# Multi-Stage Dynamic Transmission Network Expansion Planning Using LSHADE-SPACMA
###### Abstract  
This paper introduces a multi-stage dynamic transmission network expansion planning (MSDTNEP) model considering the N-1 reliability constraint. The integrated planning problem of N-1 security and transmission expansion planning is essential because a single line outage could be a triggering event to rolling blackouts. Two suggested scenarios were developed to obtain the optimal configuration of the Egyptian West Delta Network's realistic transmission (WDN) to meet the demand of the potential load growth and ensure the system reliability up to the year 2040. The size of a blackout, based on the amount of expected energy not supplied, was calculated to take both scenarios. The load forecasting (up to 2040) was obtained based on an adaptive neuro-fuzzy inference system because it gives excellent results compared to conventional methods. The linear population size reduction--Success-History-based Differential Evolution with semi-parameter adaptation (LSHADE-SPA) hybrid--covariance matrix adaptation evolution strategy (CMA-ES) algorithm (LSHADE-SPACMA)--is applied to solve the problem. The semi-adaptive nature of LSHADE-SPACMA and the hybridization between LSHADE and CMA-ES are able to solve complex optimization problems. The performance of LSHADE-SPACMA in solving the problem is compared to other well-established methods using three testing systems to validate its superiority. Then, the MSDTNEP of the Egyptian West Delta Network is presented, and the numerical results of the two scenarios are compared to obtain an economic plan and avoid a partial or total blackout. transmission network expansion planning (TNEP); multi-stage dynamic transmission network expansion planning (MSDTNEP); adaptive neuro-fuzzy inference system (ANFIS); LSHADE with semi-parameter adaptation hybrid with CMA-ES (LSHADE-SPACMA)  
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M.M.A.A., S.H.E.A., Y.A., A.M.M., M.M. capacity limits; however, financial conditions indicate the maximum amount available for investment over a planning period. The service quality constraints concern a system's safe operation under normal and single-contingency conditions [1; 2; 3; 4]. In 1970, [PERSON] [4] was the first person to solve the TNEP problem, using a transportation model that only considers each bus's active balance of power. Later, several studies introduced the TNEP problem, showing the major contributions made by TNEP modeling and solution methods. The main features used to classify TNEP models are static or dynamic evaluation and AC or DC power flow. In the static TNEP (STNEP) approach, the location and number of new lines are calculated based on the demand for electrical power at the end of the planning horizon [1]. To improve the STNEP method, a dynamic TNEP (DTNEP) solution was implemented [1; 5; 6; 7; 8]. In DTNEP, unlike STNEP, the planning horizon can be divided into many time intervals. This approach accounts for features such as annual load growth, inflation rate, market behavior, and environmental change, which lead to a more accurate and realistic assessment of the network. However, the implementation of DTNEP increases the complexity and need for high computational effort. The type of power flow is another feature used to classify TNEP models. Due to the TNEP issue's complexity, the DC power flow (DCPF) model is widely used to develop TNEP models. On the other hand, the use of an AC power flow model to solve TNEP problems is seldom discussed in the literature. The AC TNEP model accurately represents the electricity grid; however, the model's nonlinear and non-convex nature makes the problem difficult to solve and obtain a desirable solution [9; 10]. It is challenging to solve the TNEP optimization problem because the feasible search space in TNEP is usually large, non-convex, and difficult to explore. The literature on this topic contains several solving methods that can be organized into three classes: (1) mathematical methods, (2) heuristic methods (HMs), and (3) meta-heuristic methods.