(373j) An Estimation-Assisted Real-Time AC Optimal Power Flow

Ensuring a cost-effective and reliable electricity supply in power systems requires computing accurate solutions of the AC optimal power flow (ACOPF) problem, which is a cornerstone in real-time operations [1], [2], [3]. The effectiveness of traditional operational models for real-time operation of modern power systems is primarily challenged by: (i) the integration of variable renewable energy sources due to their uncertainty and variability, and (ii) the increasing demand driven by important electrification efforts across various sectors. Both challenges necessitate decision-making tools, such as the ACOPF, considering more accurate models and operating on a more granular temporal scale. This work introduces a tractable approximation of the ACOPF problem that leverages the nodal voltage estimations from existing real-time monitoring tools in power systems.

The ACOPF problem is an optimization-based control tool in power systems that aims at determining the generation setpoints of power generating units distributed over the power grid to supply the demand at the minimum cost while satisfying engineering constraints and the nonconvex governing physical laws, known as power flow equations [4]. From the modeling perspective, decision-control tools, like the ACOPF, in modern power systems are adjusting to tackle the challenges induced by uncertain generation and increased demand.

The challenges induced by uncertain generation can be mitigated by two main alternatives: (i) using stochastic models of the weather-dependent generation [5], [6], [7], [8], [9], [10], [11], and (ii) considering deterministic models of the uncertain generation but increasing the time granularity of solving the ACOPF problem. The first alternative results in a large-scale problem whose solution times are not compatible with the time needs of the real-time operations. The challenges induced by increased demand arise because they drive the operation of power systems to conditions where simplified linear models can be highly inaccurate. To this end, linear and convex approximations of the power flow equations [12], [13], [14], [15], [16] have been proposed in the literature. However, most of these models do not leverage available system information during real time operations.

This works presents a model of the ACOPF problem based on a tractable convex approximation of the power flow equations, which leverages the estimation of nodal voltages readily available from existing real-time monitoring tools. We formulate the ACOPF in rectangular coordinates whose nonconvex constraints pertaining to the power flow equations are expressed as a difference of convex functions. The nonconvexities are linearized using a first-order Taylor series approximation around the estimated nodal voltages available from the state estimator. Such convexification renders a second-order conic problem, which can be efficiently solved for real-time operations. We present to strategies to restore the feasibility of the solution of the proposed model with respect to the original ACOPF problem based on (i) a nonlinear Euclidean projection and (ii) the solution of a system of nonlinear equations.

The proposed model is tested on several realistic test systems under a wide range of operating conditions. The performance of the convexified model is studied in terms of solution time, optimality gap, and approximation error with respect to the solution of the original nonconvex problem using an interior point solver. Our numerical experiments show the benefits of the proposed model with respect to well-documented linear approximations and convex relaxations.

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