An Effective Solution to Single-Area Dynamic Dispatch Using Improved Chimp Optimizer

This paper proposes the Improved Chimp Algorithm (ICHIMP) to solve single area dynamic economic load dispatch (ELD) problem of electric power system. Chimp is a biologically-stimulated heuristic optimization technique, which is embedded on impersonating the technique chimps hunt for food and remain existent by escaping from their adversary. The particularity of ICHIMP is that the chimps move in group for hunting but each chimp searches the prey independently. The single area dynamic dispatch problem is described as non-linear, complex and forced optimization problem with objective function to curtail the total generation price, whereas fulfilling the correspondence and dissimilarity constraints of the system. This proposed algorithm has been tested on five different test systems consisting of 3, 6, 13, 20 and 40- generating units.. The test results of ICHIMP determine its superiority over other existing algorithms addressed in literature and show that it outperforms for Single area dynamic dispatch problem of electric power system.


INTRODUCTION
Single area scalar objective economic dispatch Problem (ELDP) of electric power system is a key optimization issue in the power system network due to its complex, nonconvex, non-smooth and non-linear, characteristics [1]. In addition, economic dispatch is subjected to various kinds of correspondence and dissimilarity imperatives such as Balance power, transmission losses and ramp limits [2], [3]. According to [4], [5], To congregate the load demand at feasible price within the limits of transmission and operational capability of the system is achieved by Economic load dispatch, which is the best outcome of many electricity generation units. The static economic dispatch as well as dynamic economic dispatch is categorized from economic dispatch as it is mentioned in [6],this static economic dispatch provides the optimum of the entire fuel price in a specified duration devoid of allowing for the fundamental relation of the systems between dissimilar operating periods whereas much attention is also required to pay when considering dynamic economic dispatch issue in connection of different operating times like as ramp rate limits, prohibited operating zones of generating units. This traditional representation of ED difficulty formulates the price purpose of generating unit as a single quadratic function, this formulation ignores the valve-point effects hence the inaccurate results [5], [7].The realistic ED difficulty is nonlinear, non-smooth, non-convex and more complex owed in occurrence of valve-point loading and ramp limits which complicates the global optimum search [5], [8]. In excess of the precedent decades, a lot of classical techniques have been used for solving the ED problem like linear programming [9], non-linear programming [10], quadratic programming [11], dynamic programming [12], interior point programming [13], mixed integer programming [14], Pattern Search method [15], Lagrangian relaxation algorithm [16] , Newton-Raphson method [17],Lambda iteration [18] and Gradient method. These classical methods suffer from some limitations and inconveniences such as: Worse convergence and computational complexity [19], High sensitivity of initial approximate calculations [20], Difficulties in handling nonlinear, non-convex and non-smooth problems [21], The accurate optimum solution is only guaranteed to continuous cost function which does not coincide with the practical ED problem [22], Not applicable to several real-life problems. The metaheuristics search algorithms have been developed in order to overcome the limits and defaults presented by classical methods [23]. Many metaheuristics algorithms have been used for solving economic dispatch problem as addressed in literature e.g. Differential evolution (DE) [24], genetic algorithm [30], biography algorithm [25], particle swarm optimization algorithm (PSO) [26], artificial bee colony algorithm [27], cuckoo search algorithm [28], bat algorithm [29], bacterial foraging algorithm [36], firefly algorithm [30], flower pollination algorithm [21], chemical reaction optimization [31], grey wolf optimization [32], immune algorithm [33], social spider algorithm [34], teaching learning algorithm [35], gravitational search algorithm [36]. Literature in [45], [37] provides several criteria for classifying metaheuristics algorithms, the highly used among them is the number of candidate solutions handled by every iteration. Based on this criterion [38], [48]: The metaheuristic algorithms are characterized by their natural phenomena imitation and are categorized into two types: single solution based (e.g. Vortex Search Algorithm (VS) [39], Variable Neighborhood Search [40], Simulated Annealing (SA) [41], Tabu Search (TS) [42]) and population-based (e.g. Genetic Algorithm (GA) [43]Cuckoo Search [28],Gravitational Search Algorithm (GSA) [36]). The single solution based algorithm proceeds with only one solution throughout the optimization phase whereas the population based algorithm deals with several solution in the course of optimization. In population-based techniques, the optimal or suboptimal solution coincides to the optimum or is neighborly situated at/or nearly neighbors the optimum. The population based metaheuristics (P-metaheuristic) algorithms are characterized by their natural phenomena imitation and are categorized in four types [38], [44]: Evolutionary Algorithms (EAs), Physics-based, Human-based and Swarm Intelligence (SI) algorithms. As I is addressed in [45] EAs imitate characteristics of biological evolution such as recombination, mutation, and selection. Some examples of EA are Genetic Algorithm that is inspired by the Darwinian theory of Evolution, Differential Evolution (DE), Evolutionary Strategy (ES), Evolutionary Programming (EP), and Biogeography-Based Optimization (BBO) algorithm. According to [44], [46] [47] Teaching Learning Based Optimization (TLBO) [48], Socio Evolution and Learning Optimization (SELO) [49].The fourth category of P-metaheuristics algorithms consists of algorithms that are inspired by the social conducts of organisms that live in swarms, flocks, or herds, shoals [50].Some examples of this category are Particle Swarm Optimization (PSO), Bat Algorithm (BA), Ant Colony Optimization (ACO),Artificial Bee Colony (ABC),Cuckoo Search Algorithm(CSA), Any metaheuristic algorithms has two main components which are: intensification (exploitation) and diversification (exploration) [38]. Diversification aims at generating different solutions in order to explore the search space to a great extent, whereas intensification concentrates on searching in the local region based on the knowledge ensuring that this region is the location of the current good solution. It is imperative to satisfactorily balance between exploitation and exploration in algorithm so as to avoid the decrease or the increase rate of convergence, and also preventing the algorithm from being caught into local optimum or global optimum [51], [52]. As addressed in [53], the basic single-solution based metaheuristics highly tend to be exploitation oriented while basic populated highly tend to be exploration oriented. In the proposed research, an Improved Chimp Algorithm (ICHIMP) is applied to solve the single area Economic Load Dispatch problem and simulation results show that it outperforms other algorithms addressed in literature.

SINGLE AREA ECONOMIC LOAD DISPATCH PROBLEM FORMULATION
The foremost purpose of the single area dynamic dispatch is to diminish the entire fuel price of the power generating units subject to the fulfillments of different constraints.
The overall objective function of the single area dynamic dispatch problem can be categorized to the following subsections:

Single Area Dynamic Dispatch-Conventional Approach
The mathematical formulation of conventional single area dynamic dispatch for one hour can be represented as: The dispatch of power generating units for 'H' Hours may be represented as: This eqn. (2)

PROPOSED IMPROVED CHIMP OPTIMIZER
The advantage of memorization of hunt space clue above the track of iteration compared to other metaheuristics optimization algorithms (MOA) a novel metaheuristic algorithm known as Chimp Optimization Algorithm (chOA) which belongs to Swarm Intelligence Algorithm is proposed. Solitarily the significant swarming behaviors in temperament are the Intelligent Group Haunting (IGH) of chimps. The key sense used for electing the chimps betwixt the various swarming behavior are solitary brilliance and sensual incentive. The procedure of hunting is branched into two aspects: exploration and exploitation. The four major strides of trapping are driving, chasing, blocking and attacking.
The mathematical of independent group, driver, barrier, chaser and attacker are presented.
The prey is sought after during the exploration and exploitation aspects. To mathematically model driving and chasing the prey, eqns. (11) and (12)   Regularly an attacker chimp conducts the hunting process in which driver, barrier and chaser participates. An array to imitate the actions of chimps mathematically, firstly the attacker, driver, barrier and chaser are improved to notify position of the prey. The point of the chimps up till now is to be updated and the message is stored confer to the best chimp positions. This intermediary is suggested by the eqns. (16), (17) and (18) The initial random position of search agents can be generated using the following mathematical equation:

TEST SYSTEMS, RESULTS AND DISCUSSION
Test System-1: The First Test system consist three generators with a load demand of 210 MW. Transmission loss as well as the valve-point effects has been taken into consideration in this test system. The system data are taken from [54]. Using ICHIMP the cost and optimal generations are obtained for Test System and has been shown in Table-1. Table-1 shows the lowest cost for the system as 3192.6059 $/hr. According to the results, ICHIMP performs in obtaining the superlative result for the test system. Since the size is small for this system, it has revealed that a huge numeral of algorithms converged to the same optimal. Test System-2: It is comprised of a six generating units supplying a load demand of 283.4 MW and including transmission losses. The information of this system is used from [18], [55] [56]. Table-2 illustrates the costs and optimal generations obtained, The best fuel cost and the related transmission loss achieved are 925.4682 $/hr and 10.9813MW respectively. Test System-4: This test system consist of 20-generators with multiple fuels and valve-point load effects. A load demand of 5400 MW is considered for this system. The information is taken from [2] and the input data of ten units with 2700 MW load demand are duplicated, so that they correspond to 20 units. The transmission losses are neglected in the price function. Table-4 lists the finest fuel price resulted as 1247.8624 $/hr. It shows that ICHIMP has the lowest cost in comparison with other methods found in [65].  [56]. Table-5 shows the best fuel price obtained as 121415.1246 $/hr. ICHIMP has the lowest cost in comparison with other methods [43], [56], [26], [66], [67], as seen in Table-5.

CONCLUSION
This paper emphasizes the ICHIMP algorithm to Single Area ELD problems in the power systems networks. The improved chimp algorithm has been tested for 3, 6, 13, 20 and 40 -generating units system and it has been experimentally found that the results of the proposed IChimp algorithm are better than other hybrid and recently proposed meta-heuristics search algorithm and such a powerful algorithm may be considered for the solution of Multi-Area Dynamic dispatch problems of electric power system.