International Journal of Advanced Robotics
and Automation

This paper presents Modified Particle Swarm Optimization (MPSO) algorithm for solving reactive power problem. A nonlinear decreasing weight factor used to change the fundamental ways of Particle Swarm Optimization (PSO). To allow full play to the approximation capability of the function of Back Propagation neural network & overcome the main shortcomings of its liability to fall into local extreme value this study proposed a concept of modified PSO algorithm. Back Propagation network jointly to optimize the original weight, threshold value of network and incorporating the PSO algorithm into Back Propagation network to establish a Modified PSOBP network system. Proposed method MPSO progresses convergence speed and the capability to search optimal value. In order to evaluate the proposed MPSO algorithm, it has been tested on IEEE 30 bus system and compared to other reported standard algorithms and simulation results show that (MPSO) is more efficient than other algorithms in reducing the real power loss & voltage profiles are within the limits.

Keywords: Modified Particle Swarm Optimization; Back Propagation; optimal reactive power; Transmission loss;

Reactive power problem is one of the difficult optimization problems in power systems. Various mathematical techniques have been adopted to solve this optimal reactive power dispatch problem. These include the gradient method [1, 2], Newton method [3] and linear programming [4-7].The gradient and Newton methods suffer from the difficulty in handling inequality constraints. To apply linear programming, the input- output function is to be expressed as a set of linear functions which may lead to loss of accuracy. Recently global optimization techniques such as genetic algorithms have been proposed to solve the reactive power flow problem [8, 9]. In recent years, the problem of voltage stability and voltage collapse has become a major concern in power system planning and operation. To enhance the voltage stability, voltage magnitudes alone will not be a reliable indicator of how far an operating point is from the collapse point [10]. The reactive power support and voltage problems are intrinsically related. Hence, this paper formulates the reactive power dispatch as a multi-objective optimization problem with loss minimization and maximization of Static Voltage Stability Margin (SVSM) as the objectives. The Particle Swarm Optimization (PSO) [11-15] was based on the optimal algorithm of swarm intelligence and it guides optimal search through swarm intelligence producing by the corporation and competition among particles. The artificial Neural Network possesses the ability of processing database in parallel, organizing and learning by itself. It has made great achievements in many fields. Especially neural network technique has been used in reliability and few researchers apply the method [16-20] to predict failures. Theoretically, Network [21- 32] may approach any continual nonlinear function. However, affected greatly by the sample, it may fall into local minimum value, thus it can’t ensure that it converge the minimum value in overall situations. In our paper PSO algorithm is introduced into BP network optimization by using iterate algorithm of particle swarm instead of gradient correction algorithm of BP network. This method can shorten the time of training network and improve the convergence speed of BP algorithm. However, according to different system object, if basic particle swarm algorithm is modified, the performance of BP network is improved and its practicality is better. For balancing between the global search and the local search and improving the precision of the result, this study proposed the nonlinear strategies for decreasing inertia weight based on the idea of the existing linear decreasing inertia weight. The result of simulation shows that the optimizing methods speed the rapidity of convergence obviously and the precision of simulation increase greatly. The performance of Modified Particle Swarm Optimization (MPSO) has been evaluated in standard IEEE 30 bus test system and the simulation results show the best performance of the proposed algorithm.

The objective of the reactive power dispatch problem is to minimize the active power loss and can be written in equations as follows:

Where F- objective function, P_L – power loss, g_k - conductance of branch,V_i and V_j are voltages at buses i,j, Nbr- total number of transmission lines in power systems. $$F=P_L+{\omega }_v\times VD$$ $$VD={\displaystyle \sum }_{i=1}^{Npq}\left|V_i-1\right|$$ $$P_G=P_D+P_L$$ $$P_{gslack}^{min}\le P_{gslack}\le P_{gslack}^{max}$$ $$Q_{gi}^{min}\le Q_{gi}\le Q_{gi}^{max},i\in N_g$$ $$V_i^{min}\le V_i\le V_i^{max},i\in N$$ $$T_i^{min}\le T_i\le T_i^{max},i\in N_T$$ $$Q_c^{min}\le Q_c\le Q_C^{max},i\in N_C$$ All the particles to the h times, the optimal position was $P_{gd}=\left(P_{i1},P_{i2},\mathrm{..}{P}_{id}\right)$ The basic formulas are as follows:

Where, $c_1$ &$c_2$ : Speeding coefficient, adjusting the maxim step length that flying the best particle in whole situation and the individual best particle respectively. Appropriate c1 and c2 speed up the convergence and avoid falling into partial optimality r1&r2: Random number between 0 and 1, for controlling the weight of speed W: Inertia factor. It was oriented toward overall searching .We usually take the original value as 0.9 and make it to 0.1 with the addition and reduction of the times of iteration. It mainly used to total searching, making the searching space converge to a certain space. Then we can get the solution in high degree of accuracy by partial refined researching. With the increasing number of dimension of problems, basic PSO algorithm is easily falling into partial extreme value, thus influence the optimal function of algorithm. Someone brought up with improved algorithm. Many scholars’ research shows [11- 15] that “w” has a great influence on the algorithm of particle swarm. When the “w” is bigger, the algorithm has a strong ability in total searching and when the “W” is smaller, it is good for partial searching. Therefore, in recent years, some scholars brought up many schemes. LDW (Linearly Decreasing Inertia Weight) is given by,

Where $w_{max}$ & $w_{min}$ The maximum and minimum value of W, t : The step of iteration, $t_{max}$ The maximum iteration step.

However, there are still problems in equation (12), so in the primary period of operation, if it detects the optimal point, it wants to converge to the optimal point promptly. However, the linear reduction slows down the speed of convergence of algorithm. In the later period of function, with the reduction of “w”, it may make the ability of total searching decline and the variety awaken. Finally it may easily fall into partial optimum. In this text, we use the PSO method of nonlinear variation weight with momentum to improve this method is given by,

2^θ is momentum, when in θ = t / t_max ,t is smaller, 2^θ is near to 1 and w is near to $w_{max}$ ., it ensure the ability of total searching. With the increasing of t, w reduces in non linearity, ensuring the searching ability in partial areas. In the later t = t _max avoiding the problems caused by the decrease of w. That is, the reduction ability of total searching and the decline of variety.

$$f\left(x\right)=\frac{1}{1+e^{-x}}$$ $$R=\frac{{{\displaystyle \sum }}^{\text{}}{\left(Y_{mj}-Y_j\right)}^2}{2}\left(j=1,2,\mathrm{..},n\right)$$ $$D=n_i\times n_h+n_h\times n_{°}+n_h++n_{°}$$ $$E=\frac{1}{M}{\displaystyle \sum }_K^m{\displaystyle \sum }_{j-1}^{n_o}\left(y_{kj}-\stackrel{-}{y_{kj}}\right)$$ $y_{kj}$ The output in theory based on sample K
$\stackrel{-}{y_{kj}}$ The virtual output based on sample K

M: The number of Neural Network

c. Using the improved particle swarm algorithm to optimize the weight and the threshold value of BP network.

Coming to the optimal weight and the threshold value based on equation given below, $$g_{best}=\left[\begin{array}{c}{h}_1,h_2,\mathrm{..},h_{n_h},{\text{o}}_1,{\text{o}}_2,\mathrm{..},{\text{o}}_{{\text{n}}_{\text{o}}},{\text{ih}}_1,{\text{ih}}_2,\mathrm{..},{\text{ih}}_{{\text{n}}_{\text{i}}\times {\text{n}}_{\text{h}}},\\ {\text{ho}}_1,{\text{ho}}_2,\mathrm{..},{\text{h}}_{{\text{o}}_{\text{h}}\times {\text{n}}_{\text{o}}}\end{array}\right]$$
${\text{h}}_{\text{i}}\left(=1,2,\mathrm{..},{\text{n}}_{\text{k}}\right)$The threshold value in the hidden layer
${\text{o}}_{\text{i}}\left(\text{i}=1,2,\mathrm{..},{\text{n}}_{\text{o}}\right)$ The threshold value in the output layer
${\text{ih}}_{\text{i}}\left(\text{i}1,2,\mathrm{..},{\text{n}}_{\text{i}}\times \right)$ The weight between the hidden layer and the input layer
${\text{ho}}_{\text{i}}\left(\text{i}=1,2,\mathrm{..},{\text{n}}_{\text{h}}\times {\text{n}}_{\text{o}}\right)$ The weight between the hidden layer and the output layer

d. Let the optimal weight and the threshold value be as the original weight and then put them into Neural Network for training. Adjusting the weight and the threshold value based on BP algorithm until the function index of the network’s Mean Square Error (MSE) < e. “e” is the preset expected index.

Validity of proposed Modified particle swarm optimization (MPSO) algorithm has been verified by testing in IEEE 30-bus, 41 branch system and it has 6 generator-bus voltage magnitudes, 4 transformer-tap settings, and 2 bus shunt reactive compensators. Bus 1 is taken as slack bus and 2, 5, 8, 11 and 13 are considered as PV generator buses and others are PQ load buses. Control variables limits are given in Table 1. In Table 2 the power limits of generators buses are listed.

Table 3 shows the proposed MPSO approach successfully kept the control variables within limits.Table 4 narrates about the performance of the proposed MPSO algorithm. Figure 1 show about the voltage deviations during the iterations and Table 5

list out the overall comparison of the results of optimal solution obtained by various methods.

In this paper an inventive approach Modified Particle Swarm Optimization (MPSO) algorithm is used to solve reactive power problem, by considering various constraints. The efficiency of the projected Modified particle swarm optimization (MPSO) method is demonstrated by testing it on standard IEEE 30-bus system and the real power loss has been considerably reduced when compared to other reported standard algorithms & voltage profile are well within the specified limits .

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