Multiobjective Optimal Placement of Public Fast Charging Station on Power Distribution Network Using Hybrid Ant Colony Optimization and Bees Algorithm

— The multiobjective hybrid ant colony optimization (ACO) and bees algorithm (BA) is proposed to solve multiobjective optimal placement of public fast charging station (FCS) for battery electric vehicle (BEV) on power distribution system. This new algorithm is named as MOHACOBA. It is used to minimize simultaneously both total cost associated with FCS and feeder loss on distribution network under many constraints of the power distribution system and traffic condition. The IEEE-69-bus in Tianjin Development Zone is the test system for the proposed approach with three case studies on fast charging head size. In order to verify performance of algorithm, four performance metrics (Hypervolume ratio, error ratio, spread and epsilon indicator) is applied to measure quality of Pareto optimal front of proposed method and it is compared with other multiobjective optimization methods i

Objective function of the best solution Di Q Reactive power demand at the th i bus (kVar) limit cput CPU time limit in computation I. INTRODUCTION Battery electric vehicles (BEVs) are driven by an electric motor powered by rechargeable battery packs. It is known that they do not emit the pollution produced with the internal combustion engine car (ICEs). BEVs can convert about around 80% of the electrical energy from electric power source to mechanical power. It shows that the energy efficiency of BEV is higher than ICE. However, BEVs can run about around 150 kilometres before recharging at charging station while ICE can run over 500 kilometres before refuelling [1]. In order to release this problem, charging station for electric vehicle (EV) should be installed sufficiently along the street or service area.
Fast charging station (FCS) could possibly release the speed issue in charging for BEV but it causes some negatives effect to the power distribution network like real power loss [2]. Thus, the FCS planner must plan to reduce this loss. Moreover, they should consider total cost in traveling from BEV owner house to FCS for recharging a day. The investment and operating cost of FCS should be combined as total cost. The optimal placement of FCS is studied in many research works [2][3][4]. Total cost of charging station and feeder loss cost of distribution network is combined to be single objective under many constraints and it is solved by the modified primal-dual interior point algorithm [2]. The charging station planning with single objective of the total cost under traffic constraints is solved by genetic algorithm [3]. The primary investment, operation and mobility cost is combined to be single objective for optimization problem solved by program processing [4]. However, the multiobjective optimization of both cost associated with FCS and feeder loss in the power distribution system is not yet developed subject to factors of traffic condition, electric power supply of FCS, power distribution system.
Various multiobjective optimization techniques such as multiobjective ant colony optimization (MOACO) [5], nondominated sort genetic algorithm II (NSGA II) [6], and multiobjective particle swarm optimization (MOPSO) [7] can solve multiobjective problems in electrical system. Also, multiobjective hybrid swarm optimization is developed to solve multiobjective optimization problems [8]. However, MOACO is more successful in searching Pareto optimal front [5]. From these reason, hybridizing bi-swarm intelligence for the multiobjective optimal placement of FCS is proposed in this paper to improve performance and efficient of MOACO with Bees algorithm.
This paper proposes the multiobjective optimal placement of FCS on power distribution system under many constraints of the power distribution system and traffic condition. The multiobjective hybrid ant colony optimization and bees algorithm (MOHACOBA) for the optimal allocation of FCS is proposed to minimize simultaneously both cost associated with FCS and feeder loss of distribution network and compared with other multiobjective optimization. The IEEE-69-test system in Tianjin Development Zone is used to test the proposed approachwith three case studies on fast charging head size. Hypervolume ratio, error ratio, spread and epsilon indicator are brought to find performance of MOPSO, NSGA II, MOACO and MOHACOBA. Numerical results and conclusion is presented in last section.

II. PROBLEM FORMULATION A. Location Graph of FCS Planning on Power Distribution System
A Tianjin Development Zone of about 10.5 square kilometres as residential area with 3,140 electric vehicles and the location of BEV load points can be found in reference [3]. A FCS can be constructedat bus of IEEE-69bus system in Tianjin Development Zone and its system data of bus and branch can be found in reference [9]. The backward-forward sweep distribution power flow is used to calculate the system operating condition of the systems [10]. In this paper, BEVs use a rapid recharged battery and FCS is constructed as 3-phase with many dc fast charging head. One bus of the IEEE-69-bus has to be chosen from a set of bus numbers in order to install a station of FCS.

B. Mathematic Model of the FCS Planning on Power Distribution System
The mathematic model of the FCS planning comprises two objective functions under many constraints as follow.
Objective Functions: 1) The total cost associated with FCS: The total cost associated with FCS in the residential area can be expressed as follows.

NV O&M TRV
Cost (1) i) Initial investment cost: Initial investment cost of FCSs is formulated as uniform series capital recovery cost or annual payment for recovery [6] as following equation.
Total travelling time   allEV T for recharging of all BEVs is shown as following equation.
2) The total real power loss in the feeder of the power distribution: The total real power loss in the feeder of the power distribution system is formulated as follows.
Constraints:The constraints include the equality and inequality of electric power flow of the power distribution, power supply constraints of FCS, power distribution system and traffic constraints as follows.
1) Active and reactive power flow balance equation as follows: 2) Constraint of daily power supplying of FCSs for all BEVs: Electric power consumption of all BEVs which select to charge its battery at the FCS once per a day must be less than daily power supplying of the FCS as follows.
3) System quality constraint of power distribution network: System quality constraint is defined as voltage limit and voltage deviation of distribution network due to the connection of the FCSs. The constraints of voltage magnitudes of all buses on the distribution network must be within acceptable range and can be written as. min max , The summation of voltage deviation is expressed as follows.
4) Security constraint of distribution system: Security constraints are of feeder line loading limit and substation capacity limit.

5) Constraints of the service radius of FCS:
The service radius of FCS must be within the maximum limit of distance as follows.

6) Constraints of distance between two adjacent FCSs:
The distance between two adjacent FCSs must be within the minimum and maximum limit.

7) Constraints of service number of FCS:
The summation of service parameters of all FCSs must be more than or equal to the number of BEV load points as follows. x is on worse )the operator  denotes worse)than 2 x in all objectives, or objectives.
2. The solution 1 x is strictly better (the operator  denotes better) than 2 x in at least one objective or If any of the above conditions is violated, the solution 1 x does not dominate the solution 2 x .

Definition 2.
* x is said to be a Pareto optimal solution of multiobjective optimization problem if there exists no other feasible x such that for at least one objective function j f .

B) Principle of Ant Colony Optimization
Ant colony optimization (ACO)is motivated by the collective behavior of a real ant colony in nature. Ant colony optimization is a probabilistic technique and an iterative algorithm which can find best paths in optimization problem designed in pattern of graph. While an ant walk on the path, it will drop pheromone on path. Consequently, accumulated pheromone on the path will continually guide the ants in walking and the path which has many pheromones can be the candidate of best path in current iteration of computation. Each ant will walk until finishing its tour and the best path will be acquired from these mechanisms at last iteration.

C) Principle of Bees algorithm
Bees algorithm (BA) is an optimization technique motivated by the natural forging behaviour of honeybees. The process of algorithm can be described as follows. Scout bees initially find the food source. They will return to the hive and be raised as an employed forager. Recruited employed foragers will follow an employed forager who memorizes the location of the food source. A number of recruited employed foragers of each food source will depend on the importance of a food source. They will exploit the nectar around neighbourhood area of the food source. After the employed foraging food source, bee loads a portion of nectar from the food source, and then returns to the hive. Moreover, bees will abandon food source that has little nectar. Those bees become new scout bees to search new food source. BA uses these mechanisms in searching optimal solution.

D) Multiobjective Hybrid Ant Colony Optimization with Bees Algorithm for Solving FCS placement
The computation flow of the proposed MOHACOBA algorithm is described as follows.
Step 0:Initialization, the process of this step is the following; -Read system data and set initial parameter of MOHACOBA -Start iteration; -Initial trail intensity on route is set as (0) 1 hi   and initial probability distribution on the route is set as -Calculating two heuristic functions which are defined as visibilities of objective function of the th h station at th i the bus can be expressed as follow.
The parameter 0 q can be set from 0 to 1 and q is a random number in a range of [0,1]. , the selection process on the bus î of the h station of ant k is based on discrete spinning the roulette wheel between 1 and B N with the probability calculated in (25).
Step 2: Evaluating both objective functions and find Pareto optimal solution;Evaluating both objective functions of feasible solutions and finding the non-dominated solution this iteration by non-dominated sort function: The non-dominated solution in this iteration will be set as the Pareto optimal solution   .where np is the number of the Pareto optimal solutions.
Step 3:Recruit bees around Pareto optimal solution;The process of bees algorithm is used in this step.
Where kb is a positive number.
Step 6: Stopping criteria If limit _ cpu time cput  then end; else go to Step 1.  1) It can efficiently overcome the drawback of MOACO that have stagnation behavior in searching.
2) The candidate paths to be selected by the ants has new alternative paths rather than to be fixed because of additional process from bees algorithm. Consequently, the solution will tend to be diverse and various in finding Pareto optimal front. 3) It can find Pareto solutions of multiobjective optimization problems very efficiently.

E) Quality Measurement of the Pareto Fronts
Following four metrics are used in this paper to measure the quality of the Pareto-optimal front obtained by various algorithms: 1. Spread: This metric measures the extent of spread or equal spacing of Pareto-optimal solutions along the Pareto-optimal front. As long as the spread is uniform, this metric produces a small value [11].
2. Hypervolume ratio (HV): This metric calculates the normalized volume in the objective space covered by the members of the Pareto optimal front. It is said that whenever a set of Pareto-optimal solution is better than another Pareto set, its hyper volume is higher than the latter one [11].
3. Error ratio: This metric uses the true Pareto front as reference set. Lower values of error ratio are preferable [12].
4. Epsilon indicator: This metric uses the worst-case distance between Pareto front and true Pareto front. The metric is harder to meet, if it have a large gap, it will have poorer metric performance [13].
This paper uses boxplots to present the statistical data of four performance metrics from all methods. The results were computed by using Pentium core2duo, 2.2 GHz processor, 2GB ram coding by Matlab® programming language. Enumeration is operated to find true Pareto front on the IEEE-69-bus system. 100 trial runs were carried out for all algorithms with limit cput = 250 seconds. The optimal parameters of MOHACOBA and other optimization techniques for all cases can be obtained from trial and error and is shown in Table I.   Fig. 2 show best compromise solution and Pareto optimal front from all methods and true Pareto front. The best compromise solution and location of FCS can be calculated as 286,563.27 CNY and 215.31 kW at bus [5 19 29 49 56 66] and its location on IEEE-69-Bus system can be shown in Fig.3.  Table 2.show minimum value, best compromise solution, and error ratio of Pareto optimal front from all methods. It can be found that Pareto optimal front of MOHACOBA is closer to true Pareto front.   26  22  18  14  10  6   64  62  60  58  56  54  52  50  48  44  39  34  30   45  40  36  32  27  23  19  15  11  7  4   20  16