective short-free from-learning algorithm (MOSFLA), wherein the optimal solution set is a Pareto optimal solution set.
And selecting a cooperative optimization configuration scheme of the current-limiting reactor and the fault current limiter in the flexible direct-current power grid from the optimal solution set by combining the actual operation condition of the flexible direct-current power grid system.
In the multi-objective optimization configuration mathematical model provided by the invention, an objective function is specifically as follows:
(1) current limiting effect objective function
The optimal current limiting effect is taken as an optimization target, and the arithmetic mean value of the ratio of fault current on two sides of a fault point to the maximum on-off current of the circuit breaker under all fault conditions is taken as an index reflecting the overall current limiting effect of the direct current system. The current limiting effect objective function is thus defined as:
in the formula, n is the number of considered fault scenarios; setting the time of occurrence of a fault as 0 time, the main breaker of the dc breaker is operated after the occurrence of the faultThe segment time is denoted as t2；Iγi(t2) And
are each t2Fault current constantly flows through two sides of a line where a fault point i is located; i isDmaxThe maximum cut-off current of a single direct current breaker. The smaller the value of the current limiting effect objective function is, the better the current limiting effect is.
(2) Target function of total inductance value of current limiting reactor
The total inductance value of the CLR is taken as an optimization target, and the total inductance value of the CLR configured by the system is reduced as much as possible under the condition that the direct-current system realizes reliable fault ride-through when the direct-current line fails, so that the system performance can be improved, and the equipment investment cost can be reduced. The total inductance value objective function of the current limiting reactor is thus defined as:
in the formula, NCThe total number of the CLRs installed on the direct current line; l isCiThe inductance value of the ith CLR.
(3) Target function of installation number of fault current limiter
The minimum number of installation stations of the FCL is taken as an optimization target, and the installation number and the installation position of the FCL are determined to be matched with the selection of the CLR parameters because the FCL is expensive. The smaller the number of FCL installations, the lower the equipment investment cost, and therefore the objective function for the number of installations of the fault current limiter is defined as:
f3＝min NF
in the formula, NFThe total number of FCLs installed on the dc link.
In the multi-objective optimization configuration mathematical model provided by the invention, the constraint conditions are as follows:
(1) the open current constraint condition of the direct current breaker is as follows:
considering a certain margin, the fault current flowing through the direct current circuit breaker after the fault occurs should always be smaller than the maximum cut-off current of the direct current circuit breaker. In the formula, NDThe total number of the direct current circuit breakers is; the time when the failure occurs is denoted as 0 time, and the time from the failure occurrence to the FCL operation is denoted as t1；IDi(t1) And IDi(t2) Are each t1And t2Fault current constantly flows through the ith direct current breaker; a is a reliability factor, and a<1。
(2) Converter valve overcurrent protection constraint conditions:
and when the fault current flowing through the bridge arm of the MMC reaches 2 times of rated current of the IGBT, the converter station is locked. Considering a certain margin, the maximum value of the current of a bridge arm of a converter valve before the action of a main breaker in the direct current breaker is less than 2 times of rated current. In the formula, NMThe total number of the converter stations; i isi(t1) And Ii(t2) Are each t1And t2The direct current is output from the converter station i at the moment; i isaiThe amplitude of the phase current on the alternating current side of the converter station i is obtained; i isGRated current of IGBT; i isAIs a safety margin of consideration.
(3) Current limiting reactor constraint condition
Lmin≤LCi≤Lmax
The value of the current-limiting reactor should have a reasonable interval. In the formula, LminThe minimum inductance value of the boundary of the direct current line protection area is formed to meet the CLR; l ismaxThe maximum inductance value required to meet the dynamic response of the system.
In the collaborative optimization configuration method provided by the invention, a multi-objective optimization configuration mathematical model is solved by adopting the MOSFLA, and the specific steps are as follows:
step S1, inputting system parameters and initializing mosfet parameters:
the system parameters include: rated parameters of a converter in the flexible direct-current power grid, rated parameters of a converter transformer and equivalent parameters of a power transmission line.
Initializing the mosfet la parameters includes: the number of groups of frog population related in the algorithm, the individual number of frogs in each group, the number of iterations in the group, the total number of evolutions of the population, and the maximum distance S allowed for jumping of the frogsmax。
Step S2, generating an initial frog population:
setting an initial frog population, defined as X ═ X1,...,xF]TWherein, subscript F is population scale, and the numerical value is equal to the product of the frog population group number and the individual frog number in each group; x is the number ofiThe ith frog individual;
each individual frog xiRepresents a cooperative configuration scheme of a current limiting device, i-th individual frog xiComprises the following steps:
in the formula, CLRjRepresenting, for continuous variables, the inductance value of a current-limiting reactor arranged at the j-node in the grid-flexible system, CLRjValue range of [ Lmin，Lmax]；FCLkFCL, a discrete variable, representing the configuration of a fault current limiter in a flexible grid systemk0 means that no fault current limiter, FCL, is configured at kk1 denotes that a fault current limiter is arranged at k.
Step S3, calculating frog individual xiCorresponding to a target function under a current limiting equipment configuration scheme and constructing an out-of-limit penalty function:
based on individual x of frogiThe corresponding current limiting equipment configuration scheme is used for calculating fault current and comprises the following steps:
the method comprises the steps of obtaining branch resistances of all power transmission branches, establishing a node conductance matrix of a system, further calculating steady-state load flow of the system, obtaining voltages of all nodes of the system under a steady-state working condition and currents of all nodes on a circuit connected with a corresponding modular multilevel converter, and taking the voltages as initial values for calculating transient fault currents.
According to the symmetry of a flexible direct current power grid, a converter station is equivalent to a node, a modular multilevel converter before locking after a fault occurs is equivalent to a resistor, inductor and capacitor series circuit, an inter-station direct current circuit is equivalent to a resistor and inductor series equivalent impedance, and a current limiting reactor and a fault current limiter under a current limiting equipment configuration scheme corresponding to the frog individual are equivalent to an inductor and a resistor; respectively establishing equivalent circuit models of the flexible direct current power grid before and after the action of the fault current limiter, writing a network state equation of the flexible direct current power grid after the fault according to a kirchhoff voltage law and a kirchhoff current law, and solving the established network state equation by using a computer to obtain the fault current on the direct current line.
And (3) solving the direct current fault current at the outlet of each converter station by using kirchhoff current law, wherein the converter station bridge arm fault current calculation formula is as follows:
in the formula iijTAnd iijBFault currents flowing through the j-th phase upper bridge arm and the j-th phase lower bridge arm of the ith converter station respectively; i.e. iijThe current flows through the jth phase on the ith converter station alternating current valve side; i.e. iiAnd outputting the direct current fault current for the ith converter station.
Solving a current limiting effect objective function, a total inductance value objective function of the current limiting reactor and an installation number objective function of the fault current limiters in the multi-objective optimization configuration mathematical model; verifying the constraint conditions of the on-off current of the direct-current circuit breaker, the overcurrent protection constraint conditions of the converter valve and the constraint conditions of the current-limiting reactor of the multi-objective optimization configuration mathematical model;
the out-of-limit penalty function is individual x of frogiIs defined as:
in the formula, NbAnd NnRespectively determining the number of times of the out-of-limit times of the constraint condition of the cut-off current of the direct current breaker and the number of times of the out-of-limit times of the constraint condition of the overcurrent protection of the converter valve; i isDBj(xi) And Iarmk(xi) Respectively obtaining a jth direct current breaker cut-off current out-of-limit current difference value and a kth converter valve overcurrent protection out-of-limit current difference value; and a and b are weight coefficients respectively reflecting the importance degrees of the on-off current constraint of the direct current breaker and the overcurrent protection constraint of the converter valve.
Step S4, calculating frog individual xiThe fitness of (2):
the smaller the value of the defined fitness function is, the higher the fitness is; when the frog is in the individual xiWhen the corresponding current-limiting equipment configuration scheme meets the constraint condition, the objective function is unchanged; when the frog is in the individual xiWhen the corresponding current-limiting equipment configuration scheme does not meet the constraint condition, punishing is carried out on the target function, so that the individual fitness of the frog is poor and the frog is easier to eliminate; for each individual frog xiIn other words, the fitness function of the objective function is defined as:
in the formula, fitness1(xi)、fitness2(xi) And fitness3(xi) Respectively a current-limiting effect objective function, a total inductance value objective function of the current-limiting reactor and a fitness function corresponding to the installation quantity objective function of the fault current limiters; lambda [ alpha ]1、λ2And λ3And the out-of-limit penalty coefficients are respectively corresponding to a current limiting effect objective function, a total inductance value objective function of the current limiting reactor and an installation number objective function of the fault current limiter, the values of the out-of-limit penalty coefficients are positive integers, and the out-of-limit penalty coefficients are set according to the orders of magnitude of the objective function and the out-of-limit penalty function.
Step S5, sorting the initial frog population by adopting a quick non-dominant sorting method and finding out a global optimal individual:
for individual frog xiFrog assembly W governed therebyiDefined as:
Wi＝{xj|xidominating xj,xj∈X}
Random set of frogs WiInner frog individual xiThe corresponding number is niThe frog individuals in the initial frog population X are arranged according to niThe numerical values are arranged in descending order, if n of any two individual frogsiIf the values are the same, randomly arranging to finally obtain the sequenced frog population; n in the sorted frog populationiThe frog individual with the maximum value is stored in an external group, the external group is a current non-dominated solution set, and one frog individual is randomly selected from the external group to serve as an overall fitness optimal individual;
step S6, intra-group local search: updating the frog individual with the worst fitness in a group;
the intra-group local search specifically comprises the following steps:
step S6-1, firstly, dividing the sequenced frog population into m groups in total, wherein each group comprises n frogs; putting 1 st frog individual into the 1 st group, 2 nd frog individual into the 2 nd group, the mth frog individual into the mth group, the m +1 st frog individual into the 1 st group, the m +2 nd frog individual into the 2 nd group, and so on until all the frogs are grouped;
step S6-2, for each group of frogs, at all niRandomly selecting one of the frog individuals with the maximum value as the individual with the optimal fitness in the group, wherein the fitness is the highest among all niRandomly selecting one of the frog individuals with the minimum value as an individual with worst fitness in the group;
step S6-3, generating a first new individual in the group by using the individual with the optimal fitness in the group and the individual with the worst fitness in the group, and calculating the fitness of the first new individual according to the step S4;
the update mode of the individual with the worst fitness in the group is as follows:
wherein S is a displacement matrix; r is a random number between 0 and 1, and considering that the configuration position of the current-limiting reactor is a discrete variable, the discrete variable is obtained by adopting a real number nearest integer mode in the updating process;
step S6-4, whether the first new individual in the group matches the individual with the worst fitness in the group is judged: if the first new individual in the group matches the individual with the worst fitness in the group, replacing the individual with the worst fitness in the group by the first new individual in the group, and proceeding to step S6-8; otherwise, entering step S6-5;
step S6-5, replacing the global fitness optimal individual generated in step S5 with the global fitness optimal individual to regenerate a second new individual in the group, and calculating the fitness of the second new individual according to step S4;
step S6-6, whether the second new individual in the group matches the individual with the worst fitness in the group is judged: if the second new individual in the group matches the individual with the worst fitness in the group, replacing the individual with the worst fitness in the group with the second new individual in the group, and entering the step S6-8; otherwise, entering step S6-7;
step S6-7, randomly generating a third new individual in the group in the feasible region, replacing the individual with the worst fitness in the group with the third new individual in the group, and proceeding to step S6-8;
and step S6-8, completing local search once in the group, and completing the group updating of the frog individual with the worst fitness in the group.
Step S7, repeating step S6 until the number of iterations in the group is reached, and updating the frog individual with poor fitness in the group;
step S8, global iteration optimizing: remixing all the frog individuals and executing the steps S5, S6 and S7, and repeating the operation until the set population total evolutionary times are reached;
and step S9, obtaining a Pareto optimal solution set.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
by adopting the CLR and FCL cooperative optimization configuration method provided by the invention, the multi-objective optimization configuration model is solved through the MOSFLA to obtain a Pareto optimal solution set, and a decision maker can select a proper configuration scheme in the Pareto optimal solution set by combining the current actual situation, so that the global optimization target of the best current limiting effect, the minimum total inductance value of the current limiting reactor and the minimum installation number of fault current limiters is realized, and the continuous and stable operation of the healthy part of the flexible direct current power grid is ensured when a fault occurs.
Drawings
FIG. 1 is a schematic structural diagram of a four-terminal flexible direct current power grid based on MMC;
FIG. 2 is a flow chart of the steps of the method for cooperatively and optimally configuring the current-limiting reactor and the fault current limiter in the flexible direct current power grid according to the present invention;
FIG. 3 is a Pareto optimal leading edge of CLR and FCL cooperative optimization configuration;
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples.
The invention provides a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in a flexible direct current power grid, which comprises the following steps:
and constructing a target function of the cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid based on the system performance and the current-limiting equipment cost of the flexible direct current power grid. The objective function includes: a current limiting effect objective function, a total inductance value objective function of the current limiting reactor, and an installation number objective function of the fault current limiters.
And constructing a constraint condition of a cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid. The constraint conditions include: the current limiting device comprises a direct current breaker breaking current constraint condition, a converter valve overcurrent protection constraint condition and a current limiting reactor constraint condition.
And obtaining a multi-objective optimization configuration mathematical model of the cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid by combining the objective function and the constraint condition.
And obtaining an optimal solution set by adopting an MOSFLA algorithm, wherein the optimal solution set is a Pareto optimal solution set.
And selecting a cooperative optimization configuration scheme of the current-limiting reactor and the fault current limiter in the flexible direct-current power grid from the optimal solution set by combining the actual operation condition of the flexible direct-current power grid system.
In the multi-objective optimization configuration mathematical model provided by the invention, an objective function is specifically as follows:
(1) current limiting effect objective function
The optimal current limiting effect is taken as an optimization target, and the arithmetic mean value of the ratio of fault current on two sides of a fault point to the maximum on-off current of the circuit breaker under all fault conditions is taken as an index reflecting the overall current limiting effect of the direct current system. The current limiting effect objective function is thus defined as:
in the formula, n is the number of considered fault scenarios; the time when the fault occurs is recorded as 0 time, and the time from the fault occurrence to the action of the main breaker of the direct current breaker is recorded as t2；Iγi(t2) And
are each t2Fault current constantly flows through two sides of a line where a fault point i is located; i isDmaxThe maximum cut-off current of a single direct current breaker. The smaller the value of the current limiting effect objective function is, the better the current limiting effect is.
(2) Target function of total inductance value of current limiting reactor
The total inductance value of the CLR is taken as an optimization target, and the total inductance value of the CLR configured by the system is reduced as much as possible under the condition that the direct-current system realizes reliable fault ride-through when the direct-current line fails, so that the system performance can be improved, and the equipment investment cost can be reduced. The total inductance value objective function of the current limiting reactor is thus defined as:
in the formula, NCThe total number of the CLRs installed on the direct current line; l isCiIs as followsi the inductance value of the CLR.
(3) Target function of installation number of fault current limiter
The minimum number of installation stations of the FCL is taken as an optimization target, and the installation number and the installation position of the FCL are determined to be matched with the selection of the CLR parameters because the FCL is expensive. The smaller the number of FCL installations, the lower the equipment investment cost, and therefore the objective function for the number of installations of the fault current limiter is defined as:
f3＝min NF
in the formula, NFThe total number of FCLs installed on the dc link.
In the multi-objective optimization configuration mathematical model provided by the invention, the constraint conditions are as follows:
(1) the open current constraint condition of the direct current breaker is as follows:
considering a certain margin, the fault current flowing through the direct current circuit breaker after the fault occurs should always be smaller than the maximum cut-off current of the direct current circuit breaker. In the formula, NDThe total number of the direct current circuit breakers is; the time when the failure occurs is denoted as 0 time, and the time from the failure occurrence to the FCL operation is denoted as t1；IDi(t1) And IDi(t2) Are each t1And t2Fault current constantly flows through the ith direct current breaker; a is a reliability factor, and a<1。
(2) Converter valve overcurrent protection constraint conditions:
and when the fault current flowing through the bridge arm of the MMC reaches 2 times of rated current of the IGBT, the converter station is locked. Considering a certain margin, the maximum value of the current of a bridge arm of a converter valve before the action of a main breaker in the direct current breaker is less than 2 times of rated current. In the formula, NMThe total number of the converter stations; i isi(t1) AndIi(t2) Are each t1And t2The direct current is output from the converter station i at the moment; i isaiThe amplitude of the phase current on the alternating current side of the converter station i is obtained; i isGRated current of IGBT; i isAIs a safety margin of consideration.
(3) Current limiting reactor constraint condition
Lmin≤LCi≤Lmax
The value of the current-limiting reactor should have a reasonable interval. In the formula, LminThe minimum inductance value of the boundary of the direct current line protection area is formed to meet the CLR; l ismaxThe maximum inductance value required to meet the dynamic response of the system.
Specific example 1:
taking the four-terminal flexible direct-current power grid based on the MMC shown in fig. 1 as an example, specific steps of the flexible direct-current power grid current-limiting reactor and fault current limiter cooperative optimization configuration method provided by the invention are specifically described with reference to fig. 2.
In the collaborative optimization configuration method provided by the invention, a multi-objective optimization configuration mathematical model is solved by adopting the MOSFLA, and the specific steps are as follows:
step S1, inputting system parameters, initializing the MOSFLA parameters:
(1) inputting system parameters
When the four-terminal flexible direct current power grid system based on the MMC operates normally, the first converter station MMC1 serves as a main control station to control the direct current voltage to be 500 kV. The second converter station MMC2, the third converter station MMC3 and the fourth converter station MMC4 adopt a constant active power control mode, 800MW, 600MW and-600 MW active power are respectively injected into a direct current power grid, and basic parameters of the four-end flexible direct current power grid system are shown in table 1. After a fault occurs, the resistance type FCL actively puts a 10 omega resistance, and the time from the fault occurrence to the FCL action is set to be 3 ms; the maximum breaking current of the hybrid direct-current circuit breaker is 9kA, and the time from the occurrence of a fault to the action of a main circuit breaker of the direct-current circuit breaker is set to be 6 ms; the rated current of the IGBT in the converter valve is 2 kA.
(2) Initializing mosfet la parameters
Setting the frog population group number m as 20, each timeThe number N of individual frog groups is 25, and the number of the intra-group iteration is Ne25, total number of evolutions N of populationg1000, maximum distance S the frog is allowed to jumpmax＝0.01。
TABLE 1 basic parameters of Flexible DC grid
Step S2, generating an initial frog population:
setting an initial population as X ═ X1,...,xF]TWherein the subscript F is the population size, which is equal to the product of the number of groups of frog populations (m) and the number of individual frogs per group (n). x is the number ofiThe ith frog is an individual.
Each individual frog represents a coordinated configuration of a current limiting device, the ith individual frog (x)i) Comprises the following steps:
in the formula, CLRjRepresenting, for continuous variables, the inductance value of a current-limiting reactor arranged at the j-node in the grid-flexible system, CLRjValue range of [ Lmin，Lmax]；FCLkFCL, a discrete variable, representing the configuration of a fault current limiter in a flexible grid systemk0 means that no fault current limiter, FCL, is configured at kk1 denotes configuring a fault current limiter at k;
as seen from step S1, the population size F is 500; setting the CLR value lower limit Lmin0.1H, CLR has an upper limit Lmax＝0.2H。
Step S3, calculating an objective function under the current limiting device configuration scheme corresponding to each frog and constructing an out-of-limit penalty function:
calculating fault current based on the current limiting equipment configuration scheme corresponding to each frog individual, and solving a current limiting effect objective function, a total inductance value objective function of a current limiting reactor and an installation number objective function of a fault current limiter in a multi-objective optimization configuration mathematical model; and verifying the constraint conditions of the breaking current of the direct-current circuit breaker, the overcurrent protection constraint conditions of the converter valve and the constraint conditions of the current-limiting reactor of the multi-objective optimization configuration mathematical model.
Calculating fault current based on the current limiting equipment configuration scheme corresponding to each frog individual, comprising the following steps:
(1) obtaining branch resistances of the power transmission branches, establishing a node conductance matrix of the system, and further calculating the steady-state load flow of the system to obtain the voltage of each node of the system under the steady-state working condition and the current of each node on a connecting line corresponding to the MMC, wherein the voltage of each node and the current are used as initial values for calculating the transient fault current.
(2) According to the symmetry of the flexible direct current power grid, the converter station is equivalent to a node, the MMC before locking after the fault occurs is equivalent to an RLC series circuit, the direct current circuit between the stations is equivalent to RL series equivalent impedance, and the CLR and the FCL under the current limiting equipment configuration scheme corresponding to the frog individual are equivalent to inductance and resistance. Respectively establishing equivalent circuit models of the flexible direct-current power grid before and after the FCL acts, writing a network state equation of the flexible direct-current power grid after the fault according to a kirchhoff voltage law and a kirchhoff current law, and solving the established network state equation by means of a computer to obtain the fault current on the direct-current line.
(3) And (3) solving the direct current fault current at the outlet of each converter station by using kirchhoff current law, wherein the converter station bridge arm fault current calculation formula is as follows:
iijTand iijBFault currents flowing through an upper bridge arm and a lower bridge arm of the jth phase of the converter station i are respectively; i.e. iijThe current flows through the jth phase on the AC valve side of the converter station i; i.e. iiAnd (5) outputting direct current fault current for the converter station i.
The out-of-limit penalty function is defined as:
in the formula, V (x)i) Is an individual xiTotal out-of-limit degree of constraint.
Step S4, calculating the fitness of each frog:
defining the smaller the value of the fitness function, the higher the fitness, and when the current limiting equipment configuration scheme corresponding to the individual frog meets the constraint condition, keeping the objective function unchanged; and when the current-limiting equipment configuration scheme corresponding to the individual frog does not meet the constraint condition, punishment is carried out on the target function so that the individual fitness is deteriorated and the individual fitness is easier to eliminate. The fitness function is defined as:
in the formula, fitness1(xi)、fitness2(xi) And fitness3(xi) Respectively as a fitness function of a current-limiting effect objective function and a total inductance value objective function of the current-limiting reactor; lambda [ alpha ]1、λ2And λ3The out-of-limit punishment coefficients are respectively a current-limiting effect objective function, a total inductance value objective function of the current-limiting reactor and an out-of-limit punishment coefficient corresponding to the installation quantity objective function of the fault current limiter, the values of the out-of-limit punishment coefficients are positive integers, and the out-of-limit punishment coefficients are set according to the orders of magnitude of the objective function and the out; n is a radical ofbAnd NnRespectively limiting times of the open-circuit current constraint of the direct current breaker and limiting times of the overcurrent protection constraint of the converter valve; i isDBj(xi) And Iarmk(xi) Respectively obtaining a jth direct current breaker cut-off current out-of-limit current difference value and a kth converter valve overcurrent protection out-of-limit current difference value; and a and b are weight coefficients respectively reflecting the importance degrees of the on-off current constraint of the direct current breaker and the overcurrent protection constraint of the converter valve.
The reliability coefficient a is 0.9, and the safety margin I isAAt 0.3kA, the weighting coefficients a and b were taken to be 0.5.
Step S5, adopting fast non-dominant sorting method to the initial speciesGroup sorting and finding globally optimal individuals xg：
Sequencing the initial frog population by adopting a rapid non-dominant sequencing mode, and sequencing individual frogs xiThe set of frogs dominated by it is WiAnd is recorded as:
Wi＝{xj|xidominating xj,xj∈X}
Random set of frogs WiInner frog individual xiThe corresponding number is niThe frog individual X in the initial frog population X is treatediAccording to niThe numerical values are arranged in descending order if any two individual frogs are xiN of (A) to (B)iIf the values are the same, randomly arranging to finally obtain a sequenced frog population X'; n in the sequenced frog population XiFrog individual x with maximum valueiSaving to the external population XpMiddle, outer population XpI.e. the current non-dominated solution set, from the external population XpRandomly selecting a frog individual as an optimal global fitness individual xg。
Step S6, local search in the group, specifically including the following steps:
step S6-1, firstly, dividing the sequenced frog population X' into m groups in total, wherein each group comprises n frogs; putting 1 st frog individual into the 1 st group, 2 nd frog individual into the 2 nd group, the mth frog individual into the mth group, the m +1 st frog individual into the 1 st group, the m +2 nd frog individual into the 2 nd group, and so on until all the frogs are grouped;
step S6-2, for each group of frogs, at all niFrog individual x with maximum valueiRandomly selecting one individual x as the optimal individual x of the group fitnessbAt all niFrog individual x of minimum valueiRandomly selecting one of the individuals as the individual x with the worst fitness in the groupw；
Step S6-3, using the individual x with the best fitness in the groupbAnd the individual with the worst fitness in the group xwGenerating a first new entity x in the groupnewAnd calculating the fitness according to the step S4;
individual x with worst fitness in groupwThe update method of (1) is as follows:
wherein S is a displacement matrix; r is a random number between 0 and 1, and considering that the configuration position of the current-limiting reactor is a discrete variable, the discrete variable is obtained by adopting a real number nearest integer mode in the updating process;
step S6-4, determining the first new individual x in the groupnewWhether to support individual x with worst fitness in groupw: if the first new entity x in the groupnewIndividual x with worst fitness in supporting and matching groupwThen use the first new entity x in the groupnewReplace the individual with the worst fitness in the group xwAnd proceeds to step S6-8; otherwise, entering step S6-5;
step S6-5, using the global fitness optimal individual x generated in step S5gReplacing the individual x with optimal fitness in the groupbRegenerating the second new individual within group x'newAnd calculating the fitness according to the step S4;
step S6-6, determining the second new individual x 'in the group'newWhether to support individual x with worst fitness in groupw: if the second new individual within the group x'newIndividual x with worst fitness in supporting and matching groupwThen x 'from the second new individual within the group'newReplace the individual with the worst fitness in the group xwAnd proceeds to step S6-8; otherwise, entering step S6-7;
step S6-7, randomly generating a third new individual x in the group within the feasible region "newUsing the third new individual x in the group "newReplace the individual with the worst fitness in the group xwAnd proceeds to step S6-8;
step S6-8, completing a local search in the group, and completing the frog individual x with the worst fitness in the groupwIs updated within the group.
Specific example 2:
taking the scheme A in Table 2 as an example, the configuration scheme is shown in the figure1, a first current limiting reactor CLR in a four-end flexible direct current power grid1Is 0.161H, and a second current limiting reactor CLR2Is 0.165H, and a third current limiting reactor CLR3Is 0.168H, and a fourth current limiting reactor CLR4Is 0.142H, a fifth current limiting reactor CLR5The inductance value of (1) is 0.169H, and a sixth current limiting reactor CLR6The inductance value of (1) is 0.163H, and a seventh current limiting reactor CLR7Is 0.155H, an eighth current limiting reactor CLR8Has an inductance value of 0.148H, and only the second fault current limiter FCL is arranged2Third fault current limiter FCL3Fourth fault current limiter FCL4Fifth fault current limiter FCL5Seventh fault current limiter FCL7Eighth fault current limiter FCL8There are 6 fault current limiters.
In consideration of more acquired Pareto optimal solutions, table 2 only lists the value of the CLR parameter and the installation position of the FCL under some configuration schemes.
TABLE 2 partial optimization configuration scheme
Table 3 lists the simulation comparison cases for some of the configuration schemes. As can be seen from table 3, although the configuration scheme in which the CLR is configured with only 0.2H at both ends of the line has a good current limiting effect, the system cannot realize fault ride-through due to the fact that the overcurrent protection constraint condition of the converter valve is not satisfied under extreme conditions. The scheme obtained by the CLR and FCL collaborative optimization configuration method provided by the invention can ensure the survival capability of the system under the fault condition. The decision maker can select a proper configuration scheme in the Pareto optimal solution set by combining the current practical situation.
Table 3 simulation comparison under partial configuration
Fig. 3 shows that the sum of inductance values of the system configuration CLR and the current limiting effect are in an inverse relationship with each other at the Pareto optimal leading edge obtained by the collaborative optimization configuration method provided by the present invention. Meanwhile, as the number of FCLs configured in the system increases, the overall current limiting effect of the system is improved.
The above specific implementation manner and embodiments are specific support for the technical idea of the cooperative optimization configuration method for the current-limiting reactor and the fault current limiter in the flexible direct-current power grid, and the protection scope of the present invention cannot be limited thereby, and any equivalent changes or equivalent changes made on the basis of the technical scheme according to the technical idea of the present invention still belong to the protection scope of the technical scheme of the present invention.
Claims (4)
1. The cooperative optimization configuration method of the current-limiting reactor and the fault current limiter in the flexible direct current power grid is characterized by comprising the following steps:
based on the system performance and the cost of the current limiting equipment of the flexible direct current power grid, constructing an objective function of a cooperative optimization configuration method of a current limiting reactor and a fault current limiter in the flexible direct current power grid, wherein the objective function comprises the following steps: a current limiting effect objective function, a total inductance value objective function of the current limiting reactor and an installation number objective function of the fault current limiters;
constructing a constraint condition of a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in a flexible direct current power grid, wherein the constraint condition comprises the following steps: the method comprises the following steps of (1) limiting conditions of the cut-off current of a direct current breaker, overcurrent protection of a converter valve and a current-limiting reactor;
obtaining a multi-objective optimization configuration mathematical model of a cooperative optimization configuration method of a current-limiting reactor and a fault current limiter in the flexible direct-current power grid by combining a target function and a constraint condition;
solving the multi-target optimization configuration mathematical model by adopting a multi-target mixed frog leaping algorithm to obtain an optimal solution set, wherein the optimal solution set is a Pareto optimal solution set;
selecting a cooperative optimization configuration scheme of a current-limiting reactor and a fault current limiter in the flexible direct-current power grid from the optimal solution set by combining the actual operation condition of the flexible direct-current power grid system;
the current limiting effect objective function is defined as follows:
taking the arithmetic mean value of the ratio of fault current on two sides of a fault point to the maximum on-off current of the circuit breaker under all fault conditions as an index for reflecting the global current limiting effect of the direct current system, wherein the current limiting effect objective function is as follows:
in the formula, n is the number of fault situations considered, the time when a fault occurs is recorded as 0 time, and the time from the fault occurrence to the main breaker action of the direct current breaker is recorded as t2，Iγi(t2) And Iφi(t2) Are each t2A fault current, I, flowing constantly on both sides of the line at fault point IDmaxThe maximum cut-off current of a single direct current breaker is obtained;
the total inductance value objective function of the current-limiting reactor is defined as follows:
under the condition that the direct current system realizes reliable fault ride-through when the direct current line fault is met, the total inductance value of a current-limiting reactor configured by the system is reduced, and the target function of the total inductance value of the current-limiting reactor is as follows:
in the formula, NCFor the total number of current-limiting reactors installed on the DC line, LCiThe inductance value of the ith current-limiting reactor;
the target function of the installation number of the fault current limiter is defined as follows:
f3＝min NF，
in the formula, NFThe total number of fault current limiters installed on the direct current line;
the constraint condition of the breaking current of the direct current breaker is defined as follows:
in the formula, NDThe time of the occurrence of the fault is recorded as 0 time for the total number of the direct current circuit breakers, and the time from the occurrence of the fault to the action of the fault current limiter is recorded as t1，IDi(t1) And IDi(t2) Are each t1Time t and2a fault current constantly flowing through the ith DC breaker, a is a reliability coefficient, and a<1；
The converter valve overcurrent protection constraint condition is defined as follows:
in the formula, NMIs the total number of converter stations, Ii(t1) And Ii(t2) Are each t1Time t and2at the moment of the ith converter station outlet direct current, IaiFor the amplitude of the phase current on the AC side of the ith converter station, IGIs rated current of the insulated gate bipolar transistor, IAIs a safety margin of consideration;
the constraint condition of the current-limiting reactor is defined as follows:
Lmin≤LCi≤Lmax，
in the formula, LminIn order to satisfy the minimum inductance value, L, of the boundary of the protection region of the DC line formed by the current-limiting reactormaxThe maximum inductance value required to meet the dynamic response of the system.
2. The method for cooperatively and optimally configuring the current-limiting reactor and the fault current limiter in the flexible direct current power grid according to claim 1, is characterized in that:
solving the multi-target optimized configuration mathematical model through a multi-target mixed frog leaping algorithm, which comprises the following specific steps:
step S1, inputting system parameters and initialization parameters:
the system parameters include: rated parameters of a converter in the flexible direct current power grid, rated parameters of a converter transformer and equivalent parameters of a power transmission line,
the initialization parameters include: the number of groups of frog population m, the number of individual frogs in each group N and the number of iterations in each group N related to the algorithmeTotal number of evolutionary cycles N of populationgMaximum distance S allowed for frog to jumpmax；
Step S2, generating an initial frog population:
setting an initial frog population X, defining X ═ X1,···,xF]TWherein, subscript F is population scale, and the numerical value is equal to the product of the frog population grouping number m and the individual number n of the frogs in each group; x is the number ofiThe ith frog is the individual frog,
each individual frog represents a coordinated configuration scheme of a current limiting device, and the ith individual frog xiComprises the following steps:
in the formula, CLRjRepresenting, for continuous variables, the inductance value of a current-limiting reactor arranged at the j-node in the grid-flexible system, CLRjValue range of [ Lmin，Lmax]，FCLkFCL, a discrete variable, representing the configuration of a fault current limiter in a flexible grid systemk0 means that no fault current limiter, FCL, is configured at kk1 denotes configuring a fault current limiter at k;
step S3, calculating frog individual xiCorresponding to a target function under a current limiting equipment configuration scheme and constructing an out-of-limit penalty function:
based on individual x of frogiCalculating fault current according to the corresponding current-limiting equipment configuration scheme, and solving a current-limiting effect objective function, a total inductance value objective function of a current-limiting reactor and an installation number objective function of a fault current limiter in the multi-objective optimization configuration mathematical model; direct-current breaker on-off current contract for verifying multi-objective optimization configuration mathematical modelA bundling condition, a converter valve overcurrent protection constraint condition, a current limiting reactor constraint condition,
the out-of-limit penalty function is individual x of frogiIs defined as:
in the formula, NbAnd NnRespectively the out-of-limit times of the constraint condition of the breaking current of the direct current breaker and the out-of-limit times of the constraint condition of the overcurrent protection of the converter valve, IDBj(xi) And Iarmk(xi) Respectively setting a limiting current difference value of the switching-on and switching-off current of the j-th direct current breaker and a limiting current difference value of the overcurrent protection of the k-th converter valve, wherein a and b are weight coefficients reflecting the importance degrees of the switching-on and switching-off current constraint of the direct current breaker and the overcurrent protection constraint of the converter valve respectively;
step S4, calculating frog individual xiThe fitness of (2):
the smaller the value of the defined fitness function is, the higher the fitness is, and when the frog individual x isiKeeping the objective function unchanged when the corresponding current-limiting device configuration scheme meets the constraint condition, and keeping the objective function unchanged when the individual frog x is in the single bodyiPunishment is carried out on the target function when the corresponding current-limiting equipment configuration scheme does not meet the constraint condition, so that the frog individual xiThe fitness becomes worse and is easier to be eliminated, for each frog individual (x)i) In other words, the fitness function of the objective function is defined as:
in the formula, fitness1(xi)、fitness2(xi) And fitness3(xi) Respectively as a fitness function, lambda, corresponding to a current-limiting effect objective function, a total inductance value objective function of the current-limiting reactor and an installation number objective function of the fault current limiter1、λ2And λ3Respectively, current limiting effect objective functionThe total inductance value objective function of the current-limiting reactor and the out-of-limit penalty coefficients corresponding to the installation number objective function of the fault current limiters, wherein the values of the out-of-limit penalty coefficients are positive integers and are set according to the order of magnitude of the objective function and the out-of-limit penalty function;
step S5, sorting the initial frog population X by adopting a rapid non-dominant sorting method and finding out a global optimal individual Xg：
For individual frog xiFrog assembly W governed therebyiDefined as:
Wi＝{xj|xidominating xj,xj∈X}
Random set of frogs WiInner frog individual xiThe corresponding number is niThe frog individual X in the initial frog population X is treatediAccording to niThe numerical values are arranged in descending order if any two individual frogs are xiN of (A) to (B)iIf the values are the same, randomly arranging to finally obtain a sequenced frog population X'; n in the sequenced frog population XiFrog individual x with maximum valueiSaving to the external population XpMiddle, outer population XpI.e. the current non-dominated solution set, from the external population XpRandomly selecting a frog individual as an optimal global fitness individual xg；
Step S6, intra-group local search: frog individual x with worst fitnesswPerforming intra-group updating;
step S7, repeating step S6 until the number N of iterations in the group is reachedeCarrying out group updating on the frog individual with poor fitness;
step S8, global iteration optimizing: all frogs are separated into xiRemixing and executing the steps S5, S6 and S7, and repeating the operation until the set population total evolutionary times N are reachedg；
And step S9, obtaining a Pareto optimal solution set.
3. The method for cooperatively and optimally configuring the current-limiting reactor and the fault current limiter in the flexible direct current power grid according to claim 2, is characterized in that:
the step S6, local search in a group, specifically includes the following steps:
step S6-1, firstly, dividing the sequenced frog population X' into m groups in total, wherein each group comprises n frogs; putting 1 st frog individual into the 1 st group, 2 nd frog individual into the 2 nd group, the mth frog individual into the mth group, the m +1 st frog individual into the 1 st group, the m +2 nd frog individual into the 2 nd group, and so on until all the frogs are grouped;
step S6-2, for each group of frogs, at all niFrog individual x with maximum valueiRandomly selecting one individual x as the optimal individual x of the group fitnessbAt all niFrog individual x of minimum valueiRandomly selecting one of the individuals as the individual x with the worst fitness in the groupw；
Step S6-3, using the individual x with the best fitness in the groupbAnd the individual with the worst fitness in the group xwGenerating a first new entity x in the groupnewAnd calculating the fitness according to the step S4;
individual x with worst fitness in groupwThe update method of (1) is as follows:
wherein S is a displacement matrix; r is a random number between 0 and 1, and considering that the configuration position of the current-limiting reactor is a discrete variable, the discrete variable is obtained by adopting a real number nearest integer mode in the updating process;
step S6-4, determining the first new individual x in the groupnewWhether to support individual x with worst fitness in groupw: if the first new entity x in the groupnewIndividual x with worst fitness in supporting and matching groupwThen use the first new entity x in the groupnewReplace the individual with the worst fitness in the group xwAnd proceeds to step S6-8; otherwise, entering step S6-5;
step S6-5, using the global fitness optimal individual x generated in step S5gSubstitute for optimum number of fitness in groupBody xbRegenerating the second new individual within group x'newAnd calculating the fitness according to the step S4;
step S6-6, determining the second new individual x 'in the group'newWhether to support individual x with worst fitness in groupw: if the second new individual within the group x'newIndividual x with worst fitness in supporting and matching groupwThen x 'from the second new individual within the group'newReplace the individual with the worst fitness in the group xwAnd proceeds to step S6-8; otherwise, entering step S6-7;
step S6-7, randomly generating a third new individual x in the group within the feasible region "newUsing the third new individual x in the group "newReplace the individual with the worst fitness in the group xwAnd proceeds to step S6-8;
step S6-8, completing a local search in the group, and completing the frog individual x with the worst fitness in the groupwIs updated within the group.
4. The method for cooperatively and optimally configuring the current-limiting reactor and the fault current limiter in the flexible direct current power grid according to claim 2, is characterized in that:
in step S3, x is determined for each individual frogiThe corresponding current limiting equipment configuration scheme is used for calculating fault current and comprises the following steps:
acquiring branch resistances of all power transmission branches, establishing a node conductance matrix of the system, and further calculating the steady-state load flow of the system to obtain voltages of all nodes of the system under the steady-state working condition and currents of all nodes on a line connected with the corresponding modular multilevel converter, wherein the voltages are used as initial values for calculating transient fault currents;
according to the symmetry of a flexible direct current power grid, a converter station is equivalent to a node, a modular multilevel converter before locking after a fault occurs is equivalent to a resistor, inductor and capacitor series circuit, an inter-station direct current circuit is equivalent to a resistor and inductor series equivalent impedance, and a current limiting reactor and a fault current limiter under a current limiting equipment configuration scheme corresponding to the frog individual are equivalent to an inductor and a resistor; respectively establishing equivalent circuit models of the flexible direct-current power grid before and after the action of the fault current limiter, writing a network state equation of the flexible direct-current power grid after the fault according to a kirchhoff voltage law and a kirchhoff current law, and solving the established network state equation by using a computer to obtain fault current on a direct-current line;
and (3) solving the direct current fault current at the outlet of each converter station by using kirchhoff current law, wherein the converter station bridge arm fault current calculation formula is as follows:
in the formula iijTAnd iijBThe fault currents i respectively flow through the j-th phase upper bridge arm and the j-th phase lower bridge arm of the ith converter stationijFor the j phase of the AC current i flowing through the AC valve side of the i-th converter stationiAnd outputting the direct current fault current for the ith converter station.
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