NSGA-II algorithm-based multi-objective optimization power grid voltage reduction and energy saving method

Abstract

The invention is suitable for the technical field of power systems, and provides a multi-objective optimization power grid voltage reduction and energy saving method based on an NSGA-II algorithm, and the method comprises the following steps: 1, building a random primary population with the size of N; step 2, carrying out rapid non-dominated sorting on the initial population; 3, determining the virtual fitness by calculating the congestion distance between the individuals; 4, performing selection, crossover and variation to obtain a new offspring group with the size of N; 5, synthesizing the parent generation and the filial generation into a group with the size of 2N, and carrying out rapid non-dominated sorting; step 6, selecting the previous N individuals to form a new population according to a sorting result; and 7, repeating the steps 2-6 until a set genetic algebra is reached. According to the invention, the output of the reactive power compensation device is optimized based on the NSGA-II multi-objective optimization algorithm, so that the step-down energy-saving operation of the power system is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and in particular relates to a multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm. Background Art

[0002] With the rapid development of social economy, problems such as environmental pollution and energy shortage have emerged one after another. Electric energy has become one of the most important secondary energy sources in society today due to its cleanliness, safety and other characteristic advantages. However, in recent years, with the rapid development of the power system, its scale has increased, its structure has become increasingly complex, and users' electricity demand has also increased. Problems such as excessive load or insufficient reactive power compensation have caused many nodes in the system to have low voltages, which cannot meet the power supply quality requirements, and also cause large system line losses. With the clarification of the carbon neutrality goal, reducing social energy costs through technical means is of great significance to the low-carbon transformation of energy. Based on this, the present invention proposes a multi-objective optimization operation method for voltage reduction and energy saving of active distribution networks based on the NSGA-II algorithm. Using the load index model, the voltage reduction and energy-saving operation are achieved through the adjustment of the reactive power compensation device, so as to achieve the minimum total energy consumption of the distribution system within a period of time. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-objective optimization grid voltage reduction and energy saving method based on NSGA-II algorithm, aiming to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm includes the following steps:

[0006] Step 1: Establish a random initial population of size N;

[0007] Step 2: Perform a fast non-dominated sort on the initial population;

[0008] Step 3, determine the virtual fitness by calculating the crowding distance between individuals;

[0009] Step 4: Select, crossover and mutate to obtain a new offspring population of size N;

[0010] Step 5: Combine the parent generation and the child generation into a group of size 2N and perform a fast non-dominated sort;

[0011] Step 6: Select the first N individuals to form a new population according to the sorting results;

[0012] Step 7: Repeat steps 2 to 6 until the set genetic generation is reached.

[0013] Furthermore, the specific steps of the fast non-dominated sorting are as follows:

[0014] Step 1: Search all n in the population p =0, save it to the current set Q1;

[0015] Step 2: For each individual i in set Q1, let the set of all individuals matched by it be F i , search the set F one by one i For each individual s in s =n s -1, if n s =0, then save the individual into the set H;

[0016] Step 3: All individuals obtained in set Q1 belong to the first non-dominated layer, and set H is used as the current set.

[0017] Step 4: Repeat steps 1 to 3 until all individuals in the entire population have been graded.

[0018] Furthermore, the computational complexity of the fast non-dominated sort is O(MN 2 )+O(N 2 )=O(MN 2 ).

[0019] Furthermore, the method sets an objective function and constraints; wherein x represents a decision vector, u represents a control variable, and F1, F2, and F3 represent three objective functions; and the constraints include power flow constraints and capacitor bank output constraints.

[0020] Furthermore, the objective function F1 is to minimize the deviation between the lowest node voltage and the standard voltage, and the formula is as follows:

[0021] Formula 1: MinF1(x,u)=|U B -U min |;

[0022] Among them U B is the node standard voltage; U min is the lowest node voltage.

[0023] Furthermore, the objective function F2 is to minimize the network active power loss of the system, and the formula is as follows:

[0024]

[0025] where α N The elements of I are two nodes of adjacent connecting segments in the system; ij is the current between nodes i and j; R ijis the resistance of the line between nodes i and j; ΔU ij is the voltage drop between nodes i and j; Z ij is the branch impedance between nodes i and j.

[0026] Furthermore, the objective function F3 is a penalty function of the node voltage constraint, and the formula is as follows:

[0027] Formula 3: MinF3(x,u)=∑ i∈n |U B -U i |;

[0028] Where n is the total number of system nodes; U B is the node standard voltage; U i is the voltage at node i.

[0029] Furthermore, the expression of the power flow constraint is as follows:

[0030]

[0031] Where P i is the injected active power of node i; P Gi P is the active output of the generator; Li is the active power consumed by the load; Q i is the injected reactive power of node i; Q Gi is the reactive power output of the generator; Q Ci is the reactive power of the parallel capacitor; Q Li is the reactive power consumed by the load; U i is the voltage at node i; U j is the voltage at node j; G ij is the conductance between nodes i and j; B ij is the susceptance between nodes i and j; θ ij is the voltage phase angle difference between nodes i and j.

[0032] Furthermore, the expression of the capacitor bank output constraint is as follows:

[0033] Formula 5: C min ≤C i ≤C max ,i=1,2,...,p;

[0034] Among them C i is the reactive power generated by capacitor bank i; C min C is the minimum value of reactive power allowed to be generated by capacitor bank i; max The maximum value of reactive power allowed to be emitted by capacitor bank i.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention optimizes the output of the reactive power compensation device based on the multi-objective optimization algorithm of NSGA-II, thereby realizing the voltage reduction and energy-saving operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the present invention.

[0038] Figure 2 This is a schematic diagram of the IEEE-33 node standard test system in Example 1 of the present invention.

[0039] Figure 3 : is the voltage distribution curve (T=5) in Example 1 of the present invention.

[0040] Figure 4 1 is the voltage distribution curve in Example 1 of the present invention (T=14). DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0042] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0043] An embodiment of the present invention provides a multi-objective optimization active distribution network conservation voltage reduction (CVR) technology based on a non-dominated sorting elite strategy genetic algorithm (NSGA-II). With the clarification of the carbon neutrality goal, reducing social energy costs through technical means is of great significance to the low-carbon transformation of energy. Based on this, the present invention proposes a multi-objective optimization grid voltage reduction and energy saving method based on the NSGA-II algorithm. Using a load index model, the voltage reduction and energy-saving operation is achieved through the adjustment of the reactive compensation device, so as to achieve the minimum total energy consumption of the distribution system within a period of time.

[0044] The realization of CVR technology requires the coordinated operation of reactive compensation devices and voltage regulating equipment in the system. At the same time, considering the access of a large number of distributed power sources in the active distribution network, the discussion of the application of CVR technology in the active distribution network involves the optimal operation of reactive compensation equipment, distributed power sources, etc. The corresponding optimization objectives include voltage, network loss, load response, etc., which are converted into mathematical function models as multi-objective optimization problems, and the NSGA-II algorithm is considered to be used for solution.

[0045] CVR technology can reduce the voltage of power users to the lower half of the standard voltage range (taking the standard voltage range of 0.95pu~1.05pu as an example, 0.95pu~1.00pu is the lower half of the standard voltage range), while ensuring that no damage is caused to user equipment, while achieving the purpose of reducing system load demand and system energy loss. It was first proposed by European and American countries in the 1970s. At that time, the power supply level of European and American power grids could not keep up with the corresponding user load demand. Therefore, power outages often occurred in some areas during peak load periods. CVR technology can reduce the load demand by reducing the voltage on the user side, and economically and effectively solve the problem of insufficient power supply capacity.

[0046] NSGA-II is improved and evolved on the basis of genetic algorithm. Its biggest features are elite strategy and fast non-dominated sorting. It is these two features that make this method improve the computational efficiency and robustness on the basis of traditional genetic algorithm.

[0047] As a preferred embodiment of the present invention, regarding the fast non-dominated sorting: for an optimization problem with M objective functions, let the population size be N, the traditional non-dominated sorting method will stratify the population according to the following steps:

[0048] (1)Suppose i=1;

[0049] (2) For all j = 1, 2, ..., N and j ≠ i, the fitness function is used as the basis for judging the individual x i With individual x j To determine the mutual dominance relationship between them;

[0050] (3) If x i Better than all other individuals x except itself j , then define x j is a non-dominant individual;

[0051] (4) Let i = i + 1, and continue to search for non-dominated individuals in the process of looping steps (2) and (3) until all individuals that meet the conditions are found.

[0052] The set of non-dominated individuals obtained through the above operations is called the first-level non-dominated layer. Similarly, the set of non-dominated individuals obtained by repeating the above four steps again on the basis of ignoring the marked non-dominated individuals is called the second-level non-dominated layer. Since each individual needs to be compared with all individuals except itself, each individual needs to be compared O(MN) times in total. In the process of perfecting the first non-dominated layer, the entire population needs to be searched, and the computational complexity of this process is O(MN 2), and continue the search process until the entire population is classified. The computational complexity of the algorithm in the whole process can reach up to O(MN 3 ).

[0053] In order to reduce the complexity of the above search process, the present invention proposes a fast non-dominated sorting method. The algorithm needs to calculate two parameters of each individual p in the population P:

[0054] (1) The number of individuals n that dominate individual p in the population p ;

[0055] (2) The set S of all individuals in the population that are dominated by individual p p .

[0056] The computational complexity of determining these two parameters after a complete search of the entire population is O(MN 2 ).

[0057] The main steps of the calculation process are as follows:

[0058] (1) Search all n in the population p =0, save it to the current set Q1;

[0059] (2) For each individual i in the set Q1, let the set of all individuals that are matched with it be F i , search the set F one by one i For each individual s in s =n s -1, if n s =0, save the individual into the set H;

[0060] (3) All individuals obtained in set Q1 belong to the first non-dominated layer, and then set H is used as the current set;

[0061] (4) Repeat the above steps until all individuals in the entire population have been graded.

[0062] Each iteration in the above process requires O(N) calculations, so the maximum computational complexity of the entire generation process is O(N 2 ). Then the computational complexity of the entire algorithm is O(MN 2 )+O(N 2 )=O(MN 2 ).

[0063] As a preferred embodiment of the present invention, regarding the elite strategy: the elite retention strategy can avoid the best individuals in the parent generation from being destroyed due to crossover and mutation operations, and prevent the best individuals in the parent population from being lost in the offspring, resulting in the genetic algorithm being unable to converge to the global optimal solution. The elite strategy, i.e., the elite retention strategy, prevents the better part of the individuals in the parent generation from participating in crossover and mutation, and directly saves them to the next generation. The elite individual refers to the individual with the highest fitness value searched so far in the evolution of the population, and it has the best genetic structure and excellent characteristics. In the evolutionary process, in order to keep the size of the population unchanged, when the elite individual is added to the new generation population, the individual with the smallest fitness value in the new generation population is eliminated. The elite retention strategy effectively improves the global convergence ability of the algorithm.

[0064] As a preferred embodiment of the present invention, Figure 1 As shown, the method comprises the following steps:

[0065] Step 1: Establish a random initial population of size N;

[0066] Step 2: Perform a fast non-dominated sort on the initial population;

[0067] Step 3, determine the virtual fitness by calculating the crowding distance between individuals;

[0068] Step 4: Select, crossover and mutate to obtain a new offspring population of size N;

[0069] Step 5: Combine the parent generation and the child generation into a group of size 2N and perform a fast non-dominated sort;

[0070] Step 6: Select the first N individuals to form a new population according to the sorting results;

[0071] Step 7: Repeat steps 2 to 6 until the set genetic generation is reached.

[0072] As a preferred embodiment of the present invention, for a multi-objective optimization problem, the method sets an objective function and constraints; wherein x represents a decision vector, u represents a control variable, and F1, F2, and F3 represent three objective functions; and the constraints include a power flow constraint and a capacitor bank output constraint.

[0073] The objective function F1 is to minimize the deviation between the lowest node voltage and the standard voltage, and the formula is as follows:

[0074] Formula 1: MinF1(x,u)=|U B -U min |;

[0075] Among them U B is the node standard voltage; U minis the lowest node voltage.

[0076] The objective function F2 is to minimize the network active power loss of the system, and the formula is as follows:

[0077] Formula 2:

[0078] where α N The elements of I are two nodes of adjacent connecting segments in the system; ij is the current between nodes i and j; R ij is the resistance of the line between nodes i and j; ΔU ij is the voltage drop between nodes i and j; Z ij is the branch impedance between nodes i and j.

[0079] The objective function F3 is a penalty function of the node voltage constraint, and the formula is as follows:

[0080] Formula 3: MinF3(x,u)=∑ i∈n |U B -U i |;

[0081] Where n is the total number of system nodes; U B is the node standard voltage; U i is the voltage at node i.

[0082] The expression of the power flow constraint is as follows:

[0083] Formula 4:

[0084] Where P i is the injected active power of node i; P Gi P is the active output of the generator; Li is the active power consumed by the load; Q i is the injected reactive power of node i; Q Gi is the reactive power output of the generator; Q Ci is the reactive power of the parallel capacitor; Q Li is the reactive power consumed by the load; U i is the voltage at node i; U j is the voltage at node j; G ij is the conductance between nodes i and j; B ij is the susceptance between nodes i and j; θ ij is the voltage phase angle difference between nodes i and j.

[0085] The expression of the capacitor bank output constraint is as follows:

[0086] Formula 5: C min ≤Ci ≤C max ,i=1,2,...,p;

[0087] Among them C i is the reactive power generated by capacitor bank i; C min C is the minimum value of reactive power allowed to be generated by capacitor bank i; max The maximum value of reactive power allowed to be emitted by capacitor bank i.

[0088] Example 1. In this example, the addresses of the system access capacitors are set to 5 locations, located at nodes 2, 5, 9, 15, and 29, respectively. The capacity of the capacitor is 150 MVar. In the NSGA-II algorithm, the genetic population size is set to 500, the genetic generation is set to 100, and the proportion of crossover and mutation operations is set to 20%. The simulation includes the overall operation of 33 nodes within 24 hours. Using the method of the present invention, based on the IEEE 33 node expansion system, see Figure 2 , taking time 5 and time 14 as examples, the voltage reduction and energy saving effect of CVR technology is demonstrated. Figure 3 and Figure 4 .Depend on Figure 3 and Figure 4 It can be seen that after using the CVR technology, the node voltage levels along the feeder line have decreased to a certain extent.

[0089] The comparison of daily energy consumption before and after using CVR technology is shown in Table 1.

[0090] Table 1

[0091]

[0092] As shown in Table 1, after the system uses CVR technology, the system power consumption is reduced by 1700.54kW·h, achieving 2.96% energy saving, which proves that the proposed CVR technology has a certain energy-saving effect.

[0093] The above are only preferred embodiments of the present invention. It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention. These should also be regarded as the protection scope of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent.

Claims

1. A multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm, characterized in that: The following steps are involved: Step 1: Establish a random initial population of size N; Step 2: Perform a fast non-dominated sort on the initial population; Step 3, determine the virtual fitness by calculating the crowding distance between individuals; Step 4: Select, crossover and mutate to obtain a new offspring population of size N; Step 5: Combine the parent generation and the child generation into a group of size 2N and perform a fast non-dominated sort; Step 6: Select the first N individuals to form a new population according to the sorting results; Step 7: Repeat steps 2 to 6 until the set genetic generation is reached.

2. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 1 is characterized in that: The specific steps of the fast non-dominated sort are as follows: Step 1: Search all n in the population p =0, save it to the current set Q1; Step 2: For each individual i in set Q1, let the set of all individuals matched by it be F i , search the set F one by one i For each individual s in s =n s -1, if n s =0, then save the individual into the set H; Step 3: All individuals obtained in set Q1 belong to the first non-dominated layer, and set H is used as the current set. Step 4: Repeat steps 1 to 3 until all individuals in the entire population have been graded.

3. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 2 is characterized in that: The computational complexity of the fast non-dominated sort is O(MN 2 )+O(N 2 )=O(MN 2 ).

4. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 1 is characterized in that: The method sets an objective function and constraint conditions; wherein x represents a decision vector, u represents a control variable, and F1, F2, and F3 represent three objective functions; and the constraint conditions include a power flow constraint and a capacitor bank output constraint.

5. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 4 is characterized in that: The objective function F1 is to minimize the deviation between the lowest node voltage and the standard voltage, and the formula is as follows: Equation 1: MinF1(x,u) = |U B -U min |; Among them U B is the node standard voltage; U min is the minimum node voltage.

6. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 4 is characterized in that: The objective function F2 is to minimize the network active power loss of the system, and the formula is as follows: Formula 2: where α N The elements of I are two nodes of adjacent connecting segments in the system; ij is the current between nodes i and j; R ij is the resistance of the line between nodes i and j; ΔU ij is the voltage drop between nodes i and j; Z ij is the branch impedance between nodes i and j.

7. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 4 is characterized in that: The objective function F3 is a penalty function of the node voltage constraint, and the formula is as follows: Equation 3: MinF3(x,u) = ∑ i∈n |U B -U i |; Where n is the total number of system nodes; U B is the node standard voltage; U i is the voltage at node i.

8. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 4 is characterized in that: The expression of the power flow constraint is as follows: Formula 4: Where P i is the injected active power of node i; P Gi P is the active output of the generator; Li is the active power consumed by the load; Q i is the injected reactive power of node i; Q Gi is the reactive power output of the generator; Q Ci is the reactive power of the parallel capacitor; Q Li is the reactive power consumed by the load; U i is the voltage at node i; U j is the voltage at node j; G ij is the conductance between nodes i and j; B ij is the susceptance between nodes i and j; θ ij is the voltage phase angle difference between nodes i and j.

9. The multi-objective optimization power grid voltage reduction and energy saving method based on NSGA-II algorithm according to claim 4 is characterized in that: The expression of the capacitor bank output constraint is as follows: Formula 5: C min ≤C i ≤C max ,i=1,2,...,p; Among them C i is the reactive power generated by capacitor bank i; C min C is the minimum value of reactive power allowed to be generated by capacitor bank i; max The maximum value of reactive power allowed to be emitted by capacitor bank i.

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