CN105071433A - Optimal configuration scheme of distributed power supply - Google Patents

Abstract

The invention discloses an optimal configuration scheme of a distributed power supply. From the perspective of planning, the invention mainly considers the interests of power distribution operators and takes into account the randomness of wind power generation. A multi-objective optimal configuration model composed of the minimum power loss, the minimum total voltage deviation, and the minimum risk cost; the fuzzy set theory is used to realize the normalization of multiple objectives, and there is no longer the problem of different sub-objective dimensions; The optimal configuration model is solved by adaptive mutation particle swarm optimization algorithm. Because of the introduction of mutation operation, the situation that the basic particle swarm optimization algorithm is easy to fall into local optimum is improved. Finally, the IEEE? The 33-node power distribution system verifies the optimal configuration model of DG proposed in this paper and the selected AMPSO. The simulation results show that the model and algorithm used in this paper are feasible and effective.

Description

An Optimal Configuration Scheme for Distributed Power

technical field

The invention relates to an optimal configuration scheme of a distributed power supply, which belongs to the technical field of power systems.

Background technique

Due to its high efficiency, small investment scale, reduced network loss, flexible power generation methods, diverse energy types, and environmental protection, distributed power sources are increasingly connected to the distribution network for grid-connected operation. Distributed power supply can be installed in the load center to track load changes in a timely manner. Compared with centralized power supply, it is more economical during the peak period of power consumption. The joint operation of distributed power supply and centralized power supply can save power transmission and transformation investment, stabilize voltage, Reduce energy consumption, improve power quality, power supply reliability, flexibility and security of power system operation.

The position and access power capacity of DG connected to the distribution network will have a certain impact on its planning and operation, such as affecting the system voltage distribution, voltage stability, short-circuit current, operating status, relay protection, etc., reasonably determined The access position and access power capacity of DG play a very important role in improving the efficiency and safe and stable operation of the distribution network. The main content of DG optimal configuration is to determine the entry location and access power capacity, and minimize the impact of DG access on the normal operation of the distribution network.

However, the traditional distributed power optimization configuration generally only considers a single aspect of economy or technology, and cannot comprehensively consider multiple objectives, which has certain limitations.

Contents of the invention

The purpose of the present invention is to provide an optimized configuration scheme for distributed power sources in view of the defects of the prior art, and to provide a new method for the existing distributed power sources to connect to the distribution network, so as to overcome the deficiencies of the prior art .

Technical scheme of the present invention

An optimal configuration scheme of distributed power generation. From the perspective of planning, this method mainly considers the interests of power distribution operators and the randomness of distributed power generation output. The optimal configuration of distributed power generation is studied, that is, to solve For the grid position and capacity of distributed electric energy, a multi-objective optimal configuration model consisting of the smallest active power loss, the smallest total voltage deviation, and the smallest risk cost of the distribution network is established, and constraints are set and optimized for the above multi-objective optimal configuration model. ; Using fuzzy set theory to realize the normalization of multi-objectives, coordinate the relationship between each sub-objective well, and then achieve the effect of overall optimization; solve it by adaptive mutation particle swarm algorithm.

In the above-mentioned optimal configuration scheme of a distributed power supply, the multi-objective optimal configuration model specifically includes the following:

1. Minimal active power loss;

The voltage level of the distribution network is low, and the R/X value is relatively large, so the network loss is relatively large in the power flow calculation. Reasonable access to distributed electric energy can reduce the network loss. Therefore, the minimum network loss can be used as the objective function. Bring better economic benefits. Since this article starts from the perspective of planning, the minimum active power loss is the optimization goal. The objective function of the minimum active power loss is:

$\mathrm{<span\; class="notranslate">\; min</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}$

In the formula: I _i is the current of branch i; N is the total number of branches of the system; R _i is the resistance of the branch, and h is the number of hours in the planning period.

2. The optimization target model with the smallest total voltage deviation is;

The crossing of the node voltage amplitude will affect the normal work of users and the safety of the system. Therefore, taking the total node voltage deviation as the objective function can make the node voltage closer to the reference value, guarantee the voltage level of the distribution network, and achieve The effect of improving voltage quality. The objective function with the minimum total voltage deviation is:

$\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>$

In the formula: DetV is the total voltage deviation; N is the number of network nodes; U _b is the reference voltage; U _i is the voltage value of the i-th node.

3. The risk cost is minimal;

Distributed power generation of renewable energy such as wind power generation and photovoltaic power generation is susceptible to the natural environment or other factors, making its output characterized by randomness, volatility, and uncertainty. Therefore, this paper uses risk costs to reflect the existence of distributed power generation output. Randomness, when the power generation of distributed power generation does not reach the expected value, it is characterized by the cost of power supply through the grid, that is, the superior power supply. The objective function of the risk cost is:

C _risk ＝P·C·t·n

In the formula: P is the probability that the output of the DG with randomness is less than the expected output; C is the cost of power supply from the superior power supply when the output of the DG is less than the expected output; t is the annual operation time of the DG; n is the planned number of years.

In the above-mentioned optimal configuration scheme for distributed power sources, the constraints of the multi-objective optimal configuration model are inequality constraints, and include node voltage constraints, distributed power access constraints, and branch current constraints.

1. Node voltage constraints

According to the technical principles of power grid operation in my country, the upper and lower limits of the node voltage in the 10kV power grid must be between 1.07p.u. and 0.93p.u. After accessing distributed electric energy, the local voltage may exceed the limit. Therefore, it is necessary to ensure that the node voltage meets the corresponding limit conditions. The node voltage constraints are:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ...</span>\mathrm{<span\; class="notranslate">\; ..</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>$

In the formula: are the lowest and highest voltages of node i respectively, and N is the number of network nodes.

2. Capacity constraints of distributed power access to electric energy

Distributed power generation is not subject to grid scheduling because of its output and start-up and stop. When the distribution network is connected to excessively large-capacity distributed power, it will cause a great impact on users. In order to control the distribution network due to the access of distributed power The influence of distributed electric energy needs to be restricted, as follows:

ΣS _DG ≤ηΣS _LD

In the formula: S _DG is the total capacity of distributed electric energy connected to the distribution network; S _LD is the total system load; η is the upper limit of the ratio of the total capacity of distributed electric energy to the total system load, and the value of η in this paper is 0.4 .

3. Current Constraint

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; max</span>}}$

In the formula: It is the upper limit of the current allowed to pass through for the i-th branch.

The equality constraints are the nodal power flow equations:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.$

where P _i is the injected active power of node i; Q _i is the injected reactive power of node i; G _ij is the conductance between nodes i and j; B _ij is the susceptance between nodes i and j; _i and U _j are the voltage amplitudes of node i and node j respectively.

In the above-mentioned optimal configuration scheme of a distributed power supply, the method of using fuzzy set theory to realize multi-objective normalization first improves the poor index by maximizing the minimum value of the membership degree of the multi-objective, To achieve the purpose of improving the overall performance of the system, the membership function used is a split line function. For optimization with multiple objective functions, each optimization objective is often contradictory and it is difficult to achieve the optimum at the same time. The importance of each optimization objective In the case of the same characteristics, the maximum satisfaction method is usually used to solve the problem, that is, the greater the minimum value of the membership function of the optimization target, the greater the overall satisfaction.

The specific multi-objective normalization method is as follows: due to the different dimensions of active power loss, total voltage deviation and risk cost, when using the weight coefficient method, the weight coefficient is not easy to determine, and the result obtained through optimization may be made up of poor indicators by good indicators obtained, the effect of overall optimization cannot be achieved. Therefore, this paper uses fuzzy set theory to realize the normalization of multi-objectives, and improves the poor index by maximizing the minimum value of the membership degree, so as to achieve the purpose of improving the overall performance of the system.

1. The membership function of the optimization objective

The requirements of decision makers on the objective function can be reflected by different membership functions. The more commonly used membership functions mainly include: piecewise linear function, power exponent, hyperbola, linear and inverse hyperbola, etc. For the above functions, linear and piecewise linear functions are more commonly used, mainly because inverse hyperbolic, hyperbolic and power exponents will increase the nonlinear characteristics of the decision-making process, making the solution more difficult. In this paper A piecewise linear function is selected as the membership function to optimize each sub-objective. The membership function is shown in Figure 1, and the specific function form is as follows:

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}}& {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right.$

In the formula: μ _i is the membership degree of the objective function f _i , and the value is in [0,1]. When the membership degree is 1, it means that the decision maker is completely satisfied with the optimization result; when the membership degree is 0, it means that the decision-making Those who are completely dissatisfied with the optimization results; f _i ^* is the expected value of the objective function; f _i ^max is the limit value of the objective function.

2. Multi-objective normalization

For optimization with multiple objective functions, each optimization objective is often contradictory and it is difficult to achieve the optimum at the same time. Therefore, generally in practical applications, each optimization objective is only required to achieve the optimal value as much as possible. When the importance of each optimization objective is the same, the maximum satisfaction method [62] is usually used to solve the problem. Overall satisfaction is defined as:

M=min{μ ₁ ,μ ₂ ,μ ₃ }

It can be seen from the above formula that the greater the minimum value of the membership function of the optimization objective, the greater the overall satisfaction. No matter how the membership function values of the other two optimization objectives change, their membership function values must not be higher than the minimum The value of the membership function is even smaller, so that the overall performance can be improved by increasing the minimum membership function value, so that the whole can be optimized. Then, under the corresponding constraint conditions, the original multi-objective optimization problem is transformed into the problem of maximizing the M value of the overall satisfaction:

maxM=min{μ ₁ , μ ₂ , μ ₃ }.

In the above-mentioned optimal configuration scheme of distributed power supply, the optimal configuration algorithm of distributed power supply is solved by adaptive mutation particle swarm optimization algorithm, as follows:

1. Basic particle swarm algorithm

Assuming that the particle swarm optimization algorithm searches in an N-dimensional space, the algorithm will generate a group of random particles after initialization, and each particle has a corresponding N-dimensional vector X _i =(x ₁ ,x ₂ ,x ₃ . ..., x _iN ) and V _i = (v ₁ , v ₂ , v ₃ ......, v _iN ) represent the position and velocity. Each particle can judge whether the particle is good or bad by comparing the fitness function value obtained through calculation, and evolve by constantly changing its position and speed until the global optimal solution is found. The optimal position searched by the particle in each iteration is denoted as p _best , and the optimal position searched by the entire population is denoted as g _best .

For each iteration, the velocity and position of the particles in the population are updated by the following equation:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right.$

(4-1)

In the formula: n represents the nth dimension of the N-dimensional solution space, n=l, 2, 3,..., N; k is the number of iterations; ω is the inertia weight, which is a non-negative constant; r ₁ and r ₂ are in A random number generated between [0,1]; c ₁ and c ₂ are acceleration factors, usually c ₁ =c ₂ =2.

From the formula (4-1), it can be seen that the speed change of the particle is divided into three parts: the first part Indicates the impact of the particle's velocity at the last moment on the current velocity, and has the ability to balance local and global searches, called motion inertia; the second part Indicates the self-thinking of the particle during the search process, and guides the particle to move towards the individual optimal position, which is the self-cognition part of the particle; the third part Indicates the sharing of information between particles, and guides the particles to move towards the optimal position of the group, which is the social cognition part of the particles. Through these three parts, the particle constantly changes its position according to its own experience and the experience of the population.

As a parameter in PSO, the inertia weight ω plays a very important role. It mainly characterizes the ability of the particle's inertia to affect the velocity, and introduces it into the global and local search capabilities that can control the algorithm. The larger the value of ω, the larger the search space of the particle, it is possible to expand to a new area for searching, and the global search ability is stronger; Perform a more detailed search around; when ω is 0, the particle loses its memory function, and the current speed will have nothing to do with the speed at the last moment, so the update of the particle position is only determined by the individual optimal value and the global optimal value. Location decides.

Therefore, let ω self-adaptively decrease linearly with the iterative process of the algorithm, thereby significantly improving the convergence performance of the algorithm. Using linearly decreasing weights can make the inertia weight well controlled. The k-th iteration ω is:

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

(4-2)

In the formula: ω _min and ω _max are the minimum and maximum inertia weights respectively; N is the maximum number of iterations.

The particle swarm optimization algorithm mainly follows the following five basic principles:

l) Proximity principle: Particle swarms must be able to perform simple space and time calculations;

2) Quality principle (quality): the particle swarm must be able to respond to the quality factors of the surrounding environment;

3) Diversity principle (diverseresP0nse): particle swarms should not behave in too narrow a range;

4) Qualitative principle (stability): particle swarms should not change their behavior every time the environment changes;

5) The principle of adaptability (adaptability): under an acceptable amount of calculation, particle swarms must be able to change their behavior at an appropriate time.

The basic steps of particle swarm algorithm are as follows:

1) Randomly generate the position and velocity of each particle in the population in N-dimensional space.

2) Calculate the fitness function value of each particle according to the fitness function, store the current position and fitness function value of each particle in p _best , store the position and fitness of the optimal particle in the population in g _best function value.

3) Update the velocity and position of each particle according to formula (4-1).

4) Compare the fitness value of each particle with the p _best of the particle, if it is better than p _best , replace p _best with the current particle value, otherwise it remains unchanged; compare the current p _best with the population optimal value g _best For comparison, if it is better than g _best , replace g _best with p _best , otherwise it remains unchanged.

5) If the convergence condition is met, stop searching and output the global optimal solution, otherwise turn to step 2).

2. Adaptive Mutation Particle Swarm Algorithm

If the algorithm is stuck in a local optimum, mutation operation can be performed to search other spaces to find the optimal solution, and it is possible to find new p _best and g _best in other spaces, and continue to cycle until the global optimal solution is found. Based on this idea, Adaptive Mutation Particle Swarm Optimization (AMPSO) uses the fitness variance of the population to judge the degree of convergence of the algorithm, thereby adaptively changing the mutation probability, and using the method of random disturbance to adjust the global extreme value. mutation operation.

(1) Group fitness variance

The fitness function value of each particle is determined by its position, so the aggregation degree of each particle can be reflected by the overall change of the fitness function value of all particles. When the fitness function value of each particle is close to the same, then the fitness variance of the population tends to 0. Define the fitness variance δ ² of the population as:

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

(4-3)

In the formula: n is the population size; f _k is the fitness value of particle k; f is the normalized scaling factor, which can limit the size of δ2, which is determined by the following ^formula :

f=max{max(|f _k -f _a |),1}

(4-4)

f _a is the average fitness of the population:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

(4-5)

It can be seen from formula (4-4) that the degree of aggregation of particle swarms is reflected by the size of the population fitness variance δ ² , the smaller the value of δ ² , the more convergent the population tends to be; the larger the value of δ ² , it means that the population Still doing random searches.

(2), mutation operation

When the fitness variance δ ² of the population is small, the particle swarm may fall into the local optimum. If the adaptive mutation operation is performed according to the global optimal solution at this time, the ability of the particles to jump out of the local optimal solution will be enhanced. In other words , the mutation probability should change with the size of the fitness variance δ ² . The mutation probability is determined by the following formula:

P _k ＝(P _max -P _min )(δ ² /n) ² +(P _min -P _max )(2δ ² /n)+P _max

(4-6)

In the formula: P _max and P _min are the upper and lower limits of the variation probability. It can be seen from formula 4-6 that the smaller δ ² is, the larger P _k is.

Choose random perturbation to perform mutation operation on g _best , α is a random variable that obeys Guass(0,1) distribution, and generates random number r∈[0,1]. When r<P _k , Gaussian mutation is performed:

g _best '=g _best (1+0.5α)

(4-7).

3. The steps to solve the optimal configuration of distributed power generation based on AMPSO are as follows:

1) Initialization: Input various parameter information of the power distribution system, including line parameters and load power data, and determine the corresponding constraints in Chapter 3. Initialize PSO parameters, including population size m, particle dimension n, acceleration factors c ₁ and c ₂ , minimum and maximum values of inertia weight ω _min and ω _max , and the maximum number of iterations k of the algorithm;

2) Initialize the particle swarm; randomly generate the initial value of the position and velocity of the particle. In this paper, the position of the particle represents the position of the node, that is, the position where the distributed electric energy is connected, and the speed represents the active and reactive power connected to the corresponding node;

3) Carry out power flow calculation and calculate the fitness function value of each particle. The fitness function value in this paper is the satisfaction value after multi-objective transformation into single-objective;

4) Update the optimal position of the individual and the population; compare each particle with its own p _best , if it is better than p _best , replace p _best , otherwise p _best remains unchanged; compare the fitness value p _best and g in the current population _best comparison, if it is better than g _best , use it instead of g _best , otherwise keep g _best unchanged;

5) Calculate the fitness variance and mutation probability of the current population by formula (4-3) and formula (4-6);

6) Randomly generate r∈[0,1], when r<P _k , perform mutation operation according to formula (4-7), otherwise transfer to 7);

7) Update the position and velocity of the particle according to formula (4-1);

8) If the convergence condition is satisfied, stop the search and output the global optimal solution, otherwise turn to step 3);

The solution process of distributed power optimization configuration based on AMPSO is shown in Figure 2.

Due to the adoption of the above-mentioned technical solution, compared with the prior art, the present invention mainly considers the interests of distribution operators from the perspective of planning, and takes into account the randomness of wind power generation. The multi-objective optimal configuration model composed of the smallest, the smallest total voltage deviation and the smallest risk cost; the fuzzy set theory is used to realize the normalization of multi-objectives, and there is no longer the problem of different sub-objective dimensions; the optimal configuration established in this paper The model is solved by Adaptive Mutation Particle Swarm Optimization (AMPSO). Because of the introduction of mutation operation, the situation that the basic Particle Swarm Optimization (PSO) is easy to fall into local optimum is improved. Finally, as a calculation example It is an IEEE33 node power distribution system, which verifies the optimal configuration model of DG proposed in this paper and the selected AMPSO. The simulation results show that the model and algorithm used in this paper are feasible and effective.

Description of drawings

Accompanying drawing 1 is a schematic diagram of the degree of membership function;

Accompanying drawing 2 is a schematic diagram of the solution process for the optimal configuration of distributed power sources in AMPSO;

Accompanying drawing 3 is a schematic structural diagram of the IEEE33 node power distribution system;

Accompanying drawing 4 is the convergence characteristic curve when fan stochastic output optimization;

Accompanying drawing 5 is the comparison diagram of node voltage before and after fan optimization;

Accompanying drawing 6 is the schematic diagram of convergence characteristic curve when adopting PSO algorithm to optimize;

Accompanying drawing 7 is the schematic diagram of the convergence characteristic curve when adopting AMPSO algorithm to optimize.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings, but not as any limitation to the present invention.

Embodiment of the present invention: In order to verify the effectiveness and feasibility of the proposed optimal configuration model of distributed power supply and adaptive mutation particle swarm algorithm, this embodiment selects IEEE33 node power distribution system as a calculation example, using the programming environment of MatlabR2009a, The power flow and optimization algorithm of the distribution network are programmed and calculated, and the specific analysis is as follows:

1. Parameter selection

(1) Distribution network parameters

In this embodiment, the IEEE33 node power distribution system is selected as the test object to test the influence of distributed electric energy with different capacities connected at different locations on the power distribution system, and the simulation results are summarized and analyzed. The structural diagram of the IEEE33 node power distribution system is shown in the attached As shown in Figure 3, the detailed data of branch impedance and load distribution are shown in Table 1.1 and Table 1.2. The power distribution system has one power point, namely node 0, with a total of 33 nodes and 32 branches. Node 0 is a balanced node. The remaining 32 nodes are all load nodes, which can be used as the on-grid location of distributed power generation energy. The reference voltage of the network head end is 12.66kV. Before the distributed power is connected, the active load of the entire network is 3715.0kW, and the reactive load is 2300.0kvar.

Table 1.1 Line parameter table

Table 1.2 Load power table

Continued Table 1.2 Load Power Table

Then the capacity constraints of distributed power access: the maximum capacity of distributed electric energy to be connected to the power distribution system should be less than 40% of the total system load, then the maximum active power of DG connected to the grid is:

P _max = P _total × 40% = 1486kW

(5-1)

(2) Algorithm parameters

In the particle swarm optimization algorithm, the population size m=50, the particle dimension n=32, the maximum number of iterations is K=300, the acceleration factor c ₁ =c ₂ =2, the maximum and minimum inertia weights are 0.9 and 0.4 respectively, the power flow calculation The medium wind turbine is regarded as a PQ node with a constant power factor, that is to say, the DG connected to the system is regarded as a "negative" load in the power flow calculation, and the power factor is 0.85.

(3) Parameters of distributed power supply

The domestic FD20-200kW wind turbine used in this calculation example has a rated power of 200kW, a cut-in wind speed Vci of 3m/s, a rated wind speed Vr of 13.8m/s, and a cut-out wind speed Vco of 25m/s.

2. Simulation result analysis

This paper adopts the forward-backward power flow calculation method. When no optimization is performed, that is, when the distributed power is not connected to the system, the active power loss of the IEEE33 node power distribution system obtained through matlab power flow calculation is 175.6542kW/h, and the total voltage The deviation is 0.07673, the lowest point of voltage appears at node 17, and the lowest voltage is 0.9219p.u.

(1) Simulation analysis of single random output

Assume that a wind farm has 8 FD20-200kW wind turbines, and the wind farm has four outgoing lines connected to the distribution network, and no matter how much power the wind turbines generate, it is connected to the system, and is not subject to the constraints of distributed power access power capacity Due to the limitation of conditions, AMPSO is used to conduct an optimal solution, using matlab programming, in the local wind field environment, through calculation, the wind speed of the wind field obeys the Weibull distribution with shape parameter k=2 and scale parameter c=15.5 , using the fan output simulation method to conduct a random simulation of the output of 8 fans, the results obtained are: 200kW, 184.55kW, 200kW, 182kW, 175.76kW, 148kW, 200kW, 200kW, a total of 1490.31kW. Then, when constructing the multi-objective optimization configuration model, since only one optimization is carried out and all the output of the fan is connected to the system, then there is no risk cost, and the optimization goal will become the minimum active power loss and the minimum total voltage deviation, and the optimization result See Table 2.1, see Table 2.2 for the changes in the membership functions corresponding to each sub-objective, see Figure 4 for the convergence characteristic curve during algorithm optimization, and see Figure 5 for the comparison results of node voltages before and after optimization.

Table 2.1 Random output optimization results

Note: Before the parentheses of the planning result item in the table is the node number of distributed electric energy access, the number in the parentheses is the electric energy capacity connected to the node, the unit is: kW.

Table 2.2 Change of sub-objective membership function value

It can be seen from Table 2.1 that after the distributed electric energy is connected, the active power loss and total voltage deviation of the power distribution system decrease significantly, the active power loss drops from 175.6542kW/h to 50.8484kW/h, and the total voltage deviation drops from 0.07673 to 0.01158; From Table 2.2 and Attached Figure 4, it can be seen that at the 117th iteration, the maximum satisfaction M value reaches 0.9848, and the maximum satisfaction rises from 0.9270 to 0.9848, and the membership function of the sub-goal is also gradually improving , indicating that the use of the maximum satisfaction method has improved the overall performance, and each sub-objective has obtained better optimization results; from the comparison diagram of the voltage before and after optimization in Figure 5, it can be seen that the voltage level of the node after optimization is significantly improved, and is closer to Baseline value, the voltage value of node 17 has increased from 0.9219p.u to 0.9797p.u, an increase of 6.26%, and the lowest node voltage appears at node 32, which is 0.9636p.u, which is also higher than the value at the lowest node voltage before optimization , which improves the overall voltage level of the power distribution system and improves the economy. In summary, the model and algorithm adopted in this paper are feasible.

(2) Simulation analysis of planned capacity

From the perspective of planning, this section assumes that a wind farm only provides 1200kW active capacity to the system according to the capacity limit of distributed power access to the distribution network, that is, the wind farm has 6 FD20-200kW wind turbines. The wind farm has three outgoing lines connected to the distribution network. Through the optimal configuration of distributed power sources, the location and access capacity of distributed electric energy can be determined. Then the estimated output in the risk cost of the objective function is 200kW. If the fan output does not meet 200kW, it will be powered by the superior power supply.

1) Comparison between PSO and AMPSO

Under the above conditions, a ten-year plan was carried out, and the previously established distributed power generation optimization configuration model was solved by using the PSO and AMPSO methods respectively. The optimization results only output the active power loss and the total voltage deviation. The optimization results are shown in Table 2.3. Corresponding to the data in Table 2.3, the voltage data of each node after optimization by PSO and AMPSO is shown in Table 2.4, and the corresponding convergence characteristic curves when optimized by PSO and AMPSO are shown in Figures 6 and 7.

It can be seen from Tables 2.3 and 2.4 that although the total voltage deviation in the optimization results of the particle swarm optimization algorithm is smaller than the value of the adaptive mutation particle swarm optimization algorithm, the difference is not significant. At that time, the maximum satisfaction M reached 0.9073, and there has been no change since then. The algorithm has fallen into a local optimum and has not reached the global optimum solution. From this point of view, the optimization effect is relatively poor; when using AMPSO for optimization, iterated to the 254th The sub-maximum satisfaction M value reaches the optimal value of 0.9375. Both the number of iterations and the maximum satisfaction are better than the particle swarm optimization algorithm. This is because the mutation probability that is adaptively changed according to the variance of the group fitness is introduced. When the optimal solution (from the convergence diagram can also be seen that there are multiple fluctuations during AMPSO optimization), the speed and position of the particles are changed, the diversity of the population is maintained, and the premature convergence is overcome to a certain extent, and a better result is obtained. The convergence results show that the optimal configuration of DG using AMPSO in this paper is feasible and effective.

Table 2.3 Optimization results of PSO and AMPSO

Note: Before the parentheses of the planning result items in the table is the node number of distributed electric energy access, the number in the parentheses is the electric energy capacity connected to the node, the unit is: kW.

Table 2.4 Voltage of each node in the system (p.u)

Continuation Table 2.4 Voltage of each node in the system (p.u)

2), the impact of risk costs

Under the conditions given in (2), plan for a period of ten years, and take active power loss, total voltage deviation, and active power loss, total voltage deviation, and risk costs as the objective functions respectively, that is, consider risk The cost and the risk-free cost are analyzed, and AMPSO is used to optimize the solution. The optimization result of the three-objective function is the optimal result obtained by AMPSO in 1). The optimization results of the dual-objective and three-objective are shown in Table 2.5.

Table 2.5 Optimization results of dual-objective and triple-objective

It can be seen from Table 2.5 that optimization with dual objectives can achieve a better optimization effect on the distribution system than optimization with three objectives, that is, the active power loss and total voltage deviation of the distribution system are small, indicating the existence of risk costs, namely Considering the randomness of wind turbine output, the interests of power distribution operators are reduced, but distributed power that truly reflects renewable energy is susceptible to factors such as the natural environment, making its output random.

Claims (4)

1. An optimal configuration scheme of distributed power, characterized in that: from the perspective of planning, the method mainly considers the interests of power distribution operators and the randomness of distributed power generation output, and optimizes the distribution of distributed power Conducted research, that is, to solve the grid location and capacity of distributed electric energy, and established a multi-objective optimal configuration model consisting of the smallest active power loss, the smallest total voltage deviation, and the smallest risk cost of the distribution network. The above multi-objective optimal configuration model Set up constraint conditions and optimize processing; use fuzzy set theory to realize the normalization of multi-objectives, coordinate the relationship between each sub-objective well, and then achieve the effect of overall optimization; solve it by adaptive mutation particle swarm algorithm. 2. The optimal configuration scheme of a kind of distributed power supply according to claim 1, characterized in that: the multi-objective optimal configuration model specifically includes the following: 1. Minimal active power loss; The voltage level of the distribution network is low, and the R/X value is relatively large, so the network loss is relatively large in the power flow calculation. Reasonable access to distributed electric energy can reduce the network loss. Therefore, the minimum network loss can be used as the objective function. Bring better economic benefits. Since this article starts from the perspective of planning, the minimum active power loss is the optimization goal. The objective function of the minimum active power loss is: $\mathrm{<span\; class="notranslate">\; min</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}$ In the formula: I _i is the current of branch i; N is the total number of branches of the system; R _i is the branch resistance, and h is the number of hours in the planning period. 2. The optimization target model with the smallest total voltage deviation is; The crossing of the node voltage amplitude will affect the normal work of users and the safety of the system. Therefore, taking the total node voltage deviation as the objective function can make the node voltage closer to the reference value, guarantee the voltage level of the distribution network, and achieve The effect of improving voltage quality. The objective function with the minimum total voltage deviation is: $\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>$ In the formula: DetV is the total voltage deviation; N is the number of network nodes; U _b is the reference voltage; U _i is the voltage value of the i-th node. 3. The risk cost is minimal; Distributed power generation of renewable energy such as wind power generation and photovoltaic power generation is susceptible to the natural environment or other factors, making its output characterized by randomness, volatility, and uncertainty. Therefore, this paper uses risk costs to reflect the existence of distributed power generation output. Randomness, when the power generation of distributed power generation does not reach the expected value, it is characterized by the cost of power supply through the grid, that is, the superior power supply. The objective function of the risk cost is: C _risk ＝P·C·t·n In the formula: P is the probability that the output of the DG with randomness is less than the expected output; C is the cost of power supply from the superior power supply when the output of the DG is less than the expected output; t is the annual operation time of the DG; n is the planned number of years. 3. The optimal configuration scheme of a distributed power supply according to claim 1, characterized in that: the constraints of the multi-objective optimal configuration model are inequality constraints, and include node voltage constraints, distributed power access constraints and Branch current constraints. 4. The optimal configuration scheme of a kind of distributed power supply according to claim 1, characterized in that: the method of adopting fuzzy set theory to realize the normalization of multi-objectives first passes the minimum value of the degree of membership of multi-objectives Carry out maximization processing to improve poor indicators and achieve the purpose of improving the overall performance of the system, and the membership function used is a split line function. For optimization with multiple objective functions, each optimization objective is often contradictory and difficult to simultaneously To achieve the optimum, when the importance of each optimization objective is the same, the maximum satisfaction method is usually used to solve it, that is, the greater the minimum value of the membership function of the optimization objective, the greater the overall satisfaction.