Dennice F. Gayme

Adaptive VAR Control for Distribution Circuits With Photovoltaic Generators

We show how an adaptive control algorithm can improve the performance of distributed reactive power control in a radial distribution circuit with a high penetration of photovoltaic (PV) cells. The adaptive algorithm is designed to balance the need for power quality (voltage regulation) with the desire to minimize power loss. The adaptation law determines whether the objective function minimizes power losses or voltage regulation based on whether the voltage at each node remains close enough to the voltage at the substation. The reactive power is controlled through the inverter on the PV cells. The control signals are determined based on local instantaneous measurements of the real and reactive power at each node. We use the example of a single branch radial distribution circuit to demonstrate the ability of the adaptive scheme to effectively reduce voltage variations while simultaneously minimizing the power loss in the studied cases. Simulations verify that the adaptive schemes compares favorably with local and global schemes previously reported in the literature.

Optimal power flow with large-scale storage integration

Restructuring of the electric power industry along with mandates to integrate renewable energy sources is introducing new challenges for the electric power system. Intermittent power sources, in particular, require mitigation strategies in order to maintain consistent power on the electric grid. We investigate distributed energy storage as one such strategy. Our model for optimal power flow with storage augments the usual formulation by adding simple charge/discharge dynamics for energy storage collocated with load and/or generation buses cast as a finite-time optimal control problem. We first propose a solution strategy that uses a convex optimization based relaxation to solve the optimal control problem. We then use this framework to illustrate the effects of various levels of energy storage using the topology of IEEE benchmark systems along with both time-invariant and demand-based cost functions. The addition of energy storage and demand-based cost functions significantly reduces the generation costs and flattens the generation profiles.

Quadratically Constrained Quadratic Programs on Acyclic Graphs With Application to Power Flow

This paper proves that nonconvex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. We demonstrate this theory on optimal power-flow problems over tree networks.

Optimal power flow over tree networks

The optimal power flow (OPF) problem is critical to power system operation but it is generally non-convex and therefore hard to solve. Recently, a sufficient condition has been found under which OPF has zero duality gap, which means that its solution can be computed efficiently by solving the convex dual problem. In this paper we simplify this sufficient condition through a reformulation of the problem and prove that the condition is always satisfied for a tree network provided we allow over-satisfaction of load. The proof, cast as a complex semi-definite program, makes use of the fact that if the underlying graph of an n × n Hermitian positive semi-definite matrix is a tree, then the matrix has rank at least n − 1.

Risk-mitigated optimal power flow for wind powered grids

Increased penetration of renewable energy sources poses new challenges to the power grid. Grid integrated energy storage combined with fast-ramping conventional generation can help to address challenges associated with power output variability. This paper proposes a risk mitigating optimal power flow (OPF) framework to study the dispatch and placement of energy storage units in a power system with wind generators that are supplemented by fast-ramping conventional back-up generators. This OPF with storage charge/discharge dynamics is solved as a finite-horizon optimal control problem. Chance constraints are used to implement the risk mitigation strategy. The model is applied to case studies based on the IEEE 14 bus benchmark system. First, we study the scheduling of spinning reserves and storage when generation and loads are subject to uncertainties. The framework is then extended to investigate the optimal placement of storage across different network topologies. The results of the case studies quantify the need for storage and reserves as well as suggest a strategy for their scheduling and placement.

Optimal power flow with distributed energy storage dynamics

Restructuring of the electric power industry along with mandates to integrate renewable energy sources is introducing new challenges for electric power systems and the power grid. Intermittent power sources in particular require mitigation strategies in order to maintain consistent power on the electric grid. We investigate distributed energy storage as one such strategy. Our model for optimal power flow consists of simple charge/discharge dynamics for energy storage collocated with load and/or generation buses cast as a finite-time optimal control problem. We illustrate the effects of energy storage using a modified version of the IEEE 14 bus benchmark example along with time-varying demand profiles. We use both time-invariant and demand based cost functions. The addition of energy storage along with demand based cost functions significantly reduces the generation costs and flattens the generation profiles.

Optimal placement of energy storage in the grid

This paper studies the problem of optimally placing large-scale energy storage in power grids with both conventional and wind generation. The solution technique for this infinite horizon problem assumes cyclic demand and generation profiles using a semidefinite relaxation of AC optimal power flow. Changes in storage allocation in the network are studied as a function of total storage budget and transmission line-flow constraints. These questions are investigated using an IEEE benchmark system with various generation portfolios.

Optimizing Storage Siting, Sizing, and Technology Portfolios in Transmission-Constrained Networks

In this paper, we propose a DC optimal power flow (OPF) framework for storage portfolio optimization in transmission-constrained power networks. In particular, this model is designed to investigate two problems: 1) optimizing storage operation and allocation over a network given a fixed technology portfolio and 2) optimizing the storage portfolio (i.e., the size, technology, and network allocation of these resources). We demonstrate this framework using case studies based on the IEEE 14-bus test system with four different storage technologies. Our results show that although certain technologies are generally classified as being suitable for either power or energy services, many technologies can add value to the system by performing both fast-time scale regulation (power) and load-shifting (energy) services. These results suggest that limiting the type of service that a certain technology is compensated for may result in inefficiencies at the system level and under-valuation of storage.

Large eddy simulation studies of the effects of alignment and wind farm length

Large eddy simulations of wind farms are performed to study the effects of wind turbine row alignment with respect to the incoming flow direction. Various wind farms with fixed stream-wise spacing (7.85 rotor diameters) and varying lateral displacements and span-wise turbine spacings are considered, for a fixed inflow direction. Simulations show that, contrary to common belief, a perfectly staggered (checker-board) configuration does not necessarily give the highest average power output. Instead, the highest mean wind farm power output is found to depend on several factors, the most important one being the alignment that leads to minimization of wake effects from turbines in several upstream rows. This alignment typically occurs at significantly smaller angles than those corresponding to perfect staggering. The observed trends have implications for wind farm designs, especially in sites with a well-defined prevailing wind direction.

Effects of turbine spacing on the power output of extended wind‐farms

We present results from large eddy simulations of extended wind-farms for several turbine configurations with a range of different spanwise and streamwise spacing combinations. The results show that for wind-farms arranged in a staggered configuration with spanwise spacings in the range ≈[3.5,8]D, where D is the turbine diameter, the power output in the fully developed regime depends primarily on the geometric mean of the spanwise and streamwise turbine spacings. In contrast, for the aligned configuration the power output in the fully developed regime strongly depends on the streamwise turbine spacing and shows weak dependence on the spanwise spacing. Of interest to the rate of wake recovery, we find that the power output is well correlated with the vertical kinetic energy flux, which is a measure of how much kinetic energy is transferred into the wind-turbine region by the mean flow. A comparison between the aligned and staggered configurations reveals that the vertical kinetic energy flux is more localized along turbine columns for aligned wind-farms than for staggered ones. This additional mixing leads to a relatively fast wake recovery for aligned wind-farms.