Artificial Immune System Applied to the Multi-stage Transmission Expansion Planning

Abstract

Abstract. Transmission expansion planning (TEP) is a complex optimization task to ensure that the power system will meet the forecasted demand and the reliability criterion, along the planning horizon, while minimizing investment, operational, and interruption costs. Metaheuristic methods have demonstrated the potential to find good feasible solutions, but not necessarily optimal. These methods can provide high quality solutions, within an acceptable CPU time, even for large-scale problems. This paper presents an optimization tool based on the Artificial Immune System used to solve the TEP problem. The proposed methodology includes the search for the least cost solution, bearing in mind investments and ohmic transmission losses. The multi-stage nature of the TEP will be also taken into consideration. Case studies on a small test system and on a real sub-transmission network are presented and discussed.

An Extreme Scenario Method for Robust Transmission Expansion Planning with Wind Power Uncertainty

“…Note that, the branch power flow constraints (11), (12) are derived from the polar power-voltage AC power flow model [35], where voltage angles θ i are included in sine and cosine function. For simplicity, we can set the values of θ min and θ max to be −π and π, respectively.…”

“…The TEP model established in Section 2.2 includes nonlinear terms in (12), which are the products of continuous variables and binary transmission decision-making variables I ij,k . To address this issue, we first set p ij,k = b ij,k (θ i − θ j ), and obtain f ij,k = I ij,k p ij,k .…”

“…To address this issue, we first set p ij,k = b ij,k (θ i − θ j ), and obtain f ij,k = I ij,k p ij,k . Secondly, we propose a linearization method implemented by introducing auxiliary relaxation variablesp ij,k = b ij,k (θ i −θ j ) to transform (12) into the following set of mixed-integer linear expressions:…”

“…Similarly, when transmission line k in corridor ij is not selected, the branch power flow is set to zero by substituting I ij,k = 0 into (21). Therefore, the TEP model can be transformed by replacing (12) with (20)- (23) into the mixed-integer linear expressions (1)-(11) and (13)- (23). Here, the values of auxiliary relaxation variablesθ i have no necessary relation with that of θ i , and are determined in the process of model optimization.…”

Transmission Expansion Planning: A Methodology to Include Security Criteria and Uncertainties Using Optimization Techniques

“…Although the consideration of security criteria is essential in real networks, most research works available in the literature solve the multi-stage TEP problem only for the intact network [5][6][7][8][9][10][11][12][13][14][15][16]. Deterministic approaches, as the ''N-1'', are taken into account only in a few works [18,19].…”