Key words: reactive power optimization; memory search; mode method; improved simulated annealing algorithm
REACTIVE POWER OPTIMIZATION OF POWER SYSTEM BASED ON MODIFIED
SIMULATED ANNEALING ALGORITHM
Jia Dexiang1 Tang Guoqing1 Han Jing2
(1. Dept. of Electrical Engineering, Southeast University, Nanjing 210096;
2. Maanshan Electric Power Supply Bureau, Maanshan 243000)
Traditional key programming technique and non-linear programming technique can not deal with the problem of integer variable successfully, and the simulated annealing algorithm (SA) Allowing for the characteristics of high-medium voltage distribution system, the SA is modified as follows: using remembrance-guided search method, and modifying the quasi optimum value by pattern search. Numerical experiment demonstrates that, the above method Is reasonable, feasible, and practical to some extent.
Key words: reactive power optimization; remembrance-guided search; pattern search method; modified simulated annealing algorithm
0. Introduction The problem of reactive power optimization (RPOP) has always been valued by people because the line loss rate in China has always been high. For example, in 2001, the total power generation in Anhui Province was about 40 billion kW·hr, and the actual statistical line loss rate of the power grid was about 20%, that is, the line loss was about 8 billion kW·hr, and the variable line loss was about 60. Billion kilowatts·hour [1]. Rural network losses are as high as 28% [2]. The severity of the network loss is thus evident. On the basis of the existing power grid structure, the network loss can be reduced, the voltage quality can be improved, and the economics of the grid operation can be reduced by rationally regulating the reactive power flow. The reactive power optimization problem is a large-scale nonlinear integer programming problem. The goal is usually to minimize the network loss, and to use the minimum offset, the minimum adjustment of the control device or the minimum number of operating devices as the objective function. The constraint conditions are generally the power balance of each node, and the unequal constraints include the node voltage, line power and the limitation of each control quantity adjustment range [3]. The algorithms mainly include linear programming method, nonlinear programming method, mixed integer programming method, dynamic programming method, artificial intelligence method, etc. At present, there is no way to guarantee the optimal solution of reactive power optimization problem [4].
For the 110KV-35KV high and medium voltage distribution network, the main means of regulating the reactive power flow is to change the tap position of the on-load tap changer and the number of switching groups of the shunt capacitor. These control variables are generally integer. The traditional linear programming method and nonlinear programming method first regard these integer control quantities as continuous variables. After obtaining the optimal solution, the approximate integer value is taken, and the error is large; or the branch and bound solution is used to calculate the time. Too long. In recent years, many scholars have used artificial intelligence to solve the RPOP problem. Literature 5 uses genetic algorithms combined with neural network budget grid power flow to reduce the overall computation time of large-scale grid genetic algorithms. In the literature 6, the memory-guided simulated annealing scheme is used to better realize the three-phase phase separation optimization switching problem of the distribution network capacitor.
Simulated Annealing (SA) has the characteristics of random optimization, which can better avoid the constraint of local extreme points. However, the SA solution is slow and robust. Therefore, this paper uses the improved simulated annealing algorithm (ISA) to solve the RPOP problem. The main improvement points are as follows: the memory-guided search method is used to speed up the search; the local optimization by the pattern method increases the possibility of obtaining the global optimal solution. Numerical comparison tests show that the above improved method is reasonable and feasible.
1 Mathematical model The main purpose of the reactive power operation optimization of high and medium voltage distribution network is to minimize the active network loss by changing the tap position of the on-load tap-changer and the number of switching capacitors of the shunt capacitor under various constraints. Its mathematical model is:
Wherein, the control quantity u includes the reactive power of the generator in the power grid or the continuously adjustable reactive power compensation device, the tap position of the load regulating transformer and the number of groups in which the parallel capacitor is put into operation; the state quantity x includes the voltage of each node Modulus and phase angle.
The constraint condition is the basic power flow equation group, that is, the active power and reactive power balance of each node, including the sum of load power and network loss equal to the power generation.
There are a large number of unequal constraints, including: the upper and lower limits of the node voltage modulus, the maximum power constraint passed by the line and the transformer, the constraint of the adjustment ratio of the load regulating transformer, and the upper and lower limits of the active power output. Adjust the upper and lower limits of the reactive power output [3]. Among them, the tap position of the on-load tap changer and the number of groups in which the parallel capacitor is put into operation are all integers.
In SA, unequal constraints are usually attached to the objective function as penalty terms. The objective function used in this paper is: Ps(u,x)+cK. Where Ps(u,x) is the active network loss, K is the number of violations of the unequal constraint, and c is the penalty factor. For different types of unequal constraints, the penalty factor c can take different values. When the constraint condition is more important, such as the upper limit of the voltage (more than 1.1 times the rated voltage) and the line power limit, c may take 1; when the constraint is not important, such as the lower limit of the voltage (less than 0.95 times but greater than 0.9 times) Rated voltage), etc., c can take 0.5.
2 Algorithm SA was proposed by Metropolis et al. in 1953. It simulates the annealing process of solid matter (such as metal) in physics to solve the combinatorial optimization problem. During the physical annealing process, the metal is usually first heated to melt so that the particles therein can move freely, that is, in a high energy state. The temperature is then gradually lowered to cause the particles to form a lattice of low energy states. As long as the temperature drops sufficiently slow near the freezing point, the material can get rid of the local stress and form the lowest energy ground state-crystal [7]. The crystal is correlated with the optimal value, the cooling process, and the optimization process to form an SA algorithm. The SA solution steps are as follows [8]:
1) Select an initial state x0 from the feasible solution space, calculate its objective function value f(x0), and select the length of the initial control temperature T0 and the Markov chain.
2) Generate a random perturbation in the feasible solution space, get the new state x1, and calculate its objective function value f(x1).
3) Determine whether to receive: If f(x1) < f(x0), accept the new state x1 as the current state. Otherwise, according to the Metropolis guidelines, whether to accept x1, if accepted, the current state is equal to x1; if not, the current state is equal to x0.
4) According to a certain convergence criterion, judge whether the sampling process is terminated, if it is 5, otherwise it will be 2.
5) Reduce the control temperature T according to a certain temperature cooling scheme.
6) According to a certain convergence criterion, determine whether the annealing process is terminated. If yes, turn to 7, otherwise turn 2.
7) Use the current solution as the optimal solution output.
The SA can converge to the global best advantage with a sufficiently high probability (close to 1), provided that the initial temperature is sufficiently high, the temperature drop is slow enough and the termination temperature is sufficiently low. It is difficult to meet these requirements in practical applications, so the solution results are not ideal. In addition, the SA search efficiency is low, and the final output may be worse than the intermediate result. Over the years, SA's main improvements have been the choice of initial temperature, cooling strategy and termination criteria. The initial temperature is typically taken to be a value of the same order of magnitude as the objective function. In the neighborhood search process, when the probability of the quality of the solution deteriorates as Boltzmann distribution, S. Geman and D. Geman prove that the T=T0/log(1+t) cooling strategy can make the SA search globally optimal. , where t is the number of cooling times [9]. In the later stage of the search, when the probability of the quality of the solution deteriorates as a Cahchy distribution, H. Szu and R. Hartley propose that the fast cooling strategy by T=T0/(1+t) can make the SA search globally optimal [10] ], thereby avoiding the search to fluctuate within the neighborhood of the global optimal solution. There are also many ways to terminate the criteria, such as taking the control temperature down to a set minimum temperature, the number of Markov Chains experienced by the current optimal value, and so on.
Considering the complexity and programmability of the calculation, this paper uses the memory-guided search method combined with the local optimization of the pattern method to solve the RPOP problem. The so-called memory guidance refers to taking the optimal value in the search result of the previous stage (ie memory length) as the starting point of the next stage search. This method avoids the blindness of the search to some extent. The poor local search ability is almost a common problem of all random search methods, and the Pattern Search (PS) is more suitable for local optimization. Therefore, this paper uses the pattern method to locally optimize the optimal value in each chain. And the optimal value in the whole search result is used as the output result, thereby increasing the possibility of obtaining the global optimal solution. The termination criterion is a combination of the minimum control temperature and the optimal value retention chain number.
PS is a direct solution to the optimization problem proposed by Hooke and Jeeves in 1961. The strength of PS is the ability to track the valley line (ridge line) to accelerate to the optimal solution [11]. In this paper, PS is used to locally optimize the optimal value in each chain of SA. The specific steps are: take the most advantage in each chain as the initial base point B1; determine the step size of each independent control variable Ui; The two directions are perturbed, and the sagittal point is moved in the direction in which the objective function value is optimized; when all the variables are perturbed, the new base point B2 is obtained; a similar photograph is taken from the B1+2 (B2-B1) point. Then, the new base point B3 is obtained; then the above steps are repeated from the B2+2 (B3-B2) point to explore and accelerate until the target function value no longer drops, and the local optimization iteration terminates. PS improves the local optimization ability of SA.
3 Example This paper takes the reactive power optimization problem of IEEE-30 node system as an example to verify the proposed algorithm. The data of the IEEE-30 node system is shown in document 12. The system consists of 6 generators, 4 transformers and 2 parallel capacitors. The control variables are 4 transformers and 2 parallel capacitors. In order to highlight the characteristics of the high and medium voltage distribution network, it is easy to analyze and compare, and the reactive power generation of the generator is not controlled. The line transformer ratio is adjustable, the upper and lower limits of the ratio are 1.1 and 0.9 respectively, the step size is 2.5%, and the tap position variable is set to integer, and the value range is [-4, 4]. Let the node 24 capacitors be divided into two groups, and the number of switching groups is set to integer, and the value range is [0, 2]. The node 10 capacitors are divided into four groups of equal size, and the number of switching groups is set to integer, and the value range is [0, 4]. The power reference value is 100 MVA. The initial temperature T0 of SA is taken as 10, and the cooling strategy adopts a simplified method of T=kT0, in which the temperature attenuation coefficient k takes a larger value (0.95), which leads to an increase in the number of iterations, but can search for a larger range of solution space, Conducive to obtaining the global optimal solution. The Markov chain length is shorter (50) in order to reduce algorithm time. The disturbance amount is generated by moving one bit up or down by 1/3 probability in each of the integer control component value sequences. For the deterioration solution point x, the probability exp((f(x')-f(x))/T) is accepted, where x' is the previous solution point, and f(x') and f(x) are the corresponding solutions. The target function value of the point. The initial step size of the PS local optimization is taken as 1. The termination criterion takes a minimum control temperature of 0.05 or an optimal value of 40. The length of memory optimization is 10. Since PS is closely related to the initial value selection and is easy to fall into local extreme points, the initial objective function value of SA is generally too large. In order to speed up the calculation, when the temperature drops below 1, the optimality in each chain is started. Individuals perform local optimization.
Considering that the calculation of reactive power optimization is mainly based on solving the power flow equations, with the expansion of the grid size, the time consumed by SA itself is not much different, so this paper only deals with the number of times and the distribution of optimal values. Compare the aspects. Under the above assumptions, the exact solution of reactive power optimization is 7.05014 MW. In order to obtain this solution, a total of 94*5*3 = 98415 flow equations need to be calculated. The table below compares the experimental data for several SA improvement methods. Each method performed a total of 20 tests. Each method listed by serial number in the table is an improvement point based on the former method.
The above table shows that each additional improvement measures improves the quality of the understanding points and the stability of convergence. Among them, the memory optimal value method significantly shortens the distance between the understanding point and the global best advantage. The combination termination criterion significantly reduces the number of iterative solutions to the power flow equations and speeds up the calculation. The disadvantage is that the quality of the solution point is slightly deteriorated. Memory-guided search further speeds up the calculation and improves the quality of understanding. PS local optimization is particularly effective for obtaining high-quality solution points. In the 20 trials of PS local optimization, 11 times converge to the global best, and the other 9 convergence points are slightly lower than the global best. The disadvantage is to solve The number of tidal equations increased by 10.5%, but the test results were satisfactory.
4 Conclusions In this paper, the improved simulated annealing algorithm (ISA) is used to solve the reactive power optimization problem of high and medium voltage distribution networks. The global optimal solution can be obtained with a large probability, and the stability of convergence is better. Simulation experiments verify that the method described in this paper is reasonable and feasible. The experiment found that ISA solves the RPOP problem and still has the following problems:
1). Determination of the cooling strategy. Although they are based on the principle of large-scale rough search and small-scale accurate search, different cooling strategies have a greater impact on the overall calculation speed and the quality of the final solution. For different optimization problems, it is often necessary to go through multiple tests to find a suitable cooling strategy.
2). Improvement of the local optimization method. In the experiment done in this paper, the local optimization has to solve 782 power flow equations on average, accounting for 19.56% of the total number, which is one of the main factors affecting the solution speed.
These issues will be the follow-up points of this article, and experts and scholars are welcome to give guidance.
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