CN102170137A - ORP (optimal reactive power) method of distribution network of electric power system - Google Patents

Abstract

The invention discloses an ORP (optimal reactive power) method of a distribution network of an electric power system in the technical field of ORP of the distribution network of the electric power system. The method comprises the following main steps: introducing an accelerated evolution operation and an investigation operation in an ABC (artificial bee colony) algorithm to a basic differential evolution operation; and judging whether conditions of convergence of a hybrid algorithm are met, and ending the optimization and outputting the optimal result if the conditions of convergence are met. The hybrid algorithm for solving the ORP problem exerts the advantages that the operation is simple, robustness is good and the like, of the differential evolution algorithm, and can be used to shorten the running time of the algorithm and improve the probability of finding out the global optimal value.

Description

A reactive power optimization method for power system distribution network

technical field

The invention belongs to the technical field of reactive power optimization of power system distribution network, and in particular relates to a reactive power optimization method of power system distribution network.

Background technique

Reactive power optimization means that when the structural parameters and load conditions of the system are given, through the optimization of certain control variables, one or more performance indicators of the system can be found under the premise of satisfying all specified constraints. Optimum reactive power adjustment means. The reactive power optimization problem is a branch problem gradually differentiated from the development of optimal power flow. Reactive power optimization of distribution networks in power systems can control voltage levels and reduce active power losses. Commonly used reactive power/voltage control methods include adjusting the terminal voltage of the generator, adjusting the tap position of the on-load tap changer, adjusting the number of shunt capacitors and reactor switching groups, etc. Reactive power operation planning is to use reactive power compensation equipment to improve the reactive power operation of the system, that is, to control the voltage level and reduce active power loss.

In mathematics, reactive power optimization is a typical nonlinear programming problem, which has the characteristics of nonlinearity, discontinuity, and many uncertain factors. Multi-variable and multi-constraint mixed nonlinear programming problems, the control variables include both continuous variables (generator terminal voltage) and discrete variables (on-load voltage regulator tap position, compensation capacitor, reactor input The number of cut groups) is very difficult to solve, and the differential evolution algorithm is a method that is widely used in reactive power optimization.

The differential evolution algorithm was proposed by Rainer Storn and Kenneth Price in 1995 to solve Chebyshev polynomials. A probabilistic search method to solve various difficult problems quickly and effectively. The reproduction of differential evolution algorithms is driven by genetic differences among randomly sampled individuals in the current population.

The differential evolution algorithm is simple in principle, low in operation complexity, and has the advantages of simple parameter setting, small amount of calculation and good robustness. Although the differential evolution algorithm is simple to operate and easy to implement, and has been well applied to solve power system reactive power optimization problems, it is difficult to achieve a balance between diversity and convergence, and it is easy to converge to a local optimum. In order to make up for the defects of the differential evolution algorithm, the present invention introduces the idea of accelerating evolution and expanding space in the artificial bee colony algorithm into the differential evolution algorithm, which can shorten the running time of the algorithm and increase the probability of searching for the global optimal value.

Contents of the invention

Aiming at the deficiency that the differential evolution algorithm mentioned in the background technology is difficult to achieve a balance between diversity and convergence, and is easy to converge to a local optimal value, the present invention proposes a reactive power optimization method for power system distribution network .

The technical solution of the present invention is a reactive power optimization method for power system distribution network, characterized in that the method includes the following steps:

Step 1: Input the original distribution network parameters;

Step 2: Construct an individual composed of system reactive power optimization control variables, and initialize the population;

Step 3: Perform power flow calculation and fitness evaluation according to the initial population and grid parameters;

Step 4: Hybrid optimization of differential evolution algorithm and artificial bee colony algorithm;

Step 5: The optimization process ends, and the optimization result is output.

The original distribution network parameters in the step 1 include:

a. Inherent data of the distribution network: including the network structure of the distribution network, branch data, the load of each node and the active output of the generator under various operating modes;

b. Generator terminal voltage with adjustable voltage;

c. Transformer ratio;

d. The location and capacity of reactive power compensation equipment;

e. All control variable constraints and state variable constraints.

In said step 2, reactive power optimization control variables include:

a. Generator terminal voltage;

b. On-load tap changer tap position;

c. Number of shunt capacitors and reactor switching groups.

Described step 2 comprises the following steps:

Step 2.1: Composing individual vectors from system reactive optimization control variables;

Step 2.2: Randomly generate initial values that meet the constraint conditions for all individuals in the population.

Described step 3 comprises the following steps:

Step 3.1: Perform power flow calculation according to the initial population and grid parameters;

Step 3.2: Calculate the fitness fit _i of all individuals in the initial population;

Step 3.3: Record the optimal individual x _best and the optimal fitness value fit _best of the initial population.

The calculation formula of the power flow calculation in the step 3.1 is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; L</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>}}{\mathrm{<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">\; ij</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; L</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>}}{\mathrm{<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">\; ij</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; ;</span>$ $\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Subset;</span>\mathrm{<span\; class="notranslate">\; N</span>}$

in:

为节点i注入的有功功率；

Active power injected for node i;

reactive power injected for node i;

为节点i负荷的有功功率；

is the active power of node i load;

为节点i负荷的无功功率；

is the reactive power of node i load;

is the reactive power compensation capacity of node i, which is controlled by the number of shunt capacitor switching groups;

U _i is the voltage of node i;

U _j is the voltage of node j;

G _ij is the conductance between node i and node j;

B _ij is the susceptance between node i and node j;

δ _ij is the voltage phase angle difference between node i and node j;

N is the node set of the distribution network system.

The calculation formula of the fitness fit _i in the step 3.2 is:

${\mathrm{<span\; class="notranslate">\; fit</span>}}_{\mathrm{<span\; class="notranslate">\; i</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>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u\; i"\; filenames="HDA0000057560500000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="2"\; label="u\; i"\; filenames="HDA0000057560500000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

in:

fit _i is the fitness of node i;

n ₁ is the total branch number of the network;

G _{k(i, j)} is the conductance from branch i to branch j;

δ _i is the phase angle of node i;

δ _j is the phase angle of node j.

Described step 4 specifically comprises the following steps:

Step 4.1: use differential evolution to generate a new generation of population based on the previous generation of population;

Step 4.2: Calculate the fitness distribution ratio of all individuals in the population;

Step 4.3: Calculate the number of individual accelerated evolution according to the fitness distribution ratio of the individual and the number of individuals in the population;

Step 4.4: Artificial bee colony accelerated evolution operation;

Step 4.5: Record the optimal individual x _best and the optimal fitness value fit _best of the population;

Step 4.6: Judging whether there are discarded individuals, if so, go to step 4.7, otherwise go to step 4.8;

Step 4.7: Artificial bee colony detection operation;

Step 4.8: Determine whether the population optimization termination condition is satisfied, if the convergence condition is satisfied, end step 4, otherwise, return to step 4.1.

The calculation formula of the fitness distribution ratio in the step 4.2 is:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; fit</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; NP</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; fit</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

in:

P _i is the fitness distribution ratio of the i-th individual;

NP is the population size.

The calculation formula for the number of times of individual accelerated evolution in the step 4.3 is:

N _i =P _i ×NP

in:

N _i is the number of accelerated evolution of the i-th individual.

While utilizing the existing advantages of the differential evolution algorithm, the method of the present invention overcomes the defect that the differential evolution algorithm is easy to obtain local extremums, and achieves a better balance between diversity and convergence, shortening the calculation time of the algorithm , which increases the probability of searching for the global optimum.

Description of drawings

Figure 1 is a flowchart of the reactive power optimization method.

Figure 2 is a modified IEEE14 node wiring diagram.

Fig. 3 is a flow chart of hybrid optimization of differential evolution algorithm and artificial bee colony algorithm.

Fig. 4 is a basic differential evolution flow chart.

Fig. 5 is a flowchart of accelerated evolution of artificial bee colony.

Detailed ways

The implementation of the reactive power optimization method of the present invention will be described in detail below in conjunction with the accompanying drawings, taking the modified IEEE14 node system as an example. It should be emphasized that the following description is only exemplary and not intended to limit the scope of the invention and its application.

Fig. 1 is a flowchart of a reactive power optimization method for a power system distribution network provided by the present invention. In Fig. 1, the method provided by the invention comprises the following steps:

Step 1: Input the original distribution network parameters;

The original distribution network parameters specifically include:

a. Intrinsic data of distribution network: including network structure of distribution network, branch data, load of each node under various operation modes, active output of generator;

b. Generator terminal voltage with adjustable voltage;

c. Transformer ratio;

d. The location and capacity of reactive power compensation equipment;

e. All control variable constraints and state variable constraints.

Figure 2 is a modified IEEE14 node wiring diagram, the whole system contains 14 nodes and 20 branches. On-load tap-changing transformers are respectively installed on branches 4-7, 4-9, and 5-6. The adjustable range of the transformer transformation ratio is [0.90, 1.10], and the tap position of the on-load tap-changing transformer is a discrete variable. The range is [0, 20]. Among the 14 nodes, nodes 1, 2, 3, 6, and 8 are generator nodes, of which node 1 is a balance node; nodes 9 and 14 are reactive power compensation nodes, equipped with shunt capacitors, and the range of reactive power output can be adjusted is [0, 18], the number of parallel capacitor switching groups is a discrete variable, and the range is [0, 3]; the voltage constraint range of all nodes is [0.90, 1.10], and the terminal voltage of the adjustable voltage generator is also affected by this voltage Constraint limit.

Step 2: Construct an individual composed of system reactive power optimization control variables, and initialize the population;

Step 2.1: Composing individual vectors from system reactive optimization control variables;

Power system reactive power optimization control variables mainly include: generator terminal voltage; tap position of on-load tap changer; shunt capacitor and reactor switching group number. As mentioned in step 1, there are 10 control variables in the modified IEEE14 node system, the generator terminal voltage includes: U ₁ , U ₂ , U ₃ , U ₆ and U ₈ , and the adjustable range is [0.90, 1.10]; The tap positions of the on-load tap changer include: T ₄₇ , T ₄₉ and T ₅₆ , this variable is an integer, and the adjustable range is [0, 20]; the number of parallel capacitor switching groups includes: N ₉ and N ₁₄ , this The variable is an integer, and the adjustable range is [0, 3]. For convenience, yi is used to represent the control variables uniformly, and the system reactive power optimization control variables can be composed of 10-dimensional individual vectors as:

(y ₁ ,...,y _D )

Where: D=10.

Step 2.2: Randomly generate initial values that meet the constraints for all individuals in the population;

The population is initialized according to the control variable constraints, and the population size is NP. In the control variable constraint range [y _jmin , y _jmax ], take a random value to initialize the population individual x _i (0):

$x_i\left(0\right)=(x_i^1\left(0\right),\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,x_i^{\mathrm{D.}}\left(0\right)),$ where i = {1,...,NP}

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; rand</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 0,1</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span>$

The initial population is:

X(0)={x ₁ (0), x ₂ (0), ..., x _NP (0)}

In the formula:

y _jmax and y _jmin respectively represent the upper limit and lower limit of the control variable y _j ;

x _i (0) represents the i-th individual in the initial population;

Represents the j-th dimension variable value of the i-th individual in the initial population, the number in brackets represents the population algebra, and 0 represents the initial population, where: j={1,...,D}.

In the modified IEEE14-node system, the control variable constraint range [y _jmin , y _jmax ] can be replaced by the specific data described in step 2.1, and the constraint range of generator terminal voltage is [0.90, 1.10]; The constraint range of the joint position is [0, 3]; the constraint range of the number of shunt capacitor switching groups is [0, 3]. For two discrete variables, the tap position of the on-load tap changer and the number of shunt capacitor switching groups, the random value will be rounded in the encoding.

Step 3: Perform power flow calculation and fitness evaluation according to the initial population and grid parameters;

Step 3.1: Perform power flow calculation according to the individual and grid parameters of the initial population;

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; L</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>}}{\mathrm{<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">\; ij</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; L</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>}}{\mathrm{<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">\; ij</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; ;</span>$ $\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Subset;</span>\mathrm{<span\; class="notranslate">\; N</span>}$

in:

为节点i注入的有功功率；

Active power injected for node i;

为节点i注入的无功功率；

reactive power injected for node i;

为节点i负荷的有功功率；

is the active power of node i load;

为节点i负荷的无功功率；

is the reactive power of node i load;

为节点i的无功补偿容量，由并联电容器投切组数控制；

is the reactive power compensation capacity of node i, which is controlled by the number of shunt capacitor switching groups;

U _i is the voltage of node i;

U _j is the voltage of node j;

G _ij is the conductance between node i and node j;

B _ij is the susceptance between node i and node j;

δ _ij is the voltage phase angle difference between node i and node j;

N is the node set of the distribution network system.

According to the data provided in step 1 and step 2, the Newton-Raphson power flow calculation method is used to solve the power flow equation for each individual of the initial population, and the values of all state variables can be obtained, including the voltage and phase angle of each node.

Step 3.2: Calculate the fitness fit _i of all individuals in the initial population;

Taking the active power loss of the distribution network as the fitness function in the optimization process:

${\mathrm{<span\; class="notranslate">\; fit</span>}}_{\mathrm{<span\; class="notranslate">\; i</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>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="u\; i"\; filenames="HDA0000057560500000011.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="2"\; label="u\; i"\; filenames="HDA0000057560500000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

in:

fit _i is the fitness of node i;

n ₁ is the total branch number of the network;

G _{k(i, j)} is the conductance from branch i to branch j;

δ _i is the phase angle of node i;

δ _j is the phase angle of node j.

The values of all unknown variables can be obtained after the power flow calculation in step 3.1, and the fitness fit _i is calculated for all individuals.

Step 3.3: Record the optimal individual x _best of the initial population and the optimal fitness value fit _best ;

The constraints in the reactive power optimization model include equality constraints and inequality constraints. Equality constraints satisfy the power flow equation; inequality constraints mainly consider the upper and lower limits of variables. Therefore, the violation of variable constraints after power flow calculation should be considered when selecting the optimal individual of the population.

Variable constraints can be divided into state variable constraints and control variable constraints. The inequality constraints on the state variables are:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; NG</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; NG</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; NG</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}\end{array}\right.<span\; class="notranslate">\; ,</span>$

The inequality constraints on the control variables are:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}\end{array}\right.<span\; class="notranslate">\; ,</span>$

In the formula:

和为其上界、下界；Q _G is the reactive power injected by the generator,

and as its upper bound and lower bound;

和

为其上界、下界；U _NG is the non-generator node voltage,

and

its upper bound and lower bound;

和

为其上界、下界；Q _C is the reactive power injected by the reactive power compensation node,

and

its upper bound and lower bound;

和

为其上界、下界；U _G is the terminal voltage of the generator node,

and

its upper bound and lower bound;

T is the tap position of the on-load tap changer, and T _max and T _min are its upper and lower bounds.

Among these constraint conditions, the constraint conditions of generator node terminal voltage U _G , tap position T of on-load tap changer and reactive power injected into reactive power compensation node Q _C (adjusted by the number of shunt capacitor switching groups) can be found in Satisfied in the coding, the constraint conditions of the generator injected reactive power Q _G and the non-generator node voltage U _NG may be violated, so define the out-of-bounds penalty function:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</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>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; spec</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; min</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>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; spec</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; min</span>}}}$

In the formula:

F is an out-of-bounds penalty function;

n is the set of all non-generator nodes;

n ₁ is the set of all generator nodes that can provide reactive power output;

U_j小于下界时，令

U _jmax and U _jmin are the upper bound and lower bound of voltage U _j respectively, when U _j is greater than the upper bound, let

When U _j is less than the lower bound, let

Q_k小于下界时，令

Q _kmax and Q _kmin are the upper bound and lower bound of the reactive power Q _k injected by node k respectively. When Q _k is greater than the upper bound, let

When Q _k is less than the lower bound, let

When comparing the advantages and disadvantages of any two individuals, the selection strategy is as follows:

Step 1: If both individuals have out-of-bounds situations, compare the fitness fit _i of the two individuals, and the smaller one is superior;

Step 2: If one individual has out-of-bounds situation and the other has no out-of-bounds situation, the individual without out-of-bounds situation is superior;

Step 3: If both individuals have out-of-bounds situations, compare the two out-of-bounds penalty function values F _i , and the smaller one is superior.

After comparing among individuals according to the above selection strategy, record the optimal individual x _best and the corresponding optimal fitness value fit _best in the initial population.

Step 4: Hybrid optimization of differential evolution algorithm and artificial bee colony algorithm;

Figure 3 shows the detailed operation flow of step 4. Step 4 specifically includes the following steps:

Step 4.1: Use differential evolution operations such as mutation, crossover, and selection to generate a new generation of populations on the basis of previous generation populations; Figure 4 shows a detailed operation process of a basic differential evolution operation;

Step 1: Mutation Operation

For each individual x _i (t) in the population, generate three different random integers r1, r2, r3 ∈ {1, 2, ..., NP}, and require that the three random integers are not equal to i, press The following formula generates mutant individuals v _i (t):

$v_i\left(t\right)=(v_i^1\left(0\right),...v_i^{\mathrm{D.}}\left(0\right)),$ where i={1,...NP}

$v_i^j=v_{r_1}^j\left(t\right)+f(v_{r_2}^j\left(t\right)-v_{r_3}^j\left(t\right)),$ where j={1,...D}

In the formula:

为第t代种群中第i个变异个体的第j维变量值；

is the j-th dimension variable value of the i-th mutant individual in the t-generation population;

F is the evolution parameter scaling factor, F ∈ (0, 2).

Step 2: Crossover

First generate a random integer j_rand ∈ {1, 2, ..., D}, and then generate test individual _{u i} (t) for x _i (t) and v _i (t) according to the following formula:

$u_i\left(t\right)=(u_i^1\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,u_i^{\mathrm{D.}}\left(t\right)),$ where i = {1,...,NP}

其中j＝{1，…，D}

where j = {1,...,D}

In the formula:

为第t代种群中第i个试验个体的第j维变量值；

is the j-th dimension variable value of the i-th test individual in the t-th generation population;

CR is the evolution parameter cross factor, CR ∈ (0, 1).

Step 3: Power flow calculation and fitness evaluation

For all test individuals u _i (t) refer to step 3 to perform power flow calculation and calculate fitness.

Step 4: Select an action

j = 1, 2, ..., D

In the formula:

x _i (t+1) is the i-th individual in the t+1th generation population after the evolution of the tth generation population;

fit( _xi (t)) is the fitness value of individual x _i (t).

By comparing the fitness of the test individual and the original individual, the individual with better fitness is selected as the new generation of individual. When applying the basic differential evolution algorithm to the reactive power optimization problem, the selection strategy of this step can refer to step 3.3.

Step 4.2: Calculate the fitness distribution ratio of all individuals in the population

According to the fitness of all individuals recorded in step 4.1, calculate the fitness distribution ratio of all individuals in the population Among them: NP is the population size, and fit _i represents the fitness value of the i-th individual.

Step 4.3: Calculate the number of individual accelerated evolution N _i =P _i ×NP according to the fitness distribution ratio of the individual and the number of individuals in the population, where P _i is the fitness distribution ratio of the i-th individual in the population;

Step 4.4: Artificial bee colony accelerated evolution operation;

That is, a new generation of individuals is generated by circulating N _i times of differential evolution operations on individuals; Figure 5 shows the detailed operation process of the accelerated evolution operation of artificial bee colonies. Specifically include the following steps:

The first step: initialize the counter, k=0;

Step 2: Determine whether the counter is smaller than the number of accelerated evolution of the individual, if k<N _i is established, enter the third step, otherwise end the operation process;

The third step: a differential evolution operation to generate a new individual, the operation steps refer to step 4.1;

The fourth step: add one to the counter, k=k+1, jump to the second step.

Step 4.5: Record the best individual x _best and the best fitness value fit _best in the population;

Refer to step 3.3 to compare the pros and cons of individuals, and record the optimal individual x _best and the optimal fitness value fit _best in the population.

Step 4.6: Determine whether there are discarded individuals;

Define the upper limit of evolution times limit=NP×D, where NP is the population size, and D represents the dimension of the individual. If the individual has not been improved after the limit number of evolution tests, the individual is a discarded individual. If there are discarded individuals, go to step 4.7, otherwise go directly to step 4.8.

Step 4.7: Artificial bee colony detection operation;

Regenerate random individuals that meet the constraint conditions, replace discarded individuals with regenerated random individuals, and refer to step 2.2 for the operation steps of randomly generating new individuals, and at the same time, the number of evolution trials of this individual is reset to zero.

Step 4.8: Determine whether the population optimization termination condition is satisfied, if the convergence condition is satisfied, end step 4, otherwise, return to step 4.1.

The optimization termination condition can be taken as the evolution process reaches a certain number of generations, or the value of the objective function of reactive power optimization has not been improved for several successive generations of evolution.

Step 5: the optimization process ends, and the optimization result is output;

The optimization results include the values of each control variable and state variable, the power flow level of the system, and the active power loss of the system after optimization.

The invention introduces the operation of observing bees and scouting bees in the artificial bee colony algorithm into the differential evolution algorithm. Compared with the basic differential evolution algorithm, the algorithm shortens the running time of the algorithm and improves the probability of searching for the global optimal value.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of changes or modifications within the technical scope disclosed in the present invention. Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims (10)

1. the idle work optimization method of a system for distribution network of power is characterized in that said method comprising the steps of:

Step 1: import original power distribution network parameter;

Step 2: the individuality that structure is made up of system's idle work optimization control variables, initialization population;

Step 3: carry out trend calculating and carry out fitness evaluation according to initial population and electrical network parameter;

Step 4: differential evolution algorithm and artificial ant colony algorithm hybrid optimization;

Step 5: optimizing process finishes, and the result is optimized in output.

2. according to the idle work optimization method of the described a kind of system for distribution network of power of claim 1, it is characterized in that original power distribution network parameter comprises in the described step 1:

A. power distribution network inherent data: comprise under power distribution network network structure, a circuit-switched data, the various operational mode each node load and generator is meritorious exerts oneself;

B. the generator terminal voltage of adjustable voltage;

C. transformer voltage ratio;

D. the position of reactive-load compensation equipment and capacity;

E. all control variables constraintss and state variable constraints.

3. according to the idle work optimization method of the described a kind of system for distribution network of power of claim 1, it is characterized in that the idle work optimization control variables comprises in the described step 2:

A. generator terminal voltage;

B. on-load transformer tap changer position;

C. shunt capacitor and reactor switching group number.

4. the idle work optimization method of a kind of system for distribution network of power according to claim 1 is characterized in that described step 2 may further comprise the steps:

Step 2.1: form individual vector by system's idle work optimization control variables;

Step 2.2: all individualities in the population are generated the initial value that meets constraints respectively at random.

5. according to the idle work optimization method of the described a kind of system for distribution network of power of claim 1, it is characterized in that described step 3 may further comprise the steps:

Step 3.1: carry out trend calculating according to initial population and electrical network parameter;

Step 3.2: calculate all individual fitness fit of initial population _i

Step 3.3: the optimum individual x of record initial population _BestWith fitness optimal value fit _Best

6. according to the idle work optimization method of the described a kind of system for distribution network of power of claim 5, it is characterized in that the computing formula that trend is calculated in the described step 3.1 is:

$\left\{\begin{array}{c}{P}_{G_i}-P_{L_i}=U_i\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&delta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&delta;}}_{\mathrm{ij}})\\ Q_{G_i}+Q_{C_i}-Q_{L_i}=U_i\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&delta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\&delta;}}_{\mathrm{ij}})\end{array}\right.;$ $i\&Subset;N$

Wherein:

Active power for the node i injection;

Reactive power for the node i injection;

Active power for the node i load;

Reactive power for the node i load;

Be the reactive compensation capacity of node i, by shunt capacitor switching group numerical control system;

U _iVoltage for node i;

U _jVoltage for node j;

G _IjFor the electricity between node i and the node j is led;

B _IjBe the susceptance between node i and the node j;

δ _IjBe the phase difference of voltage between node i and the node j;

N is the node set of distribution network system.

7. according to the idle work optimization method of the described a kind of system for distribution network of power of claim 5, it is characterized in that fitness fit in the described step 3.2 _iComputing formula be:

${\mathrm{fit}}_i=\underset{k=1}{\overset{n_1}{\mathrm{\&Sigma;}}}{G}_{k(i,j)}[U_i^2+U_j^2-{2U}_i{U}_j\cos ({\mathrm{\&delta;}}_i-{\mathrm{\&delta;}}_j)]$

Wherein:

Fit _iFitness for node i;

n ₁Be network general branch way;

G _{K (i, j)}For branch road i leads to the electricity of branch road j;

δ _iPhase angle for node i;

δ _jPhase angle for node j.

8. according to the idle work optimization method of the described a kind of system for distribution network of power of claim 1, it is characterized in that described step 4 specifically comprises the following step:

Step 4.1: operate in differential evolution and produce population of new generation on the basis of former generation population;

Step 4.2: calculate all individual fitness distribution proportions in the population;

Step 4.3: fitness distribution proportion and population individual amount according to individuality calculate individual accelerated evolutionary number of times;

Step 4.4: artificial bee colony accelerated evolutionary operation;

Step 4.5: the optimum individual x of record population _BestWith fitness optimal value fit _Best

Step 4.6: judge whether to exist discarded individuality, if exist, then execution in step 4.7, otherwise execution in step 4.8;

Step 4.7: artificial bee colony investigation operation;

Step 4.8: judge whether the swarm optimization end condition satisfies, if the condition of convergence satisfies, end step 4, otherwise, return step 4.1.

9. the idle work optimization method of described a kind of system for distribution network of power according to Claim 8 is characterized in that the computing formula of fitness distribution proportion in the described step 4.2 is:

$P_i=\frac{{\mathrm{fit}}_i}{\underset{n=1}{\overset{\mathrm{NP}}{\mathrm{\&Sigma;}}}{\mathrm{fit}}_n}$

Wherein:

P _iBe i individual fitness distribution proportion;

NP is a population scale.

10. the idle work optimization method of described a kind of system for distribution network of power according to Claim 8 is characterized in that the computing formula of individual accelerated evolutionary number of times in the described step 4.3 is:

N _i＝P _i×NP

Wherein:

N _iBe i individual accelerated evolutionary number of times.

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