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Register a new userRisk-Aware Dimensioning and Procurement of Contingency Reserve
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Current contingency reserve criteria ignore the likelihood of individual contingencies and, thus, their impact on system reliability and risk. This paper develops an iterative approach, inspired by the current security-constrained unit commitment (SCUC) practice, enabling system operators to determine risk-cognizant contingency reserve requirements and their allocation with minimal alterations to the current SCUC practice. The proposed approach uses generator and transmission system reliability models, including failure-to synchronize and adverse conditions, to compute contingency probabilities, which inform a risk-based system reliability assessment, and ensures reserve deliverability by learning the response of generators to post-contingency states within the SCUC. The effectiveness of the proposed approach is demonstrated using the Grid Modernization Lab Consortium update of the Reliability Test System.
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We consider some crucial problems related to the secure and reliable operation of power systems with high renewable penetrations: how much reserve should we procure, how should reserve resources distribute among different locations, and how should we price reserve and charge uncertainty sources. These issues have so far been largely addressed empirically. In this paper, we first develop a scenario-oriented energy-reserve co-optimization model, which directly connects reserve procurement with possible outages and load/renewable power fluctuations without the need for empirical reserve requirements. Accordingly, reserve can be optimally procured system-wide to handle all possible future uncertainties with the minimum expected system total cost. Based on the proposed model, marginal pricing approaches are developed for energy and reserve, respectively. Locational uniform pricing is established for energy, and the similar property is also established for the combination of reserve and re-dispatch. In addition, properties of cost recovery for generators and revenue adequacy for the system operator are also proven.
Chance-constrained optimization (CCO) has been widely used for uncertainty management in power system operation. With the prevalence of wind energy, it becomes possible to consider the wind curtailment as a dispatch variable in CCO. However, the wind curtailment will cause impulse for the uncertainty distribution, yielding challenges for the chance constraints modeling. To deal with that, a data-driven framework is developed. By modeling the wind curtailment as a cap enforced on the wind power output, the proposed framework constructs a Gaussian process (GP) surrogate to describe the relationship between wind curtailment and the chance constraints. This allows us to reformulate the CCO with wind curtailment as a mixed-integer second-order cone programming (MI-SOCP) problem. An error correction strategy is developed by solving a convex linear programming (LP) to improve the modeling accuracy. Case studies performed on the PJM 5-bus and IEEE 118-bus systems demonstrate that the proposed method is capable of accurately accounting the influence of wind curtailment dispatch in CCO.
Simultaneously with the transformation in the energy system, the spot and ancillary service markets for electricity have become increasingly flexible with shorter service periods and lower minimum powers. This flexibility has made the fastest form of frequency regulation - the frequency containment reserve (FCR) - particularly attractive for large-scale battery storage systems (BSSs) and led to a market growth of these systems. However, this growth resulted in high competition and consequently falling FCR prices, making the FCR market increasingly unattractive to large-scale BSSs. In the context of multi-use concepts, this market may be interesting especially for a pool of electric vehicles (EVs), which can generate additional revenue during their idle times. In this paper, multi-year measurement data of 22 commercial EVs are used for the development of a simulation model for marketing FCR. In addition, logbooks of more than 460 vehicles of different economic sectors are evaluated. Based on the simulations, the effects of flexibilization on the marketing of a pool of EVs are analyzed for the example of the German FCR market design, which is valid for many countries in Europe. It is shown that depending on the sector, especially the recently made changes of service periods from one week to one day and from one day to four hours generate the largest increase in available pool power. Further reductions in service periods, on the other hand, offer only a small advantage, as the idle times are often longer than the short service periods. In principle, increasing flexibility overcompensates for falling FCR prices and leads to higher revenues, even if this does not apply across all sectors examined. A pool of 1,000 EVs could theoretically generate revenues of about 5,000 EUR - 8,000 EUR per week on the German FCR market in 2020.
The standard approach to risk-averse control is to use the Exponential Utility (EU) functional, which has been studied for several decades. Like other risk-averse utility functionals, EU encodes risk aversion through an increasing convex mapping $varphi$ of objective costs to subjective costs. An objective cost is a realization $y$ of a random variable $Y$. In contrast, a subjective cost is a realization $varphi(y)$ of a random variable $varphi(Y)$ that has been transformed to measure preferences about the outcomes. For EU, the transformation is $varphi(y) = exp(frac{-theta}{2}y)$, and under certain conditions, the quantity $varphi^{-1}(E(varphi(Y)))$ can be approximated by a linear combination of the mean and variance of $Y$. More recently, there has been growing interest in risk-averse control using the Conditional Value-at-Risk (CVaR) functional. In contrast to the EU functional, the CVaR of a random variable $Y$ concerns a fraction of its possible realizations. If $Y$ is a continuous random variable with finite $E(|Y|)$, then the CVaR of $Y$ at level $alpha$ is the expectation of $Y$ in the $alpha cdot 100 %$ worst cases. Here, we study the applications of risk-averse functionals to controller synthesis and safety analysis through the development of numerical examples, with emphasis on EU and CVaR. Our contribution is to examine the decision-theoretic, mathematical, and computational trade-offs that arise when using EU and CVaR for optimal control and safety analysis. We are hopeful that this work will advance the interpretability and elucidate the potential benefits of risk-averse control technology.
This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal control problem, where a random maximum cost is assessed using the Conditional Value-at-Risk (CVaR) functional. The solution to the control problem represents the maximum extent of constraint violation of the state trajectory, averaged over the $alphacdot 100$% worst cases, where $alpha in (0,1]$. This problem is well-motivated but difficult to solve in a tractable fashion because temporal decompositions for risk functionals generally depend on the history of the systems behavior. Our primary theoretical contribution is to derive under-approximations to risk-sensitive safe sets, which are computationally tractable. Our method provides a novel, theoretically guaranteed, parameter-dependent upper bound to the CVaR of a maximum cost without the need to augment the state space. For a fixed parameter value, the solution to only one Markov decision process problem is required to obtain the under-approximations for any family of risk-sensitivity levels. In addition, we propose a second definition for risk-sensitive safe sets and provide a tractable method for their estimation without using a parameter-dependent upper bound. The second definition is expressed in terms of a new coherent risk functional, which is inspired by CVaR. We demonstrate our primary theoretical contribution using numerical examples of a thermostatically controlled load system and a stormwater system.
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