Line Roald

Line Roald, Sidhant Misra, Michael Chertkov et al.

Over the past years, the share of electricity production from wind power plants has increased to significant levels in several power systems across Europe and the United States. In order to cope with the fluctuating and partially unpredictable nature of renewable energy sources, transmission system operators (TSOs) have responded by increasing their reserve capacity requirements and by requiring wind power plants to be capable of providing reserves or following active power set-point signals. This paper addresses the issue of efficiently incorporating these new types of wind power control in the day-ahead operational planning. We review the technical requirements the wind power plants must fulfill, and propose a mathematical framework for modeling wind power control. The framework is based on an optimal power flow formulation with weighted chance constraints, which accounts for the uncertainty of wind power forecasts and allows us to limit the risk of constraint violations. In a case study based on the IEEE 118 bus system, we use the developed method to assess the effectiveness of different types of wind power control in terms of operational cost, system security and wind power curtailment.

Andreas Venzke, Lejla Halilbasic, Adelie Barre et al.

The integration of large-scale renewable generation has major implications on the operation of power systems, two of which we address in this work. First, system operators have to deal with higher degrees of uncertainty due to forecast errors and variability in renewable energy production. Second, with abundant potential of renewable generation in remote locations, there is an increasing interest in the use of High Voltage Direct Current lines (HVDC) to increase transmission capacity. These HVDC transmission lines and the flexibility and controllability they offer must be incorporated effectively and safely into the system. In this work, we introduce an optimization tool that addresses both challenges by incorporating the full AC power flow equations, chance constraints to address the uncertainty of renewable infeed, modelling of point-to-point HVDC lines, and optimized corrective control policies to model the generator and HVDC response to uncertainty. The main contributions are twofold. First, we introduce a HVDC line model and the corresponding HVDC participation factors in a chance-constrained AC-OPF framework. Second, we modify an existing algorithm for solving the chance-constrained AC-OPF to allow for optimization of the generation and HVDC participation factors. Using realistic wind forecast data, for 10 and IEEE 39 bus systems with HVDC lines and wind farms, we show that our proposed OPF formulation achieves good in- and out-of-sample performance whereas not considering uncertainty leads to high constraint violation probabilities. In addition, we find that optimizing the participation factors reduces the cost of uncertainty significantly.

Joe Gorka, Tim Hsu, Wenting Li et al.

Higher variability in grid conditions, resulting from growing renewable penetration and increased incidence of extreme weather events, has increased the difficulty of screening for scenarios that may lead to catastrophic cascading failures. Traditional power-flow-based tools for assessing cascading blackout risk are too slow to properly explore the space of possible failures and load/generation patterns. We add to the growing literature of faster graph-neural-network (GNN)-based techniques, developing two novel techniques for the estimation of blackout magnitude from initial grid conditions. First we propose several methods for employing an initial classification step to filter out safe "non blackout" scenarios prior to magnitude estimation. Second, using insights from the statistical properties of cascading blackouts, we propose a method for facilitating non-local message passing in our GNN models. We validate these two approaches on a large simulated dataset, and show the potential of both to increase blackout size estimation performance.

Kaarthik Sundar, Harsha Nagarajan, Line Roald et al.

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch. In particular, the variability of wind generation increases the risk of unexpected overloads and cascading events. To address these questions, we present an N-1 Security and Chance-Constrained Unit Commitment (SCCUC) that includes models of generation reserves that respond to wind fluctuations and component outages. We formulate the SCCUC as a mixed-integer, second-order cone problem that limits the probability of failure. We develop a modified Benders decomposition algorithm to solve the problem to optimality and present detailed case studies on the IEEE RTS-96 three-area and the IEEE 300 NESTA test systems. The case studies assess the economic impacts of contingencies and various degrees of wind power penetration and demonstrate the effectiveness and scalability of the algorithm.

T. Mühlpfordt, L. Roald, V. Hagenmeyer et al.

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the full nonlinear AC power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model the effects of arbitrary uncertainties of finite variance, which enables to predict and optimize the system state for a range of operating conditions. We apply chance constraints to limit the probability of violations of inequality constraints. Our method incorporates a more detailed and a more flexible description of both the controllable variables and the resulting system state than previous methods. Two case studies highlight the efficacy of the method, with a focus on satisfaction of the AC power flow equations and on the accurate computation of moments of all random variables.

Line Roald, Sidhant Misra, Michael Chertkov et al.

Due to the increasing amount of electricity generated from renewable sources, uncertainty in power system operation will grow. This has implications for tools such as Optimal Power Flow (OPF), an optimization problem widely used in power system operations and planning, which should be adjusted to account for this uncertainty. One way to handle the uncertainty is to formulate a Chance Constrained OPF (CC-OPF) which limits the probability of constraint violation to a predefined value. However, existing CC-OPF formulations and solutions are not immune to drawbacks. On one hand, they only consider affine policies for generation control, which are not always realistic and may be sub-optimal. On the other hand, the standard CC-OPF formulations do not distinguish between large and small violations, although those might carry significantly different risk. In this paper, we introduce the Weighted CC-OPF (WCC-OPF) that can handle general control policies while preserving convexity and allowing for efficient computation. The weighted chance constraints account for the size of violations through a weighting function, which assigns a higher risk to a higher overloads. We prove that the problem remains convex for any convex weighting function, and for very general generation control policies. In a case study, we compare the performance of the new WCC-OPF and the standard CC-OPF and demonstrate that WCC-OPF effectively reduces the number of severe overloads. Furthermore, we compare an affine generation control policy with a more general policy, and show that the additional flexibility allow for a lower cost while maintaining the same level of risk.