Multi Dimension-Based Optimal Allocation of Uncertain Renewable Distributed Generation Outputs with Seasonal Source-Load Power Uncertainties in Electrical Distribution Network Using Marine Predator Algorithm

Abstract

In the last few years, the integration of renewable distributed generation (RDG) in the electrical distribution network (EDN) has become a favorable solution that guarantees and keeps a satisfying balance between electrical production and consumption of energy. In this work, various metaheuristic algorithms were implemented to perform the validation of their efficiency in delivering the optimal allocation of both RDGs based on multiple photovoltaic distributed generation (PVDG) and wind turbine distributed generation (WTDG) to the EDN while considering the uncertainties of their electrical energy output as well as the load demand’s variation during all the year’s seasons. The convergence characteristics and the results reveal that the marine predator algorithm was effectively the quickest and best technique to attain the best solutions after a small number of iterations compared to the rest of the utilized algorithms, including particle swarm optimization, the whale optimization algorithm, moth flame optimizer algorithms, and the slime mold algorithm. Meanwhile, as an example, the marine predator algorithm minimized the seasonal active losses down to 56.56% and 56.09% for both applied networks of IEEE 33 and 69-bus, respectively. To reach those results, a multi-objective function (MOF) was developed to simultaneously minimize the technical indices of the total active power loss index (APLI) and reactive power loss index (RPLI), voltage deviation index (VDI), operating time index (OTI), and coordination time interval index (CTII) of overcurrent relay in the test system EDNs, in order to approach the practical case, in which there are too many parameters to be optimized, considering different constraints, during the uncertain time and variable data of load and energy production.

Optimizing the hybrid PVDG and DSTATCOM integration in electrical distribution systems based on a modified homonuclear molecules optimization algorithm

“…The first parameter is the TAPL [25], as follows: $$$$\begin{equation}TAP{L_{i,j}} = \mathop \sum \limits_{i = 1}^{{N_{bus}}} \mathop \sum \limits_{j = 2}^{{N_{bus}}} AP{L_{i,j}}\ \end{equation}$$$$ $$$$\begin{eqnarray}AP{L_{i,j}} &=& \frac{{{R_{ij}}}}{{{V_i}{V_j}}}\ \cos ({\delta _i} - {\delta _j}) ( {{P_i}{P_j} + {Q_i}{Q_j}} )\nonumber\\ &&+ \frac{{{R_{ij}}}}{{{V_i}{V_j}}}\sin ( {{\delta _i} - {\delta _j}}) ( {{Q_i}{P_j} + {P_i}{Q_j}})\end{eqnarray}$$$$…”

Enhancing PV distributed generator planning in medium‐voltage DC distribution networks: A multi‐design techno‐economic analysis with load demand response

“…Equations ( 1) and ( 2) serve as the standard mathematical representation of active and reactive power demand uncertainty [40,41]:…”

“…Equations (1) and (2) serve as the standard mathematical representation of active and reactive power demand uncertainty [40, 41]: $$$$\begin{equation}{P}_k\ \left( t \right) = \ \lambda \left( t \right) \times {P}_{ok}\end{equation}$$$$ $$$$\begin{equation}{Q}_k\ \left( t \right) = \lambda \left( t \right) \times {Q}_{ok}\end{equation}$$$$where P k , Q k represent the active/reactive powers injected at bus k. λ is the load demand's parameter, and Q ok , P ok are the reactive/active powers at bus k. t is the time in hours.…”

“…The active power loss (APL ) would be formulated as [41, 42]: $$$$\begin{equation}AP{L}_{i,j} = {\alpha }_{ij}\ \left( {{P}_i{P}_j + {Q}_i{Q}_j} \right) + {\beta }_{ij}\left( {{Q}_i{P}_j + {P}_i{Q}_j} \right)\end{equation}$$$$ $$$$\begin{equation}{\alpha }_{ij} = \frac{{{R}_{ij}}}{{{V}_i{V}_j}}\ \cos ({\delta }_i - {\delta }_j)\end{equation}$$$$ $$$$\begin{equation}{\beta }_{ij} = \frac{{{R}_{ij}}}{{{V}_i{V}_j}}\ \sin \left( {{\delta }_i - {\delta }_j} \right)\end{equation}$$$$where P ij , Q ij are line's active/reactive powers, R ij is the resistance of line, V i , V j refer to voltage at bus i , and j. δ i , δ j are the angles at buses i, j, N bus is the bus number, and P PVDG is the PVDG number.…”

Probabilistic Planning of Renewable Energy Source with Different Load Models

“…The goal of the study in Ref. Belbachir, N. et al [23] was to find the best location and size for DGs to minimize the technical indices of the total active power loss index (APLI) and reactive power loss index (RPLI), voltage deviation index (VDI) considering generation and load uncertainties using Marine Predator Algorithm. An Particle swarm optimization (PSO) technique approach to properly deploy multiple DG units is presented to reduce power losses, reliability in distribution systems (Salam, I. U et al, [24]).…”