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Severe weather events such as floods, hurricanes, earthquakes, and large wind or ice storms can cause extensive damage to electrical distribution networks, requiring a multi-day restoration effort. Complicating the recovery process is the lack of complete and accurate information regarding the extent and locations of damages, at least during the initial part of the recovery process. These factors make workforce planning challenging. In this paper, we adopt a rolling horizon restoration framework whereby repairs are planned for adjustable finite length restoration windows. Considering both repair times as well as travel times, we show that the optimal scheduling problem with multiple crews, each with their own time budget, can be recast in terms of a cost constrained reward maximizing mTSP (traveling salesman problem) on doubly weighted graphs, where the objective is to maximize the aggregate reward earned during the upcoming restoration window, provided no crew violates its time budget and certain electrical continuity constraints are met. We propose a mixed integer linear programming (MILP) model for solving the above problem which is validated on standard IEEE PES test feeder networks., Comment: 26 pages, 17 figures

This paper discusses how a cyber attack could take advantage of torsional resonances in the shaft of turbo-generators to inflict severe physical damage to a power system. If attackers were able to take over the control of a battery energy storage device, they could modulate the injection of this device at a frequency that matches one of the sub-synchronous resonance frequencies of a generator. Small changes in injection might be sufficient to excite one of these mechanical resonances, resulting in metal fatigue and ultimately a catastrophic failure in the shaft of the generator. Using a state-space model of the electromechanical system, the paper develops transfer functions linking the magnitude of the malicious injections to the magnitude of oscillations in the speed and angle of the various masses connected to the shaft. Numerical results from a two-area power system demonstrate the existence of vulnerable frequencies and show that damaging mechanical oscillations can be triggered without causing easily detectable signals at the generator terminals., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

Further electrification of the economy is expected to sharpen ramp rates and increase peak loads. Flexibility from the demand side, which new technologies might facilitate, can help these operational challenges. Electric utilities have begun implementing new tariffs and other mechanisms to encourage the deployment of energy storage. This paper examines whether making these new tariffs technology agnostic and extending them to flexible demand would significantly improve the procurement of operational flexibility. In particular, we consider how a commercial consumer might adjust its flexible demand when subject to Pacific Gas and Electric Company's storage-centric electric tariff. We show that extending this tariff to consumers with flexible demand would reduce the utility's net demand ramp rates during peak hours. If consumers have a high level of demand flexibility, this tariff also reduces the net demand during peak hours and decreases total electric bills when compared to the base tariff., Comment: Accepted to the 2022 IEEE Power and Energy Society (PES) General Meeting. arXiv admin note: text overlap with arXiv:2105.07106

Optimal Volt/VAR control (VVC) in distribution networks relies on an effective coordination between the conventional utility-owned mechanical devices and the smart residential photovoltaic (PV) inverters. Typically, a central controller carries out a periodic optimization and sends setpoints to the local controller of each device. However, instead of tracking centrally dispatched setpoints, smart PV inverters can cooperate on a much faster timescale to reach optimality within a PV inverter group. To accommodate such PV inverter groups in the VVC architecture, this paper proposes a bi-level optimization framework. The upper-level determines the setpoints of the mechanical devices to minimize the network active power losses, while the lower-level represents the coordinated actions that the inverters take for their own objectives. The interactions between these two levels are captured in the bi-level optimization, which is solved using the Karush-Kuhn-Tucker (KKT) conditions. This framework fully exploits the capabilities of the different types of voltage regulation devices and enables them to cooperatively optimize their goals. Case studies on typical distribution networks with field-recorded data demonstrate the effectiveness and advantages of the proposed approach.

High penetrations of photovoltaic (PV) systems can cause severe voltage quality problems in distribution networks. This paper proposes a distributed control strategy based on the dynamic formation of coalitions to coordinate a large number of PV inverters for voltage regulation. In this strategy, a rule-based coalition formation scheme deals with the zonal voltage difference caused by the uneven integration of PV capacity. Under this scheme, PV inverters form into separate voltage regulation coalitions autonomously according to local, neighbor as well as coalition voltage magnitude and regulation capacity information. To coordinate control within each coalition, we develop a feedback-based leader-follower consensus algorithm which eliminates the voltage violations caused by the fast fluctuations of load and PV generation. This algorithm allocates the required reactive power contribution among the PV inverters according to their maximum available capacity to promote an effective and fair use of the overall voltage regulation capacity. Case studies based on realistic distribution networks and field-recorded data validate the effectiveness of the proposed control strategy. Moreover, comparison with a centralized network decomposition-based scheme shows the flexibility of coalition formation in organizing the distributed PV inverters. The robustness and generalizability of the proposed strategy are also demonstrated.

There is an opportunity in modern power systems to explore the demand flexibility by incentivizing consumers with dynamic prices. In this paper, we quantify demand flexibility using an efficient tool called time-varying elasticity, whose value may change depending on the prices and decision dynamics. This tool is particularly useful for evaluating the demand response potential and system reliability. Recent empirical evidences have highlighted some abnormal features when studying demand flexibility, such as delayed responses and vanishing elasticities after price spikes. Existing methods fail to capture these complicated features because they heavily rely on some predefined (often over-simplified) regression expressions. Instead, this paper proposes a model-free methodology to automatically and accurately derive the optimal estimation pattern. We further develop a two-stage estimation process with Siamese long short-term memory (LSTM) networks. Here, a LSTM network encodes the price response, while the other network estimates the time-varying elasticities. In the case study, the proposed framework and models are validated to achieve higher overall estimation accuracy and better description for various abnormal features when compared with the state-of-the-art methods., Comment: Author copy of the manuscript submitted to IEEE Trans on Power Systems

Changes in the profile of prices in wholesale electricity markets prompt utilities to redesign their tariffs and adjust their time-of-use periods to ensure a more adequate cost recovery. However, changing the rate structures could adversely affect commercial consumers by increasing their electricity bills and hindering their ability to reduce costs using techniques like net energy metering. As time-of-use periods are adjusted, consumers will need to rely on the flexibility of distributed energy resources to achieve cost reductions. This paper explores the effect that Pacific Gas and Electric Company's redesigned rates have on the electricity bills of consumers with different demand profiles. Sensitivity analyses are conducted to examine the effect of asset sizing on reducing costs under each tariff., Comment: Accepted to the 2021 IEEE Power and Energy Society (PES) General Meeting

This paper presents a trajectory tracking control strategy that modulates the active power injected by geographically distributed inverter-based resources to support transient stability. Each resource is independently controlled, and its response drives the local bus voltage angle toward a trajectory that tracks the angle of the center of inertia. The center-of-inertia angle is estimated in real time from wide-area measurements. The main objectives are to stabilize transient disturbances and increase the amount of power that can be safely transferred over key transmission paths without loss of synchronism. Here we envision the actuators as utility-scale energy storage systems; however, equivalent examples could be developed for partially-curtailed photovoltaic generation and/or Type 4 wind turbine generators. The strategy stems from a time-varying linearization of the equations of motion for a synchronous machine. The control action produces synchronizing torque in a special reference frame that accounts for the motion of the center of inertia. This drives the system states toward the desired trajectory and promotes rotor angle stability. For testing we employ a reduced-order dynamic model of the North American Western Interconnection. The results show that this approach improves system reliability and can increase capacity utilization on stability-limited transmission corridors., Comment: 31 pages, 15 figures, 2 tables, IET pre-print

Increasing the penetration of variable generation has a substantial effect on the operational reliability of power systems. The higher level of uncertainty that stems from this variability makes it more difficult to determine whether a given operating condition will be secure or insecure. Data-driven techniques provide a promising way to identify security rules that can be embedded in economic dispatch model to keep power system operating states secure. This paper proposes using a sparse weighted oblique decision tree to learn accurate, understandable, and embeddable security rules that are linear and can be extracted as sparse matrices using a recursive algorithm. These matrices can then be easily embedded as security constraints in power system economic dispatch calculations using the Big-M method. Tests on several large datasets with high renewable energy penetration demonstrate the effectiveness of the proposed method. In particular, the sparse weighted oblique decision tree outperforms the state-of-art weighted oblique decision tree while keeping the security rules simple. When embedded in the economic dispatch, these rules significantly increase the percentage of secure states and reduce the average solution time., Comment: 8 pages, 6 figures

While energy arbitrage from energy storage can lower power system operating costs, it can also increase greenhouse gas emissions. If power system operations are conducted with the constraint that energy storage operation must not increase emissions, how does this constraint affect energy storage investment decisions? Two bi-level energy storage investment problems are considered, representing 'philanthropic' (profitability-constrained) and profit-maximizing storage investors (PhSI, PMSI). A MILP heuristic is developed to obtain good candidate solutions to these inherently MINLP bi-level problems. A case study is conducted on a 30% renewable system, with sensitivity analyses on the price of storage and the price of carbon emissions. Regardless of the emissions-neutrality constraint, a PhSI installs significantly more energy storage than a PMSI, increasing system flexibility. The effect of the emissions-neutrality constraint in the absence of a carbon price is to reduce the quantity of storage purchased and reduce annual system emissions (~3%), with only minor increases in overall cost (~0.1%). In cases with a carbon price, storage does not tend to increase emissions and the emissions constraint does not tend to decrease storage investment. The emissions-neutrality constraint is seen to deliver similar emissions reductions even in a system with much higher renewable penetration (46%).

For decades, power system stabilizers paired with high initial response automatic voltage regulators have served as an effective means of meeting sometimes conflicting system stability requirements. Driven primarily by increases in power electronically-coupled generation and load, the dynamics of large-scale power systems are rapidly changing. Electric grids are losing inertia and traditional sources of voltage support and oscillation damping. The system load is becoming stiffer with respect to changes in voltage. In parallel, advancements in wide-area measurement technology have made it possible to implement control strategies that act on information transmitted over long distances in nearly real time. In this paper, we present a power system stabilizer architecture that can be viewed as a generalization of the standard $\Delta\omega$-type stabilizer. The control strategy utilizes a real-time estimate of the center-of-inertia speed derived from wide-area measurements. This approach creates a flexible set of trade-offs between transient and small-signal response, making synchronous generators better able to adapt to changes in system dynamics. The phenomena of interest are examined using a two-area test case and a reduced-order model of the North American Western Interconnection. To validate the key findings under realistic conditions, we employ a state-of-the-art co-simulation platform called HELICS to combine high-fidelity power system and communication network models. The benefits of the proposed control strategy are retained even under pessimistic assumptions of communication network performance., Comment: 11 pages, 17 figures, 2 tables

Natural disasters require repairing all damaged components in electricity distribution networks. Optimal scheduling repair crews to minimize the aggregate duration of interruptions reduces the harm. We consider the fact that the number of switches is much smaller than the number of edges. The problem is modeled by a parallel identical machine scheduling with group soft precedence constraints to minimize the total weighted energization time. We propose an LP-based list scheduling algorithm and a conversion algorithm and analyze their theoretical performances.

This paper addresses the problem of how best to coordinate, or `stack,' energy storage services in systems that lack centralized markets. Specifically, its focus is on how to coordinate transmission-level congestion relief with local, distribution-level objectives. We describe and demonstrate a unified communication and optimization framework for performing this coordination. The congestion relief problem formulation employs a weighted $\ell_{1}$-norm objective. This approach determines a set of corrective actions, i.e., energy storage injections and conventional generation adjustments, that minimize the required deviations from a planned schedule. To exercise this coordination framework, we present two case studies. The first is based on a 3-bus test system, and the second on a realistic representation of the Pacific Northwest region of the United States. The results indicate that the scheduling methodology provides congestion relief, cost savings, and improved renewable energy integration. The large-scale case study informed the design of a live demonstration carried out in partnership with the University of Washington, Doosan GridTech, Snohomish County PUD, and the Bonneville Power Administration. The goal of the demonstration was to test the feasibility of the scheduling framework in a production environment with real-world energy storage assets. The demonstration results were consistent with computational simulations., Comment: 11 pages, 7 figures, 10 tables

Multi-energy systems can provide a constant level of service to end-use energy demands, while deriving delivered energy from a variety of primary/secondary energy sources. This fuel-switching capability can be used to reduce operating expenses, reduce environmental impacts, improve flexibility to accommodate renewable energy, and improve reliability. This paper presents four frameworks for incentivizing energy hub equipment investments for low-carbon operation targets. These frameworks vary in the measures taken to achieve low-carbon operation (explicit constraint vs. carbon pricing) and in the relationship between the hub builder and operator (cooperative vs. uncoordinated). The underlying energy hub model upon which these frameworks are built is an enhanced greenfield model, introducing 'energy buses' to reduce dimensionality. A case study is conducted for a campus being designed in Beijing, and results from each framework are compared to illustrate their relative costs. When the operator cannot be trusted to cooperate in controlling emissions, the system must be 'overbuilt' with more expensive equipment to ensure emissions target are met. A taxation-based approach increases overall costs at moderate emissions targets, but this effect decreases at aggressive targets. This paper also compares the cost of less efficient institutional frameworks with the most efficient approach, i.e. cooperation between builder and operator with constraints on emissions.

This paper addresses the problem of predicting duration of unplanned power outages, using historical outage records to train a series of neural network predictors. The initial duration prediction is made based on environmental factors, and it is updated based on incoming field reports using natural language processing to automatically analyze the text. Experiments using 15 years of outage records show good initial results and improved performance leveraging text. Case studies show that the language processing identifies phrases that point to outage causes and repair steps., Comment: Appears in IEEE Transactions on Power Systems

Probabilistic load forecasts provide comprehensive information about future load uncertainties. In recent years, many methodologies and techniques have been proposed for probabilistic load forecasting. Forecast combination, a widely recognized best practice in point forecasting literature, has never been formally adopted to combine probabilistic load forecasts. This paper proposes a constrained quantile regression averaging (CQRA) method to create an improved ensemble from several individual probabilistic forecasts. We formulate the CQRA parameter estimation problem as a linear program with the objective of minimizing the pinball loss, with the constraints that the parameters are nonnegative and summing up to one. We demonstrate the effectiveness of the proposed method using two publicly available datasets, the ISO New England data and Irish smart meter data. Comparing with the best individual probabilistic forecast, the ensemble can reduce the pinball score by 4.39% on average. The proposed ensemble also demonstrates superior performance over nine other benchmark ensembles., Comment: Submitted to IEEE Transactions on Smart Grid

Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. In this paper, we propose a novel approach to controlled islanding based on weak submodularity. Our formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. We relax the problem to a formulation with bounded submodularity ratio and a matroid constraint, and propose an approximation algorithm which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems.

Controllable building loads have the potential to increase the flexibility of power systems. A key step in developing effective and attainable load control policies is modeling the set of feasible building load profiles. In this paper, we consider buildings whose source of flexibility is their HVAC loads. We propose a data-driven method to empirically estimate a robust feasible region of the load using coarse data, that is, using only total building load and average indoor temperatures. The proposed method uses easy-to-gather coarse data and can be adapted to buildings of any type. The resulting feasible region model is robust to temperature prediction errors and is described by linear constraints. The mathematical simplicity of these constraints makes the proposed model adaptable to many power system applications, for example, economic dispatch, and optimal power flow. We validate our model using data from EnergyPlus and demonstrate its usefulness through a case study in which flexible building loads are used to balance errors in wind power forecasts.

This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a discrete optimization problem with bounded submodularity ratio, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system., Comment: This is a revised version of the paper that appeared in the proceedings of the 56th IEEE Conference on Decision and Control (CDC), Melbourne, Australia, December, 2017

In this paper, we develop semidefinite programming (SDP) models aimed at solving optimal power flow (OPF) problems in distribution systems. We propose two models: the symmetrical SDP model which modifies the existing BFM-SDP model. Then based on the symmetrical SDP model, we develop a voltage regulation model that solves OPF problems with binding voltage constraints. To evaluate the accuracy of our proposed OPF models, we rely on OpenDSS, a power flow solver, to generate power flow solutions as the benchmarks. Comprehensive case studies are conducted showing our SDP models have better numerical stability and yield more accurate results than existing approaches

Distribution systems are often crippled by catastrophic damage caused by a natural disaster. Well-designed hardening can significantly improve the performance of post-disaster restoration operations. Such performance is quantified by a resilience measure associated with the operability trajectory. The distribution system hardening problem can be formulated as a two-stage stochastic problem, where the inner operational problem addresses the proper sequencing of post-disaster repairs and the outer problem the judicious selection of components to harden. We propose a deterministic robust reformulation with two solution methods, an MILP formulation and a heuristic approach. We provide computational evidence on various IEEE test feeders which illustrates that the heuristic approach provides near-optimal hardening solutions efficiently.

Battery participants in performance-based frequency regulation markets must consider the cost of battery aging in their operating strategies to maximize market profits. In this paper we solve this problem by proposing an optimal control policy and an optimal bidding policy based on realistic market settings and an accurate battery aging model. The proposed control policy has a threshold structure and achieves near-optimal performance with respect to an offline controller that has complete future information. The proposed bidding policy considers the optimal control policy to maximize market profits while satisfying the market performance requirement through a chance-constraint. It factors the value of performance and supports a trade-off between higher profits and a lower risk of violating performance requirements. We demonstrate the optimality of both policies using simulations. A case study based on the PJM regulation market shows that our approach is effective at maximizing operating profits.

We study the optimal control of battery energy storage under a general "pay-for-performance" setup such as providing frequency regulation and renewable integration. In these settings, batteries need to carefully balance the trade-off between following the instruction signals and their degradation costs in real-time. Existing battery control strategies either do not consider the uncertainty of future signals, or cannot accurately account for battery cycle aging mechanism during operation. In this work, we take a different approach to the optimal battery control problem. Instead of attacking the complexity of battery degradation function or the lack of future information one at a time, we address these two challenges together in a joint fashion. In particular, we present an electrochemically accurate and trackable battery degradation model called the rainflow cycle-based model. We prove the degradation cost is convex. Then we propose an online control policy with a simple threshold structure and show it achieve near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize the optimality gap and show it is independent to the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results., Comment: Appears in IEEE Transactions on Automatic Control

Power systems are increasingly operated in corrective rather than preventive security mode, which means that appropriate control actions must be taken immediately after a contingency has occurred. This paper proposes an online algorithm for automatically alleviating contingencies such as voltage limit violations and line overloads. Unlike previously proposed approaches, the network itself serves as a natural solver of the power flow equations. This makes it possible to start the implementation immediately and avoids problems caused by modeling errors. Every time the controller receives measurements from the grid, it evaluates the presence of contingencies and computes the optimal corrective actions that can be implemented before the next sampling period, subject to ramping constraints of the generators. These corrective actions are implemented through the standard Automatic Generation Control. Finding the optimal incremental corrective actions is fast because this problem is linearized. The effectiveness of this algorithm at correcting both line overloads and voltage violations is demonstrated using the IEEE-118 Bus test system., Comment: To Appear in IEEE Transactions on Power Systems

Scenario generation is an important step in the operation and planning of power systems with high renewable penetrations. In this work, we proposed a data-driven approach for scenario generation using generative adversarial networks, which is based on two interconnected deep neural networks. Compared with existing methods based on probabilistic models that are often hard to scale or sample from, our method is data-driven, and captures renewable energy production patterns in both temporal and spatial dimensions for a large number of correlated resources. For validation, we use wind and solar times-series data from NREL integration data sets. We demonstrate that the proposed method is able to generate realistic wind and photovoltaic power profiles with full diversity of behaviors. We also illustrate how to generate scenarios based on different conditions of interest by using labeled data during training. For example, scenarios can be conditioned on weather events~(e.g. high wind day) or time of the year~(e,g. solar generation for a day in July). Because of the feedforward nature of the neural networks, scenarios can be generated extremely efficiently without sophisticated sampling techniques., Comment: Accepted to IEEE Transactions on Power Systems; code available at https://github.com/chennnnnyize/Renewables_Scenario_Gen_GAN

When participating in electricity markets, owners of battery energy storage systems must bid in such a way that their revenues will at least cover their true cost of operation. Since cycle aging of battery cells represents a substantial part of this operating cost, the cost of battery degradation must be factored in these bids. However, existing models of battery degradation either do not fit market clearing software or do not reflect the actual battery aging mechanism. In this paper we model battery cycle aging using a piecewise linear cost function, an approach that provides a close approximation of the cycle aging mechanism of electrochemical batteries and can be incorporated easily into existing market dispatch programs. By defining the marginal aging cost of each battery cycle, we can assess the actual operating profitability of batteries. A case study demonstrates the effectiveness of the proposed model in maximizing the operating profit of a battery energy storage system taking part in the ISO New England energy and reserve markets.

When providing frequency regulation in a pay-for-performance market, batteries need to carefully balance the trade-off between following regulation signals and their degradation costs in real-time. Existing battery control strategies either do not consider mismatch penalties in pay-for-performance markets, or cannot accurately account for battery cycle aging mechanism during operation. This paper derives an online control policy that minimizes a battery owner's operating cost for providing frequency regulation in a pay-for-performance market. The proposed policy considers an accurate electrochemical battery cycle aging model, and is applicable to most types of battery cells. It has a threshold structure, and achieves near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize this gap and show it is independent of the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.

Natural disasters, such as hurricanes, earthquakes and large wind or ice storms, typically require the repair of a large number of components in electricity distribution networks. Since power cannot be restored before these repairs have been completed, optimally scheduling the available crews to minimize the cumulative duration of the customer interruptions reduces the harm done to the affected community. Considering the radial network structure of the distribution system, this repair and restoration process can be modeled as a scheduling problem with soft precedence constraints. As a benchmark, we first formulate this problem as a time-indexed ILP with valid inequalities. Three practical methods are then proposed to solve the problem: (i) an LP-based list scheduling algorithm, (ii) a single to multi-crew repair schedule conversion algorithm, and (iii) a dispatch rule based on $\rho$-factors which can be interpreted as Component Importance Measures. We show that the first two algorithms are $2$ and $\left(2 - \frac{1}{m}\right)$ approximations respectively. We also prove that the latter two algorithms are equivalent. Numerical results validate the effectiveness of the proposed methods.

Reduced installation and operating costs give energy storage systems an opportunity to participate actively and profitably in electricity markets. In addition to providing ancillary services, energy storage systems can also arbitrage temporal price differences. Congestion in the transmission network often accentuates these price differences and will under certain circumstances enhance the profitability of arbitrage. On the other hand, congestion may also limit the ability of a given storage device to take advantage of arbitrage opportunities. This paper analyzes how transmission congestion affects the profitability of arbitrage by storage devices in markets with perfect and imperfect competition. Imperfect competition is modeled using a bilevel optimization where the offers and bids submitted by the storage devices can alter the market outcome. Price-taker and price-maker assumptions are also investigated through market price duration curves. This analysis is based on simulating an entire year of market operation on the IEEE Reliability Test system., Comment: To appear in PESGM 2017

Energy storage can facilitate the integration of renewable energy resources by providing arbitrage and ancillary services. Jointly optimizing energy and ancillary services in a centralized electricity market reduces the system's operating cost and enhances the profitability of energy storage systems. However, achieving these objectives requires that storage be located and sized properly. We use a bi-level formulation to optimize the location and size of energy storage systems which perform energy arbitrage and provide regulation services. Our model also ensures the profitability of investments in energy storage by enforcing a rate of return constraint. Computational tractability is achieved through the implementation of a primal decomposition and a subgradient-based cutting-plane method. We test the proposed approach on a 240-bus model of the Western Electricity Coordinating Council (WECC) system and analyze the effects of different storage technologies, rate of return requirements, and regulation market policies on ES participation on the optimal storage investment decisions. We also demonstrate that the proposed approach outperforms exact methods in terms of solution quality and computational performance.

Because energy storage systems have better ramping characteristics than traditional generators, their participation in frequency regulation should facilitate the balancing of load and generation. However, they cannot sustain their output indefinitely. System operators have therefore implemented new frequency regulation policies to take advantage of the fast ramps that energy storage systems can deliver while alleviating the problems associated with their limited energy capacity. This paper contrasts several U.S. policies that directly affect the participation of energy storage systems in frequency regulation and compares the revenues that the owners of such systems might achieve under each policy., Comment: This paper will be presented in IEEE PES General Meeting 2016