Secure operation in low-voltage power systems : embedding inverter control into optimal power flow

Abstract

Because of the increasing integration of renewable energy sources (RESs) and distributed generators (DGs) interfaced inverters, low-voltage power systems are being changed with new structures including microgrids, which lead to new security problems. How to facilitate the security under uncertainties while fully exploiting the droop-controlled inverters needs a deeper reconsideration. Consequently, in this thesis, we investigate a series of optimal operation strategies facilitating security constraints both in distribution networks and microgrids. Our contributions are fivefold.

First, we propose a conditional value at risk (CVaR)-averse distributionally robust chance constrained optimal power flow (OPF) which considers the voltage regulation from a risk perspective. By applying the duality theory, we reformulate the proposed OPF as a second-order cone programming, which can be solved in polynomial processing time. Numerical results on the modified 118-bus distribution system show the efficiency and superiority of the proposed OPF in voltage regulation over other benchmark models.

Second, to fill the research gap on the stability sensitivity, we deduce an analytical formula for stability sensitivity in a general power system. Based on the Lyapunov equation, we define the stability index which characterizes the convergence rate of system oscillation by semi-definite programming (SDP) which holds the convexity. By using the duality of SDP, we give the stability sensitivity to any entries of the dynamic Jacobian matrix. The simulation results verify the accuracy and computational efficiency enhancements of the proposed sensitivity compared to numerical approaches. The proposed analytical stability sensitivity is applied in the following threefold contributions.

Third, to accommodate unpredictable plug-and-play (PnP) of DGs in inverter-dominant microgrids, we propose a preventive-corrective stability constrained OPF (SC-OPF). Considering that DG droops are restricted by load sharing, we introduce the battery energy storage system (BESS) with adjustable droops, which acts as a new control resource. From simulation results, the proposed model significantly improves the economic cost, stability, and computational efficiency compared to other SC-OPF models without considering BESS droop control or PnPs.

Fourth, we propose a chance constrained SC-OPF with non-Gaussian uncertainties in isolated microgrids. By applying Gaussian mixture model to fit RES non-Gaussian forecast errors, analytical sensitivity cuts are designed to linearly approximate chance constraints (CC) of the stability index and other operational variables. We design a supplementary correction to mitigate the possible linear approximation error. Simulation results demonstrate that the proposed model converges 30 times faster compared to traditional approaches.

Fifth, to facilitate the stability issues brought by uncertainties from another perspective, we propose a two-stage robust optimization model. A day-ahead schedule of DGs with the RESs interval predictions is provided in the first stage, and a deterministic OPF is derived hourly in the second stage. An adaptive stability constraint generation algorithm is developed to solve the robust optimization problem. Simulation results show the proposed model facilitates the stability with relatively low cost and guarantees robustness against the uncertainties.

To sum up, this thesis provides novel insights into secure operations in low-voltage power systems by embedding inverter control to overcome RESs uncertainties.