arXiv subjects
Publications and source records attributed to Josh A. Taylor.
We derive distance relay characteristics in terms of incremental phasors. We use a circuit model of the network to estimate the incremental remote current. If we assume that all sources are stationary, i.e., remain periodic shortly after a fault, then the incremental remote current, and thus the characteristics, do not depend on the real-time voltages or current injections of the sources.
Optimized charging of electric vehicles (EVs) at public locations consists of two decisions: how much energy to deliver at what times, which is continuous, and where to plug in, which is binary. This makes optimizing EV charging a mixed-integer linear program (MILP). This discreteness undermines traditional marginal pricing methods. In this paper, we develop the first marginal-price-based mechanism for pricing EV charging with binary station access constraints. Using the result of Burer (2009), we express the EV charging as a completely positive program (CPP), whose dual is a copositive program (COP). This convex dual admits valid shadow prices even though the original allocation problem is discrete and nonconvex. By interpreting the COP dual variables as marginal prices, we construct a pricing mechanism that captures EV supply equipment (EVSE) congestion as well as charging-capacity limits. We prove that the resulting mechanism is revenue-adequate for the operator and individually rational for every EV user, in the strong sense that each user maximizes their own welfare by accepting their assigned charging plan rather than deviating to any alternative option. We further develop problem-specific inner-approximation and dimension-reduction techniques that substantially improve the computational tractability of solving the COP in our setting. Numerical experiments on both small and large scale charging instances demonstrate that our pricing mechanism captures discrete congestion effects and aligns user incentives with the system-optimal assignment, outperforming time-of-use (TOU) and convex relaxation benchmarks.
Distance relays detect faults on transmission lines. They face uncertainty from the fault's location and resistance, as well as the current from the line's remote terminal. In this paper, we aggregate this uncertainty with the Minkowski sum. This allows us to explicitly model the power grid surrounding the relay's line, and in turn accommodate any mix of synchronous machines and inverter-based resources. To make the relay's task easier, inverters can inject perturbations, or auxiliary signals, such as negative-sequence current. We use Farkas' lemma to construct an optimization for designing inverter auxiliary signals.
Power system protection schemes today rely on currents rising by several orders of magnitude when faults occur. In inverter-dominated power systems, a fault current might be just a few percent larger than normal, making fault detection more difficult. One solution is for the inverter to slightly perturb its output current and/or voltage, i.e., to inject an auxiliary signal, so as to make the system's behavior under faults easier to distinguish from normal. In this paper, we optimize auxiliary signals for fault detection with distance relays. We begin with a standard auxiliary signal design problem for generic static systems. We use duality to reformulate the problem as a bilinear program, which we solve using the convex-concave procedure. We implement the framework in an example based on distance protection, in which the auxiliary signal is negative sequence current.
The converters in an AC/DC grid form actuated boundaries between the AC and DC subgrids. We show how in both simple linear and balanced dq-frame models, the states on either side of these boundaries are coupled only by control inputs. This topological property imparts all AC/DC grids with poset-causal information structures. A practical benefit is that certain decentralized control problems that are hard in general are tractable for poset-causal systems. We also show that special cases like multi-terminal DC grids can have coordinated and leader-follower information structures.
This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.
Aggregations of flexible loads can provide several power system services through demand response programs, for example load shifting and curtailment. The capabilities of demand response should therefore be represented in system operators' planning and operational routines. However, incorporating models of every load in an aggregation into these routines could compromise their tractability by adding exorbitant numbers of new variables and constraints. In this paper, we propose a novel approximation for concisely representing the capabilities of a heterogeneous aggregation of flexible loads. We assume that each load is mathematically described by a convex polytope, i.e., a set of linear constraints, a class which includes deferrable loads, thermostatically controlled loads, and generic energy storage. The set-wise sum of the loads is the Minkowski sum, which is in general computationally intractable. Our representation is an outer approximation of the Minkowski sum. The new approximation is easily computable and only uses one variable per time period corresponding to the aggregation's net power usage. Theoretical and numerical results indicate that the approximation is accurate for broad classes of loads.
Energy storage can absorb variability from the rising number of wind and solar power producers. Storage is different from the conventional generators that have traditionally balanced supply and demand on fast time scales due to its hard energy capacity constraints, dynamic coupling, and low marginal costs. These differences are leading system operators to propose new mechanisms for enabling storage to participate in reserve and real-time energy markets. The persistence of market power and gaming in electricity markets suggests that these changes will expose new vulnerabilities. We develop a new model of strategic behavior among storages in energy balancing markets. Our model is a two-stage game that generalizes a classic model of capacity followed by Bertrand-Edgeworth price competition by explicitly modeling storage dynamics and uncertainty in the pricing stage. By applying the model to balancing markets with storage, we are able to compare capacity and energy-based pricing schemes, and to analyze the dynamic effects of the market horizon and energy losses due to leakage. Our first key finding is that capacity pricing leads to higher prices and higher capacity commitments, and that energy pricing leads to lower, randomized prices and lower capacity commitments. Second, we find that a longer market horizon and higher physical efficiencies lead to lower prices by inducing the storage to compete to have their states of charge cycled more frequently.