Publications

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The New York State Public Service Commission recently made significant changes to the compensation mechanisms for distributed energy resources, such as solar generation. The new mechanisms, called the Value of Distributed Energy Resources (VDER), alter the value proposition of potential installations. In particular, multiple time-of-generation based pricing alternatives were established, which could lead to potential benefits from pairing energy storage systems with solar installations. This paper presents the calculations to maximize revenue from a solar photovoltaic and energy storage system installation operating under the VDER pricing structures. Two systems in two different zones within the New York Independent System Operator area were modeled. The impact of AC versus DC energy storage system interconnections with solar generation resources was also explored. The results show that energy storage systems could generate significant revenue depending on the pricing alternative being targeted and the zone selected for the project.

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A generic constant-efficiency energy flow model is commonly used in techno-economic analyses of grid energy storage systems. In practice, charge and discharge efficiencies of energy storage systems depend on state of charge, temperature, and charge/discharge powers. Furthermore, the operating characteristics of energy storage devices are technology specific. Therefore, generic constant-efficiency energy flow models do not accurately capture the system performance. In this work, we propose to use technology-specific nonlinear energy flow models based on nonlinear operating characteristics of the storage devices. These models are incorporated into an optimization problem to find the optimal market participation of energy storage systems. We develop a dynamic programming method to solve the optimization problem and perform two case studies for maximizing the revenue of a vanadium redox flow battery (VRFB) and a Li-ion battery system in Pennsylvania New Jersey Maryland (PJM) interconnection's energy and frequency regulation markets.

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Energy storage systems are flexible and controllable resources that can provide a number of services for the electric power grid. Many technologies are available, and corresponding models vary greatly in level of detail and tractability. In this work, we propose an adaptive optimal control and estimation approach for real-time dispatch of energy storage systems that neither requires accurate state-of-energy measurements nor knowledge of an accurate state-of-energy model. Specifically, we formulate an online optimization problem that simultaneously solves moving horizon estimation and model predictive control problems, which results in estimates of the state-of-energy, estimates of the charging and discharging efficiencies, and future dispatch signals. We present a numerical example in which the plant is a nonlinear, time-varying Lithium-ion battery model and show that our approach effectively estimates the state-of-energy and dispatches the system without accurate knowledge of the dynamics and in the presence of significant measurement noise.

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As batteries become more prevalent in grid energy storage applications, the controllers that decide when to charge and discharge become critical to maximizing their utilization. Controller design for these applications is based on models that mathematically represent the physical dynamics and constraints of batteries. Unrepresented dynamics in these models can lead to suboptimal control. Our goal is to examine the state-of-the-art with respect to the models used in optimal control of battery energy storage systems (BESSs). This review helps engineers navigate the range of available design choices and helps researchers by identifying gaps in the state-of-the-art. BESS models can be classified by physical domain: state-of-charge (SoC), temperature, and degradation. SoC models can be further classified by the units they use to define capacity: electrical energy, electrical charge, and chemical concentration. Most energy based SoC models are linear, with variations in ways of representing efficiency and the limits on power. The charge based SoC models include many variations of equivalent circuits for predicting battery string voltage. SoC models based on chemical concentrations use material properties and physical parameters in the cell design to predict battery voltage and charge capacity. Temperature is modeled through a combination of heat generation and heat transfer. Heat is generated through changes in entropy, overpotential losses, and resistive heating. Heat is transferred through conduction, radiation, and convection. Variations in thermal models are based on which generation and transfer mechanisms are represented and the number and physical significance of finite elements in the model. Modeling battery degradation can be done empirically or based on underlying physical mechanisms. Empirical stress factor models isolate the impacts of time, current, SoC, temperature, and depth-of-discharge (DoD) on battery state-of-health (SoH). Through a few simplifying assumptions, these stress factors can be represented using regularization norms. Physical degradation models can further be classified into models of side-reactions and those of material fatigue. This article demonstrates the importance of model selection to optimal control by providing several example controller designs. Simpler models may overestimate or underestimate the capabilities of the battery system. Adding details can improve accuracy at the expense of model complexity, and computation time. Our analysis identifies six gaps: deficiency of real-world data in control literature, lack of understanding in how to balance modeling detail with the number of representative cells, underdeveloped model uncertainty based risk-averse and robust control of BESS, underdevelopment of nonlinear energy based SoC models, lack of hysteresis in voltage models used for control, lack of entropy heating and cooling in thermal modeling, and deficiency of knowledge in what combination of empirical degradation stress factors is most accurate. These gaps are opportunities for future research.

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Energy storage systems are flexible resources that accommodate and mitigate variability and uncertainty in the load and generation of modern power systems. We present a stochastic optimization approach for sizing and scheduling an energy storage system (ESS) for behind-the-meter use. Specifi-cally, we investigate the use of an ESS with a solar photovoltaic (PV) system and a generator in islanded operation tasked with balancing a critical load. The load and PV generation are uncertain and variable, so forecasts of these variables are used to determine the required energy capacity of the ESS as well as the schedule for operating the ESS and the generator. When the forecasting uncertainties can be fit to normal distributions, the probabilistic load balancing constraint can be reformulated as a linear inequality constraint, and the resulting optimization problem can be solved as a linear program. Finally, we present results from a case study considering the balancing of the critical load of a water treatment plant in islanded operation.

Energy storage is a unique grid asset in that it is capable of providing a number of grid services. In market areas, these grid services are only as valuable as the market prices for the services provided. This paper formulates the optimization problem for maximizing energy storage revenue from arbitrage and frequency regulation in the CAISO market. The optimization algorithm was then applied to three years of historical market data (2014-2016) at 2200 nodes to quantify the locational and time-varying nature of potential revenue. The optimization assumed perfect foresight, so it provides an upper bound on the maximum expected revenue. Since California is starting to experience negative locational marginal prices (LMPs) because of increased renewable generation, the optimization includes a duty cycle constraint to handle negative LMPs. The results show that participating in frequency regulation provides approximately 3.4 times the revenue of arbitrage. In addition, arbitrage potential revenue is highly location-specific. Since there are only a handful of zones for frequency regulation, the distribution of potential revenue from frequency regulation is much tighter.

Energy storage systems are flexible resources that accommodate and mitigate variability and uncertainty in the load and generation of modern power systems. We present a stochastic optimization approach for sizing and scheduling an energy storage system (ESS) for behind-the-meter use. Specifi-cally, we investigate the use of an ESS with a solar photovoltaic (PV) system and a generator in islanded operation tasked with balancing a critical load. The load and PV generation are uncertain and variable, so forecasts of these variables are used to determine the required energy capacity of the ESS as well as the schedule for operating the ESS and the generator. When the forecasting uncertainties can be fit to normal distributions, the probabilistic load balancing constraint can be reformulated as a linear inequality constraint, and the resulting optimization problem can be solved as a linear program. Finally, we present results from a case study considering the balancing of the critical load of a water treatment plant in islanded operation.