Abstract
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.
Highlights
Research on the security of power systems generally focuses on stability security based on differential equations and adequate security based on algebraic equations [1]
The minimum load shedding of the best system state is zero when the number of the lines out k equals to 1, 2, . . . , 23
Because interval load is discretized by trisection for linearization, load demand at each load bus has four options: upper bound, the first value in interval, the second value in interval and lower bound
Summary
Research on the security of power systems generally focuses on stability security based on differential equations and adequate security based on algebraic equations [1]. This paper studies the deterministic analysis of power systems under the loss of k components for expansion planning. Under certain load demands, which k components that include transmission lines and generators out produce the best N-k contingency, and which k components out produce the worst. Under uncertain load demands, which k components out and which load blocks produce the best system state, and which k components out and load blocks produce the worst-case system state (WSS). The WSS refers to the worst-case scenario under uncertain conditions of N-k contingency and load demand. Power system operators or planners are concerned about worst-case scenarios under uncertain N-k contingencies and with varied loads, conditions that are weaker than all other power system scenarios given uncertainties of N-k contingency and load demand. Our main goal is to identify the worst N-k contingency with varied load
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