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We study risk-aware linear policy approximations for the optimal operation of an energy system with stochastic wind power, storage, and limited fuel. The resulting problem is a sequential decision-making problem with rolling forecasts. In addition to a risk-neutral objective, this paper formulates two risk-aware objectives that control the conditional value-at-risk of system cost and the buffered probability of exceeding a predefined threshold of unserved load. The resulting policy uses a parameter-modified cost function approximation that reduces the computational load compared to the direct inclusion of those risk measures in the problem objective. We demonstrate our method on a numerical case study.

The rise of advanced data technologies in electric power distribution systems enables operators to optimize operations but raises concerns about data security and consumer privacy. Resulting data protection mechanisms that alter or obfuscate datasets may invalidate the efficacy of data-driven decision-support tools and impact the value of these datasets to the decision-maker. This paper derives tools for distribution system operators to enrich data-driven operative decisions with information on data quality and, simultaneously, assess data usefulness in the context of this decision. To this end, we derive an AC optimal power flow model for radial distribution systems with data-informed stochastic parameters that internalize a data quality metric. We derive a tractable reformulation and discuss the marginal sensitivity of the optimal solution as a proxy for data value. Our model can capture clustered data provision, e.g., from resource aggregators, and internalize individual data quality information from each data provider. We use the IEEE 33-bus test system, examining scenarios with varying photovoltaic penetration, to demonstrate the application of our approach and discuss the relationship between data quality and its value.

We propose an enhancement to wholesale electricity markets whereby the exposure of consumers to increasingly large and volatile consumer payments arising as a byproduct of volatile real-time net loads -- i.e., loads minus renewable outputs -- and prices, both compared to day-ahead cleared values. We incorporate a robust estimate of such excess payments into the day-ahead computation and specifically seek to account for volatility in real-time net loads and renewable generation. Our model features a data-driven uncertainty set based on principal component analysis, which accommodates both load and wind production volatility and captures locational correlation of uncertain data. To solve the model more efficiently, we develop a decomposition algorithm that can handle nonconvex subproblems. Our extensive experiments on a realistic NYISO data set show that the risk-aware model protects the consumers from potential high costs caused by adverse circumstances.

For a timely decarbonization of our economy, power systems need to accommodate increasing numbers of clean but stochastic resources. This requires new operational methods that internalize this stochasticity to ensure safety and efficiency. This paper proposes a novel approach to compute adaptive safety intervals for each stochastic resource that internalize power flow physics and optimize the expected cost of system operations, making them ``prescriptive''. The resulting intervals are interpretable and can be used in a tractable robust optimal power flow problem as uncertainty sets. We use stochastic gradient descent with differentiable optimization layers to compute a mapping that obtains these intervals from a given vector of context parameters that captures the expected system state. We demonstrate and discuss the proposed approach on two case studies., Comment: Accepted to PSCC 2024

With the ongoing investment in data collection and communication technology in power systems, data-driven optimization has been established as a powerful tool for system operators to handle stochastic system states caused by weather- and behavior-dependent resources. However, most methods are ignorant to data quality, which may differ based on measurement and underlying privacy-protection mechanisms. This paper addresses this shortcoming by (i) proposing a practical data quality metric based on Wasserstein distance, (ii) leveraging a novel modification of distributionally robust optimization using information from multiple data sets with heterogeneous quality to valuate data, (iii) applying the proposed optimization framework to an optimal power flow problem, and (iv) showing a direct method to valuate data from the optimal solution. We conduct numerical experiments to analyze and illustrate the proposed model and publish the implementation open-source.

This paper addresses the challenge of efficiently solving the optimal power flow problem in real-time electricity markets. The proposed solution, named Physics-Informed Market-Aware Active Set learning OPF (PIMA-AS-OPF), leverages physical constraints and market properties to ensure physical and economic feasibility of market-clearing outcomes. Specifically, PIMA-AS-OPF employs the active set learning technique and expands its capabilities to account for curtailment in load or renewable power generation, which is a common challenge in real-world power systems. The core of PIMA-AS-OPF is a fully-connected neural network that takes the net load and the system topology as input. The outputs of this neural network include active constraints such as saturated generators and transmission lines, as well as non-zero load shedding and wind curtailments. These outputs allow for reducing the original market-clearing optimization to a system of linear equations, which can be solved efficiently and yield both the dispatch decisions and the locational marginal prices (LMPs). The dispatch decisions and LMPs are then tested for their feasibility with respect to the requirements for efficient market-clearing results. The accuracy and scalability of the proposed method is tested on a realistic 1814-bus NYISO system with current and future renewable energy penetration levels.

Envisioning a future 100% electrified transportation sector, this paper uses socio-economic, demographic, and geographic data to assess electric energy demand from commuter traffic. We explore the individual mode choices, which allows to create mode-mix scenarios for the entire population, and quantify the electric energy demand for each scenario using technical specifications of battery and electric drives technology in combination with different charging scenarios. Using data sets for New York City, our results highlight the need for infrastructure investments, the usefulness of flexible charging policies, and the positive impact of incentivizing micromobility and mass-transit options. Our model and results are publicly available as interactive dashboard., Comment: Accepted for publication at the 2023 IEEE PES General Meeting

The growing penetration of variable renewable energy sources (VRES) requires additional flexibility reserve to ensure reliable power system operations. Current industry practice typically assumes a certain fraction of the VRES power production forecast as flexibility reserve, thus ignoring other relevant information, such as weather conditions. To address this, probability- and risk-based reserve sizing models have been proposed, which use probabilistic VRES power forecasts that mostly rely on historical forecast and actual VRES power data for model training. Hence, these approaches are not suitable for planned or newly installed wind farms, where no or insufficient historical data is available. This paper addresses this caveat. First, we propose a weather-driven probabilistic forecasting method for wind power installations using publicly available weather data. Second, we apply the resulting probabilistic forecasts to a novel risk-based flexibility reserve sizing model that is compatible with the current reserve procuring pipeline used by US ISOs. Finally, we compare the risk-based reserve requirements to industry practice, state-of-the-art reserve procurement methods, and a weather-ignorant benchmark with respect to system cost and security. Our results are obtained from real-world data on a 1819-bus NYISO system model with both on- and projected off-shore wind power installations, which highlight the usefulness of weather information wind power forecasting and demonstrate efficiency gains from risk-aware reserve procurement.

With the advancement in smart grid and smart energy devices, demand response becomes one of the most economic and feasible solutions to ease the load stress of the power grids during peak hours. In this work, we propose a fully decentralized ensemble control framework with consensus for demand response (DR) events and compatible control methods based on random policies. We show that under the consensus that is tailored to DR, our proposed decentralized control method yields the same optimality as the centralized control method in both myopic and multistage settings.

Electrical outages continue to occur despite technological innovations and improvements to electric power distribution infrastructure. In this paper, we describe a tool that was designed to acquire and collect data on electric power outages in New York City since July 2020. The electrical outages are then displayed on a front-end application, which is publicly available. We use the collected outage data to analyze these outages and their socio-economic impacts on electricity vulnerable population groups. We determined that there was a slightly negative linear relationship between income and number of outages. Finally, a Markov Influence Graph was created to better understand the spatial and temporal relationships between outages., Comment: Accepted for the 2022 IEEE PES General Meeting

This paper proposes a modified conditional generative adversarial network (cGAN) model to generate net load scenarios for power systems that are statistically credible, conditioned by given labels (e.g., seasons), and, at the same time, "stressful" to the system operations and dispatch decisions. The measure of stress used in this paper is based on the operating cost increases due to net load changes. The proposed operation-adversarial cGAN (OA-cGAN) internalizes a DC optimal power flow model and seeks to maximize the operating cost and achieve a worst-case data generation. The training and testing stages employed in the proposed OA-cGAN use historical day-ahead net load forecast errors and has been implemented for the realistic NYISO 11-zone system. Our numerical experiments demonstrate that the generated operation-adversarial forecast errors lead to more cost-effective and reliable dispatch decisions.

The effective allocation of cross-border trading capacities is one of the central challenges for the implementation of a pan-European internal energy market. In contrast to traditional power flow-ignorant methods like net transfer capacities (NTC), flow-based market coupling (FBMC) has been shown to increase price convergence between market areas, while improving congestion management effectiveness. However, explicitly analysing FBMC for a future power system with a very high share of intermittent renewable generation is often overlooked in the current literature. This paper provides a comprehensive summary on the technical specification of the FBMC process and FBMC modeling methods. It discusses implications of policy considerations and explicitly discusses the impact of high-shares of intermittent generation on FBMC performance. Further, we propose probabilistic security margins compatible with the current FBMC implementation to better account for renewable uncertainty in FBMC modeling. We conduct numerical experiments on the IEEE 118 bus test system to showcase the proposed model formulations and our data and implementation is published open source.

Cyberattacks in the energy sector are commonplace. Load-altering cyberattacks launched via the manipulations of high-wattage appliances and assets are particularly alarming, as they are not continuously monitored by electric power utilities. Public Electric Vehicle Charging Stations (EVCSs) are among such high-wattage assets. Even EVCSs monitored by the electric power utilities and protected by state-of-the-art defense mechanisms are vulnerable to cyberattacks. Such cyberattacks cause financial losses to the EVCSs. In this paper, we propose cyber insurance for EVCSs to hedge the economic loss due to such cyberattacks and develop a data-driven cyber insurance design model for public EVCSs. Under mild modeling assumptions, we derive an optimal cyber insurance premium. Then, we ensure the robustness of this optimal premium and investigate the risk of insuring the EVCSs using a suitable risk assessment metric (Conditional Value-at-Risk). A case study with data from EVCSs in Manhattan, New York illustrates our results. Our results demonstrate that risk assessment is crucial for designing insurance premiums. Furthermore, the premium increases in proportion to the loss coverage offered for the EVCSs. This work informs the stakeholders involved in the roll-out and operation of public EVCSs about the benefits of cyber insurance and suggests that insurance premiums can be reduced by deploying state-of-the-art defense mechanisms.

Maintaining the stability of renewable-dominant power systems requires the procurement of virtual inertia services from non-synchronous resources (e.g., batteries, wind turbines) in addition to inertia traditionally provided by synchronous resources (e.g., thermal generators). However, the pricing of inertia provision has not been studied in a stochastic electricity market, where the uncertainty characteristics of renewable energy sources (RES) are considered. To fill in this research gap, this paper formulates a chance-constrained stochastic unit commitment model with inertia requirements and computes equilibrium energy, reserve and inertia prices using convex duality. Numerical experiments on an illustrative system and a modified IEEE 118-bus system show the performance of the proposed pricing mechanism. By allowing new virtual inertia providers to contribute to system inertia requirements, the total operating cost reduces. Moreover, the proposed stochastic electricity market internalizes RES uncertainty, which yields additional cost reductions by co-optimizing energy, reserve and inertia procurement.

Recently, chance-constrained stochastic electricity market designs have been proposed to address the shortcomings of scenario-based stochastic market designs. In particular, the use of chance-constrained market-clearing avoids trading off in-expectation and per-scenario characteristics and yields unique energy and reserves prices. However, current formulations rely on symmetric control policies based on the aggregated system imbalance, which restricts balancing reserve providers in their energy and reserve commitments. This paper extends existing chance-constrained market-clearing formulations by leveraging node-to-node and asymmetric balancing reserve policies and deriving the resulting energy and reserve prices. The proposed node-to-node policy allows for relating the remuneration of balancing reserve providers and payment of uncertain resources using a marginal cost-based approach. Further, we introduce asymmetric balancing reserve policies into the chance-constrained electricity market design and show how this additional degree of freedom affects market outcomes.

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.

The proposed open-source Power Market Tool (POMATO) aims to enable research on interconnected modern and future electricity markets in the context of the physical transmission system and its secure operation. POMATO has been designed to study capacity allocation and congestion management (CACM) policies of European zonal electricity markets, especially flow-based market coupling (FBMC). For this purpose, POMATO implements methods for the analysis of simultaneous zonal market clearing, nodal (N-k secure) power flow computation for capacity allocation, and multi-stage market clearing with adaptive grid representation and redispatch. The computationally demanding N-k secure power flow is enabled via an efficient constraint reduction algorithm. POMATO provides an integrated environment for data read-in, pre- and post-processing and interactive result visualization. Comprehensive data sets of European electricity systems compiled from Open Power System Data and Matpower Cases are part of the distribution. POMATO is implemented in Python and Julia, leveraging Python's easily maintainable data processing and user interaction features and Julia's well readable algebraic modeling language, superior computational performance and interfaces to open-source and commercial solvers.

Existing electricity market designs assume risk neutrality and lack risk-hedging instruments, which leads to suboptimal market outcomes and reduces the overall market efficiency. This paper enables risk-trading in the chance-constrained stochastic electricity market by introducing Arrow-Debreu Securities (ADS) and derives a risk-averse market-clearing model with risk trading. To enable risk trading, the probability space of underlying uncertainty is discretized in a finite number of outcomes, which makes it possible to design practical risk contracts and to produce energy, balancing reserve and risk prices. Notably, although risk contracts are discrete, the model preserves the continuity of chance constraints. The case study illustrates the usefulness of the proposed risk-averse chance-constrained electricity market with risk trading.

The ability to make optimal decisions under uncertainty remains important across a variety of disciplines from portfolio management to power engineering. This generally implies applying some safety margins on uncertain parameters that may only be observable through a finite set of historical samples. Nevertheless, the optimized decisions must be resilient to all probable outcomes, while ideally providing some measure of severity of any potential violations in the less probable outcomes.It is known that the conditional value-at-risk (CVaR) can be used to quantify risk in an optimization task, though may also impose overly conservative margins. Therefore, this paper develops a means of co-controlling the value-at-risk (VaR) level associated with the CVaR to guarantee resilience in probable cases while providing a measure of the average violation in less probable cases. To further combat uncertainty, the CVaR and VaR co-control is extended in a distributionally robust manner using the Wasserstein metric to establish an ambiguity set constructed from finite samples, which is guaranteed to contain the true distribution with a certain confidence.

US transmission systems and wholesale electricity markets, albeit federally regulated, often span across multiple state jurisdictions. In this environment, state regulators can strategically exploit this techno-economic coupling to advance their clean energy policy goals at the expense of neighboring jurisdictions. This paper investigates strategic regulatory competition to understand its effect on achieving Renewable Portfolio Standards (RPS). We formulate a chance-constrained equilibrium problem with equilibrium constraints (CC-EPEC), which considers multiple state regulators, acting in coordination with in-state power companies, to implement RPS goals in the least-cost manner. To solve this CC-EPEC, we customize a Progressive Hedging (PH) algorithm. The case study uses the CCEPEC and PH algorithm to analyze the effects of state regulatory competition in the ISO New England system.

Demand response (DR) programs aim to engage distributed demand-side resources in providing ancillary services for electric power systems. Previously, aggregated thermostatically controlled loads (TCLs) have been demonstrated as a technically viable and economically valuable provider of such services that can effectively compete with conventional generation resources in reducing load peaks and smoothing demand fluctuations. Yet, to provide these services at scale, a large number of TCLs must be accurately aggregated and operated in sync. This paper describes a Markov Decision Process (MDP) that aggregates and models an ensemble of TCLs. Using the MDP framework, we propose to internalize the exogenous uncertain dynamics of TCLs by means of stochastic and distributionally robust optimization. First, under mild assumptions on the underlying uncertainty, we derive analytical stochastic and distributionally robust control policies for dispatching a given TCL ensemble. Second, we further relax these mild assumptions to allow for a more delicate treatment of uncertainty, which leads to distributionally robust MDP formulations with moment- and Wasserstein-based ambiguity sets that can be efficiently solved numerically. The case study compares the analytical and numerical control policies using a simulated ensemble of 1,000 air conditioners.

Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational requirements. This problem becomes more severe when the SCOPF has to be solved not only for a single instance, but for multiple periods, e.g. in the context of electricity market analyses. This paper proposes an algorithm that identifies the minimal set of constraints that exactly define the space of feasible nodal injections for a given network and contingency scenarios. By internalizing the technical limits of the nodal injections and enforcing a minimal worst-case impact of contingencies to line flows, computational effort can be further improved. The case study applies and analyzes the methods on the IEEE 118 and A&M 2000 bus systems, as well as the German and European transmission systems. In all tested cases the proposed algorithm identifies at least 95% of the network and security constraints as redundant, leading to significant SCOPF solve time reductions. Scalability and practical implementation are explicitly discussed. The code and input data of the case study is published supplementary to the paper under an open-source license.

The roll-out of stochastic renewable energy sources (RES) undermines the efficiency of power system and market operations. This paper proposes an approach to derive electricity prices that internalize RES stochasticity. We leverage a chance-constrained AC Optimal Power Flow (CC AC-OPF) model, which is robust against RES uncertainty and is also aware of the resulting variability (variance) of the system state variables. Using conic duality theory, we derive and analyze energy and balancing reserve prices that internalize the risk of system limit violations and the variance of system state variables. We compare the risk- and variance-aware prices on the IEEE 118-node testbed., Comment: Accepted for publication in PSCC 2020

Distribution locational marginal prices (DLMPs) facilitate the efficient operation of low-voltage electric power distribution systems. We propose an approach to internalize the stochasticity of renewable distributed energy resources (DERs) and risk tolerance of the distribution system operator in DLMP computations. This is achieved by means of applying conic duality to a chance-constrained AC optimal power flow. We show that the resulting DLMPs consist of the terms that allow to itemize the prices for the active and reactive power production, balancing regulation, and voltage support provided. Finally, we prove the proposed DLMPs constitute a competitive equilibrium, which can be leveraged for designing a distribution electricity market, and show that imposing chance constraints on voltage limits distorts the equilibrium.

Flexible demand response (DR) resources can be leveraged to accommodate the stochasticity of some distributed energy resources. This paper develops an online learning approach that continuously estimates price sensitivities of residential DR participants and produces such price signals to the DR participants that ensure a desired level of DR capacity. The proposed learning approach incorporates the dispatch decisions on DR resources into the distributionally robust chance-constrained optimal power flow (OPF) framework. This integration is shown to adequately remunerate DR resources and co-optimize the dispatch of DR and conventional generation resources. The distributionally robust chance-constrained formulation only relies on empirical data acquired over time and makes no restrictive assumptions on the underlying distribution of the demand uncertainty. The distributional robustness also allows for robustifying the optimal solution against systematically misestimating empirically learned parameters. The effectiveness of the proposed learning approach is shown via numerical experiments. The paper is accompanied by the code and data supplement released for public use, see [27].

Distribution system operators (DSO) world-wide foresee a rapid roll-out of distributed energy resources. From the system perspective, their reliable and cost effective integration requires accounting for their physical properties in operating tools used by the DSO. This paper describes an approach to leverage the dispatch flexibility of thermostatically controlled loads (TCLs) for operating distribution systems with a high penetration level of photovoltaic resources. Each TCL ensemble is modeled using the Markov Decision Process (MDP). The MDP model is then integrated with the chance-constrained optimal power flow that accounts for the uncertainty of PV resources. Since the integrated optimization model cannot be solved efficiently by existing dynamic programming methods or off-the-shelf solvers, this paper proposes an iterative Spatio-Temporal Dual Decomposition algorithm (ST-D2). We demonstrate the usefulness of the proposed integrated optimization and ST-D2 algorithm on the IEEE 33-bus test system., Comment: 8 pages, 9 figures, 29 references

Increasing penetration of distributed energy resources complicate operations of electric power distribution systems by amplifying volatility of nodal power injections. On the other hand, these resources can provide additional control means to the distribution system operator (DSO). This paper takes the DSO perspective and leverages a data-driven distributionally robust decision-making framework to overcome the uncertainty of these injections and its impact on the distribution system operations. We develop an AC OPF formulation for radial distribution systems based on the LinDistFlow AC power flow approximation and exploit distributionally robust optimization to immunize the optimized decisions against uncertainty in the probabilistic models of forecast errors obtained from the available observations. The model is reformulated to be computationally tractable and tested on multiple IEEE distribution test systems. We also release the code supplement that implements the proposed model in Julia and can be used to reproduce our numerical results., Comment: 6 pages, 6 figures, 27 references. v4: Final Version as accepted for Publication in IEEE L-CSS