Optimal Allocation of Hybrid Renewable Energy System by Multi-Objective Water Cycle Algorithm

: This article o ﬀ ers a multi-objective framework for an optimal mix of di ﬀ erent types of distributed energy resources (DERs) under di ﬀ erent load models. Many renewable and non-renewable energy resources like photovoltaic system (PV), micro-turbine (MT), fuel cell (FC), and wind turbine system (WT) are incorporated in a grid-connected hybrid power system to supply energy demand. The main aim of this article is to maximize environmental, technical, and economic beneﬁts by minimizing various objective functions such as the annual cost, power loss and greenhouse gas emission subject to di ﬀ erent power system constraints and uncertainty of renewable energy sources. For each load model, optimum DER size and its corresponding location are calculated. To test the feasibility and validation of the multi-objective water cycle algorithm (MOWCA) is conducted on the IEEE-33 bus and IEEE-69 bus network. The concept of Pareto-optimality is applied to generate trilateral surface of non-dominant Pareto-optimal set followed by a fuzzy decision-making mechanism to obtain the ﬁnal compromise solution. Multi-objective non-dominated sorting genetic (NSGA-III) algorithm is also implemented and the simulation results between two algorithms are compared with each other. The achieved simulation results evidence the better performance of MOWCA comparing with the NSGA-III algorithm and at di ﬀ erent load models, the determined DER locations and size are always righteous for enhancement of the distribution power system performance parameters.


Introduction
In recent years, worldwide switching towards reliable and workable hybrid renewable energy systems is mainly because of two reasons, the potential technical and economic benefits of hybrid combinations and the rapid depletion of conventional sources of energy [1]. Hybrid renewable energy (RE) systems based on photovoltaic and wind energy systems are known and implemented successfully in different locations and have a long lifetime [2]. Focusing on improving the hybrid energy sources economically and technically receives much attention from the researchers in both off-grid and on-grid. The implementation of hybrid energy sources provides better performance, and more economic than implementing PV energy system or wind energy system individually. On the other hand the hybrid (1) We proposed a multi-objective Water Cycle Algorithm for optimal allocation of the hybrid power system model in distribution systems. Also, an NSGA-III algorithm is performed and the simulation results between two algorithms are compared with each other (2) Studying the impact of different load models in summer day and winter day on the optimum placement of the hybrid power system model in radial distribution systems (3) Considering the uncertainty of renewable energy sources by using Hong's 2m +1 PEM method. (4) Studying the impact of the hybrid power system model to enhance the technical, economic and environmental issues of distribution systems. (5) Reducing the power loss is considered as a technical benefit for achieving the improve system performance, reliability, and efficiency. (6) Minimizing energy costs because of the reduction in power loss can also be translated into economic benefits by using multiple distributed energy resources (DER) placements. (7) Minimizing the greenhouse gas emission is considered as environmental benefit. (8) Eventuality of the aforesaid approach is conducted on the standard IEEE 33 and IEEE 69 bus power system.  [18] a second-order cone programming model [19] Cuckoo search algorithm [20] The Flower Pollination Algorithm (FPA) [21] biogeography-based optimization algorithm [22] PSO algorithm [23] Multi-objective ant lion optimizer [24] Breeder genetic algorithm (BGA). The organization of the remainder of the current article is as the following, Load and uncertainty modeling discusses in part II. The formulation of the mathematical problem objective functions and constraints are presented in part III. The concept of MOWCA is briefed in part IV. Part V presents the obtained results and discussion. The article's conclusion is given in the final part of part VI.

Load Models
For evaluating the impact of hybrid power system model on DER planning for various load models i.e. summer day load model (SDM) and winter day load model (WDM) loads are adopted in. The real and complex power of the load is considered as constant power in the classical load flow problems, despite, the load may be nonlinear such as industrial load residential and commercial which discussed by models in [25]. The nonlinear dependent voltage load model is represented by exponential function as the following form: In the classical power flow solution, the load is suggested to be fixed power, where α = β = 0. For nonlinear loads representing commercial and residential, the real and complex power components are given in Table 2 [25]. The produced energy of FC is described as follows [26]: The output power of MT is presented as follows [26]:

Photovoltaic System (PVS)
Assume the irradiance of the solar irradiance performance β PDF and CDF are implemented to represent it according to (5) and (6) [27].
α & β: beta PDF parameters, that can be used as the following equation: when applying Equation (5) The PDF and CDF can be expressed according to the following equations [27]: when assuming the V m is the mean wind speed, the parameters can be obtained as the following: When substituting α w in PDF and CDF, the Rayleigh model for WT can be obtained as a function of average wind speed according to the Equations (12) and (13).
The output power generated by WT is obtained in terms of wind speed V wind as follows: The characteristics of different DER technologies (i.e., MT, FC, WT, and PV) are listed in Table 3.

Fundamental of Point Estimated Method (PEM)
The point estimate method is a numerical method exerted to calculate the true unknown value. PEM is a stochastic technique developed by Hong which consists of km and km+1 scheme (K) is a parameter depending on the type of Hong's PEM schemes. The 2m+1 scheme is more accurate than 2m scheme due to its use the kurtosis of the input random variables. So this research work uses 2×m + 1 Hong's PEM [29]. General Procedure of Point Estimate Method: Step 1: Calculate the statistical information of the input variables.
Step 2: Calculate the concentrations for each input variable x l .
Step 4: Compute the statistical information of the output variable (Z) Z(l, k) = F p 1 , p 2 , . . . , p l , . . . , p m (17) For each random variable p l , the three locations are calculated using mean value (µ p,l ) and variance value (σ p,l ) of p l p l,k = µ pl + ξ pl,k .σ pl k = 1, 2, 3 The standard location, weighting factor ω l,k of the uncertain parameters are determined by the following equation: For k = 1, 2 ξ l,3 = 0 (20) The parameters λ pl,3 , λ pl,4 are the third and the fourth standard central moments of p l which are defined as coefficients of skewness and kurtosis as follows: In current work, (K = 3,ξ l,k = 0) is applied for wind and PV power uncertainties.After computing two pairs of locations and weights (p l, k , ω l, k , k=1, 2) for each point, the output function Z will be computed for each variable and for each concentrated point Z(l, k) based on F µ p1 , µ p2 , . . . , p l,k , . . . , µ pm . The jth order moment of Zj can be computed as follow:

Objective Functions
The goal of multi-objective optimal allocation of DER units is to obtain an accurate solution in the optimization process. In this article, three objective functions are examined for optimization as shown below:

Power Loss (Technical Benefit):
Reducing the total system power loss is mainly affected by the optimal allocation of the DERs problem. The power loss equation can be defined as follows [30].

Total Annual Energy Cost (Annual Economic Benefit)
After installing DERs in the network, the overall real losses (P wDER L ) is decreased when compared to that without DER (P woDER L ). The cost provided by DERs is given in [31]. Annual cost has been calculated as the difference in energy loss cost without DER and with DER. The DER cost includes the cost of DER and its installation. So the total annual cost is given by the following equation [32].

Total Greenhouse Gas Emission (Environmental Benefit)
The third objective function (F 3 ) is considered to minimize the harmful gas emission into the environment resulted from the substation and DER units. The values of emission coefficients of DER units and the grid are given in [31].

Equality Constraints
The basics of equilibrium effect on the equality constraints. Real and interactive power balance equations can be written as below [32]: The real and complex power that can be injected when the energy sources are taking into account for distribution system can be calculated as the following equations

Inequality Constraints
• Bus Voltage constraints The bus voltages amplitude at the radial network should be limited by prescribed operating conditions, which appear as the following equation: where, V min i = 0.95 and V max i = 1.05

• Power generation limit
It contains the limits of the maximum real power of the DERs and assuring that the whole DERs capable to work within the permissible limits as the following equation:

Review of WaterCycle Algorithm
The water cycle optimization algorithm (WCA) mimics the stream of rivers and flow directly to the sea and derived by the notification of the water cycle process [33]. The complete details are used from [32]. The general procedures of the multi-objective water cycle algorithm (MOWCA) are summarized as follows [32].
Step 1: Choose the initial parameters for the MOWCA: N sr , dmax , N pop , Max Iteration, and Pareto archive size.
Step 2: Generate a random initial population and form the initial streams, rivers, and sea by using equations as below.
N sr = Numbers of River + 1(sea) (34) Step 3: Calculate the value of multi-objective functions for each stream using Equation (36).
Step 4: Determine the non-dominated solutions in the initial population and save them in the Pareto archive.
Step 5: Determine the non-dominated solutions among the feasible solutions and save them in the Pareto archive Step 6: Calculate the crowding-distance for each Pareto archive member.
Step 7: Select a sea and rivers based on the crowding-distance value.
Step 8: Determine the intensity of the flow for rivers and sea-based on the crowding distance values using Equation (37).
Step 9: Streams flow into the rivers using Equation (38).
Step 10: Exchange positions of the river with a stream which gives the best solution.
Step 11: Some streams may directly flow into the sea using Equation (39).
Step 12: Exchange positions of the sea with a stream which gives the best solution.
Step 13: Rivers flow into the sea using Equation (40).
Step 14: Exchange positions of the sea with a river which gives the best solution.
Step 15: Check the evaporation condition.
Step 16: If the evaporation condition is satisfied, the raining process will occur using Equation (41).
Step 17: Reduce the value of d max which is a user-defined parameter using Equation (42).
Step 18: Determine the new feasible solutions in the population.
Step 19: Determine the new non-dominated solutions among the feasible solutions and save them in the Pareto archive.
Step 20: Eliminate any dominated solutions in the Pareto archive.
Step 21: If the number of members in the Pareto archive is more than the determined Pareto archive size, go to Step 22, otherwise, go to Step 23.
Step 22: Calculate the crowding-distance value for each Pareto archive member and remove as many members as necessary with the lowest crowding-distance value.
Step 23: Calculate the crowding-distance value for each Pareto archive member to select new sea and rivers.
Step 24: Check the convergence criteria. If the stopping criterion is satisfied, the algorithm will be stopped, otherwise return to Step 9.

Non-Dominated Sorting Genetic Algorithm (NSGA-III)
A modified version of NSGA, called NSGA-II, developed by Deb et al. (2000) and Deb et al. (2002), utilizes a fast non-dominated sorting genetic algorithm. This method is computationally efficient, non-elitism preventing, and less dependent on a sharing parameter for diversity preservation. Recently, a reference-point based multi-objective NSGA-II algorithm (called NSGA-III) is proposed by Deb and Jain, which is more efficient to solve problems with more than two objectives [33]. The main procedure of NSGA-III can be briefly described below. NSGA-III starts with the definition of a set of reference points. Then an initial population with N members is randomly generated, where N is the population size. The next steps are iterated until the termination criterion is satisfied. At the t-th generation, the current parent population Pt is used to produce an offspring population Q t by using random selection, simulated binary crossover (SBX) operator and polynomial mutation. The size of Pt and Qt are both N. subsequently, the two populations P t and Q t are merged together to form a new population R t = P t ∪Q t (of size 2N). To choose the best N members from R t for the next generation, the non-dominated sorting based on the usual domination principle [34,35] is first used, which classifies R t into different non-domination levels (F 1 , F 2 , and so on). Then, a new population S t is constructed by filling members of different non-domination levels one at a time, starting from F 1 , until the size of St equals to N or for the first time becomes greater than N. Let us suppose that the last level included is the l-th level. Hence, the solutions from the level l + 1 onwards are simply rejected. Members in S t \F l are already chosen for P t+1 , and the remaining population slots are chosen from F l such that the desired diversity is maintained in the population. In the original NSGA-II, the solutions in F l with the largest crowding distance values are selected. However, the crowding distance measure does not perform well for many-objective problems. Thus, the selection mechanism in NSGA-III is modified by conducting a more systematic analysis of members in S t with respect to the supplied reference points. To achieve this, objective values and supplied reference points are first normalized so that they have an identical range. After normalization, the ideal point of the set S t is the zero vectors. Thereafter, the perpendicular distance between a member in St and each of the reference lines (joining the ideal point with a reference point) is calculated. Each member in S t is then associated with a reference point having the minimum perpendicular distance. Next, the niche count ρj for the j-th reference point, defined as the number of members in S t \F l that are associated with the j-th reference point, can be obtained based on the above process. Further, a niche-preservation operation is executed to select members from Fl, and it works as follows. First, the reference point set J min = {j:argmin j ρ j } having the minimum ρ j value is identified. In case of |J min | > 1, one¯j ∈ J min is randomly chosen. If ρ¯j = 0, we choose the one having the shortest perpendicular distance to the j-th reference line among members associated with the j-th reference point in F l and add it to P t+1 . The count of ρ¯j is then increased by one. In the event ρ j ≥ 1, a randomly chosen member from front Fl that is associated with the j-th reference point is added to P t+1 , and the count of ρ¯j also needs increasing by one. In both of the two cases, once there exists no such member to be selected, the j-th reference point is excluded from further consideration for the current generation. After niche counts are updated, the above niche operation is repeated for a total of K = N − |S t \ F l | times to fill the remaining population slots of P t+1 . For more details of NSGA-III, please refer to [33].The pseudo-codes of NSGA-III are shown in Figure 1.

Non-dominated sorting genetic algorithm (NSGA-III ) procedure
Input: H processed reference points Zs or predefined desired points

IEEE 33-bus system
For examining the feasibility of the suggested MOWCA optimization technique, a test system consists of 33-bus and 32 branches is used. 100 MVA, and 12.66 kV operating parameters, and loading parameters are 3720 kW and 2300 kVAr respectively. The active and reactive losses without installing DER units are 202.7 kW and 140.03 kVAr, respectively. The system parameters are found in [31].

Case 1:Constant load model
The results calculated by the suggested MOWCA algorithm are shown as in Table 4. It is compared to the results obtained by other technique like NSGA-III for comparative study with the suggested algorithm. It is observed from

Best Compromise Solution
The power system operators may have imprecise goals for the DERs planning problem. Therefore, a fuzzy-based mechanism is employed over the tradeoff curve of the Pareto optimal set obtained by the MOWCA and NSGA-III algorithm to extract the best compromise solution. The value of the membership function µ k i is calculated for the kth solution of the ith objective function, as follows [34]: For each non-dominated solution in the archive set, the normalized membership function U k is calculated as follows: The solution that has the maximum value of U k is considered the best compromise solution. In this paper, all objective functions have the same importance (weight factor).
The values of input data parameters used in NSGA-III and MOWCA are summarized in Table 4.

Results and Discussion
To define the impact of the suggested algorithm carried out on a test system of IEEE-33 bus systems and the IEEE-69 bus network. The cost of the energy losses per kWh is supposed to be $0.05 [31]. The planning of hybrid power system model added to different load models, like constant, residential and commercial load models at summer day load (SDM) and winter day load (WDM) are made by employing MOWCA and NSGA-III form minimization of total power loss, total annual energy cost, and emission while placing the DERs in appropriate locations. The simulations have been carried out over six different cases as shown in Table 5.

IEEE 33-Bus System
For examining the feasibility of the suggested MOWCA optimization technique, a test system consists of 33-bus and 32 branches are used. 100 MVA, and 12.66 kV operating parameters, and loading parameters are 3720 kW and 2300 kVAr respectively. The active and reactive losses without installing DER units are 202.7 kW and 140.03 kVAr, respectively. The system parameters are found in [31].

Case 1: Constant Load Model
The results calculated by the suggested MOWCA algorithm are shown in Table 4. It is compared to the results obtained by other techniques like NSGA-III for comparative study with the suggested algorithm. It is observed from Table 6 that a significant reduction is achieved by MOWCA in the annual energy cost (683,595.915 $) and Emission (5489.94691 Ib/h) in comparison with NSGA-III while the power loss achieved by MOWCA method (103.9202 kW) is higher than NSGA-III method. Figure 2 shows a set of non-dominated solutions or Pareto optimal fronts of constant load model.

Case 2: Summer Day Load Model (SDM)
• Residential load Table 6 depicts the multi-objective output for the residential load model. The network losses are 164 kW before the installation of any DER, and after installing they are reduced to 71.2596 kW.From Table 4 it is clear that the MOWCA method significantly improves the system performance in terms of reduction of the power loss of (71.2596kW) and annual energy cost (710,536.85$)as compared with NSGA-III. However, the emission (5078.22182Ib/h) is less in NSGA-III.
• Commercial load Table 6 illustrates the obtained results from implementing multi-objective optimization for the commercial load model. Before installing any DER the system losses are 152 kW and after installing they are reduced to 54.95 kW. The simulation results show that the MOWCA method reduces power losses and emissions. However, the annual energy cost is less in NSGA-III. Figure 3 shows Pareto optimal fronts and three dimensional residential and commercial load models at summer day load model. The output results using MOWCA optimization algorithms are compared to the NSGA-III method and summarized in Table 6. The comparison proves that the suggested MOWCA provides the most reduction is achieved in annual cost and emission as compared with NSGA-III method. While the power loss achieved by MOWCA (69.68398 kW) is higher than NSGA-III (53.64945 kW).

• Commercial load
The output results deduced using the suggested MOWCA are compared to NSGA-III as presented in Table 6. It may be notified that MOWCA significantly reduces the power loss and emission as compared with the NSGA-III algorithm. However, the annual cost is less in NSGA-III. Figure 4 shows Pareto optimal fronts and three dimensional residential and commercial load models at the winter day load model.

IEEE 69-Bus System
To show the performance of the proposed optimization techniques on a huge network is developed using a 69-bus network, the second test system used is 69-bus systems with a load of 3800 kW and 2690 kVAr, respectively and the data related to this test system was taken from [31]. Before the placement of DG units, the total active and reactive power losses are 224.95 kW and 102.12 kVAr, respectively.

Case 4: Constant Load Model
From Table 7, it is clearly notified that the results obtained by MOWCA show that significant reduction is achieved in the active power losses (135.852 kW) and annual energy cost (653,778.637$) in comparison with NSGA-III while the emission achieved by MOWCA method (5622.082 Ib/h) is higher than NSGA-III method. A group of non-dominated solutions or Pareto optimal fronts of constant load model are shown in Figure 5.  • Residential load Before installing any DER the system losses are 177 kW active power loss and after installing they are reduced to 88.02824 kW. Form Table 7, it can be noticed that the results obtained by MOWCA show that significant reduction is achieved in power loss (88.02824 kW) and emission (5270.99823 Ib/h) as compared with the NSGA-III while the annual economic benefit achieved by MOWCA(713,190.234$) is higher than NSGA-III (537,874.808$).
• Commercial load Before installing any DER, the system losses are 162 kW active power loss and after installing they are reduced to 97.75 kW. Form Table 7, it can be seen that the MOWCA method significantly improve the system performance in terms of reduction of power loss of (87.47904 kW) and emission (5066.35384 Ib/h) as compared with NSGA-III. However, the annual economic benefit is less in NSGA-III method. Figure 6 shows Pareto optimal fronts and three dimensional of residential and commercial load model at summer day load.  (a) Residential load model (b) Commercial load model Figure 6. Distribution of Pareto-optimal solutions for residential and commercial load models at summer day load in the IEEE-69 bus system.

Case 6: Winter Day Load Model (WDM)
• Residential load Without allocation DER, the network losses are 161 kW and after installing they are reduced to 78.90383 kW. The simulation results show that the MOWCA method reduces power losses and emission in an effective manner. However, the total annual energy cost is high compared with the method NSGA-III.

• Commercial load
Without installing DER, the network losses are 159 kW and after installing they are reduced to (96.37189 kW). It may further be noted from Table 7 that the power losses and emission obtained by the MOWCA method which provides highly accurate results in compared with that obtained by NSGA-III method while the annual energy cost achieved by NSGA-III is lower than MOWCA method. Figure 7 shows Pareto optimal fronts and three dimensional residential and commercial load models at winter day load. Figure 7. Distribution of Pareto-optimal solutions for residential and commercial load models at winter day load in the IEEE-69 bus system.

Conclusions
In this article, the Multi-objective Water Cycle Algorithm (MOWCA) is proposed to determine the optimum placement and size of a hybrid power system model consisting of various combinations of a conventional system and renewable energy resources. Various optimization problems are addressed in this article such as real power loss, annual energy cost, and greenhouse gas emission as objective functions. The prime aim of considering these objectives is minimization of power loss, annual energy cost, and greenhouse gas emission. The DER planning with MOWCA method is tested for different voltage-dependent load models, namely constant, residential, and commercial load at summer and winter day load models in IEEE 33 bus and 69 bus distribution systems. The attained results by MOWCA method are compared with NSGA-II algorithm to validate its performance. It is clear from the comparison of simulation results that MOWCA was capable of obtaining better solutions than NSGA-III approach for multi-objective problems. The results indicated that enhancement of the distribution power system performance parameters depends on the size of DERs and their suitable placement in the distribution power systems. It was clear the proposed MOWCA method proves that the economic and environmental benefit is achieved with the optimal allocation of DERs at the constant load and residential load in the winter day load model regarding to other load models for IEEE 33-bus system while technical and economic benefit is got at the constant load with respect to other load models for the IEEE 69-bus system. The technical and environmental benefit is obtained at commercial load in summer and winter day load model for the IEEE 33-bus system and also at residential load for the IEEE 69-bus system while the technical and e economic benefit is attained at residential load in summer day load model for IEEE 33-bus system. Acknowledgments: The authors would like to thank the reviewer committee for their valuable comments, which help the authors to raise the article quality.

Conflicts of Interest:
The authors declare no conflict of interest with any other researchers. Real output power of the ith Photovoltaic P WTi

Nomenclature
Real output power of the ith wind turbine P gi Active powers of the ith energy source