A Novel Formulation for Optimal Placement of Diesel/Wind/PV in Distribution System by Honey- Bee Mating Optimization Algorithm

A Novel Formulation for Optimal Placement of Diesel/Wind/PV in Distribution System by Honey- Bee Mating Optimization Algorithm

Mojtaba Jamiati

Faculty member, Department of Physics, Naragh Branch, Islamic Azad University, Naragh, Iran

Shapour Haddadipour, Amirabbas Safaie, Majid Bataghva

Department of Electrical Engineering, Naragh Branch, Islamic Azad University, Naragh, Iran

Abstract In this paper, a novel formulation has been suggested to solve optimal placement of hybrid system based on diesel generator, wind farm and photo voltaic. For this, the proposed objective function has been formulated based on: cost of purchasing equipment, cost of gas split, distance from electrical substation, cost of land acquisition, costs of water split. The problem has been optimized by Honey-bee mating optimization (HBMO) algorithm. Simulation has been performed on a practical test system in Iran. Results of the proposed algorithm has been compared with related values of Particle Swam Optimization (PSO) algorithm.

Keywords hybrid system, Diesel generator, Wind farm, Photo voltaic, Honey-bee mating optimization (HBMO) algorithm.

1. INTRODUCTION

   In optimal design of standalone hybrid renewable energy systems (HRES), reliability of the system in supplying power for a demand load is as important as the levelised cost of energy (LCE) produced by the system. Reliability of a standalone HRES in supplying power depends on various parameters, including, system configuration, size of its components, reliability of each component in terms of operation and the availability of renewable resources [1].

   Objective function in [2] has been coded by combination of genetic algorithm to evaluate impacts of DG placement in reliability enhancement and loss reduction as well as voltage profile improvement. In formulation of objective function in [3], technical factor (e.g. minimization of the line loss, reduction in the voltage sag) and economical factor (installation and maintenance cost of the DGs) have been considered. The multi-objective function has been solved using GA and tested on 14, 30 and 34 distribution networks. The proposed objective function in [4] is based on nodal pricing which has been employed to find optimal size and location of DG units for loss reduction, and voltage profile improvement including voltage rise phenomenon. In [5] objective function has been formulated as the weighted sum of reliability indices and power loss, whereas load models, investment costs and DG types have not been considered.

   Evolutionary techniques are used in [6-9] to solve this problem. variety of methods have been used in these papers such as combination of algorithms, defining vulnerable buses from voltage stability point of view and finding DG places by dynamic programming search, sensibility test and heuristic curve-fitted technique [10] and straightforward algorithm. The fuzzy algorithm goes beyond zero and one values in traditional programming and opens new horizon in programming and computer world. References [11-13] use fuzzy algorithm to find optimum place and capacity for DGs. Authors in [14] applied Mixed Integer Non-Linear Programming (MINLP) algorithm to overcome the problem.

   In this paper, a novel objective function has been suggested to calculate cost of hybrid system cost. This problem has been solved by HBMO algorithm. This context consists of five sections.

2. PROBLEM FORMULATION

   As it has been noted before, the main contribution of this paper is to calculate the net revenue of the investor and the capital investment return time period of installation and operation three type of DGs. The DGs are: gas turbine, wind turbine and photovoltaics. Therefore the problem is formulated to minimize duration of capital investment return time for private sector. The calculations are done based on amount of investment for each 3 types of DGs, generating time of each, operation and maintenance costs and bank financial supports (loans). In following formulations, subscript g or gas indicates gas turbine, subscript w refers to wind turbine and the s subscript is for photovoltaics.

   The technologies used in allocating each of these three types of DGs are different, thus capital investment for each one of them could be formulated as eq. (1-3). In wind turbine and photovoltaic generation, gas and water piping costs do not add to other expenses, consequently these factors are eliminated from the cost function:

   Costtg CoEg CoGS g CoCg COLAg CoWS g CoS g (1)

   Costtw

   CoEw

   CoCw

   COLAw

   CoSw

   (2)

   Costts

   CoEs CoCs COLAs CoS s

   (3)

   In these equations, CoE is the cost of equipment, CoGS stands for Cost of Gas Split, CoC is the Cost of Cabling, CoLA is the Cost of Land Acquisition, CoWS is Cost of Water Split, and CoB is the Cost of the Switch. g, w and s indexes are for gas turbine, wind turbine and photovoltaic respectively.

   1. Cost of purchasing equipment

      The value of this factor is corresponded to the installed

      MVA and the amount.

   2. Cost of Gas Split

      If the DG needs the natural gas, cost of gas split and piping from gas station to DG station (depends on distance) should be calculated.

3. HONEY-BEE MATING OPTIMIZATION (HBMO) ALGORITHM [15-16]

   The honey bee is a social insect that can only survive as a member of a community, or colony. Behavior of each class provides the needs of the community. The structure of their community involves three different forms: The queen to spawn, the drone to intercourse with the queen to produce and the worker bee for the task of keeping the broods and take care of queen and drones and other jobs of the hive. HBMO as many algorithms which are formed based on the real behavior of social insects, is formed based on the read behavior of honey bee when process of mating. HBMO can be summarized as following steps:

   • The algorithm starts by mating flight, where a queen selects drones to form the spermatheca probabilistically.

     CoGS

     gas .PDgas .Lgas

     (4)

   • New broods are generated with crossover genotypes of the drones and the queens.

     In which gas is a given coefficient and its unit is Toman/meter (Toman is Iranian money unit) and Dgas is the diameter of pipe and is dependent on MW. Lgas is the distance between DG power plant and gas station.

     1. Distance from electrical substation

        Some cabling should be done from DG station to 63/20 substation, and it can be calculated as follows:

   • Workers are used to do the local search on broods (trial solutions).

   • The available queen is replaced by a brood of prominent.

   DfS

   DfS .LDfS

   (5)

   In this equation DfS is the substation distance coefficient.

   1. Cost of land acquisition

      This term has been included in the main function based on policy made about industrial zone in Iran. In Iran, the land for DG station located within industrial zone is free and the closer the location could get to the industrial zone, the cheaper will be the land. To consider industrial zone, a part of it will be dedicated to network bar. Thus the following equation could be concluded:

      CoLA aCoLA .Land 800 P 200

      (6)

      In eq. (6), DfS is either zero or one. If the DG station is located in the industrial zone, this coefficient is set to be zero, and if not it would be 1. Land is price of the land outside the zone. Land prices are varying inside the cities, therefore we consider 60,000 to 100,000Toman per meter (T/m) for this price. Some of the buses are assumed to be in 60,000 T/m land, some in 70,000 T/m and others are considered to be in 100,000 T/m. DGA is the area occupied the DG power plant.

   2. Costs of water split

   Some of the DGs need water for cooling procedure, which the corresponding costs should be added to cost function:

   CoWS

   water .PDwater .Lwater

   (7)

   In above equation, water is e predefined value and it has T/m unit and PDwater is the diameter of water pipes and it is proportional to MW. Lgas is the length of pipe between power plant and gas station. It should be noted that the pipe length is a geometrical component and value of water.

   Fig. 1. The HBMO algorithm

   The start of the process is performed by mating flight by the queen and drones pursuits the queen. In the mating process the queen copulates multiple times with multiple drones. When mating with drone, its sperm enters the queen spermatheca. The queen fertilizes the eggs using the sperms collected in spermetheca. Among the process, at each step in space, the queen copulates with the drone which encounters probabilistically with, according to following probability role which works like a annealing function.

   (f )

4. SIMULATION RESULTS

   A radial distribution network in Northwest of Iran has been investigated as test systems. Fig.2 shows single diagram of this system. Results of the HBMO algorithm are compared with related values of genetic algorithm. In GA, Mutation rate, selection factor and the numbers of population and iteration are 0.2, 0.5, 12 and 500, respectively. In HBMO algorithm, Mutation rate and the numbers of population and iteration are 0.2, 12 and 500, respectively. Simulations have been carried out by SONY VAIO Corei5, 2.3 GHz.

   prob (D ) e

   (8)

   s (t )

   21

   29 20

   where, Prob(Q,D) is the probability of adding the sperm of drone (D) to the spermatheca of the queen (Q), (f) is the

   58

   57

   44

   28

   17

   16

   18 19

   absolute difference between the fitness of drone (f(D)) and the fitness of the queen (f(Q)) and S(t) is the speed of the

   56 43

   49

   55 42

   48

   36 27 6

   35 26 15 5

   queen at time t. Mating flight may resemble the prowl and

   movement in space and time which the queen encounters

   54 53 50 47 45 41 40 37 34 30 25 22

   14 13 7 4 3 2 1

   with drones in different locations with different speeds.

   59 51 46

   38 31 23

   8

   11 12

   According to the function nature, it is clear that the probability of mating is very high when starting of the flight with higher speed of the queen and or when sufficiency of the drone is close to queens. After each of relocations in space

   60 52

   61 68

   62 67

   39 32 24 9

   33 10

   and passage of time, the queens speed and energy is dies down according to the following equations:

   63 64 65 66 69 71 72 73

   70

   S(t 1) S(t)

   En(t 1) En(t)

   (9)

   (10)

   Fig. 2. Single line diagram of practical 73-bus distribution network

   where, is a factor dependent to the interval [0, 1] and is queens speed and energy drop rate in each transfer. Queens speed is selected probabilistically at the start of the process.

   At the start of each flight, a drone is selected by the queen probabilistically according to above probabilistic function. If the mating is successful, the drones sperm is saved in queens spermatheca. This continues until the spermatheca fills or queens speed and energy ends. As the queen saves sperms of different drones in its spermatheca, it can use various parts of drones genotype to produce new broods which helps to generate broods (suitable solution).

   When the queen ends the mating, generation of broods to predefined numbers is started. Each queen selects a sperm from its spermatheca probabilistically and mates. New brood (trial solution) is generated using queens and drones genotypes. Then the workers come in action to local search to improve burned broods. At the end, if a brood is superior to the queen, the queen is replaced. As HBMO employs the objective function itself and not other auxiliary data, and as the its search is performed in a set of points and not in a single point, and due to using probability roles instead of deterministic roles and because of having suitable mutation operators, all the above factors makes special characteristics of this algorithm with respect to other optimization algorithms to achieve real optimal solution with suitable rate.

   In this stage, optimal numbers of the hybrid system that should be installed are determined based on optimal values and capability of the proposed algorithm has been compared with PSO. Table I illustrates optimal values of investment cost for hybrid system.

   TABLE I. OPTIMAL VALUES OF INVESTMENT COST

   Parameter	DGen	WT	PV
   equipment	80.00	80.00	80.00
   DfS	556.1568	340.4483	49.55950
   COGS	180.5978	0.00	0.00
   CoWS	89.10946	0.00	0.00
   COLA	1177.9600	179.7540	1220.5000
   Cost	19675	15850	8320

   From data of Table I, switches costs for all three types are the same. Cabling and land acquisition cost for photovoltaic is significantly higher, but photovoltaic and wind turbine do not require water and gas piping. As for land acquisition cost, wind turbine comprises the least,

   To prove advantages of proposed algorithm, we compared them with corresponding results from genetic algorithm. Simulation was run for 100 times for each test system and the best solution, average of obtained solutions and Best/Iteration (B/It) listed in Table 2. For each test system, simulations have been performed for 100 times and results in three sections have been presented in Table II. These sections are best solution (overall), average of all solutions and best/ iteration (B/It).

   TABLE II. COMPARING THE RESULTS OF PROPOSED ALGORITHM AND THE PSO ALGORITHM

   Parameters	Technique	Value
   Best	HBMO	0.499628
   	PSO	0.377812
   Mean	HBMO	0.613788
   	PSO	0.418202
   B/It	HBMO	43
   	PSO	21
   Running time	HBMO	411.005135
   	PSO	254.827210

   Regarding to Table II, proposed algorithm delivers a better solution. Best possible solution by this method is 0.1218 lower than relative result from PSO. In average of all solutions, this reduction is about 0.1956 and HBMO algorithm reaches the desired optimal result in 21 iterations very much faster than PSO algorithm (almost in half of time PSO reaches the optimal result).

5. CONCLUSION

Main contribution of this paper is proposing a novel objective function to calculate investment and operation cost of hybrid system. For this, a complete hybrid system based on wind turbine and photo voltaic as well as diesel generator has been placed in a practical test system in Iran. The HBMO algorithm has been used to solve the problem. Five parameters have been defined in formulation which are: cost of purchasing equipment, cost ofgas split, distance from electrical substation, cost of land acquisition, costs of water split. Capability of the proposed algorithm has been confirmed by comparing its results with PSO algorithm.

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