CN112329210A - Solving method for quadratic form optimal load tracking model of power price driving of power system - Google Patents

Solving method for quadratic form optimal load tracking model of power price driving of power system Download PDF

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CN112329210A
CN112329210A CN202011114425.7A CN202011114425A CN112329210A CN 112329210 A CN112329210 A CN 112329210A CN 202011114425 A CN202011114425 A CN 202011114425A CN 112329210 A CN112329210 A CN 112329210A
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竺迪
秦晓多
张笑天
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Suzhou Yingmaifei Intelligent Technology Co ltd
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Abstract

The invention discloses a solving method of a quadratic optimal load tracking model driven by power price of a power system, which comprises the following steps: s1, aiming at the mathematical characteristics of a quadratic optimal load curve tracking model of the power system, applying the idea of information fusion estimation and designing an estimation algorithm for solving an electric energy price sequence by combining reverse order rollback and forward order recursion; s2, under the drive of an electricity price sequence, a quadratic optimum tracking model with the electricity price as a decision variable is established, and accurate tracking of the power output to the system load is realized; s3, constructing a power flow overrun quadratic term in the objective function, and designing a self-adaptive adjustment mechanism of the power flow weight during solving; and aiming at the power flow overrun with different severity degrees, an appropriate weight value is obtained in an iterative manner, and the output of the distributed power supply driven by the optimal electricity price sequence is ensured to meet the power flow constraint. The actual physical meaning of each weight in the model is more definite, the actual concept of each covariance matrix in the solution algorithm is clearer, and the program has stronger interpretability.

Description

Solving method for quadratic form optimal load tracking model of power price driving of power system
Technical Field
The invention relates to the technical field of optimal load tracking models of power systems, in particular to a quadratic optimal load tracking model solving method for power price driving of a power system.
Background
Various power loads in the power system change along with time, and the power load is the basis for scheduling power of the power system and planning the power system. Due to the constraint of physical laws, in order to ensure the frequency and voltage stability of power supply, the power system must ensure the real-time balance of the relation between supply and demand, i.e. the accurate tracking of the power output to the system load. The traditional power system adopts a top-down scheduling mode: the power supply adjusts the generated output under the control of a system scheduling instruction, and tracks and predicts a load curve. The power supply and demand balance is realized by the dispatching instruction mode, so that the power supply and demand balance is simple and effective, but the income condition of the power supply as an economic main body is ignored, and the positivity of the power supply for responding to the dispatching instruction is not considered. Therefore, the established model does not conform to the new trend of the market-oriented innovation of the power system.
Under the new situation of the electric power market, the income condition of the power supply as a market main body must be fully considered, the electric energy price should be fully utilized, and the guidance control is applied to the generating behavior of the controllable power supply by a marketization means, so that the physical significance of the conventional commercial solver is not clear enough, the solving process is not transparent enough, the interpretability is poor, and the like.
In order to solve the problems, an optimal method for solving an electric energy price sequence needs to be researched, the method applies proper electric energy price to each controllable power supply through a system, a quadratic optimal load tracking model is driven by the electric price of an electric power system, the actual physical meaning of each weight in the model is more definite according to the tracked electric energy price sequence, the actual concept of each covariance matrix in a solving algorithm is clear, a program has stronger interpretability, and the method is suitable for different actual scene requirements.
Disclosure of Invention
In view of the above, the present invention aims to provide a method for solving a quadratic optimal load tracking model driven by electricity price of a power system, so as to solve the problems that the physical significance of the existing commercial solver is not clear enough, the solving process is not transparent enough, the interpretability is poor, and the like.
In order to achieve the purpose, the invention adopts the technical scheme that: a solving method of a quadratic form optimal load tracking model driven by power price of a power system comprises the following specific steps:
s1, aiming at mathematical characteristics of a quadratic optimal load curve tracking model of the power system, applying the idea of multi-source information fusion estimation, and designing an optimal estimation algorithm for solving an electric energy price sequence by combining reverse order rollback and forward order recursion;
s2, under the drive of an electricity price sequence, a quadratic optimal tracking model with the electricity price as a decision variable is established, and the electricity generation output is guided by actively changing the electricity price, so that the accurate tracking of the distributed power output on the system load is realized;
s3, constructing a power flow overrun quadratic term in the objective function, and designing a self-adaptive adjustment mechanism of the power flow weight during solving; and aiming at the power flow overrun with different severity degrees, an appropriate weight value is obtained in an iterative manner, and the output of the distributed power supply driven by the optimal electricity price sequence is ensured to meet the power flow constraint.
In a preferred embodiment of the present invention, in S1, the optimal estimation algorithm for solving the electric energy price sequence is: for the state χ, measured using M sensors, there is ζm＝Γmχm+emM is 1, …, M, wherein, ζm,emThe measurement results of m pairs of states x of the sensor and the error, gamma, thereofmFor the information transfer matrix of sensor m, the error e is measuredmSatisfies the mathematical expectation E (E) for a white noise sequencem) 0, covariance
Figure BDA0002726040280000021
The optimal information fusion estimate for the state χ is
Figure BDA0002726040280000022
Wherein the content of the first and second substances,
Figure BDA0002726040280000023
for measuring zetamThe amount of information about the state χ contained in (a).
In a preferred embodiment of the present invention, in S2, the quadratic optimal tracking model with the price of electric energy as the decision variable is:
Figure BDA0002726040280000024
wherein C is a vector of all 1 s, and the decision variable is the electric energy price lambdak。
In a preferred embodiment of the present invention, the objective function satisfies the minimization of deviation of the actual electricity price from the reference base price and the minimization of tracking error of the generated output to the load curve.
In a preferred embodiment of the present invention, the minimum satisfying condition of the deviation between the actual electricity price and the reference price is: lambda [ alpha ]*＝λk+rkWherein r iskIs white noise with a covariance of R-1The optimal estimation of the price of electric energy is
Figure BDA0002726040280000031
The minimum requirement of the tracking error of the generated output to the load curve is as follows:
Figure BDA0002726040280000032
wherein h iskIs white noise with covariance of H-1。
In a preferred embodiment of the present invention, the calculation is performed in a solution algorithm,
Figure BDA0002726040280000033
Pj＝CTHC+AT[(Pj+1)-1+BR-1BT]a, wherein j ═ N, N-1, …, k +1 with the initial condition PN+1＝CTHC+AT[εIn+BR-1BT]A，
Figure BDA0002726040280000034
Wherein, InIs an n-order identity matrix, and epsilon is a correction factor for avoiding matrix singularity.
In a preferred embodiment of the present invention, in S3, the two quadratic terms are respectively the minimum tracking error of the generated output to the system load and the minimum tracking error of the electric energy price to the reference standard, when the power transmission line is congested, the upper limit of the line capacity, that is, the current constraint, is considered, and one term is added to the objective function as:
Figure BDA0002726040280000035
wherein S is a line tide weight matrix and is a diagonal, and each element on the diagonal is each line weight in turn; f is the impedance matrix of the power grid, and psi is the power flow of each line.
In a preferred embodiment of the invention, the corresponding solving algorithm adopts an iterative adaptive adjustment weight matrix, the initial value of the weight is small, and the optimization of two targets is not influenced; and when the power flow of a certain line exceeds the limit, gradually increasing the weight of the certain line, and repeating the iteration for multiple times until the power flow constraint of the line is met.
In a preferred embodiment of the present invention, the pseudo code of the corresponding solution algorithm is:
step 1: setting a weight matrix H, S, R and the maximum iteration number ncmax；
Step 2: the iteration serial number nc is equal to 1, and the power flow out-of-limit zone bit ov is equal to 0;
and step 3: inputting each state vector q, q*Calculating
Figure BDA0002726040280000036
And 4, step 4: successive calculation in reverse order
Figure BDA0002726040280000041
j＝N,…,1；
And 5: successive calculation of positive sequence
Figure BDA0002726040280000042
k＝1,…,N-1；
Step 6: calculating the power flow of each line, and if the power flow of the line i exceeds the limit: setting the load flow out-of-limit zone bit ov to 1 (setting), and expanding S according to the corresponding weighti,i←κSi,iOtherwise: the load flow out-of-limit zone bit ov is equal to 0 (reset), and the weight is reduced
Figure BDA0002726040280000043
And 7: if nc > ncmaxOr ov ═ 0: finishing; otherwise: go back to step 4.
The invention solves the defects in the background technology, and has the following beneficial effects:
(1) according to the method, the idea of multi-source information fusion estimation is used for solving the electric energy price sequence tracked by aiming at the quadratic optimal load curve, the actual physical meaning of each weight in the model is more definite, and the actual concept of each covariance matrix in the solution algorithm is clearer.
(2) The method is different from the solving process of a common commercial solver black box type, the algorithm is established on the basis of clear physical significance, the solving process is completely transparent, and the program has stronger interpretability; therefore, the system can be flexibly modified or expanded according to the actual scene needs.
(3) The method aims at the electric energy price sequence model tracked by the quadratic optimal load curve, fully considers the income condition of the power supply as a market main body, fully utilizes the electric energy price, applies guide control to the power generation behavior of the controllable power supply by a marketization means, and takes the electric energy price as a decision so as to realize the accurate tracking of the total power generation amount to the system load.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a 24h supply and demand graph for a power system of comparative example 1 in example 1;
FIG. 2 is a graph of the results of the algorithm solution of comparative example 2 in example 1 at different segment lengths;
FIG. 3 is a graph of the effect of different renewable power generation ratios on the results of the algorithm solution for comparative example 3 in example 1;
FIG. 4 is a 72-hour power flow graph showing different transmission capacities of a #54 line and a #96 line of comparative example 4 in example 1;
fig. 5 is a 72-hour power flow graph showing the #8 line and the #121 line under different transmission capacities of the comparative example 5 in the example 1;
fig. 6 is a histogram of the average power price of 72h at the node where 9 controllable power sources are located in embodiment 1.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
In the description of the present application, it is to be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in the orientation or positional relationship indicated in the drawings for convenience in describing the present application and for simplicity in description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated in a particular manner, and are not to be considered limiting of the scope of the present application. Furthermore, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first," "second," etc. may explicitly or implicitly include one or more of that feature. In the description of the invention, the meaning of "a plurality" is two or more unless otherwise specified.
In the description of the present application, it is to be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art through specific situations.
A solving method of a quadratic form optimal load tracking model driven by power price of a power system comprises the following specific steps:
s1, aiming at mathematical characteristics of a quadratic optimal load curve tracking model of the power system, applying the idea of multi-source information fusion estimation, and designing an optimal estimation algorithm for solving an electric energy price sequence by combining reverse order rollback and forward order recursion;
s2, under the drive of an electricity price sequence, a quadratic optimal tracking model with the electricity price as a decision variable is established, and the electricity generation output is guided by actively changing the electricity price, so that the accurate tracking of the distributed power output on the system load is realized;
s3, constructing a power flow overrun quadratic term in the objective function, and designing a self-adaptive adjustment mechanism of the power flow weight during solving; and aiming at the power flow overrun with different severity degrees, an appropriate weight value is obtained in an iterative manner, and the output of the distributed power supply driven by the optimal electricity price sequence is ensured to meet the power flow constraint.
In S1, the optimal estimation algorithm for solving the power price sequence of the present invention is: for the state χ, measured using M sensors, there is ζm＝Γmχm+emM is 1, …, M, wherein, ζm,emThe measurement results of m pairs of states x of the sensor and the error, gamma, thereofmFor the information transfer matrix of sensor m, the error e is measuredmSatisfies the mathematical expectation E (E) for a white noise sequencem) 0, covariance
Figure BDA0002726040280000061
The optimal information fusion estimate for the state χ is
Figure BDA0002726040280000071
Wherein the content of the first and second substances,
Figure BDA0002726040280000072
for measuring zetamThe amount of information about the state χ contained in (a).
In S2, the quadratic optimal tracking model using the electric energy price as the decision variable is as follows:
Figure BDA0002726040280000073
wherein C is a vector of all 1 s, and the decision variable is the electric energy price lambdak。
The target function of the invention meets the minimum deviation between the actual electricity price and the reference standard price and the minimum tracking error of the generated output to the load curve.
The minimum satisfying condition of the deviation between the actual electricity price and the reference standard price is as follows: lambda [ alpha ]*＝λk+rkWherein r iskIs white noise with a covariance of R-1The optimal estimation of the price of electric energy is
Figure BDA0002726040280000074
Satisfaction condition for minimizing tracking error of generated output to load curveComprises the following steps:
Figure BDA0002726040280000075
wherein h iskIs white noise with covariance of H-1。
The present invention requires computation in the solution algorithm of the tracking model,
Figure BDA0002726040280000076
Pj＝CTHC+AT[(Pj+1)-1+BR-1BT]a, wherein j ═ N, N-1, …, k +1 with the initial condition PN+1＝CTHC+AT[εIn+BR-1BT]A，
Figure BDA0002726040280000077
Wherein, InIs an n-order identity matrix, and epsilon is a correction factor for avoiding matrix singularity.
In S3, two quadratic terms are respectively the minimum tracking error of the generated output to the system load and the electric energy price to the reference standard, when the power transmission line is congested, the upper limit of the line capacity, namely the current constraint, is considered, and one term is added into the objective function as follows:
Figure BDA0002726040280000078
wherein S is a line tide weight matrix and is a diagonal, and each element on the diagonal is each line weight in turn; f is the impedance matrix of the power grid, and psi is the power flow of each line.
The corresponding solving algorithm of the invention adopts an iterative adaptive adjustment weight matrix, the initial weight value is small, and the optimization of two targets is not influenced; and when the power flow of a certain line exceeds the limit, gradually increasing the weight of the certain line, and repeating the iteration for multiple times until the power flow constraint of the line is met.
The corresponding pseudo code of the solving algorithm of the invention is as follows:
step 1: setting a weight matrix H, S, R and the maximum iteration number ncmax；
Step 2: the iteration serial number nc is equal to 1, and the power flow out-of-limit zone bit ov is equal to 0;
and step 3: inputting each state vector q, q*Calculating
Figure BDA0002726040280000081
And 4, step 4: successive calculation in reverse order
Figure BDA0002726040280000082
j＝N,…,1；
And 5: successive calculation of positive sequence
Figure BDA0002726040280000083
k＝1,…,N-1；
Step 6: calculating the power flow of each line, and if the power flow of the line i exceeds the limit: setting the load flow out-of-limit zone bit ov to 1 (setting), and expanding S according to the corresponding weighti,i←κSi,iOtherwise: the load flow out-of-limit zone bit ov is equal to 0 (reset), and the weight is reduced
Figure BDA0002726040280000084
And 7: if nc > ncmaxOr ov ═ 0: finishing; otherwise: go back to step 4.
Example 1
Example 1 the algorithm can be flexibly applied to the situations of various power flow constraints through the test results of a plurality of groups of comparative examples.
Comparative example 1, a small electric power system is taken as an example, comprising 3 controllable power sources and 1 renewable power source. Each time interval is 15 minutes, and then 24 hours are carried out for 96 time intervals, referring to fig. 1, a 24h supply and demand curve of a certain power system; the system load, the renewable power output and the controllable power output are respectively shown in fig. 1, and the tracking error of the system load caused by the various power outputs is shown by a label x. The system load is in the order of magnitude of 50MW, the output of the renewable power supply is in the order of magnitude of 10MW, and the tracking errors in 24 hours are all +/-5 multiplied by 10-6Within kW.
Comparative example 2, with reference to fig. 2, is the effect of different segment lengths on the algorithm solution. The abscissa is divided into 1, 2, 3, 4, 6 and 12 time periods (i.e. the time periods are 1h, 30min, 20min, 15min, 10min and 5min) in one hour, and the algorithm solution results under different time periods are obtained. The shorter the visible time period is, the better the solution result of the algorithm is: the tracking error is reduced and the electric energy price is reduced. But the improvement of the solution quality mainly occurs when the time interval length is shortened from 1h to 30 min; after the period length was below 20min, although there was still improvement, the magnitude of the improvement was no longer significant; meanwhile, due to the fact that the time interval length is shortened, the solving frequency of the optimization problem is remarkably improved (when the optimization problem is the most serious, the optimization problem needs to be solved once every 5min), and therefore higher requirements are provided for the solving speed of the algorithm.
Comparative example 3, with reference to fig. 3, the effect on the algorithm solution results for different renewable power generation ratios. The abscissa is 5%, 10%, 15%, 20%, 25%, 30% of the total load of the system for renewable power generation. As the renewable power generation ratio increases, the solution results of the algorithm become worse: increased tracking error and increased electricity price. This is because with the increase of renewable power generation, the uncertainty of the system increases, and the difficulty in realizing the balance of supply and demand increases; under the marketization condition, the output of the controllable power supply can be adjusted according to the renewable power generation fluctuation only by using higher electric energy price.
Comparative example 4, taking an IEEE-118 node system as an example, and assuming that there is a power flow constraint in the #54 line and the #96 line, as shown in fig. 4, a 72-hour power flow curve representing the #54 line and the #96 line under different transmission capacities is shown. When the transmission capacity is infinite (inf), the current in both lines is a free-running curve. With the gradual reduction of transmission capacity, it can be seen that the power flows in the #54 line and the #96 line are limited to 400MW and 350MW, 380MW and 300MW, 200MW and 150MW at the highest.
Comparative example 5, assuming that there is a power flow constraint in the #8 line and the #121 line, as shown in fig. 5, 72-hour power flow curves of the #8 line and the #121 line are respectively shown under different transmission capacities. When the transmission capacity is infinite (inf), the current in both lines is a free-running curve. As transmission capacity is scaled down, it can be seen that the power flow in lines #8 and #121 is limited to 900MW and 800MW, 830MW and 750MW, 620MW and 700MW, at the highest.
Therefore, through the multiple groups of test results in comparative examples 1-5, it is verified that the algorithm can be flexibly applied to the situations of multiple power flow constraints, and for the four line power flow constraints in fig. 4, as shown in fig. 6, 72h average electric energy prices of the nodes where 9 controllable power supplies are located are respectively given. Therefore, along with the gradual tightening of the power flow constraint, the difference of the electric energy prices among different nodes becomes more and more obvious, and the capacity of realizing the congestion management of the power transmission line by taking the electric energy prices as means of a model and an algorithm is displayed.
In light of the foregoing description of the preferred embodiment of the present invention, it is to be understood that various changes and modifications may be made by one skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (9)

1. A solving method of a quadratic form optimal load tracking model driven by power price of a power system comprises the following specific steps:
s1, aiming at mathematical characteristics of a quadratic optimal load curve tracking model of the power system, applying the idea of multi-source information fusion estimation, and designing an optimal estimation algorithm for solving an electric energy price sequence by combining reverse order rollback and forward order recursion;
s2, under the drive of an electricity price sequence, a quadratic optimal tracking model with the electricity price as a decision variable is established, and the electricity generation output is guided by actively changing the electricity price, so that the accurate tracking of the distributed power output on the system load is realized;
s3, constructing a power flow overrun quadratic term in the objective function, and designing a self-adaptive adjustment mechanism of the power flow weight during solving; and aiming at the power flow overrun with different severity degrees, an appropriate weight value is obtained in an iterative manner, and the output of the distributed power supply driven by the optimal electricity price sequence is ensured to meet the power flow constraint.
2. The method for solving the quadratic form optimal load tracking model driven by the electricity price of the power system according to claim 1, characterized in that: in S1, the optimal estimation algorithm for solving the power price sequence is: to pairAt state χ, measured using M sensors, having ζm＝Γmχm+emM is 1, …, M, wherein, ζm,emThe measurement results of m pairs of states x of the sensor and the error, gamma, thereofmFor the information transfer matrix of sensor m, the error e is measuredmSatisfies the mathematical expectation E (E) for a white noise sequencem) 0, covariance
Figure FDA0002726040270000011
The optimal information fusion estimate for the state χ is
Figure FDA0002726040270000012
Wherein the content of the first and second substances,
Figure FDA0002726040270000013
for measuring zetamThe amount of information about the state χ contained in (a).
3. The method for solving the quadratic form optimal load tracking model driven by the electricity price of the power system according to claim 1, characterized in that: in S2, the quadratic optimal tracking model using the price of electric energy as a decision variable is:
Figure FDA0002726040270000021
wherein C is a vector of all 1 s, and the decision variable is the electric energy price lambdak。
4. The method for solving the quadratic form optimal load tracking model driven by the electricity price of the power system according to claim 1, characterized in that: in S3, the objective function satisfies 2 conditions: the deviation of the actual electricity price from the reference base price is minimized and the tracking error of the generated output to the load curve is minimized.
5. The method for solving the quadratic form optimal load tracking model driven by the electricity price of the power system according to claim 4, characterized in that:the satisfaction condition for minimizing the deviation of the actual electricity price from the reference base price is as follows: lambda [ alpha ]*＝λk+rkWherein r iskIs white noise with a covariance of R-1The optimal estimate of the price of electrical energy is:
Figure FDA0002726040270000022
the minimum requirement of the tracking error of the generated output to the load curve is as follows:
Figure FDA0002726040270000023
wherein h iskIs white noise with covariance of H-1。
6. The method for solving the quadratic form optimal load tracking model driven by the electricity price of the power system according to claim 5, characterized in that: it is calculated in the solution algorithm that,
Figure FDA0002726040270000024
Pj＝CTHC+AT[(Pj+1)-1+BR-1BT]a, wherein j ═ N, N-1, …, k +1 with the initial condition PN+1＝CTHC+AT[εIn+BR-1BT]A，
Figure FDA0002726040270000025
Wherein, InIs an n-order identity matrix, and epsilon is a correction factor for avoiding matrix singularity.
7. The method for solving the quadratic optimal load tracking model driven by the electricity price of the power system according to claim 1 or 3, characterized in that: in S3, the two quadratic terms are respectively the minimum tracking error of the generated output to the system load and the electric energy price to the reference standard, when the power transmission line is congested, the upper limit of the line capacity, that is, the current constraint, is considered, and one term is added to the objective function as follows:
Figure FDA0002726040270000026
wherein S is a line tide weight matrix and is a diagonal, and each element on the diagonal is each line weight in turn; f is the impedance matrix of the power grid, and psi is the power flow of each line.
8. The method for solving the quadratic optimal load tracking model driven by the electricity price of the power system according to claim 1 or 3, characterized in that: the corresponding solving algorithm adopts an iterative adaptive adjustment weight matrix, the initial weight value is small, and the optimization of two targets is not influenced; and when the power flow of a certain line exceeds the limit, gradually increasing the weight of the certain line, and repeating the iteration for multiple times until the power flow constraint of the line is met.
9. The method for solving the quadratic optimal load tracking model driven by the electricity price of the power system according to claim 1 or 3, characterized in that: the corresponding pseudo code of the solving algorithm is:
step 1: setting a weight matrix H, S, R and the maximum iteration number ncmax；
Step 2: the iteration serial number nc is equal to 1, and the power flow out-of-limit zone bit ov is equal to 0;
and step 3: inputting each state vector q, q*Calculate PN+1,
Figure FDA0002726040270000031
And 4, step 4: successive calculation in reverse order
Figure FDA0002726040270000032
And 5: successive calculation of positive sequence
Figure FDA0002726040270000033
Step 6: calculating the power flow of each line, and if the power flow of the line i exceeds the limit: setting the load flow out-of-limit zone bit ov to 1 (setting), and expanding S according to the corresponding weighti,i←κSi,iOtherwise: the power flow threshold crossing flag bit ov is 0 (complex)Bits), weight reduction
Figure FDA0002726040270000034
And 7: if nc > ncmaxOr ov ═ 0: finishing; otherwise: go back to step 4.
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