Joshua A. Taylor

Convex Models of Distribution System Reconfiguration

We derive new mixed-integer quadratic, quadratically constrained, and second-order cone programming models of distribution system reconfiguration, which are to date the first formulations of the ac problem that have convex, continuous relaxations. Each model can be reliably and efficiently solved to optimality using standard commercial software. In the course of deriving each model, we obtain original quadratically constrained and second-order cone approximations to power flow in radial networks.

Linear Relaxations for Transmission System Planning

We apply a linear relaxation procedure for polynomial optimization problems to transmission system planning. The approach recovers and improves upon existing linear models based on the DC approximation. We then consider the full AC problem, and obtain new linear models with nearly the same efficiency as the linear DC models. The new models are applied to standard test systems, and produce high-quality approximate solutions in reasonable computation time.

Conic AC transmission system planning

We formulate mixed-integer conic approximations to AC transmission system planning. The first applies lift-and-project relaxations to a nonconvex model built around a semidefinite power flow relaxation. We then employ a quadratically constrained approximation to the DistFlow equations in constructing a second-order cone model that is convex without relaxation. We solve mixed integer linear and second-order cone programs using commercial software and assess their performance on two benchmark problems. As with DC power flow models and linear AC relaxations, the new models usually produce solutions which are infeasible under the original constraints. However, they are nearer to feasibility, and therefore represent stronger alternatives.

Competitive energy storage in the presence of renewables

A large fraction of new distributed generation will use renewable sources, and cannot be treated as conventional generators due to high variability. Energy storage is a natural mechanism for absorbing variability, and hence minimizing costly reliance on generator reserves. We consider a simple scenario in which energy imbalances are allocated to energy storage, representing either cooperation with a renewable producer or competitive operation in markets. The optimal storage scheduling strategy is shown to be an inventory control-like policy, which through mild approximation yields affine relationships with the state variables. We develop and numerically evaluate suboptimal policies that approximately incorporate the effects of correlation. Further approximation enables us to characterize the Nash equilibria arising between generation and storage, which we use to analyze strategic effects. Specifically, we find that inefficient storage can lead to non-socially optimal behavior.

Aggregate flexibility of a collection of loadsπ

We consider a collection of flexible loads. Each load is modeled as requiring energy E on a service interval [a; d] at a maximum rate of m. The collection is serviced by available generation g(t) which must be allocated causally to the various tasks. Our objective is to characterize the aggregate flexibility offered by this collection. In the absence of rate limits, we offer necessary and sufficient conditions for the generation g(t) to service the loads under causal scheduling without surplus or deficit. Our results show that the flexibility in the collection can be modeled as electricity storage. The capacity Q(t) and maximum charge/discharge rate m(t) of the equivalent storage can be computed in real time. Ex ante, these parameters must be estimated based on arrival/departure statistics and charging needs. Thus, the collection is equivalent a stochastic time-varying electricity storage. We next consider the case with charging rate limits. Here, we offer bounds on the capacity and rate of the equivalent electricity storage. We offer synthetic examples to illustrate our results.

Index Policies for Demand Response

Demand response programs incentivize loads to actively moderate their energy consumption to aid the power system. Uncertainty is an intrinsic aspect of demand response because a loads capability is often unknown until the load has been deployed. Algorithms must therefore balance utilizing well-characterized, good loads and learning about poorly characterized but potentially good loads; this is a manifestation of the classical tradeoff between exploration and exploitation. We address this tradeoff in a restless bandit framework, a generalization of the well-known multi-armed bandit problem. The formulation yields index policies in which loads are ranked by a scalar index, and those with the highest are deployed. The policy is particularly appropriate for demand response because the indices have explicit analytical expressions that may be evaluated separately for each load, making them both simple and scalable. This formulation serves as a heuristic basis for when only the aggregate effect of demand response is observed, from which the state of each individual load must be inferred. We formulate a tractable, analytical approximation for individual state inference based on observations of aggregate load curtailments. In numerical examples, the restless bandit policy outperforms the greedy policy by 5%-10% of the total cost. When the states of deployed loads are inferred from aggregate measurements, the resulting performance degradation is on the order of a few percent for the (now heuristic) restless bandit policy.

Decentralized Supplementary Control of Multiple LCC-HVDC Links

This paper presents a decentralized wide-area coordinated supplementary control of multiple line-commutated converter (LCC)-HVDC links to 1) prevent interactions among the HVDC links and 2) enhance the damping of the inter-area oscillatory modes. The proposed approach is based on the sparsity-promoting optimal control. The main features of the proposed approach are 1) it requires minimal communication infrastructure to achieve the control objectives and thus reduces the impacts of communication delays and noise, 2) it entails in an optimal gain which preserves the closed-loop stability and 3) it does not require the estimates of the system states. The performance of the proposed controller is evaluated based on eigen analysis and time-domain simulation of an interconnected AC system that includes five LCC-HVDC links. Performance of the proposed controller is also compared with those of fully centralized and conventional local supplementary controllers and its merits are highlighted. The studies indicate the proposed controller, based on 13 remotely communicated signals, provides similar performance as that of a fully centralized optimal controller using 2050 communicated signals and is far superior to the conventional local supplementary controllers.

Financial Storage Rights

Should energy storage buy and sell power at wholesale prices like utilities and generators, or should its physical and financial operation be asynchronyous as with transmission lines? In the first case, storage straightforwardly profits through intertemporal arbitrage, also known as load shifting and peak shaving. In this paper, the latter case, referred to as passive storage, is examined. Because passive storage does not make nodal price transactions, new mechanisms are necessary for its integration into electricity markets. This issue is addressed by further developing the analogy between energy storage and transmission. Specifically, financial rights are defined for storage, and tracing is extended to multiperiod power flows linked by storage. Like flowgate transmission rights, the new financial storage rights redistribute the system operators merchandising surplus and enable risk-averse market participants to hedge against nodal price volatility resulting from storage congestion. Simple examples are given demonstrating the implementation of the new mechanisms. Game-theoretic analysis suggests that financial storage rights mitigate gaming when both the generator and load bid strategically.

Consolidated Dynamic Pricing of Power System Regulation

The cost and quality of regulation have been brought to the forefront of power system operations by renewable variability. We propose a regulation pricing methodology based on an idea of Berger and Schweppe: in the same manner that locational marginal prices are derived from the dual of economic dispatch, let regulation prices be the dual multipliers or costate of an optimal control problem. By specializing to the linear quadratic regulator, we formulate a regulation pricing policy, which in turn allows us to derive statistically correct payments such as imbalance fees. We then construct a Vickrey-Clarke-Groves mechanism to induce selfish agents to honestly report their private valuations and costs of regulation. Semidefinite programming descriptions of the formulation can be embedded within standard convex economic dispatch constraint sets, enabling cooptimization of base load and regulation pricing. The approach mechanistically produces prices for any dynamic scenario, and can therefore be used to consolidate diverse regulation services. We demonstrate this feature by combining traditional frequency regulation, area control error, and the California Independent System Operators Flexible Ramping Product in an example.

Optimal power and reserve capacity procurement policies with deferrable loads

Deferrable loads can be used to mitigate the variability associated with renewable generation. In this paper, we study the impact of deferrable loads on forward market operations. Specifically, we compute cost-minimizing ex-ante bulk power and reserve capacity procurement policies in the cases of fully deferrable and non-deferrable loads. For non-deferrable loads, we analytically express this policy on a partition of procurement prices. We also formulate a threshold policy for deferrable load scheduling in the face of uncertain supply, that minimizes grid operating costs.