CN113629715A - UPFC multi-objective optimization configuration method considering power transmission capacity - Google Patents

UPFC multi-objective optimization configuration method considering power transmission capacity Download PDF

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CN113629715A
CN113629715A CN202110802494.5A CN202110802494A CN113629715A CN 113629715 A CN113629715 A CN 113629715A CN 202110802494 A CN202110802494 A CN 202110802494A CN 113629715 A CN113629715 A CN 113629715A
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load
upfc
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CN113629715B (en
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杨晓雷
石博隆
叶琳
项中明
孙维真
张静
周正阳
陶欢
方江晓
屠一艳
张涛
陶然
霍然
李逸鸿
郭玥彤
刘景�
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China Three Gorges University CTGU
Jiaxing Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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Jiaxing Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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    • H02J3/144—Demand-response operation of the power transmission or distribution network
    • H—ELECTRICITY
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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    • H—ELECTRICITY
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Abstract

A UPFC multi-objective optimization configuration method considering the power transmission capacity comprises the following steps: inputting network original parameters and algorithm related parameters; constructing a UPFC multi-objective optimization configuration model taking the maximum available transmission capacity and the minimum voltage deviation and voltage stability as objective functions; establishing constraint conditions meeting the stable operation of the system, wherein the constraint conditions comprise equality constraint and inequality constraint, the equality constraint is a power flow equation of the system, and the inequality constraint comprises control variable constraint and state variable constraint; processing the state variable constraint by adopting an adaptive penalty function; and solving the UPFC multi-objective optimization configuration model based on the improved NSGA-III algorithm. The invention relates to a UPFC multi-target optimization configuration method considering the power transmission capacity, which optimizes UPFC site selection and capacity by using the maximum available power transmission capacity and the minimum voltage deviation and L index, and solves a model by adopting an improved NSGA-III algorithm to obtain an optimal configuration scheme.

Description

UPFC multi-objective optimization configuration method considering power transmission capacity
Technical Field
The invention relates to the technical field of optimal configuration of power systems, in particular to a UPFC multi-objective optimal configuration method considering power transmission capacity.
Background
With the continuous expansion of modern power systems and the improvement of the demand on the transmission capacity of the systems, how to increase the available transmission capacity and improve the voltage stability of the power systems without changing the existing structure of the power transmission network has great significance. The advent of Flexible AC Transmission System (FACTS) has become an effective means for solving this problem. The FACTS device is based on high-voltage and high-power electronic equipment, and can effectively change the tide distribution of a power transmission line through a flexible and quick control technology, reduce the line loss caused by long-distance power transmission, and improve the transmission capacity and the voltage quality of a power system, thereby improving the operation stability and the economic benefit of the power system.
Since the FACTS technology is proposed, many different FACTS devices appear, wherein a Unified Power Flow Controller (UPFC) can adjust line voltage and phase, and has the functions of improving Power Flow distribution and reactive compensation, and a wide application prospect. If the installation position and the capacity of the UPFC equipment are not properly configured, the transmission capacity and the voltage stability are reduced, the investment cost of the equipment is high, and the like. Therefore, optimal configuration of the UPFC equipment has become an urgent problem to be solved in practical engineering.
Disclosure of Invention
In order to improve the operation economy and stability of a power system, the invention provides a UPFC multi-objective optimization configuration method considering the power transmission capacity.
The technical scheme adopted by the invention is as follows:
a UPFC multi-objective optimization configuration method considering the power transmission capacity comprises the following steps:
step 1: inputting network original parameters including system branch parameters, loads of all nodes and upper and lower limits of compensation device parameters; inputting algorithm related parameters including the population size, the maximum iteration times, the upper and lower limits of the variation coefficient and the upper and lower limits of the cross coefficient;
step 2: constructing a UPFC multi-objective optimization configuration model taking the maximum available transmission capacity and the minimum voltage deviation and voltage stability as objective functions;
and step 3: establishing constraint conditions meeting the stable operation of the system, wherein the constraint conditions comprise equality constraint and inequality constraint, the equality constraint is a power flow equation of the system, and the inequality constraint comprises control variable constraint and state variable constraint;
and 4, step 4: processing the state variable constraint by adopting an adaptive penalty function;
and 5: and solving the UPFC multi-objective optimization configuration model based on the improved NSGA-III algorithm.
In the step 2, the voltage deviation is represented by the sum of the voltage deviations in all the branches, the voltage stability reflects the voltage stability of the system by using an L index, and the objective function is specifically as follows:
the power transmission capacity:
Figure BDA0003165183320000021
voltage deviation:
Figure BDA0003165183320000022
l index:
Figure BDA0003165183320000023
in the formulae (1), (2) and (3), f1For the available transmission capacity of the system, i.e. ATC, λ between areasLiRepresents the increase ratio of the ith load; pLiRepresenting the active load of the ith load node; n is a radical ofPQThe number of PQ nodes in the power receiving area; p0Representing the active load in the case of ground state power flow.
f2Is the total voltage deviation; u shapeiFor the actual voltage at the end of the line, UNIs the nominal voltage at the end of the line;
f3is an L index; l isjThe L index of the jth load node is represented, and the L index of the whole system is evaluated by taking the maximum value of the L indexes of all the load nodes; n isGRepresenting the number of generator nodes in the system; alpha is alphaL、αGRepresenting the set of all load nodes and generator nodes in the system; u shapeiRepresenting the i-th generator node voltage, UjIs the jth load node voltage; fjiIs the jth row and ith column element of the load participation factor matrix F.
The specific calculation expression of the load participation factor matrix is as follows:
Figure BDA0003165183320000024
in the formula (4), YLLAnd YLGBeing a sub-array of the nodal admittance matrix, YLL -1Represents YLLThe inverse matrix of (c).
YLLAnd YLGCan be obtained by the following formula:
Figure BDA0003165183320000025
equation (5) represents a node voltage equation written for the column after the system node is divided into two groups, i.e., a generator node and a load node, where UG、IGA column vector formed by representing the voltage and the current of all the motor nodes; u shapeL、ILA column vector formed by representing the voltage and the current of all load nodes; y isLL、YGGRepresenting a node admittance matrix formed by all load nodes and generator nodes; y isLG、YGLAnd expressing node admittance matrixes formed by the load nodes and the generator nodes and the load nodes. In the step 3, according to the operating characteristics of the system, the state variable constraints include generator node voltage, generator active power output constraints, node voltage constraints, transformer gear constraints and control variables of the UPFC.
In the step 3, the constraint conditions are specifically as follows:
and (3) constraint of an equation:
Figure BDA0003165183320000031
the inequality constrains:
and (3) controlling variable constraints:
Figure BDA0003165183320000032
and (3) state variable constraint:
Figure BDA0003165183320000033
in the formulae (6), (7) and (8), Ui、UjRespectively representing the voltage amplitudes of the nodes i and j; thetaijRepresents the voltage phase difference between nodes i, j; gij、BijRespectively representing the conductance and susceptance among the branches i-j; lambda [ alpha ]iG、λiLThe active output and the load power of the generator are respectively increased proportion; pGiAnd QGiRespectively representing active and reactive power output of a generator arranged at a node i; pLiAnd QLiRespectively representing the active power and the reactive power of the load; pCiAnd QCiRespectively representing active power and reactive power equivalently injected at a node i when the UPFC is configured; n is the total number of system nodes; u shapeGi、UGmax、UGminRespectively representing the voltage amplitude and the upper and lower limits of the generator node; u shapeLi、ULmax、ULminThe voltage amplitude and the upper and lower limits of the load node are respectively; t isi、Tmax、TminThe tap position and the upper and lower limits of the transformer can be adjusted; pij、PijmaxThe transmission power and the upper limit among the branches i-j; u shapeT、UTmax、UTminRespectively representing the voltage amplitude and the upper and lower limits of an equivalent voltage source on the series side of the UPFC; thetaT、θTmax、θTminRespectively representing the voltage phase angle and the upper and lower limits of an equivalent voltage source on the series side of the UPFC; i isq、Iqmax、IqminTo representAnd the reactive component and the upper and lower limits of the current of the equivalent current source on the parallel side of the UPFC.
In the step 4, the process of the step,
the state variables are processed by an adaptive penalty function, and the objective function taking the minimum value is constructed as follows:
minF(x)＝f(x)+p(k)·H(x) (9)
in the formula (9), f (x) is the original objective function value; p (k) is a penalty factor 1, the penalty factor 1 is dynamically changed according to the change of the iteration number, and p (k) k (k)1/2(ii) a H (x) is a penalty term, and the expression is shown in formula (10):
Figure BDA0003165183320000034
in the formula (10), n is the number of state variables needing punishment; t ═ max {0, hi(x) Represents the magnitude of the cross-boundary volume; h isi(x) A cross-border function representing an inequality constraint; theta (t) is a penalty coefficient 2, and the penalty coefficient 2 is dynamically selected according to the size of the out-of-bounds quantity; gamma (t) is punishment, the punishment gamma (t) is dynamically selected according to the size of the out-of-limit quantity t, if the out-of-limit quantity is less, the gamma (t) takes 1, and at the moment, the t is the punishmentγ(t)The linear increase punishment quantity is represented, if the linear increase punishment quantity exceeds a large quantity, if the linear increase punishment quantity exceeds one time of the range of the upper limit value interval and the lower limit value interval, the gamma (t) is 2, and at the moment, the t isγ(t)Represents a large amplification penalty in the form of a square.
Figure BDA0003165183320000041
Figure BDA0003165183320000042
The step 5 comprises the following steps:
step 5.1: firstly, initializing a parent population based on upper and lower limits of parameters of a compensation device and the population size in the step 1;
step 5.2: and introducing a mutation operator and a crossing strategy in a difference algorithm, carrying out mutation and crossing treatment on the parent population to generate an offspring population, and mixing the parent population and the offspring population.
Step 5.3: and (3) rapidly sequencing the recombined population without domination to divide domination levels, and for the individuals of the same domination level, selecting N individuals associated with the reference point with the minimum relevance as the parent of the next cycle through a reference point mechanism.
Step 5.4: and judging whether the current iteration number reaches the maximum iteration number, if not, repeating the step 5.2 to the step 5.4, and if so, selecting the compromise solution with the highest satisfaction degree by adopting the fuzzy membership degree to obtain the optimal configuration scheme of the UPFC.
In the step 5.2, the step of the method,
the introduction of the variation and the intersection of the differential algorithm is to balance and improve the global search capability and the local search capability of the multi-target NSGA-III algorithm, and meanwhile, the variation coefficient and the intersection coefficient in the variation and the intersection are subjected to self-adaptive adjustment. The mutation and crossover operations are as follows
Figure BDA0003165183320000043
In formula (13), F is a scaling factor; CR is the probability of crossover; x _ newi,jIs a new gene generated by mutation and crossing of the jth gene on the ith individual, xi,jThe gene is the j gene of the original i individual. x is the number ofr1,j、xr2,jAnd xr3,jRespectively being randomly selected r1、r2And r3The jth gene on individuals, r1, r2 and r3 are 3 random numbers different from each other; rand denotes a random number; q is the position number of a certain randomly selected gene (q. epsilon. 1,2, …, j);
and (3) carrying out self-adaptive adjustment on the scaling factor and the value of the cross probability to ensure that the scaling factor and the value of the cross probability dynamically change in a range, obtaining stronger global search capability by taking larger F and CR at the initial stage, and gradually reducing the scaling factor and the value of the cross probability to enhance the local search capability at the later stage. F and CR have the following values:
Figure BDA0003165183320000051
Figure BDA0003165183320000052
in the formulae (14) and (15), Fmax、FminRepresents the maximum and minimum values of the scaling factor; CRmax、CRminThe maximum value and the minimum value of the cross probability; k. k is a radical ofmaxCurrent and maximum number of iterations. FkRepresenting the scale factor value at the kth iteration; CRkRepresenting the probability of intersection at the k-th iteration.
In the step 5.4, the step of the method,
selecting a compromise solution by adopting a fuzzy membership method, wherein the fuzzy membership is calculated in the following way:
Figure BDA0003165183320000053
in the formula (16), uijFuzzy degree of membership, f, of the ith objective function of the jth individualimax、fiminThe maximum value and the minimum value of each objective function are respectively.
After the fuzzy membership degree is calculated, the maximum value is selected from the fuzzy membership degree according to the formula (16), and the maximum value is the compromise optimal solution comprehensively considering all target values.
Figure BDA0003165183320000054
In the formula (17), N represents the number of objective functions; mu is the compatibility of the corresponding solution, and the better the result is, the closer to 1. Mu.siIndicating the overall satisfaction of the ith individual.
The invention relates to a UPFC multi-objective optimization configuration method considering the power transmission capacity, which has the following technical effects:
1) in the aspect of model construction, the UPFC is selected as a regulating and compensating device, and the functions of flow distribution and reactive compensation are improved by using the UPFC, so that the operation stability of the power transmission network is improved. And selecting the indexes of available power transmission capacity, voltage deviation and voltage stability L as objective functions to construct a UPFC multi-objective optimization configuration model.
2) In the aspect of algorithm improvement, variation and crossover in a differential algorithm are introduced, and the global and local searching capability of the NSGA-III algorithm is balanced. Meanwhile, on the basis of rapid non-dominated sorting of the original algorithm, a compromise solution with the highest satisfaction degree is selected by introducing a fuzzy membership function, and the multi-target problem in the configuration model can be effectively processed.
3) The UPFC multi-objective optimization configuration method considering the available transmission capacity introduces the UPFC device to be connected into a transmission network for reactive compensation, thereby effectively regulating and controlling the power flow of a power system and improving the voltage stability. And carrying out optimization configuration on the UPFC multi-objective optimization configuration model, and establishing the UPFC multi-objective optimization configuration model by taking the maximum available transmission capacity, the minimum voltage deviation and the minimum L index as targets. In order to solve the problem of multiple targets, the original NSGA-III algorithm is improved, variation in a difference algorithm and cross and fuzzy membership functions are introduced to process the multiple targets, a compromise solution is selected, and a final UPFC configuration scheme is obtained. The result shows that the installation of FACTS equipment can improve various indexes of the system, improve the power transmission capacity of the system to a great extent and improve the quality and stability of voltage. In addition, the improved NSGA-III can obtain better effect compared with the original NSGA-III, and the effectiveness of the algorithm improvement strategy is shown.
Drawings
Fig. 1 is a flow chart of the improved NSGA-III algorithm applied to UPFC optimization configuration according to the present invention.
Fig. 2 is a structural diagram of an IEEE14 node system according to the present invention.
FIG. 3 is a comparison graph of the optimization effect of STATCOM and UPFC according to the present invention.
FIG. 4 is a graph comparing the algorithms for improved NSGA-III and NSGA-III according to the present invention.
Detailed Description
The technical solution of the present invention will be specifically described below with reference to the accompanying drawings.
A UPFC multi-objective optimization configuration method considering available transmission capacity comprises the following steps:
step 1: inputting the original parameters of the power system network, specifically comprising the branch parameters of the system, the load of each node, and the upper and lower limits Q of the capacity of the compensating devicemax,Qmin. Inputting algorithm related parameters, specifically including population size nPop, maximum iteration number Iter, and upper and lower limits of variation coefficient Fmax,FminUpper and lower cross coefficient limits CRmax,CRmin。
Step 2: and constructing a UPFC multi-objective optimization configuration model taking the maximum available transmission capacity and the minimum voltage deviation and voltage stability as objective functions. The voltage deviation is represented by the sum of voltage offsets in all branches, the voltage stability reflects the voltage stability of the system by an L index, and the objective function is specifically as follows:
A. available transmission capacity:
Figure BDA0003165183320000061
B. voltage deviation:
Figure BDA0003165183320000062
C. l index:
Figure BDA0003165183320000063
in the formulae (1), (2) and (3), f1For the available transmission capacity of the system, i.e. ATC, λ between areasLiRepresents the increase ratio of the ith load; pLiRepresenting the active load of the ith load node; n is a radical ofPQThe number of PQ nodes in the power receiving area; p0Representing the active load in the case of ground state power flow. f. of2Is a voltage deviation; u shapeiFor the actual voltage at the end of the line, UNIs the nominal voltage at the end of the line; f. of3Is an L index; l isjThe L index of the jth load node is represented, and the L index of the whole system is evaluated by taking the maximum value of the L indexes of all the load nodes; n isGRepresenting generator nodes in a systemThe number of the cells; alpha is alphaL、αGRepresenting the set of all load nodes and generator nodes in the system; u shapeiRepresenting the i-th generator node voltage, UjIs the jth load node voltage; fjiIs the jth row and ith column element of the load participation factor matrix F.
The specific calculation expression of the load participation factor is as follows:
Figure BDA0003165183320000071
in the formula (4), YLLAnd YLGIs a sub-array of the nodal admittance matrix,
Figure BDA0003165183320000072
represents YLLThe inverse matrix of (c) can be obtained by the following equation:
Figure BDA0003165183320000073
equation (5) represents a node voltage equation written for the column after the system node is divided into two groups, i.e., a generator node and a load node, where UG、IGA column vector formed by representing the voltage and the current of all the motor nodes; u shapeL、ILA column vector formed by representing the voltage and the current of all load nodes; y isLL、YGGRepresenting a node admittance matrix formed by all load nodes and generator nodes; y isLG、YGLAnd expressing node admittance matrixes formed by the load nodes and the generator nodes and the load nodes.
And step 3: and establishing constraint conditions which meet the stable operation of the system, wherein the constraint conditions comprise equality constraint and inequality constraint. The equality constraint is a power flow equation of the system, and the inequality constraint comprises a control variable constraint and a state variable constraint. According to the operating characteristics of the system, the control variable constraints mainly comprise generator node voltage, generator active power output constraints, node voltage constraints, transformer gear constraints, control variables of the UPFC and the like. The constraint conditions are specifically as follows:
A. and (3) constraint of an equation:
Figure BDA0003165183320000074
B. the inequality constrains:
(1) and (3) controlling variable constraints:
Figure BDA0003165183320000075
(2) and (3) state variable constraint:
Figure BDA0003165183320000076
in the formulae (6), (7) and (8), Ui、UjRespectively representing the voltage amplitudes of the nodes i and j; thetaijRepresents the voltage phase difference between nodes i, j; gij、BijRespectively representing the conductance and susceptance among the branches i-j; lambda [ alpha ]iG、λiLThe active output and the load power of the generator are respectively increased proportion; pGiAnd QGiRespectively representing active and reactive power output of a generator arranged at a node i; pLiAnd QLiRespectively representing the active power and the reactive power of the load; pCiAnd QCiRespectively representing active power and reactive power equivalently injected at a node i when the UPFC is configured; n is the total number of system nodes; u shapeGi、UGmax、UGminRespectively representing the voltage amplitude and the upper and lower limits of the generator node; u shapeLi、ULmax、ULminThe voltage amplitude and the upper and lower limits of the load node are respectively; t isi、Tmax、TminThe tap position and the upper and lower limits of the transformer can be adjusted; pij、PijmaxThe transmission power and the upper limit among the branches i-j; u shapeT、UTmax、UTminRespectively representing the voltage amplitude and the upper and lower limits of an equivalent voltage source on the series side of the UPFC; thetaT、θTmax、θTminRespectively representing the voltage phase angle and the upper and lower limits of an equivalent voltage source on the series side of the UPFC; i isq、Iqmax、IqminCurrent reactive power division for representing equivalent current source on parallel side of UPFCAmounts and upper and lower limits.
And 4, step 4: using an adaptive penalty function to process the state variables, the objective function, e.g., for taking a minimum, can be constructed as follows:
minF(x)＝f(x)+p(k)·H(x) (9)
in the formula (9), f (x) is the original objective function value; p (k) is a penalty factor 1, the penalty factor 1 is dynamically changed according to the change of the iteration number, and p (k) k (k)1/2(ii) a H (x) is a penalty term, and the expression is shown in formula (10):
Figure BDA0003165183320000081
in the formula (10), n is the number of state variables needing punishment; t ═ max {0, hi(x) Represents the magnitude of the cross-boundary volume; h isi(x) A cross-border function representing an inequality constraint; theta (t) is a penalty coefficient 2, and the penalty coefficient 2 is dynamically selected according to the size of the out-of-bounds quantity; gamma (t) is punishment, the punishment gamma (t) is dynamically selected according to the size of the out-of-limit quantity t, if the out-of-limit quantity is less, the gamma (t) takes 1, and at the moment, the t is the punishmentγ(t)The linear increase punishment quantity is represented, if the linear increase punishment quantity exceeds a large quantity, if the linear increase punishment quantity exceeds one time of the range of the upper limit value interval and the lower limit value interval, the gamma (t) is 2, and at the moment, the t isγ(t)Represents a large amplification penalty in the form of a square.
Figure BDA0003165183320000082
Figure BDA0003165183320000083
And 5: and solving the UPFC multi-objective optimization configuration model based on the improved NSGA-III algorithm. Firstly, initializing a parent population based on the upper and lower capacity limits and the population size in step 1.
Step 6: and introducing a mutation operator and a crossing strategy in a difference algorithm, carrying out mutation and crossing treatment on the parent population to generate an offspring population, and mixing the parent population and the offspring population. The mutation and crossover operations are as follows
Figure BDA0003165183320000084
In formula (13), F is a scaling factor; CR is the probability of crossover; x _ newi,jIs a new gene generated by mutation and crossing of the jth gene on the ith individual, xi,jThe gene is the j gene of the original i individual. xr1, j, xr2, j and xr3, j are respectively j-th genes on r1, r2 and r3 individuals which are randomly selected (r1, r2 and r3 are 3 random numbers which are different from each other); rand denotes a random number; q is the position number of a certain randomly selected gene (q. epsilon. 1,2, …, j);
and (3) carrying out self-adaptive adjustment on the scaling factor and the value of the cross probability to ensure that the scaling factor and the value of the cross probability dynamically change in a range, obtaining stronger global search capability by taking larger F and CR at the initial stage, and gradually reducing the scaling factor and the value of the cross probability to enhance the local search capability at the later stage. F and CR have the following values:
Figure BDA0003165183320000091
Figure BDA0003165183320000092
in the formulae (14) and (15), Fmax、FminRepresents the maximum and minimum values of the scaling factor; CRmax、CRminThe maximum value and the minimum value of the cross probability; k. k is a radical ofmaxCurrent and maximum number of iterations. FkRepresenting the scale factor value at the kth iteration; CRkRepresenting the probability of intersection at the k-th iteration.
And 7: and (3) rapidly sequencing the recombined population without domination to divide domination levels, and for the individuals of the same domination level, selecting N individuals associated with the reference point with the minimum relevance as the parent of the next cycle through a reference point mechanism. The fuzzy membership is calculated as follows:
Figure BDA0003165183320000093
in the formula (16), uijFuzzy degree of membership, f, of the ith objective function of the jth individualimax、fiminThe maximum value and the minimum value of each objective function are respectively.
After the fuzzy membership degree is calculated, the maximum value is selected from the fuzzy membership degree according to the formula (16), namely the optimal solution which is worthy of compromise considering all the targets comprehensively.
Figure BDA0003165183320000094
In the formula (17), N represents the number of objective functions; mu is the compatibility of the corresponding solution, and the better the result is, the closer to 1. Mu.siIndicating the overall satisfaction of the ith individual.
And 8: and judging whether the current iteration number reaches the maximum iteration number, if not, repeating the steps from 5 to 8, and if so, selecting the compromise solution with the highest satisfaction degree by adopting the fuzzy membership degree to obtain the optimal configuration scheme of the UPFC. The algorithm flow chart is shown in figure 1.
The specific embodiment is as follows:
taking an IEEE14 node system as an example, the UPFC multi-objective optimization configuration model is solved by adopting an improved NSGA-III algorithm.
The system was divided into 3 zones: the power generation system comprises a power generation area, a power receiving area and a balance area, wherein the area 1 is the power generation area, the area 2 is the power receiving area, and the area 3 is the balance area. And when calculating the ATC, keeping the power of other load nodes unchanged and only increasing the load in the power receiving area. When the load of the power receiving area increases, the power generation area supplies required power to the power receiving area, and the balance area bears the network loss caused by the increase of the system power. The size of the improved NSGA-III algorithm population is set to be 100, the iteration times are 100, the crossing rate is 0.5, the variation rate is 0.5, the differential variation rate is 0.5, and the number of reference points is 21; the system reference capacity is 100 MVA; setting the voltage value range of each PV node and each PQ node to be 0.94-1.06 p.u.; the transformer is provided with 5 gears, and the adjusting range of each gear is +/-2.5%. The UPFC installation rule is as follows: one branch is provided with at most one UPFC, and the branch with the generator has a certain regulation capacity and is not provided with the UPFC, so that 9 branches can be selected to be installed.
According to the constructed optimized configuration model, the comparison of the installation effects of the UPFC and STATCOM and the optimal solution of the table 1 are obtained as shown in FIG. 1.
TABLE 1 fuzzy satisfaction solution
Figure BDA0003165183320000101
As can be seen from table 1, the ATC of the system is significantly increased from the ground state after installation of the UPFC or STATCOM, and when the L index or voltage deviation is the same, both other indexes are better than the ground state. In the optimal solution selected from the optimal solution set, the three project scalar values of the UPFC are all superior to those of the STATCOM, and meanwhile, the installation capacity is smaller. According to the structural analysis of the UPFC, the series side and the parallel side of the UPFC can be regarded as that the SSSC and the STATCOM are coupled together through the direct current capacitor, the function characteristics of the SSSC and the STATCOM are achieved, the series side and the parallel side can be subjected to reactive compensation and voltage amplitude and phase angle regulation, the regulation range is wider, and therefore the power flow regulation and reactive compensation have more excellent effects.
FIG. 4 shows the modified NSGA-III algorithm, the original NSGA-III algorithm, at the same time for comparative analysis, and Table 2 shows the external solution comparison of the two algorithms.
TABLE 2 optimization Algorithm external solutions
Figure BDA0003165183320000102
Figure BDA0003165183320000111
The final configuration condition of the UPFC is analyzed by the above example, and the effectiveness and the accuracy of the UPFC multi-target optimization configuration method considering the available power transmission capacity are verified.

Claims (9)

1. A UPFC multi-objective optimization configuration method considering the power transmission capacity is characterized by comprising the following steps:
step 1: inputting network original parameters including system branch parameters, loads of all nodes and upper and lower limits of compensation device parameters;
inputting algorithm related parameters including the population size, the maximum iteration times, the upper and lower limits of the variation coefficient and the upper and lower limits of the cross coefficient;
step 2: constructing a UPFC multi-objective optimization configuration model taking the maximum available transmission capacity and the minimum voltage deviation and voltage stability as objective functions;
and step 3: establishing constraint conditions meeting the stable operation of the system, wherein the constraint conditions comprise equality constraint and inequality constraint, the equality constraint is a power flow equation of the system, and the inequality constraint comprises control variable constraint and state variable constraint;
and 4, step 4: processing the state variable constraint by adopting an adaptive penalty function;
and 5: and solving the UPFC multi-objective optimization configuration model based on the improved NSGA-III algorithm.
2. The UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: in the step 2, the voltage deviation is represented by the sum of the voltage deviations in all the branches, the voltage stability reflects the voltage stability of the system by using an L index, and the objective function is specifically as follows:
the power transmission capacity:
Figure FDA0003165183310000011
voltage deviation:
Figure FDA0003165183310000012
l index:
Figure FDA0003165183310000013
in the formulae (1), (2) and (3), f1For the available transmission capacity of the system, i.e. ATC, λ between areasLiRepresents the increase ratio of the ith load; pLiRepresenting the active load of the ith load node; n is a radical ofPQThe number of PQ nodes in the power receiving area; p0Representing the active load in the case of ground state power flow;
f2is the total voltage deviation; u shapeiFor the actual voltage at the end of the line, UNIs the nominal voltage at the end of the line;
f3is an L index; l isjThe L index of the jth load node is represented, and the L index of the whole system is evaluated by taking the maximum value of the L indexes of all the load nodes; n isGRepresenting the number of generator nodes in the system; alpha is alphaL、αGRepresenting the set of all load nodes and generator nodes in the system; u shapeiRepresenting the i-th generator node voltage, UjIs the jth load node voltage; fjiIs the jth row and ith column element of the load participation factor matrix F;
the specific calculation expression of the load participation factor matrix is as follows:
Figure FDA0003165183310000014
in the formula (4), YLLAnd YLGBeing a sub-array of the nodal admittance matrix, YLL -1Represents YLLThe inverse matrix of (d);
YLLand YLGCan be obtained by the following formula:
Figure FDA0003165183310000021
equation (5) represents a node voltage equation written for the column after the system node is divided into two groups, i.e., a generator node and a load node, where UG、IGA column vector formed by representing the voltage and the current of all the motor nodes;UL、ILa column vector formed by representing the voltage and the current of all load nodes; y isLL、YGGRepresenting a node admittance matrix formed by all load nodes and generator nodes; y isLG、YGLAnd expressing node admittance matrixes formed by the load nodes and the generator nodes and the load nodes.
3. The UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: in the step 3, according to the operating characteristics of the system, the state variable constraints include generator node voltage, generator active power output constraints, node voltage constraints, transformer gear constraints and control variables of the UPFC.
4. The UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: in the step 3, the constraint conditions are specifically as follows:
and (3) constraint of an equation:
Figure FDA0003165183310000022
the inequality constrains:
and (3) controlling variable constraints:
Figure FDA0003165183310000023
and (3) state variable constraint:
Figure FDA0003165183310000024
in the formulae (6), (7) and (8), Ui、UjRespectively representing the voltage amplitudes of the nodes i and j; thetaijRepresents the voltage phase difference between nodes i, j; gij、BijRespectively representing the conductance and susceptance among the branches i-j; lambda [ alpha ]iG、λiLThe active output and the load power of the generator are respectively increased proportion; pGiAnd QGiRespectively representing active and reactive power of generator mounted at node iForce is exerted; pLiAnd QLiRespectively representing the active power and the reactive power of the load; pCiAnd QCiRespectively representing active power and reactive power equivalently injected at a node i when the UPFC is configured; n is the total number of system nodes; u shapeGi、UGmax、UGminRespectively representing the voltage amplitude and the upper and lower limits of the generator node; u shapeLi、ULmax、ULminThe voltage amplitude and the upper and lower limits of the load node are respectively; t isi、Tmax、TminThe tap position and the upper and lower limits of the transformer can be adjusted; pij、PijmaxThe transmission power and the upper limit among the branches i-j; u shapeT、UTmax、UTminRespectively representing the voltage amplitude and the upper and lower limits of an equivalent voltage source on the series side of the UPFC; thetaT、θTmax、θTminRespectively representing the voltage phase angle and the upper and lower limits of an equivalent voltage source on the series side of the UPFC; i isq、Iqmax、IqminAnd the current reactive component and the upper and lower limits of the equivalent current source on the parallel side of the UPFC are represented.
5. The UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: in the step 4, the process of the step,
the state variables are processed by an adaptive penalty function, and the objective function taking the minimum value is constructed as follows:
min F(x)＝f(x)+p(k)·H(x) (9)
in the formula (9), f (x) is the original objective function value; p (k) is a penalty factor 1, the penalty factor 1 is dynamically changed according to the change of the iteration number, and p (k) k (k)1/2(ii) a H (x) is a penalty term, and the expression is shown in formula (10):
Figure FDA0003165183310000031
in the formula (10), n is the number of state variables needing punishment; t ═ max {0, hi(x) Represents the magnitude of the cross-boundary volume; h isi(x) A cross-border function representing an inequality constraint; theta (t) is a penalty factor of 2,dynamically selecting a penalty coefficient 2 according to the size of the out-of-bounds quantity; gamma (t) is punishment, the punishment gamma (t) is dynamically selected according to the size of the out-of-limit quantity t, if the out-of-limit quantity is less, the gamma (t) takes 1, and at the moment, the t is the punishmentγ(t)The linear increase punishment quantity is represented, if the linear increase punishment quantity exceeds a large quantity, if the linear increase punishment quantity exceeds one time of the range of the upper limit value interval and the lower limit value interval, the gamma (t) is 2, and at the moment, the t isγ(t)Representing a large amplification penalty in the form of a square;
Figure FDA0003165183310000032
Figure FDA0003165183310000033
6. the UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: the step 5 comprises the following steps:
step 5.1: firstly, initializing a parent population based on upper and lower limits of parameters of a compensation device and the population size in the step 1;
step 5.2: introducing a mutation operator and a crossing strategy in a difference algorithm, carrying out mutation and crossing treatment on the parent population to generate an offspring population, and mixing the parent population and the offspring population;
step 5.3: the recombined population is subjected to rapid non-domination sorting to divide domination levels, and for individuals of the same domination level, N individuals associated with a reference point with the minimum relevance are selected as parents of the next cycle through a reference point mechanism;
step 5.4: and judging whether the current iteration number reaches the maximum iteration number, if not, repeating the step 5.2 to the step 5.4, and if so, selecting the compromise solution with the highest satisfaction degree by adopting the fuzzy membership degree to obtain the optimal configuration scheme of the UPFC.
7. The UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: in the step 5.2, the step of the method,
the introduction of the variation and crossing of the differential algorithm is to improve the global search capability and the local search capability of the multi-target NSGA-III algorithm in a balanced manner, and meanwhile, the variation coefficient and the crossing coefficient in the variation and crossing are subjected to self-adaptive adjustment; the mutation and crossover operations are as follows
Figure FDA0003165183310000041
In formula (13), F is a scaling factor; CR is the probability of crossover; x _ newi,jIs a new gene generated by mutation and crossing of the jth gene on the ith individual, xi,jThe gene is the jth gene of the original ith individual; x is the number ofr1,j、xr2,jAnd xr3,jRespectively being randomly selected r1、r2And r3The jth gene on individuals, r1, r2 and r3 are 3 random numbers different from each other; rand denotes a random number; q is the position number of a certain randomly selected gene (q. epsilon. 1,2, …, j);
the scaling factor and the value of the cross probability are subjected to self-adaptive adjustment, so that the scaling factor and the value of the cross probability dynamically change within a range, larger F and CR are taken at the initial stage to obtain stronger global search capability, and the scaling factor and the value of the cross probability are gradually reduced at the later stage to enhance local search capability; f and CR have the following values:
Figure FDA0003165183310000042
Figure FDA0003165183310000043
in the formulae (14) and (15), Fmax、FminRepresents the maximum and minimum values of the scaling factor; CRmax、CRminThe maximum value and the minimum value of the cross probability; k. k is a radical ofmaxCurrent and maximum number of iterations; fkRepresents the k-th iterationA scaling factor value of the epoch; CRkRepresenting the probability of intersection at the k-th iteration.
8. The UPFC multi-objective optimization configuration method considering power transmission capacity as claimed in claim 1, wherein: in the step 5.4, the step of the method,
selecting a compromise solution by adopting a fuzzy membership method, wherein the fuzzy membership is calculated in the following way:
Figure FDA0003165183310000044
in the formula (16), uijFuzzy degree of membership, f, of the ith objective function of the jth individualimax、fiminRespectively the maximum value and the minimum value of each objective function;
after the fuzzy membership degree is calculated, selecting the maximum value from the fuzzy membership degree according to the formula (16), namely the compromise optimal solution comprehensively considering all target values;
Figure FDA0003165183310000051
in the formula (17), N represents the number of objective functions; mu is the compatibility of the corresponding solution, and the more excellent the result is, the closer to 1 is; mu.siIndicating the overall satisfaction of the ith individual.
9. A UPFC multi-objective optimization configuration model is characterized by comprising the following steps: the objective function of the model is specifically as follows:
the power transmission capacity:
Figure FDA0003165183310000052
voltage deviation:
Figure FDA0003165183310000053
l index:
Figure FDA0003165183310000054
in the formulae (1), (2) and (3), f1For the available transmission capacity of the system, i.e. ATC, λ between areasLiRepresents the increase ratio of the ith load; pLiRepresenting the active load of the ith load node; n is a radical ofPQThe number of PQ nodes in the power receiving area; p0Representing the active load in the case of ground state power flow;
f2is the total voltage deviation; u shapeiFor the actual voltage at the end of the line, UNIs the nominal voltage at the end of the line;
f3is an L index; l isjThe L index of the jth load node is represented, and the L index of the whole system is evaluated by taking the maximum value of the L indexes of all the load nodes; n isGRepresenting the number of generator nodes in the system; alpha is alphaL、αGRepresenting the set of all load nodes and generator nodes in the system; u shapeiRepresenting the i-th generator node voltage, UjIs the jth load node voltage; fjiIs the jth row and ith column element of the load participation factor matrix F;
the specific calculation expression of the load participation factor matrix is as follows:
Figure FDA0003165183310000055
in the formula (4), YLLAnd YLGBeing a sub-array of the nodal admittance matrix, YLL -1Represents YLLThe inverse matrix of (d);
YLLand YLGCan be obtained by the following formula:
Figure FDA0003165183310000056
equation (5) represents a node voltage equation written for the column after the system node is divided into two groups, i.e., a generator node and a load node, where UG、IGA column vector formed by representing the voltage and the current of all the motor nodes; u shapeL、ILA column vector formed by representing the voltage and the current of all load nodes; y isLL、YGGRepresenting a node admittance matrix formed by all load nodes and generator nodes; y isLG、YGLAnd expressing node admittance matrixes formed by the load nodes and the generator nodes and the load nodes.
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