Junjie Qin

Optimal electric energy storage operation

Estimating the arbitrage value of storage is an important problem in power systems planning. Various studies have reported different values based numerical solutions of variations of a basic model. In this paper, we instead rely on a closed form solution for storage control. The closed form highlights the right type of forecasting that is required and allows large horizon problems to be solved. We study various scenarios and provide a simple methodology for evaluating the arbitrage value of storage.

Wind Aggregation Via Risky Power Markets

Aggregation of diverse wind power sources can effectively reduce their uncertainty, and hence the cost of wind energy integration. A risky power contract is proposed, by which wind power producers (WPPs) can trade uncertain future power for efficient wind aggregation. A two-settlement market with both the risky power contract and a conventional firm power contract is shown to have a unique competitive equilibrium (CE), characterized in closed form. The marginal contribution and diversity contribution of each WPP to the group of all WPPs are fairly reflected in the profit earned by this WPP at the CE. Moreover, the CE achieves the same total profit as achieved by a grand coalition of WPPs. In a coalitional game setting, the profit allocation induced by the CE is always in the core, and is achieved via a non-cooperative risky power market. The benefits of the risky power market are demonstrated using wind generation and locational marginal price data for ten WPPs in the PJM interconnection.

Storage in Risk Limiting Dispatch: Control and approximation

Integrating energy storage into the grid in scenarios with high penetration of renewable resources remains a significant challenge. Recently, Risk Limiting Dispatch (RLD) was proposed as a mechanism that utilizes information and market recourse to reduce reserve capacity requirements, emissions and other system operator objectives. Among other benefits, it included a set of simplified rules that can be readily utilized in existing system operator dispatch systems to provide reliable and computationally efficient decisions. RLD implements stochastic loss of load control to absorb the increased uncertainty in the grid. Storage is emerging as an alternative to mitigate the uncertainty in the grid. This paper extends the RLD framework to incorporate intrahour storage. It develops a closed form scheduling rule for optimal stochastic dispatch that incorporates a sequence of markets and real-time information. Simple approximations to the optimal rule that can be easily implemented in existing dispatch systems are proposed and evaluated. The approximation relies on continuous-time approximations of solutions for a discrete time optimal control problem. Numerical experiments are conducted to illustrate the proposed procedures.

Online Modified Greedy Algorithm for Storage Control Under Uncertainty

This paper studies the general problem of operating energy storage under uncertainty. Two fundamental sources of uncertainty are considered, namely the uncertainty in the unexpected fluctuation of the net demand process and the uncertainty in the locational marginal prices. We propose a very simple algorithm termed Online Modified Greedy (OMG) algorithm for this problem. A stylized analysis for the algorithm is performed, which shows that comparing to the optimal cost of the corresponding stochastic control problem, the sub-optimality of OMG is controlled by an easily computable bound. This suggests that, albeit simple, OMG is guaranteed to have good performance in cases when the bound is small. Meanwhile, OMG together with the sub-optimality bound can be used to provide a lower bound for the optimal cost. Such a lower bound can be valuable in evaluating other heuristic algorithms. For the latter cases, a semidefinite program is derived to minimize the sub-optimality bound of OMG. Numerical experiments are conducted to verify our theoretical analysis and to demonstrate the use of the algorithm.

Modeling and online control of generalized energy storage networks

The integration of intermittent and volatile renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of general storage networks in uncertain environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems with continuous spaces suffer from curses of dimensionality, and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or near-optimal performance. This paper provides an efficient and provably near-optimal algorithm to solve this problem in a very general setting. We study the optimal control of generalized storage networks, i.e., electric networks connected to distributed generalized storages. Here generalized storage is a unifying dynamic model for many components of the grid that provide the functionality of shifting energy over time, ranging from standard energy storage devices to deferrable or thermostatically controlled loads. An online algorithm is devised for the corresponding constrained stochastic control problem based on the theory of Lyapunov optimization. We prove that the algorithm is near-optimal, and construct a semidefinite program to minimize the sub-optimality bound. The resulting bound is a constant that depends only on the parameters of the storage network and cost functions, and is independent of uncertainty realizations. Numerical examples are given to demonstrate the effectiveness of the algorithm.

Dynamic programming solution to distributed storage operation and design

Energy storage provides an important way to average temporal variability of intermittent energy generation. Grid level distributed storage enables additional spatial averaging effect by sending stored energy through the network. However, the problem of optimal storage operation in the network, coupling storage and network constraints with randomness of renewable generation, is challenging. An efficient solution method to this problem based on dynamic programming is presented in this paper. This approach also leads to analytical expressions for the expected system cost and the optimal control parametrized by dual variables, which can be computed by solving a simple deterministic convex program. These analytical expressions simplify tasks such as network storage system design. The approach is illustrated with numerical examples.

Distributed Online Modified Greedy Algorithm for Networked Storage Operation Under Uncertainty

The integration of intermittent and stochastic renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of storage networks in stochastic environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems on continuous spaces suffer from curses of dimensionality and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or provably near-optimal performance for this problem. This paper provides an efficient algorithm to solve this problem with performance guarantees. We study the operation of storage networks, i.e., a storage system interconnected via a power network. An online algorithm, termed online modified greedy algorithm, is developed for the corresponding constrained stochastic control problem. A sub-optimality bound for the algorithm is derived and a semidefinite program is constructed to minimize the bound. In many cases, the bound approaches zero so that the algorithm is near-optimal. A task-based distributed implementation of the online algorithm relying only on local information and neighborhood communication is then developed based on the alternating direction method of multipliers. Numerical examples verify the established theoretical performance bounds and demonstrate the scalability of the algorithm.

Risky power forward contracts for wind aggregation

Risky power contracts are introduced for enabling wind power aggregation. First, the problem of optimal risky and firm power contract offering in the forward market is formulated in the single wind farm setting. Analytical solutions are obtained, and the concepts of fair price of wind power and price of unitized risk are introduced. The more general setting of two wind farms both trading risky and firm power is studied, in which both wind farms seek to benefit from wind aggregation. The problem of a contract offering game in the forward market is formulated. Analytical solutions are obtained for the best responses that reveal clear insights into the optimal firm and risky contract offering for each wind farm. Complete characterization of the equilibria of the game is then obtained analytically. A generalization of the fair price to the two wind farm setting is derived, which characterizes the value of wind aggregation. With the generalized fair prices, all equilibria are also efficient, namely, they achieve the same total profit as forming a coalition of the two wind farms.

Flexible Market for Smart Grid: Coordinated Trading of Contingent Contracts

A coordinated trading process is proposed as a design for an electricity market with significant uncertainty, perhaps from renewables. In this process, groups of agents propose to the system operator (SO) a contingent trade that is balanced, that is, the sum of demand bids and the sum of supply bids are equal. The SO accepts the proposed trade if no network constraint is violated or curtails it until no violation occurs. Each proposed trade is accepted or curtailed as it is presented. The SO also provides guidance to help future proposed trades meet network constraints. The SO does not set prices, and there is no requirement that different trades occur simultaneously or clear at uniform prices. Indeed, there is no price-setting mechanism. However, if participants exploit opportunities for gain, the trading process will lead to an efficient allocation of energy and to the discovery of locational marginal prices. The great flexibility in the proposed trading process and the low communication and control burden on the SO may make the process suitable for coordinating producers and consumers in the distribution system.

Distributed storage operation in distribution network with stochastic renewable generation

The integration of distributed renewable energy generations and storages in the distribution system imposes new challenges on the paradigm of the operation. The resulting control problems are intrinsically hard because of nonlinearity in power flow equations, stochasticity in renewable generations, and inter-temporal coupling of decision problems due to energy storage. This paper provides an initial attempt to solve these nonlinear stochastic control problems numerically, within the framework of Markov decision processes (MDPs). Detailed MDPs are first designed for two-bus sub-networks of the distribution system. Optimal control policies for each sub-network are then combined to guide the design of a control policy to operate the entire storage system on a distribution network. The performance of this approach is demonstrated numerically by comparing with other typical operation policies.