CN108462184B - Power system line series compensation optimization configuration method - Google Patents

Power system line series compensation optimization configuration method Download PDF

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CN108462184B
CN108462184B CN201810250772.9A CN201810250772A CN108462184B CN 108462184 B CN108462184 B CN 108462184B CN 201810250772 A CN201810250772 A CN 201810250772A CN 108462184 B CN108462184 B CN 108462184B
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node
voltage
series compensation
compensation
generator
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CN108462184A (en
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刘志坚
严俊
宋琪
张函
孙应毕
尹冬晖
杜炎城
吴桂鸿
王洪亮
单节杉
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Kunming University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1807—Arrangements for adjusting, eliminating or compensating reactive power in networks using series compensators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

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Abstract

The invention relates to an optimal configuration method for series compensation of a power system circuit, and belongs to the technical field of power system operation. Firstly, establishing a power network mathematical model, and then determining a power flow algorithm of a power system; secondly, series compensation is added into a system circuit, a multi-objective optimization model with the minimum system network loss and the optimal voltage quality is established on the basis of load flow calculation by taking the number of series compensation, series compensation circuits, the series compensation degree, the active power output of a generator and the like as constraint conditions, and the series compensation configuration in the system is optimized by adopting an improved particle swarm algorithm based on random weight, so that the selection of the number of series compensation configuration, the series compensation configuration circuits and the series compensation degree under the steady state with the optimal load flow is achieved; and finally, simulating and solving in Matlab. The invention solves the problem of line series compensation configuration, not only reduces the system network loss and improves the system voltage quality, but also adopts the improved particle swarm optimization of random weight to ensure the optimal solution of system optimization and avoid falling into local optimization.

Description

Power system line series compensation optimization configuration method
Technical Field
The invention relates to an optimal configuration method for series compensation of a power system circuit, and belongs to the technical field of power system operation.
Background
The large-capacity high-voltage long-distance power transmission mode is the biggest characteristic of the power transmission network in China, and the voltage quality and the network loss become main factors for limiting the power transmission capacity and influencing the electric energy quality. Through scientific research, the series compensation technology of the power transmission line can improve the reactance characteristic of a long-distance power transmission line, shorten the electrical distance of a power transmission corridor, improve the power transmission capacity of a power transmission system, improve the stability of the power transmission system, improve the power transmission capacity of the power transmission system, obviously improve the system voltage and reduce the system network loss, but if the series compensation degree and the position of the series compensation are unreasonable, the operation cost of the system is increased, and the voltage quality is not ideal. When the series compensation degree of the line is very high, in order to make the voltage curve of the system smooth as much as possible, a large amount of reactive compensation is connected in parallel at the tail end of the line, and finally, the voltage of the system is too high, so that the voltage quality cannot be guaranteed; when the series compensation degree of the line is too low, the input effect of the series compensation capacitor is possibly poor, the conveying capacity of the system cannot be effectively improved, and the expected effect of adding the series compensation cannot be achieved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for optimizing configuration of the series compensation of the power system circuit is provided, the problems of the number of the series compensation of the system, the series compensation circuit selection and the series compensation degree are solved, the static voltage stability of the system is improved, the power transmission capacity is improved, the voltage quality of the system is improved, the network loss of the system is reduced, and the stability of the system is improved.
The technical scheme adopted by the invention is as follows: a power system line series compensation optimal configuration method comprises the following steps:
1) determining a power flow algorithm of the power system;
2) determining an objective function which takes the optimal voltage quality and the minimum network loss as the optimal series compensation configuration;
3) determining a constraint condition;
4) and solving a series compensation optimization configuration model after series compensation is added into the system by adopting an improved particle swarm optimization based on random weight.
Specifically, the step 1) includes the steps of:
step 1.1: the specific power flow network equation can be established by using the relations of the power, the voltage, the conductance and the susceptance on the line:
Figure GDA0003004143220000021
in the formula: piActive power for node i; qiReactive power for node i; e.g. of the typeiIs the real part of the voltage at node i, ejIs the real part of the voltage at node j; f. ofiIs the imaginary part of the voltage of node i, fjIs the imaginary part of the voltage at node j; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; n is the number of nodes;
step 1.2: and (3) obtaining a comprehensive power flow calculation method with strong applicability by combining a Newton Raphson algorithm and a PQ decomposition method:
firstly, a PQ decomposition method is set to calculate the load flow times, the system load flow is calculated by adopting the PQ decomposition method to obtain an initial value of the load flow calculated by a Newton-Raphson algorithm, and then the load flow calculation is carried out on the system by utilizing the Newton-Raphson algorithm.
Specifically, the step 2) comprises the following steps:
firstly, establishing an objective function with optimal voltage quality according to the voltage deviation:
Figure GDA0003004143220000022
in the formula: Δ U is the system voltage deviation; u shapeiIs the node i voltage; u shapeNA system voltage rating;
secondly, establishing an objective function with minimum network loss according to the loss of the line:
Figure GDA0003004143220000023
in the formula: p is the system loss; delta PiIs the voltage loss of line i;
and finally, calculating per unit value, unifying the two, and establishing a weight-based multi-objective optimization objective function:
min f＝λ1ΔU+λ2P (4)
in the formula: lambda [ alpha ]1，λ2Voltage deviation and loss weight coefficients.
Specifically, the constraint conditions in step 3) include:
the series compensation degree, the series compensation quantity and the series compensation circuit constraint condition are as follows:
kiminXi≤xi*kiXi≤kimaxXi (5)
Figure GDA0003004143220000024
in the formula: x is the number ofiThe serial compensation mark on the ith line can only be an integer and can only be 0 or 1, wherein 0 represents that no serial compensation exists on the ith line, and 1 represents that serial compensation exists on the ith line; k is a radical ofiFor degree of series compensation, X, on the lineiIs reactance, kimax，kiminThe upper and lower limits of the variation range; n is the limitation of the number of series compensation added in the system;
constraint conditions of active power output of the generator are as follows:
PGimin≤PGi≤PGimax (7)
in the formula: pGiIs the active output of the generator i; pGiminIs the minimum value of the active power output of the generator i, PGimaxIs the maximum value of the active output of the generator i;
node voltage, transformer transformation ratio and system compensation of the generator are used as constraint conditions:
UGimin≤UGi≤UGimax (8)
Timin≤Ti≤Timax (9)
QCimin≤QCi≤QCimax (10)
in the formula: u shapeGiIs the voltage value of the generator i; t isiIs the transformation ratio of the transformer i; qCiA compensation capacity for reactive compensation i; u shapeGimax、UGiminThe upper limit and the lower limit of the voltage value change range of the generator i; t isimax、TiminIs the upper and lower limits of the transformation ratio variation range of the transformer i, QCimax、QCiminThe upper limit and the lower limit of the variation range of the compensation capacity of the reactive compensation i;
the reactive output and the node voltage of the generator are used as constraint conditions:
Figure GDA0003004143220000031
in the formula: qGjIs the reactive power of a generator j in the system; u shapeiIs the node i voltage; qGjmax、QGjminIs the upper and lower limits, U, of the reactive variation range of the generator j in the systemimax、UiminThe upper and lower limits of the voltage variation range of the node i.
Specifically, the step of determining the series compensation optimization configuration model after adding the series compensation in the step 4) is specifically as follows:
step 4.1: determining an optimization model of the system after adding the series compensation:
Figure GDA0003004143220000041
in the formula: f is an objective function; lambda [ alpha ]1，λ2For voltage deviation and loss weight factor, λ1＝λ2＝0.5；UiIs the node i voltage; u shapeNIs the system voltage rating; delta PiIs the voltage loss of line i; u shapejIs the node j voltage; thetaijIs the phase angle difference between the voltages of the node i and the node j; x is the number ofiFor serial compensation marking on the ith line, kiFor the series compensation, X, on the ith lineiIs the reactance, k, on the ith lineimax，kiminOn the ith lineThe upper and lower limits of the variation range of the series compensation degree; piActive power for node i; qiReactive power for node i; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; pGiIs the active output of the generator i; pGiminIs the minimum value of the active power output of the generator i, PGimaxIs the maximum value of the active output of the generator i; u shapeGiIs the voltage value of the generator i; t isiIs the transformation ratio of the transformer i; qCiA compensation capacity for reactive compensation i; u shapeGimax、UGiminThe upper limit and the lower limit of the voltage value change range of the generator i; t isimax、TiminIs the upper and lower limits of the transformation ratio variation range of the transformer i, QCimax、QCiminThe upper limit and the lower limit of the variation range of the compensation capacity of the reactive compensation i; qGjIs the reactive power of a generator j in the system; u shapeiIs the voltage of node i in the system; qGjmax、QGjminIs the upper and lower limits, U, of the reactive variation range of the generator j in the systemimax、UiminThe upper limit and the lower limit of the voltage variation range of the node i are defined; n is the limitation of the number of series compensation added in the system;
step 4.2: when series compensation is added into a line, the equation trend solution of a node added with the series compensation line is corrected, and the power balance of a branch node containing the series compensation is shown as the following formula:
Figure GDA0003004143220000051
in the formula: u shapeiIs the node i voltage; u shapejIs the node j voltage; thetaijIs the phase angle difference between the voltages of the node i and the node j; pisActive power of a head-end node of the series compensation circuit; qisThe reactive power of a head end node of the series compensation line is obtained; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; xTCSCIs a series compensation reactance.
Specifically, the improved particle swarm optimization based on random weight in step 4) refers to that the random weight factor ω is changed:
ω＝(μmin+(μmax-μmin)*rand(0,1))+σ*N(0,1) (14)
in the formula: mu.sminIs the minimum of the random weight average; mu.smaxIs the maximum value of the random weight average; rand (0,1) is a random number from 0 to 1; σ is the variance of the random weight mean; n (0,1) is a random number of a standard normal distribution,
the velocity update formula for adding random weights is as follows:
Figure GDA0003004143220000052
in the formula:
Figure GDA0003004143220000053
is the (k + 1) th velocity of the particle;
Figure GDA0003004143220000054
the kth velocity of the particle; c. C1，c2Is a learning factor; r is1，r2Are mutually independent pseudo-random numbers;
Figure GDA0003004143220000055
the k-th individual optimal value;
Figure GDA0003004143220000056
the optimal value of the kth population;
Figure GDA0003004143220000057
is the k-th individual particle of the particle,
Figure GDA0003004143220000058
is the kth population particle.
The invention has the beneficial effects that: the method can effectively solve the difficulty of long-distance power transmission and transmission of the Yunnan power grid and the Yunnan northwest region and solve the voltage problem of the Yunnan northwest region caused by environmental factors. The method can be widely applied to an electric power system, and can be used for improving the characteristics of the system, controlling various system state quantities in a power transmission system, such as system bus voltage, line impedance, and active power and reactive power of the system, so that the performance of the electric power system can be improved, the power transmission capacity of a system power transmission line can be improved, and the stability of the system can be improved. And has good economic efficiency, so the method has good application prospect.
Drawings
FIG. 1 is a schematic view of the present invention in its entirety;
FIG. 2 is a block diagram of a comprehensive power flow algorithm;
FIG. 3 is a schematic diagram of a TCSC steady-state equivalent model added to a line;
FIG. 4 is a block diagram of a particle swarm network optimization based on random weights;
FIG. 5 is a model diagram of a network connection diagram of an IEEE14 node power transmission system;
FIG. 6 is a graph of a voltage comparison analysis of an optimized node of an IEEE14 node power transmission system;
FIG. 7 is a model diagram of a network connection diagram of an IEEE30 node power transmission system;
fig. 8 is a comparison analysis diagram of optimized node voltages of an IEEE30 node power transmission system.
Detailed Description
The invention is further described below with reference to the accompanying drawings and specific embodiments.
Example 1: as shown in fig. 1 to 8, a method for optimally configuring a series compensation circuit of an electrical power system includes the following steps:
1) determining a power flow algorithm of the power system;
2) determining an objective function which takes the optimal voltage quality and the minimum network loss as the optimal series compensation configuration;
3) determining a constraint condition;
4) and solving a series compensation optimization configuration model after series compensation is added into the system by adopting an improved particle swarm optimization based on random weight.
The specific implementation process is as follows: in order to improve the power transmission capacity of a power system, improve the voltage quality of the system and reduce the network loss of the system, series compensation is added into a high-voltage power transmission line, and a line model is optimally configured through a particle swarm algorithm based on random weight. Firstly, providing a mathematical equivalent model of a power network, deducing a system power flow equation, namely a power flow model, through a power network node equation, analyzing the system power flow, and determining a comprehensive power flow method to calculate the system; secondly, establishing a machine-network coordination optimization series compensation configuration optimization model by taking the minimum voltage quality and network loss as targets and taking the series compensation quantity, the generator generating capacity, the transformer transformation ratio, the system compensation and the like as constraint conditions; and finally, the particle swarm algorithm is improved by changing the random weight factor, and the optimized configuration model is solved by utilizing the improved particle swarm algorithm.
Further, the step 1) comprises the following steps:
step 1.1: the specific power flow network equation can be established by using the relations of the power, the voltage, the conductance and the susceptance on the line:
Figure GDA0003004143220000061
in the formula: piActive power for node i; qiReactive power for node i; e.g. of the typeiIs the real part of the voltage at node i, ejIs the real part of the voltage at node j; f. ofiIs the imaginary part of the voltage of node i, fjIs the imaginary part of the voltage at node j; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; n is the number of nodes;
step 1.2: and (3) obtaining a comprehensive power flow calculation method with strong applicability by combining a Newton Raphson algorithm and a PQ decomposition method:
flow is analyzed by a cow pulling method and a PQ decomposition method respectively. If the initial value of the power flow calculation is not set well, the iterative solution of the Newton Raphson algorithm enters a dead loop and deviates from the correct direction of the iterative derivation of the power flow solution, so that the final value of the power flow convergence cannot be found all the time; while the PQ decomposition method is an improvement on the newton-raphson algorithm under the condition of simplifying the network, if the system network parameters are not suitable, the PQ decomposition method will collapse to obtain a power flow convergence value. Therefore, the comprehensive power flow calculation method with high applicability is obtained by combining the Newton-Raphson algorithm and the PQ decomposition method, has the advantages of high calculation speed and good convergence, and is suitable for power flow solution of large and complex power networks. Firstly, a PQ decomposition method is set to calculate the load flow times, the system load flow is calculated by adopting the PQ decomposition method to obtain an initial value of the load flow calculated by a Newton-Raphson algorithm, and then the load flow calculation is carried out on the system by utilizing the Newton-Raphson algorithm.
Further, the step 2) comprises the following steps:
firstly, establishing an objective function with optimal voltage quality according to the voltage deviation:
Figure GDA0003004143220000071
in the formula: Δ U is the system voltage deviation; u shapeiIs the node i voltage; u shapeNA system voltage rating;
secondly, establishing an objective function with minimum network loss according to the loss of the line:
Figure GDA0003004143220000072
in the formula: p is the system loss; delta PiIs the voltage loss of line i;
and finally, calculating per unit value, unifying the two, and establishing a weight-based multi-objective optimization objective function:
min f＝λ1ΔU+λ2P (4)
in the formula: lambda [ alpha ]1，λ2Voltage deviation and loss weight coefficients.
Further, the constraint conditions in step 3) include:
the series compensation degree, the series compensation quantity and the series compensation circuit constraint condition are as follows:
kiminXi≤xi*kiXi≤kimaxXi (5)
Figure GDA0003004143220000073
in the formula: x is the number ofiThe serial compensation mark on the ith line can only be an integer and can only be 0 or 1, wherein 0 represents that no serial compensation exists on the ith line, and 1 represents that serial compensation exists on the ith line; k is a radical ofiFor degree of series compensation, X, on the lineiIs reactance, kimax，kiminThe upper and lower limits of the variation range; n is the limitation of the number of series compensation added in the system;
constraint conditions of active power output of the generator are as follows:
PGimin≤PGi≤PGimax (7)
in the formula: pGiIs the active output of the generator i; pGiminIs the minimum value of the active power output of the generator i, PGimaxIs the maximum value of the active output of the generator i;
node voltage, transformer transformation ratio and system compensation of the generator are used as constraint conditions:
UGimin≤UGi≤UGimax (8)
Timin≤Ti≤Timax (9)
QCimin≤QCi≤QCimax (10)
in the formula: u shapeGiIs the voltage value of the generator i; t isiIs the transformation ratio of the transformer i; qCiA compensation capacity for reactive compensation i; u shapeGimax、UGiminThe upper limit and the lower limit of the voltage value change range of the generator i; t isimax、TiminIs the upper and lower limits of the transformation ratio variation range of the transformer i, QCimax、QCiminThe upper limit and the lower limit of the variation range of the compensation capacity of the reactive compensation i;
the reactive output and the node voltage of the generator are used as constraint conditions:
Figure GDA0003004143220000081
in the formula: qGjIs the reactive power of a generator j in the system; u shapeiIs the node i voltage; qGjmax、QGjminIs the upper and lower limits, U, of the reactive variation range of the generator j in the systemimax、UiminThe upper and lower limits of the voltage variation range of the node i.
Further, the step of determining the series compensation optimization configuration model after adding the series compensation in the step 4) is specifically as follows:
step 4.1: determining an optimization model of the system after adding the series compensation:
Figure GDA0003004143220000091
in the formula: f is an objective function; lambda [ alpha ]1，λ2For voltage deviation and loss weight factor, λ1＝λ2＝0.5；UiIs the node i voltage; u shapeNIs the system voltage rating; delta PiIs the voltage loss of line i; u shapejIs the node j voltage; thetaijIs the phase angle difference between the voltages of the node i and the node j; x is the number ofiFor serial compensation marking on the ith line, kiFor the series compensation, X, on the ith lineiIs the reactance, k, on the ith lineimax，kiminThe upper limit and the lower limit of the variation range of the series compensation degree on the ith line are set; piActive power for node i; qiReactive power for node i; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; pGiIs the active output of the generator i; pGiminIs the minimum value of the active power output of the generator i, PGimaxIs the maximum value of the active output of the generator i; u shapeGiIs the voltage value of the generator i; t isiIs the transformation ratio of the transformer i; qCiA compensation capacity for reactive compensation i; u shapeGimax、UGiminIs the voltage of the generator iUpper and lower limits of the range of variation; t isimax、TiminIs the upper and lower limits of the transformation ratio variation range of the transformer i, QCimax、QCiminThe upper limit and the lower limit of the variation range of the compensation capacity of the reactive compensation i; qGjIs the reactive power of a generator j in the system; u shapeiIs the voltage of node i in the system; qGjmax、QGjminIs the upper and lower limits, U, of the reactive variation range of the generator j in the systemimax、UiminThe upper limit and the lower limit of the voltage variation range of the node i are defined; n is the limitation of the number of series compensation added in the system;
step 4.2: when series compensation is added into a line, the flow solution of a node equation added into the series compensation line is corrected, a line-added TCSC steady-state equivalent model graph shown in FIG. 4 is established, and the power balance of branch nodes containing the series compensation is shown as the following formula:
Figure GDA0003004143220000101
in the formula: u shapeiIs the node i voltage; u shapejIs the node j voltage; thetaijIs the phase angle difference between the voltages of the node i and the node j; pisActive power of a head-end node of the series compensation circuit; qisThe reactive power of a head end node of the series compensation line is obtained; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; xTCSCIs a series compensation reactance.
Further, the improved particle swarm optimization based on random weight in step 4) refers to that the random weight factor ω is changed:
ω＝(μmin+(μmax-μmin)*rand(0,1))+σ*N(0,1) (14)
in the formula: mu.sminIs the minimum of the random weight average; mu.smaxIs the maximum value of the random weight average; rand (0,1) is a random number from 0 to 1; σ is the variance of the random weight mean; n (0,1) is a random number of a standard normal distribution,
the velocity update formula for adding random weights is as follows:
Figure GDA0003004143220000102
in the formula:
Figure GDA0003004143220000103
is the (k + 1) th velocity of the particle;
Figure GDA0003004143220000104
the kth velocity of the particle; c. C1，c2Is a learning factor; r is1，r2Are mutually independent pseudo-random numbers;
Figure GDA0003004143220000105
the k-th individual optimal value;
Figure GDA0003004143220000106
the optimal value of the kth population;
Figure GDA0003004143220000107
is the k-th individual particle of the particle,
Figure GDA0003004143220000108
is the kth population particle.
Further, the improved particle swarm optimization based on random weight in step 4) solves the series compensation optimization configuration model after the series compensation is added into the system, and is shown in a flow chart in fig. 4. The initial determination quantity of the power flow calculation is initially particlized. And then optimizing by using a particle swarm algorithm based on random weight, and discarding the group of particles if the trend solution does not meet the requirement. In the simulation experiment, one of the generator nodes is selected as a balance node, other generators are used as PU nodes, and the load nodes and other nodes are used as PQ nodes. The specific algorithm steps are as follows:
1) initializing data: and setting control variable parameters of load flow calculation, such as series compensation degree, series compensation quantity, generator active power and the like, as particles of a particle swarm algorithm, and setting the size of a population and the number of evolutions.
2) And (3) load flow calculation: and obtaining a node matrix and a branch matrix of load flow calculation through the particle control quantity. And calculating corresponding network loss and voltage offset in the power network through the comprehensive power flow to obtain a fitness function, namely an objective function of optimal power flow control, and state variables such as the limit of voltage amplitude.
3) Initial optimal solution: setting a state variable of the tidal current operation, controlling the constraint range of the state variable, searching individual optimum and group optimum in a fitness function in a reasonable constraint range, and if the operation state is not in the reasonable range, carrying out particle replacement optimization.
4) Speed update and location update: and updating the values of the particles according to a speed updating formula, and performing load flow calculation according to the new particle values to obtain new fitness function values.
5) Iterative loop optimization: and comparing fitness functions obtained by the particles of the population evolved each time, and circulating according to the evolution times to obtain the fitness function value of each time.
6) Obtaining an optimal solution: when the circular evolution numerical value set by the program is reached, the program outputs a converged global optimal solution, otherwise, the program continues to perform circular optimization.
Case (2):
to further illustrate the accuracy and reliability of the method of the present invention, simulation analysis was performed on the IEEE14 node and the IEEE30 node power transmission systems by Matlab, and the models are shown in fig. 5 and 7, where numerals 1 to 14 in fig. 5 and numerals 1 to 30 in fig. 7 all represent nodes.
Case one: the IEEE14 node power transmission system considers the active power output of the generator, changes the output of the original generator, takes the network series compensation position and the series compensation degree as well as the reactive compensation of the No. 9 node and the generator terminal voltage as the parameters of network optimization, and sets the branch of the transformer to be 1 to ensure that the series compensation can be added to the branch of the transformer. Performing optimization solution by using a particle swarm algorithm based on random weight, setting control parameters as a series compensation position, wherein series compensation can be added to 20 line branches, the maximum number of the series compensation is 3, the series compensation degree is controlled within the range of reactive compensation capacity of No. 9 node from 0.1 to 0.80-0.5, terminal voltage is controlled to be 0.95-1.05, generator output is controlled to be 0-0.8, particle swarm algorithm parameters are 200 for population scale, 200 for evolution times, and c is a parameter in speed updating1＝c2＝1.49445，μmax＝0.8，μmin＝0.5，σ＝0.2。
It can be seen from fig. 6 that the optimized node voltage distribution is more reasonable, and the voltage amplitude per unit value is distributed between 0.98 and 1.02. The network loss, voltage pair ratio is shown in table 1 below:
TABLE 1
Figure GDA0003004143220000111
The trend optimization results are shown in table 2 below.
TABLE 2
Figure GDA0003004143220000112
Figure GDA0003004143220000121
It can be seen from the table that, after the IEEE14 node considers the configuration of the series compensation position and the series compensation degree, and after the optimized series compensation, the lowest voltage of the node is increased, the network voltage deviation is smaller, the network loss is also smaller, the voltage distribution is more reasonable, the voltage average value is increased, and the voltage standard deviation is reduced. The optimization effect of the series compensation configuration optimization on the IEEE14 node power transmission system is obvious.
Case two: the active output of the generator is considered, the output of the original generator is changed, the network series compensation position and the series compensation degree, the reactive compensation of nodes 10 and 24 and the terminal voltage are used as parameters for network optimization, the branch of the transformer is set to be 1, and the series compensation can be added to the branch of the transformer. Performing optimization solution by using a particle swarm algorithm based on random weight, setting the control parameter as a series compensation position, wherein series compensation can be added to 41 line branches, the number of the series compensation is at most 6, and the series compensation degreeControlling the reactive compensation capacity of a node 9 to be 0.1-0.8, controlling the terminal voltage to be 0.95-1.05, controlling the output of a generator to be 0-0.8, controlling the particle swarm algorithm parameters to be 200 in population scale, 200 in evolutionary times and c in speed updating1＝c2＝1.49445，μmax＝0.8，μmin＝0.5，σ＝0.2。
It can be seen from fig. 8 that the voltage distribution is more reasonable after the particle swarm optimization, the voltage deviation is smaller, and the voltage amplitude per unit value is distributed between 0.97 and 1.03. The net loss, voltage pair ratio is shown in table 3 below:
TABLE 3
Figure GDA0003004143220000122
The trend optimization results are shown in table 4 below.
TABLE 4
Primitive power flow Optimizing series compensation configuration flow
Lowest voltage 0.9159 0.9702
Deviation of voltage 1.1556 0.1988
Network loss 6.16MW 0.496MW
Average value of voltage 0.9615 0.9996
Standard deviation of voltage 0.02852 0.00958
As can be seen from the above table, after the IEEE30 node considers the configuration of the series compensation position and the series compensation degree, and after optimization, the lowest voltage of the node is raised, the network voltage deviation is reduced compared with the original network, but the voltage average value is increased, the voltage standard deviation is reduced, and the network loss result of the series compensation configuration optimized power flow is the best.
The invention carries out comprehensive optimization selection aiming at the selection of the series compensation position and the series compensation degree of the system, takes the reduction of the network loss and the improvement of the voltage quality of the power system as optimization targets, researches the configuration of the series compensation, and optimizes the series compensation configuration of the circuit in the power system. The invention aims at the minimum system network loss and the optimal voltage quality, takes the number of series compensation, series compensation lines, the series compensation degree, the active power output of a generator, the transformer ratio, the system compensation and the like as constraint conditions, adopts random weight factors to improve the particle swarm optimization, carries out the optimum design of series compensation configuration on a series compensation line model of the system, scientifically and reasonably configures the series compensation position, and accurately calculates the series compensation capacity to be added into the line.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit and scope of the present invention.

Claims (1)

1. A power system line series compensation optimal configuration method is characterized by comprising the following steps: the method comprises the following steps:
1) determining a power flow algorithm of the power system;
2) determining an objective function which takes the optimal voltage quality and the minimum network loss as the optimal series compensation configuration;
3) determining a constraint condition;
4) solving a series compensation optimization configuration model after series compensation is added into the system by adopting an improved particle swarm optimization based on random weight;
the step 1) comprises the following steps:
step 1.1: the specific power flow network equation can be established by using the relations of the power, the voltage, the conductance and the susceptance on the line:
Figure FDA0003004143210000011
in the formula: piActive power for node i; qiReactive power for node i; e.g. of the typeiIs the real part of the voltage at node i, ejIs the real part of the voltage at node j; f. ofiIs the imaginary part of the voltage of node i, fjIs the imaginary part of the voltage at node j; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; n is the number of nodes;
step 1.2: and (3) obtaining a comprehensive power flow calculation method with strong applicability by combining a Newton Raphson algorithm and a PQ decomposition method:
firstly, a PQ decomposition method is set to calculate the load flow times, the system load flow is calculated by adopting the PQ decomposition method to obtain an initial value of the load flow calculated by a Newton-Raphson algorithm, and then the load flow calculation is carried out on the system by utilizing the Newton-Raphson algorithm;
the step 2) comprises the following steps:
firstly, establishing an objective function with optimal voltage quality according to the voltage deviation:
Figure FDA0003004143210000012
in the formula: Δ U is the system voltageDeviation; u shapeiIs the node i voltage; u shapeNA system voltage rating;
secondly, establishing an objective function with minimum network loss according to the loss of the line:
Figure FDA0003004143210000013
in the formula: p is the system loss; delta PiIs the voltage loss of line i;
and finally, calculating per unit value, unifying the two, and establishing a weight-based multi-objective optimization objective function:
min f＝λ1ΔU+λ2P (4)
in the formula: lambda [ alpha ]1，λ2Voltage deviation and loss weight coefficients;
the constraint conditions in the step 3) comprise:
the series compensation degree, the series compensation quantity and the series compensation circuit constraint condition are as follows:
kiminXi≤xi*kiXi≤kimaxXi (5)
Figure FDA0003004143210000021
in the formula: x is the number ofiThe serial compensation mark on the ith line can only be an integer and can only be 0 or 1, wherein 0 represents that no serial compensation exists on the ith line, and 1 represents that serial compensation exists on the ith line; k is a radical ofiFor degree of series compensation, X, on the lineiIs reactance, kimax，kiminThe upper and lower limits of the variation range; n is the limitation of the number of series compensation added in the system;
constraint conditions of active power output of the generator are as follows:
PGimin≤PGi≤PGimax (7)
in the formula: pGiAs a generator iActive power output of (1); pGiminIs the minimum value of the active power output of the generator i, PGimaxIs the maximum value of the active output of the generator i;
node voltage, transformer transformation ratio and system compensation of the generator are used as constraint conditions:
UGimin≤UGi≤UGimax (8)
Timin≤Ti≤Timax (9)
QCimin≤QCi≤QCimax (10)
in the formula: u shapeGiIs the voltage value of the generator i; t isiIs the transformation ratio of the transformer i; qCiA compensation capacity for reactive compensation i; u shapeGimax、UGiminThe upper limit and the lower limit of the voltage value change range of the generator i; t isimax、TiminIs the upper and lower limits of the transformation ratio variation range of the transformer i, QCimax、QCiminThe upper limit and the lower limit of the variation range of the compensation capacity of the reactive compensation i;
the reactive output and the node voltage of the generator are used as constraint conditions:
Figure FDA0003004143210000022
in the formula: qGjIs the reactive power of a generator j in the system; u shapeiIs the node i voltage; qGjmax、QGjminIs the upper and lower limits, U, of the reactive variation range of the generator j in the systemimax、UiminThe upper limit and the lower limit of the voltage variation range of the node i are defined;
the step of determining the series compensation optimal configuration model after the series compensation is added in the step 4) is specifically as follows:
step 4.1: determining an optimization model of the system after adding the series compensation:
Figure FDA0003004143210000031
in the formula: f is an objective function; lambda [ alpha ]1，λ2For voltage deviation and loss weight factor, λ1＝λ2＝0.5；UiIs the node i voltage; u shapeNIs the system voltage rating; delta PiIs the voltage loss of line i; u shapejIs the node j voltage; thetaijIs the phase angle difference between the voltages of the node i and the node j; x is the number ofiFor serial compensation marking on the ith line, kiFor the series compensation, X, on the ith lineiIs the reactance, k, on the ith lineimax，kiminThe upper limit and the lower limit of the variation range of the series compensation degree on the ith line are set; piActive power for node i; qiReactive power for node i; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; pGiIs the active output of the generator i; pGiminIs the minimum value of the active power output of the generator i, PGimaxIs the maximum value of the active output of the generator i; u shapeGiIs the voltage value of the generator i; t isiIs the transformation ratio of the transformer i; qCiA compensation capacity for reactive compensation i; u shapeGimax、UGiminThe upper limit and the lower limit of the voltage value change range of the generator i; t isimax、TiminIs the upper and lower limits of the transformation ratio variation range of the transformer i, QCimax、QCiminThe upper limit and the lower limit of the variation range of the compensation capacity of the reactive compensation i; qGjIs the reactive power of a generator j in the system; u shapeiIs the voltage of node i in the system; qGjmax、QGjminIs the upper and lower limits, U, of the reactive variation range of the generator j in the systemimax、UiminThe upper limit and the lower limit of the voltage variation range of the node i are defined; n is the limitation of the number of series compensation added in the system;
step 4.2: when series compensation is added into a line, the equation trend solution of a node added with the series compensation line is corrected, and the power balance of a branch node containing the series compensation is shown as the following formula:
Figure FDA0003004143210000041
in the formula: u shapeiIs the node i voltage; u shapejIs the node j voltage; thetaijIs the phase angle difference between the voltages of the node i and the node j; pisActive power of a head-end node of the series compensation circuit; qisThe reactive power of a head end node of the series compensation line is obtained; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; xTCSCA series compensation reactance;
the improved particle swarm optimization based on the random weight in the step 4) refers to that the random weight factor omega is changed:
ω＝(μmin+(μmax-μmin)*rand(0,1))+σ*N(0,1) (14)
in the formula: mu.sminIs the minimum of the random weight average; mu.smaxIs the maximum value of the random weight average; rand (0,1) is a random number from 0 to 1; σ is the variance of the random weight mean; n (0,1) is a random number of a standard normal distribution,
the velocity update formula for adding random weights is as follows:
Figure FDA0003004143210000042
in the formula:
Figure FDA0003004143210000043
is the (k + 1) th velocity of the particle;
Figure FDA0003004143210000044
the kth velocity of the particle; c. C1，c2Is a learning factor; r is1，r2Are mutually independent pseudo-random numbers;
Figure FDA0003004143210000045
the k-th individual optimal value;
Figure FDA0003004143210000046
the optimal value of the kth population;
Figure FDA0003004143210000047
is the k-th individual particle of the particle,
Figure FDA0003004143210000048
is the kth population particle.
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