We propose a two-stage scenario-based stochastic optimization problem to determine investments that enhance power system resilience. The proposed optimization problem minimizes the Conditional Value at Risk (CVaR) of load loss to target low-probability high-impact events. We provide results in the context of generator winterization investments in Texas using winter storm scenarios generated from historical data collected from Winter Storm Uri. Results illustrate how the CVaR metric can be used to minimize the tail of the distribution of load loss and illustrate how risk-Aversity impacts investment decisions.
We present a procedure for randomly generating realistic steady-state contingency scenarios based on the historical outage data from a particular event. First, we divide generation into classes and fit a probability distribution of outage magnitude for each class. Second, we provide a method for randomly synthesizing generator resilience levels in a way that preserves the data-driven probability distributions of outage magnitude. Finally, we devise a simple method of scaling the storm effects based on a single global parameter. We apply our methods using data from historical Winter Storm Uri to simulate contingency events for the ACTIVSg2000 synthetic grid on the footprint of Texas.
As renewable energy penetration increases and system inertia levels drop, primary frequency control is becoming a critical concern in relatively small interconnections such as the Electric Reliability Council of Texas (ERCOT). To address this problem ERCOT is implementing a number of market rule changes including the introduction of a new Fast Frequency Response (FFR) reserve type to the electricity market. This FFR reserve type aims to help the traditional Primary Frequency Response (PFR) reserve type in arresting frequency decline in the event of a large generator outage. This paper derives reserve requirements to ensure sufficient reserve to arrest frequency decline before reaching the critical frequency threshold while coupling PFR reserve, FFR reserve, and system inertia. The general reserve requirement places limits on the amount of PFR reserve that can be provided by each unit based on its ramping capabilities. Two such limits are derived from first principles and another is proposed that is capable of accommodating the equivalency ratio introduced in previous work. These PFR reserve limits also provide first principles insight into equivalency ratios, which have only been studied empirically in the past. High-level insights are provided on a large Texas test case.
Eldridge, Brent E.; Castillo, Anya C.; Knueven, Bernard K.; Garcia, Manuel J.
This document is an online supplement for Sparse, Dense, and Compact Linearizations of the AC OPF. Here we present complete derivations of the formulations examined, details of the lazy constraint algorithm, and full computational results supporting Sparse, Dense, and Compact Linearizations of the AC OPF.