The uncertainties of the predicted load demand and N-K contingencies are very significant aspects to composite generation and transmission expansion planning (CGTEP). In this paper, multi-contingency constrained CGTEP with load uncertainty was analyzed from stringent mathematical view and formulated as a tri-level optimization model. To effectively solve the tri-level optimization, the entire problem is formulated as two problems using Benders' decomposition: master problem with expansion planning and the sub-problem with the worst case load shedding. The sub-problem is a bi-level optimization problem which can be solved mathematically using strong duality theory and linearization method. CGTEP with the tri-level optimization can endure the disturbances of interval load and N-K contingencies. A benchmark test system is simulated to validate the effectiveness of the proposed approach. Furthermore, for Bender's decomposition with many sub-problems of worst load shedding, the numerically comparable results of a special case demonstrate that all sub-problems of composite contingencies must be validated at each iteration even if certain contingency meets the standard of load shedding at the previous iteration.

N-k contingency estimation plays a very important role in the operation and expansion planning of power systems, the method of which is traditionally based on heuristic screening. This paper stringently analyzes the best and worst states of power systems given the uncertainties of N-k contingency and interval load. For the sake of simplification and tractable computation, an approximate direct current (DC) power flow model was used. Rigorous optimization models were established for identifying the worst and best scenarios considering the contingencies of generators and transmission lines together with their uncertain loads. It is very useful to identify the worst N-k contingencies with interval loads. If the worst existing scenario meets security standards, all scenarios must satisfy it. The mathematical model established for finding the worst N-k contingency with interval load is a bi-level optimization model. In this paper, strong duality theory and mathematical linearization were applied to the solution of bi-level optimization. The computational results of standard cases validate the effectiveness of the proposed method and illustrate that generator contingency has more impact on minimum load shedding than transmission line contingency.

The increasing complexity of the distribution system makes the practical distribution network operation much difficult. This paper presents an ordinal optimisation (OO) approach to solve the distribution network reconfiguration, which is an NP‐ hard problem with discrete control variables. OO uses crude and computationally fast model to reduce the search space. The spirit of OO is to seek the good enough solution instead of the best with high probability. The proposed approach is validated with two practical distribution systems, TPC 84 node test system. The results are compared with Optimal Flow Pattern (OFP), Common Genetic Algorithm (CGA), Partheno Genetic Algorithm with Tree Structure Encoding technology (TSE‐PGA) and Second‐Order Cone Programming (SOCP).

Because of the non-convex AC power flow, power system expansion planning used traditionally DC power flow which approximates to AC power flow. This paper proposed a novel method for power system expansion planning with AC power flow. In order to mathematically optimize AC power flow, a second order conic relaxation method of branch AC power flow equations has been proposed. A second order programming for optimal power flow is formulated and is compared with local optimization method (e.g. interior point method). Then, by adding the integer decision variables, composite generation and transmission expansion planning has been formulated for mixed integer second order conic programming (MICP), which can be solved by mature optimization software. Expansion planning the paper proposed has considered voltage limit and network loss. Finally, standard numerical cases have been studied to illustrate the effectiveness of conic relaxation of AC power flow and we have compared power system expansion planning with conic relaxation of AC power flow to that of DC power flow.

Future generation expansion has significant impact on transmission expansion planning, the paper proposes a mathematical model for multi-scenario generation and transmission expansion planning (MGTEP). This model is formulated for mixed integer linear programming (MILP) by the approach of disjunctive direct current power flow of existing and candidate lines, thus it can be solved by mature optimization software. Traditional expansion planning disregards temporal and spatial distribution of load and wind power. In order to consider spatial distribution of load and wind power, K-means cluster is applied to the calculation of scenarios of load and wind power. Finally case studies with Garver-6 bus system and IEEE-RTS-24 bus system validate the computational effectiveness of MGTEP and these numerical results demonstrate it is more comprehensive to MGTEP considering load spatial distribution.