Water Cycle Algorithm for Probabilistic Planning of Renewable Energy Resource, Considering Di ﬀ erent Load Models

: This work introduces multi-objective water cycle algorithm (MOWCA) to ﬁnd the accurate location and size of distributed energy resource (DERs) considering di ﬀ erent load models for two seasons (winter, and summer). The impact of uncertainties produced from load and renewable energy resource (RES) such as wind turbine (WT) and photovoltaic (PV) on the performance of the radial distribution system (RDS) are covered as this is closer to the real operation condition. The point estimate method (PEM) is applied for modeling the RES uncertainties. An optimization technique is implemented to ﬁnd the multi-objective optimal allocation of RESs in RDSs considering uncertainty e ﬀ ect. The main objectives of the work are to maximize the technical, economic and environmental beneﬁts by minimizing di ﬀ erent objective functions such as the dissipated power, the voltage deviation, DG cost and total emissions. The proposed multi-objective model is solved by using multi-objective water cycle algorithm (MOWCA), considering the Pareto criterion with nonlinear sorting based on fuzzy mechanism. The proposed algorithm is carried out on di ﬀ erent IEEE power systems with various cases.


Introduction
Nowadays, the global load demand for electricity has been greatly increased [1]. This leads to increasing the distribution system capacity by installing new distributed energy resources, therefore installing distributed energy resources (DERs) is an urgent matter. DERs have become an essential electric devices that integrated with modern distributed systems. Optimum place, capacity and number of needed DERs for accurate behavior of distribution systems are essential for ensuring optimum operating performance. The selection criteria of the DERs source is very important to ensure providing the advantages of integrating them with radial networks [1].
Nowadays, introducing the hybrid renewable energy sources to be integrated with radial networks providing technical and economic impacts. Hybrid renewable energy systems based on photovoltaic and wind energy systems are used extensively and have long lifetime. The integration of hybrid 33-bus biomass  biomass  [19] Multi-Objective Natural Aggregation Algorithm (MONAA).
The different objective functions such as total power loss, voltage deviation and, co emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 p the problem formulation. Section 4, introduces the mathematical model of the DERs. D loading models were displayed in Section 5. Load uncertainty is presented in Section 6. T estimation method is discussed in Section 7. Section 8, introduces the mathematical mode proposed technique. The results and discussions of applying the suggested technique in d cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Multi-Objective Natural Aggregation Algorithm (MONAA).
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used. The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, co emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 p the problem formulation. Section 4, introduces the mathematical model of the DERs. D loading models were displayed in Section 5. Load uncertainty is presented in Section 6. T estimation method is discussed in Section 7. Section 8, introduces the mathematical mode proposed technique. The results and discussions of applying the suggested technique in d cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Different loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pest estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in different cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in Table 1. iii.
The different objective functions such as total power loss, voltage deviation and, cost, and emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 provides the problem formulation. Section 4, introduces the mathematical model of the DERs. Differen loading models were displayed in Section 5. Load uncertainty is presented in Section 6. The pes estimation method is discussed in Section 7. Section 8, introduces the mathematical model of the proposed technique. The results and discussions of applying the suggested technique in differen cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in iii.
The different objective functions such as total power loss, voltage deviation and, co emission are used.
The rest of this paper is ordered as follows: Section 2, presents previous work, Section 3 p the problem formulation. Section 4, introduces the mathematical model of the DERs. D loading models were displayed in Section 5. Load uncertainty is presented in Section 6. T estimation method is discussed in Section 7. Section 8, introduces the mathematical mode proposed technique. The results and discussions of applying the suggested technique in d cases displays in Section 9. The conclusion of the paper is given in Section 10.

Previous Work
A review of the applied techniques for the optimal allocation of DERs in RDS is depicted in

Minimization of Power Losses (P loss )
Integration of DESs at suitable location and capacity leads to minimization of network power loss. The loss calculation is demonstrated below [29]: Energies 2020, 13, 5800 4 of 24 where p, and q = to bus and from bus for kth line; V p and V q = to bus and from bus complex voltage (pu); r k is the resistance of kth line (pu); and x k is the reactance of kth line (pu).
S pq is the complex power flow from bus p to bus q through kth line. S qp is the complex power flow from bus q to bus p through kth line.
Q loss = Imaginary (Total loss)

Minimization of Voltage Deviation (VD)
The voltage deviation is decreased after the installation of DG with optimal allocation. The voltage deviation (VD) of any of the studies system bus is evaluated related to substation bus that still has 1-pu voltage. It is calculated as given in Equation (6). Here, V nj refers to the substation voltage for kth line [34].
The objective function for decreasing power dissipated and voltage deviation is formulated as follows:

Minimization of Cost
A best dispatch problem requires achieving system loads in the most economical manner possible. The total expense is the total buying force cost of the main substation and DES, which can be calculated from the following [35]: The total buying force cost of the main substation as follows: The cost of a DES encompasses its fixed cost and a variable cost can be formulated by: From the last equation, the DERs expense includes its initial cost term and a variable term. Cost FX DERs,i is initial investment (or fixed) cost, which includes the cost of equipment, infrastructure, commissioning, as follows: where Cost DERs,i is variable cost associated with operation and maintenance (O&M) as well as fuel, which can be formulated as: The suggested (DERs) technologies are shown in Table 2.

Minimization of Emission
In this objective, decreasing of emissions created from various electric sources and grid is the goal. The following gases are considered, i.e., carbon dioxide (CO 2 ), nitrogen oxides (NO x ) and sulfur dioxide (SO 2 ). The Grid, and the DER data is given in Table 3. The values of emission coefficients of DES units and the grid are represented as follows [36]: The emission produced from MT (E MTi, ) can be calculated by the following equation: The emission produced from FC (E FCi ,) can be formulated by: The emission produced from WT (E WTi ) can be expressed as follows: The emission produced from PV (E PVi ) is formulated as follows: The emission produced from grid (E Grid ) can be calculated using the following equation:

Constraints
The active and reactive power supplied by DES, and bus voltages are examples of operational constraints needed to achieve them while finding the best DES position.

Power Balanced Constraints
In these limitations, the total power flow through the distribution system coming from DGs and grid must be equivalent to the total power flow going to load and loss of the system, as follows. nb nj=1 p gnj + p grid = nb nj=1 p dnj + p loss (19) nb nj=1 Q gnj + Q grid = nb nj=1 Q dnj + Q loss (20)

Inequality Constraints
Nonrenewable Generation limit: The upper and lower constrains of powers supplied by DES are calculated using the following equation: Q min gnj ≤ Q gnj ≤ Q max gnj (22) Voltage limit: the buses' voltage limitation is shown as follows: Line thermal limits: The complex power through any line is limited by its rated value as follows:

DERs Modeling
In this work, the DERs devices are modeled as RESs and N-RESs. The control of PV and WT in this study is adjusted to operate at unity PF.

Photovoltaic System (PVS)
In this section, the probabilistic modelling of photovoltaic system in RDS is presented. Sunlight is converted into electrical energy by a photovoltaic generator. The main parameter that affects the amount of power output from this generator is the amount of solar radiation. To model the behavior of solar irradiance, assume the irradiance of the solar irradiance performance β PDF and CDF are implemented to represent it according to (25) and (26) [37]: where α and β are the parameters of beta PDF presented as follows: Energies 2020, 13, 5800 7 of 24 The relationship between solar irradiance and solar power is expressed as follows: when applying Equation (21) the probability density function f P pv P pv for the output power of PVs can be obtained as the following equation:

Wind Energy System (WES)
The wind energy is converted into electric power by wind turbines (WT). The factors affecting the power generated from a wind turbine are accessibility and speed of wind, the power curve of wind turbines, and size and shape of the turbine. The output power produced by WT is calculated as a function of wind speed v wind according to the following equation: [1]: The probability density function f pw (P w ) for the power generated by WES is expressed as follows:

Full Cell Unit (FC)
The electric power output of FC units is described as follows [1]:

Micro Turbine Unit (MT)
The electric power output of MT units is obtained from the following equation: [1]:

Load Model
In this study, five different types of loads are considered. The considered load types are constant, residential, commercial, Industrial, and agricultural load type. 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 residential, commercial, Industrial, and agricultural which discussed by models in [23]. The effect of different types of loads is represented by exponential function as the following form: The values of α and β for different types of load models in winter and summer are listed in Table 4 [22].

Load Uncertainties Model
To enhance the flexibility and robustness of the proposed system planning and providing reliability to the analysis, the commonly used normal distribution is adopted to approximately characterize the uncertainty of load. The random active power (P d ) of load i are generated based on the probability density function of the load power, f(P di ) according to the following equation: [38]: where the standard deviation (σ P d ) of normal distribution is taken 10% of the considered load level with zero mean (µ P d ) value [39]. Therefore, the uncertainty of power demand prediction is modeled by a vector of independent Gaussian random variables, which is represented as an addition injection at each selected load bus.

Model of Uncertainties Based on PEM Method
Point estimate method (PEM) is one of the appropriate tools to deal with uncertainties. Details of this method are discussed in [38][39][40]. In this article, (2m + 1) Hong's PEM scheme [40] is employed to three buses in each distribution network to represent the load uncertainty. In each case study, the optimization methods performed (2 × 3 + 1) load-flow calculations to estimate the solution of the load-flow based on the PEM method, where three uncertain system parameters are considered in each test system. General steps of (PEM): Step 1: The statistical information of the input variables is calculated.
Step 2: The concentrations for each input variables are determined.
Step 4: The statistical information of the output variable (Z) are calculated by using: F Z = F p 1 ; p 2 ; . . . ; p l ; . . . ; p m ; c (38) Step 5: For each random variable p 1 , the three locations are Computed using mean value (µ pl ) and variance value (σ pl ) of p 1 .
Step 6: The standard location, weighting factor w lk of the uncertain parameters can be find by the following equations: Energies 2020, 13, 5800 9 of 24 Step 7: The F function at this point and its new weighting factor (w 0 ) will be calculated as follows: (42) In this work, (K = 3, ε lk = 0) is used for modeling PV and WT output power under the effect of uncertainties. After calculating two pairs of locations and weights (pl, k, ωl, k, k = 1, 2) for each point, the output function Z will be calculated for each variable and for each concentrated point Z(l, k) based on F(M p1 , M p2 , . . . , p lk , . . . , M pm) , which is computed according to:

Proposed Method
The proposed optimization technique in this study is based on (WCA). The (WCA) simulates the flow of rivers and streams toward the sea and derives from monitoring the water cycle process [41]. The complete details of the multi-objective water cycle algorithm (MOWCA) are tracked step by step as follows [42]: Step 1: The initial parameter of the WCA: Npop, Nsr, dmax, and Maximum_Iteration are chosen.
Step 2: a random initial population and the initial streams, rivers, and sea are generated by using equations as below.
N sr = Number of Rivers + 1 (45) Step 3: The value of multi-objective functions for each stream are calculated by: Step 4: Calculate the intensity of flow for river and sea by: Step 5: Calculate the flow of streams into the rivers by: Step 6: Calculate the flow of rivers into the sea by: Step 7: Replace the positions of river and stream which achieves the best solution.
Step 8: Replace the position of river with the sea which achieves the best solution.
Step 9: The evaporation condition which can be obtained from the pseudo code are review.
Step 10: The precipitation process will be started after the evaporation condition is attained as follows: Step 11: Reduce the dmax using: Step 12: If the termination criteria are satisfied, the algorithm will be ended. Otherwise, return back to step 5.
Pseudo-codes of the MOWCA algorithm is provided in Algorithm 1 [35]. The flowchart of the water cycle optimization algorithm is shown in Figure 1 [36].

Simulation Results Based on MOWCA
This part indicates the impact of the proposed method (MOWCA method) considering decreasing the power losses, voltage deviation, cost, and pollutant gas emission of the RDS. The suggested algorithm has been utilized on big RDS. An analytical software tool has been developed in MATLAB to run load flow, based Newoton-Raphson method and determine optimal location and size of DES. The study scenarios are tabulated in Table 5.

IEEE 118 bus radial distribution system
The IEEE 118-bus (RDS) is large scale study system includes 117 buses and 118 branches with a total reactive and real load powers of 17041.07 kVAr and 22,709.72 kW, respectively, as shown in Figure 2 [43]. The MVA and kV base of the test system are100 MVA and 11 kV, respectively. The total reactive and real power losses are 978.7 kVAr and 1298.1 kW, respectively. System data is taken from [44]. Regarding the uncertainty in the load demand, the normal distribution function is performed and injected at loads on buses 21, 76, and 110. The total numbers of MT, FC, PV, WT units are 4, 4, 2, and 2 units, respectively. MT, FC, PV, WT unit sizes are 150 kW, 400 kW, 300 kW, and 15 kW, respectively.

Scenario 1 (constant load model)
In this case the performance of system is analyzed under three different values of the standard deviation considering constant load model based on MOWCA. The Pareto fronts and the best compromise solution are shown in Figure 3a-c, it's clear that the Pareto solutions at SD = 0.1 of the considered load level are the best solution for improving all objective functions. The three objectives under the effect of SD are illustrated in Figure 3d, It is observed that the 10% of the considered load level is succeeded in minimizing power loss, voltage deviation, and the emission of the network effectively, but the min cost value obtained when SD equal to 0.05 or 0.01 of the considered load level is closed to the value obtained when SD = 0.1 of the considered load level. The optimal allocations of mixed DERs are listed in Table 6. The optimization results achieved by proposed the MOWCA is given in Table 7, it's clear that the power loss reduced by 15.14%.

Scenario 2 (Agricultural load model)
In this scenario, the agricultural load model is presented under a different standard deviation values, the value of α and β in the winter season is the same value in the summer season, there is one optimization result for two seasons. Pareto frontiers and their 2D projections are plotted in Figure 4a-c. It is evident that the significant reduction in all objective functions achieved by MOWCA algorithm considering SD = 5% of the considered load level. Figure 4d shows the effect of SD value on the different objective function. The size and location of different DERs and the optimization results for improving system performance at SD = 0.05 are illustrated in Tables 8 and 9, respectively, it is cleared from optimization results that the total sizes of new electric sources under using agricultural load model are higher that the sizes obtained under using constant load model. The power loss is decreased from 1012.6 kW to 901.8219 kW, the voltage deviation is reduced to 4.3731 PU. The total emission is reduced from 20,609 Ib/h to 18,936.083 Ib/h.

Scenario 3 (Industrial load model)
This scenario displays the industrial load as a load model, the Pareto solutions for proposed algorithm under three values of SD are illustrated in Figure 5a-c. Figure 5d indicates the effect of three values of SD on three objectives. Obviously, using SD = 1% of the considered load level provides highly accurate results compared to results obtained with other values of SD for reducing the power loss, voltage deviation. In addition, the results obtained at SD = 5% of the considered load level closed to the results obtained at SD = 1%. SD = 0.05 of the considered load level is the best value for minimizing cost, in addition, the sizes of DERs are reduced and power loss is increased compared to the results at SD = 0.01 or 0.1. The performance of network at SD = 0.01, and 0.05 are found in Tables 10 and 11. From the optimization result, min active and reactive loss and min voltage deviation obtained with SD = 0.01 but min cost and emission obtained from SD = 0.05. The power loss is reduced from 1235 kW to 901.8219 kW, the voltage deviation is decreased to 4.1282 PU. The total emissions are reduced from 21,750 Ib/h to 19,073.5745 Ib/h.

Scenario 4 (Residential load model)
MOWCA algorithms is employed to determine the best size and placement of DERs based on deterministic planning under residential load model and select best value of SD in winter and summer seasons. The optimization results obtained from the optimization algorithm under Residential load model in two seasons are tabulated in Tables 12 and 13.  Case 4 (at winter season) The Pareto solutions for proposed algorithm and their 2-D projections are visualized in Figure 6a-c and three objective functions are shown in Figure 6d; it is obvious that the SD = 0.1 is the suitable value for minimizing loss and voltage deviation considering residential load model in winter season. For minimizing cost and Emission, the SD value must be reduced to equal to 0.05. The power loss is reduced by 14.258%, the voltage deviation is reduced to 4.1282 PU. The total emissions are reduced from 20,483 Ib/h to 19,073.5745 Ib/h.

Case 5 (at summer season)
In this case, the optimal optimization results obtained under SD = 0.1 with a residential load model in summer season, Pareto frontiers and their 2D projections are shown in Figure 7a-c, the effect of SD values on the different objective functions are cleared in Figure 7d. The best performance of the system has been done in SD = 0.1, the power loss is decreased from 988.4 kW to 836.766 kW, the voltage deviation is decreased to 4.2342 PU. The total emissions are reduced from 20,978Ib/h to 19,561.3486 Ib/h.

Scenario 5 (Commercial load)
This scenario consist of two cases depend on the seasons operation considering commercial load model. The obtained responses were deduced by utilizing the proposed MOWCA considering commercial load model are listed in Table 14. The optimal allocation of DERs is depicted in Table 15.

Case 6 (at winter season)
The Pareto frontiers of proposed algorithm and the objective function analyzing under different standard deviation are depicted in Figure 8a-d, respectively. The results at SD = 5% are better compared to the results obtained at other values for minimizing loss and voltage deviation, however, the cost is reduced based on SD = 10%. The power loss is decreased by 15%, the voltage deviation is reduced to 4.3833 PU. The total emission is decreased from 21,078 Ib/h to 19,704.4773 Ib/h at SD = 0.05.

Case 7 (at summer season)
The effect of SD values on the Pareto solution and objective functions are plotted in Figure 9a-d, respectively, and it's clear that the min loss and voltage deviation together with minimized cost taken when SD = 0.05. In addition, SD = 0.1 is used to minimize emission. The power loss is decreased from 1033.3 kW to 871.2567 kW, the voltage deviation is reduced to 4.33336 PU. The total emissions are reduced from 21,160 Ib/h to 20,175.6564 Ib/h.

Conclusions
Water cycle algorithm (WCA) is used to identify the optimal allocation of distributed energy resource (DERs) in radial distribution systems for minimizing the total network power losses (P losses ), cost (C), voltage deviation (VD), and pollutant gas emissions considering different load model. The DERs and load uncertainties are considered in this study. The proposed method is tested on IEEE 118-bus radial distribution system. The simulation results show the impact of different values of standard deviation (SD) on the performance of the system. The point estimate method (PEM) is applied for modeling the solar and wind power uncertainties. The SD is variated according to load configuration, to improve the RDN performance. According to the summer load, when minimizing power losses, voltage deviation and emission for industrial load, the SD is 0.01. When the SD is increased with small increment, the cost is reduced. In winter load, the SD equal 0.01 to minimize the energy losses, and voltage deviation, where the emission is high. When the SD is increased to 0.05 the emission is minimized. Different values of SD are obtained for each load scenario. This assures the well-known phrase "no free launch".

Funding:
The authors extend their appreciation to the researchers supporting project at King Saud University, Riyadh, Saudi Arabia, for funding this research work through the project number-RSP-2020/278.

Conflicts of Interest:
The authors declare no conflict of interest. Energy price from the main substation