Artificial bee colony algorithm applied to optimal power flow solution incorporating stochastic wind power

Received Oct 28, 2020 Revised Jun 27, 2021 Accepted Jul 7, 2021 This paper focuses on the artificial bee colony (ABC) algorithm, which is a nonlinear optimization problem. is proposed to find the optimal power flow (OPF). To solve this problem, we will apply the ABC algorithm to a power system incorporating wind power. The proposed approach is applied on a standard IEEE-30 system with wind farms located on different buses and with different penetration levels to show the impact of wind farms on the system in order to obtain the optimal settings of control variables of the OPF problem. Based on technical results obtained, the ABC algorithm is shown to achieve a lower cost and losses than the other methods applied, while incorporating wind power into the system, high performance would be gained.


INTRODUCTION
The majority of the world's fossil-fuel power generation operations use coal and natural gas to generate electricity, which is one of the most expensive commodities used to generate electric power. Polluting emissions from electricity generation based on the combustion of fossil fuels account for a sizable portion of global greenhouse gas emissions [1], [2]. As a result of economic and environmental reasons, workers in the field of electric energy were encouraged to increase and develop renewable energy. The electrical power control are experiencing noteworthy changes due to an increase in wind energy penetration level, causing unused challenges to system operation and planning [3], [4]. Therefore, the operators of power systems both in the planning and operating stage are very interested in optimal power flow (OPF) [5]. The main objective of an optimal power flow methodology is to find the ideal working of a power system by optimizing a specific objective whereas fulfilling certain indicated physical and security limitations [6], [7].

OPF PROBLEM FORMULATION
The solution to the OPF problem involves the optimization of objective function and obtaining the optimal settings of the power system control variables. The formal OPF problem can be written as [31]: Where F refers to the target (objective) function to be minimized, x and u are state and control variables respectively. The state vector x including; i) PG1, generating power at swing (slack) bus, ii) QG, reactive generating power outputs, and iii) VL, load bus voltage. x can be written as: (4) Where NG, NL, NTL and SL are the number of generator buses, number of load buses, transmission lines and number of transmission line loading, respectively. The control vector u including; i) PG, generator active power outputs, ii) VG, generator voltages, iii) QC, shunt VAR compensations, and iv) T transformer tap settings. u can be written as: (5) Where N C and N T are the shunt VAR compensators output and the transformers regulated number, respectively [31].

OPF objective functions
Two different objective functions are chosen in the current paper. The 1 st is the economic objective whereas the 2 nd is the technical objective.

Economic objective
The main objective of the optimization problem is minimizing the operating costs in the wind-thermal power system. a. Cost model of thermal power generators Consider as a generator fuel cost, given as in (6)  The goal of the current paper's optimization problem is to minimize the overestimated and underestimated costs of wind energy caused by wind speed uncertainty. According to: Where is underestimation scaled average cost for wind power in $/MW h, is directly cost output wind power and is overestimation scaled average cost for wind power in MW.
be written as: Where w j is active power generated by j th wind turbine and q j is direct cost coefficient.
E(Y_(oe.j)) can be written as: and ∑ E(Y_(ue.j)) can be written as: Where Cpwj and Crwj are the overestimation and underestimation cost coefficient of jth wind generator in $/MW h respectively. ( ) and are the overestimation and underestimation anticipated value of wind power for jth wind turbine. kj and cj are a shape factor and a scale of the jth wind generator respectively estimating of wind speed in the Weibull probability density function (pdf). v inj , v out,I , v r,j are cut-in, cut-out and rated wind speed respectively. v 1 = v in + (v r − v in ) w 1 /w r is an intermediary parameter in [6]. Minimize the total production cost in wind-thermal power system can be expressed as [33]:

Technical objective
In this paper, two objective functions are considered for the technical category. First, minimize the total active power losses which can be expressed as: Where m is the total number of lines in the system, G k is the conductance of the k th line, V j and V i are the voltage magnitude at bus j and bus i respectively, δ j and δ i are the voltage phase angle at bus j and i respectively [34]. Second, minimize the voltage deviation (VD) of all load buses to improve the voltage profile on load buses. The voltage deviation given by (15) [35]:

OVERVIEW ON ARTIFICIAL BEE COLONY ALGORITHM
In 2005, Dervis Karaboga proposed a new optimization technique that is the artificial bee colony (ABC) algorithm. The ABC algorithm has been shaped by closely watching the exercises and actions of genuine bees while they were looking for nectar assets and sharing the sum of the assets with other colony For an optimization problem, an algorithm consists of three steps is as follows: In the first step, the employed bees are dispatched to find all the resources needed, and then the nectar amount is calculated.
Step two, the onlooker bees choose an asset that matches the information from the already-discovered honeydew assets. The employed bumblebee was sent out to the fields to select new locations in order to identify potential food sources. "Looking" bees would be further broken into two categories: the "used" bees and the "observing" bees. The algorithm works on the basis that the number of employable bees equals the number of available sources of nectar. When we understand where the issues likely lie, we'll be better equipped to deal with them [36]. ABC algorithm: a) Initialization phase In the first step, variables ( = 1, 2, 3, … ) that have not been measured yet are selected at random, using some sort of random methodology. b) Employed bee phase The new sources are identified by each employed bee whose amounts are equal to the half of the total sources. a new source can be found by: Where j is a randomly selected parameter index, is a random number between [0, 1] and it has to be different from , is a random number within the range [-1, 1], is the current position of food source which comparing two food postion visually by bee from this parameter the production of the neighbor food source can be controlled. The new food source postion is produced and evaluated by the artificial bee,by comparing the current food source with previous source taking its performance in the consider. From the information that obtained if the new source has equal or better amount of food or nectar than the old source,it used to replace the old source in the memory. Otherwise, the old source would be retained in memory.

c) Onlooker bee phase
In this phase ,the onlooker bees are work on the principle of probability by selecting the food source with probability can be written as: Where and are the fitness value and probability associated with solution respectively. In each colony, great responsibility for random research is scout bees' bear. d) Scout bee phase In this stage, the scout bee randomly investigates food sources without direction from the queen. Every scout in the swarm thinks that he or she is an explorer. If the supply of food decreases below the gainful level or as a result of applying a given level of the food application of the nectar, the bees associated with it cease feeding. When you have new information, a new understanding, or a new insight, the limit on the number of bees tells you how many from the source and how many to the destination.
Where and are the maximum and minimum limits for optimization parameter, rand (0, 1) is a random number within the range [0, 1]. The number of iterations in ABC algorithm considered as the important criterion for stopping an ABC algorithm. An optimization algorithm might therefore determine that the stopping criteria to be: 1. Number of maximum iterations 2. Maximum error between two consecutive iterations Figure 1 shown the flowchart of the ABC algorithm based OPF problem.

CASE STUDY
In this paper, two wind farms connecting to bus 10 and bus 24 are suggested. Figure 2 shown the standard IEEE 30 system with two wind farms. The wind power penetration level is defined as the ratio of the installed wind power capacity to the total-installed system generation capacity of 10%. The total power generation of six thermal generating in system are around 400MW, therefore the installed wind power capacity is 40 MW. Two wind farms included 10 wind turbines each one has rating 2 MW (Vestas V90, 2 MW) and connected at bus 10 and bus 24 (20 MW in each bus) is used to analyse the impact of incorporating wind farm on different performance analysis of system. Several scenarios with dispersed wind penetration levels from 0% to 100% have been investigated.

OPF without incorporating wind power
In this case, they used the artificial bee colony (ABC) algorithm to find a solution for OPF that did not include a wind farm. The power generation in thermal generator, active power loss and total production cost obtained by ABC algorithm is compared with other methods obtained in the [34]. Table 1 shows the results of this comparison. An 800.638 $/hr total production cost has been obtained by ABC, which is better than linear programming (LP) in [34].

OPF incorporating single wind farm site
In this case, the wind farm is incorporated on bus 10 and bus 24 separately (20 MW in each bus), for penetration levels from 25% to 100% with an interval of 25. The comparison results between ABC and the results obtained in the [34] for slack bus generation, total production cost, active power losses and voltage deviation are shown in Table 2. Figure 3 shows the load bus voltage profiles and Figure 4 shows the convergence characteristic of total production cost for this case when the wind farm is incorporated at bus 10.  Figure 4. Convergence characteristics of the ABC for penetration levels of wind power at bus 10 only

OPF incorporating multiple wind farm
This case shows the impact of incorporating a wind farm connected to bus 10 and bus 24 together (20 MW in each bus). For penetration levels from 25% to 100% with an interval of 25%. Table 3 shows the slack bus generation, the total production cost, active power losses and voltage deviation. Figure 5 shows the load bus voltage profiles and Figure 6 shows the convergence characteristic of total production cost for this case.

CONCLUSION
This paper proposes the application of artificial bee colony (ABC) algorithm optimal power flow for a system that incorporates thermal units and wind farms during normal operation. The performance of the ABC was applied to standard IEEE-30 bus system with and without incorporating wind farm to show its impact on the the slack bus generation, the total production cost, active power losses and voltage deviation, and compared its simulation results with another method. Based on technical results obtained are it can be noticed that the ABC high performance than the rest methods, and concluded that an optimal integration and location of wind farms give significant to system, such as reducing in the total production cost, active power losses and improvement in the load bus voltage profile, while high performance can be noticed when a wind farm site on bus 24 rather than its site on bus 10. Finally, the results are exceptionally much promising.