The uncertainties from deepening penetration of renewable energy resources have already shown to impact not only the market operations, but also the physical operations in large power systems. It is demonstrated that deterministic modeling of wind would lead to voltage insecurity in the reality where wind fluctuates. This could render deterministic control of reactive power ineffective. As an alternative, we propose a chance-constrained formulation of optimal reactive power dispatch which considers the uncertainties from both renewables and contingencies. This formulation of a chance constrained optimal reactive power dispatch (cc-ORPD) offers system operators an effective tool to schedule voltage support devices such that the system voltage security can be ensured with quantifiable level of risk. The cc-ORPD problem is a Mixed-Integer Non-Linear Programming (MINLP) problem with a joint chance constraint and is extremely challenging to solve. Using the Big-M approach and linearized power flow equations, the original cc-ORPD problem is approximated as a Mixed-Integer Linear Programming (MILP) problem, which is efficiently solvable. Case studies are conducted on a modified IEEE 24-bus system to investigate the optimal operating schedule under uncertainties and the out-of-sample violation probability.
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