Simultaneous placement of FACTS devices using cuckoo search algorithm

Received Jul 22, 2019 Revised Oct 9, 2019 Accepted Feb 19, 2020 The power system deregulation requires thechange in reactive power compensation in the power system. The optimal placement of FACTs (Flexi ble AC transmission system) devices is mandatory to recalculate the reactive power compensation in deregulation case. The FACTs devices generally used in series and shunt conections. Here the various facts devices connected in series & shunt combination simultaneously. The optimal placement and sizing of the devices are done in this paper by formulating the objective function with minimization of cost of the generation and minimizing the cost of Facts devices. MALAB is used for writing the code. IEEE 14 bus system is used to here for testing the system. Placing the FACTs separately and simultaneously are studied in case study. Cuckoo search algorithm is used to identify the solution to the optimization problem.


INTRODUCTION
The placement of FACTS devices is studied by many papers. The multiple number of different types like series and shunt facts devices are used together as shown in [1][2][3][4]. In the entire list of facts devices UPFC is one of that which provides both series and shunt combination [4,5]. The papers [1][2][3][4][5] deals with the optimal placement and size of facts devices. Some literatures deal with the increasing the number of FACTS devices [6][7][8][9]. In many literatures the placement problem solution is given in [10][11][12][13][14][15][16][17][18][19][20]. This paper deals with the optimal placement of FACTS devices with cuckoo search algorithm [10,[20][21][22][23][24][25]. A matlab based code is developed for placing the FACTS devices. The dual FACTS devices are placed simulataneously using this algorithm. The FACTS devices used here are combination of series and shunt devices. The combination like SVC-TCSC, TCSC-UPFC and SVC-UPFC are used here are case studies. The objective fuction is used with cost function of the generation and cost function of FACTs devices. The IEEE 14 bus system is used here for testing.

PROBLEM FORMULATION
Bidding cost is considered as the thermal system cost curve so the biding cost can be represented as [9], The incremental cost can be represented as below, Deregulated power system optimal power flow equation is given below, When ∑ =1 = -each seller is contracted amount is at its capacity lower limit.

CUCKOO SEARCH ALGORITHM (CSA)
The cuckoo bird lays eggs in other bird nests. If the host bird recognizes it, it may drop the eggs or it may abandon the nest and form a new nest. The "cuckoo search algorithm" is built on this concept. To simplify, the hypothesis is replaced by the new nest (with new arbitrary solutions) of the number of nodes. To simplify it, a depiction of the respective egg in the nest, and a crane egg represents a new solution, the goal is to use new and imaginative best answers (cuckoo) to replace the worst response in the nest. Here, it is assumed that there is only one egg in the respective nest. Based on these guidelines, the basic steps of cuckoo search (CSOA) can be summarized as pseudo-code. When making new answers x(t+1) for, about, a cuckoo i, a Levy flight is performed Where α> 0 is the step size, which relates to the rulers of the problem. In most cases, it is used as α = 1. Typically, an arbitrary style is a Markovsync, the next rank / location is in the current location (the first word in the equation above) and the probability of the conversion (the second term). Product ⊕ means organ-wise multiplications. This element-wise product is similar to the PSO, but here the levee plane is more efficient at finding the search area because its step distance is too long.
The levy plane basically provides an arbitrary walk, while the arbitrary step length is derived from the levy distribution CSA can thus be prolonged to the type of meta-population algorithm. The algorithm is given below: Step-1: Suppose that n host candidates are Xxi (i = 1, 2, .. n) and maximum iteration.
Step-2: Analyze the maximum number of epochs and select a hook arbitrarily using taxonomic planes to estimate fit or cost function (Fi).
Step-3: Select a nest between n and say arbitrarily (j).
Step-4: Test whether Fj is lower than replacing F with the new solution.
Step-5: (Pa) One of the worst candidates is abandoned and new ones are built. Have the best nest or solution Step-6: Grade the answers and find out the current.
Step-7: Confirm this for all epochs and finish when you reach maximum epochs.

RESULTS AND DISCUSSION
The test system is 3-seller CSA is taken here. As shown in the results the fitness value of CSA in [28]. As it is economic load dispatch the loss consideration also based on the loss matrix. When the same 3seller system is used in the optimal power flow the cost of the generation reduces. We use the same 3-seller system as the test system and we implement the facts devices with inclusion of investment cost.
The FACTS devices considered here are SVC & TCSC, TCSC & UPFC and SVC & UPFC. SVC & UPFC models are taken as reactive power model and the TCSC is taken as reactance model.
The objective function discussed in eq (9/10/11) is taken as a fitness equation with voltage limit and power flow constraints. The well-known metaheuristic algorithm called CSA algorithms is used for testing the fitness function for without facts devices. The results obtained are discussed below.
The Figure 1 shows the convergence curve. It can be seen that SVC with UPFC gives lesser cost compared to SVC & TCSC and TCSC & UPFC. The loss is minimized drastically from the single FACTS devices to multiple facts devices. Table 1 Table 1   And the IEEE 14 bus which is also known as 3-seller deregulated system is considered here for testing the performances. The comparison is provided in the results and discussion section.