Optimal allocation of capacitor devices on MV distribution networks using crow search algorithm

In electrical power networks, reactive power controlling is essential for improving their efficiency and performance such as reducing the power losses [1, 2], ameliorating the voltage profile of the load buses [3], minimising the loading level of the substation, and economising the penetration of the additional installed sources of reactive power [4].

For this purpose, the optimal allocation of the shunt capacitor devices in the distribution network is employed. Usually, it aims to suitably locate and size the capacitors through minimally reducing the total costs of the energy loss and the capacitor investments.

The nature of the capacitor allocation problem is non-linear, complex optimisation problem that needs an effective optimiser to deal with especially for stressed situations of network operation. It has been solved using several previous methods that differ from each other in the studied formulation and the implemented solution tool [5–9]. In [5], a two-stage methodology has been carried out based on the ant colony optimization (ACO) algorithm and the loss sensitivity index for minimising the energy loss and the capacitor costs. In [6], a modified discrete particle swarm optimiser has been applied for minimising the line losses and the investment costs of the capacitor devices. In [7], flower pollination algorithm (FPA) has been developed and applied for the same target, while power loss index (PLI) has been utilised in order to identify the candidate buses for installing the capacitors. In [8], the optimal allocation of the capacitor devices has been incorporated with the optimal reconfiguration problem for reducing the power losses as a single objective. This problem has been solved using a selective particle swarm optimization (SPSO). In [9], second-order PSO has been proposed for handling the optimal allocation problem of the capacitor devices by setting the number of rules utilising the fuzzy expert system.

Crow search algorithm (CSA) is a new optimiser for solving optimisation problems which is based on crow's intelligence in storing and retrieving its food in hiding locations [10]. Its outperformance over GA, PSO, and harmony search algorithm has been demonstrated for solving several engineering applications.

In this paper, this novel intelligence optimiser is developed for optimal allocations to deduce the optimal size of capacitor devices and their locations considering all buses as candidate locations to insert them and so enhancing the search space with all possible locations. The proposed procedure is applied on East Delta Network (EDN) as a real distribution network in the Unified Egyptian Network. Significant technical and economical merits are satisfied for the studied distribution network which proves the capability of the proposed allocation procedure.

Generally, the objective of the optimal allocations of capacitors in electrical distribution networks is to minimise the energy loss and investment costs of additional capacitor devices while various operational limits are satisfied. This is mathematically stated as follows:where F is the net costs ($/year); E_L the yearly cost per kW network losses ($/kW/year); d_L the duration of each load level; Loss_L the network losses in each load period; N_L the number of load levels; C_C the installation and purchase cost for each kVAr capacitor ($/kVAr); Q_C and N_C are, respectively, the size and the number of the installed capacitor device.

This objective function is subjected towhere V refers to the voltage magnitude; N_B is the number of buses; S^flow and S^rating are the apparent power flow and the maximum rating of the distribution lines; N_Line is the number of lines in the distribution network.

N^max refers to the maximum number of possible capacitor installations; and Q_Load is the reactive power demand.

The first constraint represents the voltage quality at consumer side by handling the voltage at each bus within their permissible limits, while the second gives attention to the loading of the distribution network lines. Equation (4) bounds the size of each capacitor device less than the feasible manufacturing limit while (5) aims to specify the number of capacitors to be installed in the distribution network as a budget constraint and so it represents suitability for various distribution companies. The last constraint limits the total reactive injection from new capacitor devices to be less than or equal the total load of reactive power in order to guarantee the lagging power factor and avoiding the leading one. Added to that, the equality constraints should be maintained which are usually represented by the load flow balance equations.

The decision variables of this problem are the optimal size (Loc) of capacitor devices and their locations (Q_C) as follows:These candidate locations are integer numbers chosen from all load buses (2–30) and so the search space is enhanced with all possible locations, while their optimal sizes are integer numbers chosen from (0–1200) kVAr with step 150 kVAr.

The installation of new capacitor devices has great impacts on electrical distribution networks through optimally reducing the energy loss, and economical penetration of shunt capacitors as considered as objective function in (1). In addition, a significant MVA capacity of transformer substation is released [11, 12] and, it is evaluated as follows:where, MVA_S/S-TR is the MVA capacity release of transformer substation where MVA₁ and MVA₂ are its MVA loading before and after installing the new capacitors, respectively (Fig. 1).

Also, the new installations of capacitor devices will control the reactive power flow through the loaded feeders and so their MVA loading will be reduced with certain percentage which is evaluated as follows:where $S_{k,1}^{\mathrm{flow}}$ and $S_{k,2}^{\mathrm{flow}}$ are the MVA line loading pre- and post-installing the new capacitors, respectively.

Furthermore, controlling the reactive power flow through the distribution network and reducing their loading will help in improving the voltage profile at load buses with certain percentage which is evaluated as follows:where V_i,1 and V_i,2 are the voltages at bus i for pre- and post-installing the new capacitors, respectively.

CSA is a new optimiser for solving optimisation problems which is based on crow's intelligence in storing and retrieving its food in hiding locations [10].

Usually, the CSA starts with a flock size of crows at random initial positions which are the values of the control variables.

As no experiences are initially existed to the crows, these positions represent their initial memories. Then, the crows update their positions searching for their best food (solution of the optimisation problems). The heart of the CSA is the update process of the position (x^{i, t+1}) of each crow (i) by selecting another crow (j) in a random way and following it to find out its hidden foods as follows:where r_i and r_j are random numbers between 0 and 1, t is the current iteration number, fl^{i, t} the flight length, and AP^{j, t} the awareness probability of crow (j) at iteration (t). m^{i, t+1} is the memory of crow (i) which is updated as follows:In this way, each crow updates its position and memory. This updating process is reiterated until the greatest number of iterations (t^max) is achieved.

Fig. 1 shows the main stages of the proposed CSA for solving the optimal allocation problem of capacitor devices in MV distribution networks.

The proposed CSA is applied on EDN as a real distribution network in the Unified Egyptian Network. Its one-line diagram is shown in Fig. 2. Its bus and line data are taken from [7]. The rated line voltage is 11 kV, the rated kW is 22,441.3, and the rated kVAr is 14,162.26. The CSA's parameters are set as follows:

The maximum number of possible locations are set to 4; the yearly cost per kW network losses (E_L) is taken 168 $/kW/year, while the installation and purchase cost for each kVAr capacitor C_C is taken 5 $/kVAr [7]. The voltage magnitudes are bounded with ±5% for the underground networks as recommended in the Electricity Distribution Code by the Egyptian Electric Utility and Consumer Protection and Regulatory Authority [13].

Table 1 tabulates the optimal locations and sizes of the capacitor devices using the proposed CSA for EDN. As shown, the locations of the capacitor devices are optimally identified at buses {21, 22, 24, 26}, while their related sizes are {600, 600, 600, 750} with total installed ratings of 2550 kVAr. With these optimal allocations, the distribution losses are minimised from 805.7368 to 705.673 kW compared with the initial case with loss reduction of 12.42%. Also, Table 1 shows a comparison between the simulation results of total costs minimisation obtained using the proposed CSA and those obtained using ACO [5] which demonstrates the CSA outperformance which acquired lower total costs than that obtained using ACO.

Fig. 3 displays the CSA's convergence curve to minimise the total costs of energy loss and investment for EDN. It is clear that, the CSA has fast convergence characteristics in obtaining the optimal solution. Further improvement in the performance of electrical distribution EDN with installation of new capacitor devices using the proposed CSA as follows:

Moreover, the changing of the switching tie-line (the open point of the MV ring) in electrical distribution network has a significant effect on the optimal allocation of the capacitor devices. Therefore, three cases are considered by changing the switching tie-line with preserving the radiality of the distribution network and consequently, the decision variables of the optimal size (Loc) of capacitor devices and their locations (QC) are optimised as shown in Table 3. It is clear that the losses have been reduced with a percentage of 13.75, 12.75, and 12.42% by switching off lines 26–27, 28–29, and 13–30, respectively. Likewise, the minimum total costs of $127,986.7 is achieved by disconnecting lines 26–27. This concludes the high impacts of the distribution reconfiguration on the optimal allocation of the capacitor devices and their technical benefits as well.

In this paper, the shunt capacitors in medium-voltage (MV) distribution networks are optimally allocated by employing a novel swarm intelligence optimiser called CSA. The proposed CSA has been efficiently applied on a real distribution network in the Unified Egyptian Network in order to minimise the energy loss, minimise the costs of the capacitors, and improve the performance of distribution networks. The proposed CSA demonstrates fast convergence characteristics in solving the considered problem. Also, it states better performance than ACO. The allocation procedure using the proposed CSA accomplishes great technical and economical merits. The loading of the transformer substation is reduced and the loading of various distribution lines are improved since their flow are reduced. Also, the voltage magnitudes of all distribution nodes are improved. Furthermore, the reconfiguration of the distribution network demonstrated great impacts on the optimal allocation of the capacitor devices and their technical benefits as well. Therefore, it is recommended to incorporate the possible reconfigurations with the optimal allocation of the capacitor devices.