The high penetration of volatile renewable energy challenges power system operation. Energy storage units (ESUs) can shift the demand over time and compensate real-time discrepancy between generation and demand, and thus improve system operation flexibility and reduce renewable energy curtailment. This paper proposes two parametric optimization models to quantify how the power (MW) and energy (MWh) capacity of ESU would impact renewable energy utilization from two aspects: renewable energy curtailment and system flexibility for uncertainty mitigation. The two indicators are characterized as multivariate functions in the capacity parameters of ESUs. A severity ranking algorithm is suggested to pick up critical scenarios of fluctuation patterns from the uncertainty set; consequently, the proposed models come down to multi-parametric mixed-integer linear programs (mp-MILPs) which can be solved by a decomposition algorithm. The proposed method provides analytical expressions of the two indicators as functions in MW and MWh capacity. Such a characterization delivers abundant sensitivity information on the impact of ESU capacity parameters, and provides a powerful tool for visualization and useful reference for storage sizing. Case studies verify the effectiveness of the proposed method and demonstrate how to use the geometric information.

Distribution systems are operated with an increasing level of uncertainty. Energy storage is playing an important role in shaving the peak load and mitigating uncertainty. This paper proposes a multistage robust optimization model for distribution system operation with energy storage under uncertainty. Unlike the conventional robust optimization paradigm which minimizes the worst-case cost, the proposed formulation optimizes the cost in the nominal scenario. In analogy to dynamic programming, we define dynamic robust feasible regions in a recursive manner. In each period, the dynamic robust feasible region is shown to be polyhedral, and a linear programming based projection algorithm is developed to compute such regions offline. In the online stage, the method is executed following a rolling horizon manner: renewable output is observed at the beginning of each period, and the cost of remaining periods in the forecast scenario is to be minimized subject to operation constraints and dynamic robust feasible regions, giving rise to a linear program. In this way, the dispatch strategy ensures multistage operation security regardless of future realizations of renewable power. In numeric tests on a modified IEEE 33-bus distribution system, the dynamic robust feasible regions are visualized and analyzed, and the proposed method is compared with two prevailing robust optimization methods, verifying its advantages in terms of optimality and robustness.

Energy storage is playing an increasingly important role in power system operation due to its ability to shave the peak and fill the valley. Advanced adiabatic compressed-air energy storage (AA-CAES) is a clean and scalable energy storage technology and has attracted wide attention recently. This paper proposes a multi-state operation model of AA-CAES capturing the dynamic change of internal physical status. A stand-by state is introduced, at which AA-CAES works like a condenser that produces only reactive power. It brings two benefits. First, the facility is started up and shut down less frequently, which helps extend its service time. Second, it can provide continuous reactive power support all day long, unlike on-load tap changers or shunt capacitors whose voltage regulation strategy is discrete and suffers from a very low switching frequency. Taking AA-CAES into account, the optimal operation of a distribution network is formulated as a bi-objective dynamic optimal power flow problem. Nash bargaining is employed to extract a single Pareto optimal solution that fairly compromises two objectives. To solve the operation problem in a tractable manner, the bargaining objective and power flow constraints are convexified, giving rise to a mixed-integer second-order cone program. A feasibility recovery algorithm is developed to find a physically meaningful solution whenever the convex relaxation on power flow is inexact. Case studies on the IEEE 33-bus system demonstrate the effectiveness and advantages of the proposed method.

The integration of volatile renewable resources and energy storage entails making dispatch decisions for conventional coal-fired units and fast-response devices in different timescales. This paper studies intraday dynamic energy-reserve dispatch following a two-timescale setting. The coarse timescale determines the hourly reference output and reserve allocation, which offers a sufficient backup for the fine-timescale operation; the fine timescale determines the adjustment of gas-fired units and energy storage system every 15 minutes in response to the actual wind power. A stochastic dynamic programming method is proposed to make decisions at the coarse timescale while guaranteeing the robust feasibility of the fast process via vertex scenarios of uncertainty set and bounding the state-of-charge intervals for energy storage; the fast-response actions at the fine timescale are updated using a truncated rolling-horizon optimization, which incorporates the cost-to-go functions calculated at the coarse timescale to prevent the fast decisions from being myopic. Case studies on the modified IEEE 5-bus system and 118-bus system validate the proposed framework.

Energy storage unit (ESU) is playing an increasingly important role in load shifting and uncertainty mitigation. This paper aims to quantify the value of ESU in the unit commitment (UC) with renewable generation. By treating the power and energy capacities of ESU as continuous parameters, the stochastic UC problem is cast as a multi-parametric mixed-integer linear program (mp-MILP), whose optimal value function (OVF) gives the relation between storage capacity and the daily UC cost in an analytical manner. It encompasses abundant sensitivity information, and its surface can be easily visualized. The reduced cost compared with the benchmark case without storage can be regarded as the value of ESU. As a potential application, the OVF is used to formulated an optimal storage sizing problem that maximizes the ratio between the reduced operation cost and the investment cost, ensuring the minimum time of cost recovery. The solution consists of two steps: the first step constructs the OVF parameterized in storage capacity; the second step reformulates the fractional storage sizing program into an MILP, leveraging the expression of the OVF and variable transformations. Case studies conducted on the IEEE 9-bus system and IEEE 118-bus system illustrate how the OVF offers useful reference for power system operation and planning. The proposed optimal sizing model shows advantages in efficient utilization of investment in terms of payback time and rate of return.