Chance-constrained Optimal Power Flow Research Articles

Chance-constrained optimal power flow with non-parametric probability distributions of dynamic line ratings

Compared to Seasonal Line Rating (SLR), Dynamic Line Rating (DLR) allows for higher power flows on overhead transmission lines, depending on the actual weather conditions. Nevertheless, the potential of DLR has to be traded off against the additional uncertainty associated with varying ratings. This paper proposes a DC-Optimal Power Flow (DCOPF) algorithm that accounts for DLR uncertainty by means of Chance-Constraints (CC). The goal is to determine the optimal day-ahead dispatch taking the cost of reserve procurement into account. The key contribution of this paper consists in considering both non-parametric predictive distributions of DLR and the combined wind power uncertainty in the optimization problem. Our results highlight the benefits of DLR in wind-dominated power systems, assuming typical risk aversion levels in the line rating estimation.

Introducing Uncertainty Components in Locational Marginal Prices for Pricing Wind Power and Load Uncertainties

With substantially increasing penetration levels of wind power, electric power system flexibility is needed to address the variability and uncertainty of wind power output. Thus, it has become an urgent issue to obtain an optimal tradeoff between economics and reliability, and to price system uncertainties. This paper proposes a new electricity market-clearing mechanism based on locational marginal prices (LMPs) for pricing uncertain generation and load. The uncertainty contained locational marginal price (U-LMP) is derived from a distributionally robust chance-constrained optimal power flow model in which only the first-order and second-order moments of the uncertain sources’ probability distribution are needed. Compared with traditional LMPs, the proposed U-LMP formulation includes two new uncertainty components: transmission line overload uncertainty price and generation violation uncertainty price. These LMP uncertainty components are the price signals reflecting the system costs as a result of wind generation and demand uncertainty at different locations. Finally, using parametric case studies, the relationship among uncertainty levels, system generation cost, and LMP uncertainty components are established. Case studies performed on the PJM 5-bus and IEEE 118-bus systems verify the proposed U-LMP method.

Decentralized wind uncertainty management: Alternating direction method of multipliers based distributionally-robust chance constrained optimal power flow

How to manage wind power uncertainty in system operation is an urgent and important issue, especially under substantially increasing penetration levels of wind generation in electric power systems. With increasing numbers of wind power plants (WPPs) integrated into power systems, their variability and uncertain power outputs become a challenge to maintaining system reliability. Traditional stochastic optimization-based models face the curse of dimensionality when the number of WPPs increases. This paper proposes a novel decentralized wind power uncertainty management model. In this model, conventional generators optimize their power capacity output and their participation to mitigate wind power uncertainty locally with only limited information exchange with the system operators. First, a distributionally-robust chance-constrained optimal power flow (DRCC-OPF) model is deployed to schedule the generation and reserve considering the wind power forecast uncertainty. Then, the alternating direction method of multipliers (ADMM) is used to reformulate the DRCC-OPF model into the distributed optimization model for each conventional generator and WPP. The tests on a small PJM 5-bus system and the IEEE 118-bus system demonstrate that the proposed decentralized model can increase the operation reliability without sacrificing system operating cost, especially when the wind power penetration levels are high. Using the proposed model, the optimal solutions can be obtained within one minute, for all studied cases, which verifies the computation efficiency of the proposed decentralized model. Furthermore, considering a large number of WPPs integrated into the system, the proposed decentralized method obtains a lower operating cost within one minute which demonstrates its efficiency to deal with high dimension of uncertainties.

A generalized framework for chance-constrained optimal power flow

Abstract Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call – among others – fora structured consideration of uncertainties in optimal power flow problems. The main challenge is to guarantee power balance while maintaining economic and secure operation. In the presence of Gaussian uncertainties affine feedback policies are known to be viable options for this task. The present paper advocates a general framework for chance-constrained opf problems in terms of continuous random variables. It is shown that, irrespective of the type of distribution, the random-variable minimizers lead to affine feedback policies. Introducing a three-step methodology that exploits polynomial chaos expansion, the present paper provides a constructive approach to chance-constrained optimal power flow problems that does not assume a specific distribution, e.g. Gaussian, for the uncertainties. We illustrate our findings by means of a tutorial example and a 300-bus test case.

Stochastic optimal reactive power reserve dispatch considering voltage control areas

Summary Conventional optimal reactive power reserve dispatch approaches are mostly modeled in deterministic forms, where the power injections are fixed. With the integration of intermittent renewable sources, the power injections could become uncertain. To maintain the security, a stochastic optimal reactive power reserve dispatch model is proposed, which is formulated as a chance-constrained optimal power flow problem. To begin, a multistage partitioning method considering both the decoupling degree and the robustness to failure is proposed to obtain the voltage control areas. Then, the original nonlinear stochastic optimal reactive power reserve dispatch model is decomposed into a successive multiarea linearized programming problem. Finally, a chance constraint relaxation–based method is proposed to solve the above problem. The results show that the proposed method can significantly enhance the voltage stability margin, and the security in uncertain scenarios can also be maintained for the satisfaction of the chance constraints.

A Robust Approach to Chance Constrained Optimal Power Flow With Renewable Generation

Optimal Power Flow (OPF) dispatches controllable generation at minimum cost subject to operational constraints on generation and transmission assets. The uncertainty and variability of intermittent renewable generation is challenging current deterministic OPF approaches. Recent formulations of OPF use chance constraints to limit the risk from renewable generation uncertainty, however, these new approaches typically assume the probability distributions which characterize the uncertainty and variability are known exactly. We formulate a Robust Chance Constrained (RCC) OPF that accounts for uncertainty in the parameters of these probability distributions by allowing them to be within an uncertainty set. The RCC OPF is solved using a cutting-plane algorithm that scales to large power systems. We demonstrate the RRC OPF on a modified model of the Bonneville Power Administration network, which includes 2209 buses and 176 controllable generators. Deterministic, chance constrained (CC), and RCC OPF formulations are compared using several metrics including cost of generation, area control error, ramping of controllable generators, and occurrence of transmission line overloads as well as the respective computational performance.

Distributionally Robust Chance-Constrained Optimal Power Flow with Uncertain Renewables and Uncertain Reserves Provided by Loads

Aggregations of electric loads can provide reserves to power systems, but their available reserve capacities are time-varying and not perfectly known when the system operator computes the optimal generation and reserve schedule. In this paper, we formulate a chance constrained optimal power flow problem to procure minimum cost energy, generator reserves, and load reserves given uncertainty in renewable energy production, load consumption, and load reserve capacities. Assuming that uncertainty distributions are not perfectly known, we solve the problem with distributionally robust optimization, which ensures that chance constraints are satisfied for any distribution in an ambiguity set built upon the first two moments. We use two ambiguity sets to reformulate the model as a semidefinite program and a second-order cone program and run computational experiments on the IEEE 9-bus, 39-bus, and 118-bus systems. We compare the solutions to those given by two benchmark reformulations; the first assumes normally distributed uncertainty and the second uses large numbers of uncertainty samples. We find that the use of load reserves, even when load reserve capacities are uncertain, reduces operational costs. Also, the approach is able to meet reliability requirements, unlike the first benchmark approach and with lower computation times than the second benchmark approach.

Approximating the parameter-space stability boundary considering post-contingency corrective controls

Lately, much work in the area of voltage stability assessment has been focused on finding post-contingency corrective controls. In this article a contribution to this area will be presented where we investigate the surface of maximal loadability while allowing for post-contingency corrective controls. This objective is different from the usual, where the aim is to include the post-contingency controls in a security-constrained optimal power flow. Our aim is rather to find approximations of the post-contingency stability boundary, in pre-contingency parameter space, while including the possibility for post-contingency corrective controls. These approximations can then be used in, for example, a chance-constrained optimal power flow routine.