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"Crow, Mariesa"
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New Infeed Correction Methods for Distance Protection in Distribution Systems
The reliability and security of power systems may be jeopardized by the increase in the amounts of renewable generation and the uncertainties produced by these devices. In particular, the protection schemes of traditional power systems have been challenged by the integration of distributed generation (DG) resources. Distance relays (DRs), which have been mainly employed to protect transmission systems, are increasingly proposed as one of the solutions to protect distribution systems with a heavy penetration of DGs. However, conventional distance protection faces several drawbacks that might lead to maloperation. One of those challenges is the “infeed effect”, which causes the impedance seen by the distance relay to be larger than the actual positive-sequence line impedance between the fault and relay location. This paper proposes three new methods to estimate the distance to the fault in the presence of infeeds, whether in a radial distribution feeder or the transmission line. Unlike other solution methodologies in the literature that require communication links to estimate the distance to the fault, the proposed methods only need the local measurement (i.e., the voltage and current measurements at the location of the distance relay) to do the same. The performance of the method is demonstrated with a radial distribution system model in PSCAD™/EMTDC™.
Journal Article
Economic Scheduling of Residential Plug-In (Hybrid) Electric Vehicle (PHEV) Charging
In the past decade, plug-in (hybrid) electric vehicles (PHEVs) have been widely proposed as a viable alternative to internal combustion vehicles to reduce fossil fuel emissions and dependence on petroleum. Off-peak vehicle charging is frequently proposed to reduce the stress on the electric power grid by shaping the load curve. Time of use (TOU) rates have been recommended to incentivize PHEV owners to shift their charging patterns. Many utilities are not currently equipped to provide real-time use rates to their customers, but can provide two or three staggered rate levels. To date, an analysis of the optimal number of levels and rate-duration of TOU rates for a given consumer demographic versus utility generation mix has not been performed. In this paper, we propose to use the U.S. National Household Travel Survey (NHTS) database as a basis to analyze typical PHEV energy requirements. We use Monte Carlo methods to model the uncertainty inherent in battery state-of-charge and trip duration. We conclude the paper with an analysis of a different TOU rate schedule proposed by a mix of U.S. utilities. We introduce a centralized scheduling strategy for PHEV charging using a genetic algorithm to accommodate the size and complexity of the optimization.
Journal Article
Multi-Objective Dynamic Economic Dispatch with Demand Side Management of Residential Loads and Electric Vehicles
In this paper, a multi-objective optimization method based on the normal boundary intersection is proposed to solve the dynamic economic dispatch with demand side management of individual residential loads and electric vehicles. The proposed approach specifically addresses consumer comfort through acceptable appliance deferral times and electric vehicle charging requirements. The multi-objectives of minimizing generation costs, emissions, and energy loss in the system are balanced in a Pareto front approach in which a fuzzy decision making method has been implemented to find the best compromise solution based on desired system operating conditions. The normal boundary intersection method is described and validated.
Journal Article
Tightening QC Relaxations of AC Optimal Power Flow through Improved Linear Convex Envelopes
AC optimal power flow (AC OPF) is a fundamental problem in power system operations. Accurately modeling the network physics via the AC power flow equations makes AC OPF a challenging nonconvex problem. To search for global optima, recent research has developed a variety of convex relaxations that bound the optimal objective values of AC OPF problems. The well-known QC relaxation convexifies the AC OPF problem by enclosing the non-convex terms (trigonometric functions and products) within convex envelopes. The accuracy of this method strongly depends on the tightness of these envelopes. This paper proposes two improvements for tightening QC relaxations of OPF problems. We first consider a particular nonlinear function whose projections are the nonlinear expressions appearing in the polar representation of the power flow equations. We construct a convex envelope around this nonlinear function that takes the form of a polytope and then use projections of this envelope to obtain convex expressions for the nonlinear terms. Second, we use certain characteristics of the sine and cosine expressions along with the changes in their curvature to tighten this convex envelope. We also propose a coordinate transformation that rotates the power flow equations by an angle specific to each bus in order to obtain a tighter envelope. We demonstrate these improvements relative to a state-of-the-art QC relaxation implementation using the PGLib-OPF test cases. The results show improved optimality gaps in 68% of these cases.
Paper
Tightening QC Relaxations of AC Optimal Power Flow Problems via Complex Per Unit Normalization
Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address these challenges, recent research has applied various convex relaxation approaches to OPF problems. The QC relaxation is a promising approach that convexifies the trigonometric and product terms in the OPF problem by enclosing these terms in convex envelopes. The accuracy of the QC relaxation strongly depends on the tightness of these envelopes. This paper presents two improvements to these envelopes. The first improvement leverages a polar representation of the branch admittances in addition to the rectangular representation used previously. The second improvement is based on a coordinate transformation via a complex per unit base power normalization that rotates the power flow equations. The trigonometric envelopes resulting from this rotation can be tighter than the corresponding envelopes in previous QC relaxation formulations. Using an empirical analysis with a variety of test cases, this paper suggests an appropriate value for the angle of the complex base power. Comparing the results with a state-of-the-art QC formulation reveals the advantages of the proposed improvements.
Paper
Computational Methods for Electric Power Systems
Electric power systems are some of the largest human-made systems ever built. The sheer size of the bulk power transmission system forced early power engineers to be among the first to develop computational approaches to solving the equations that describe them. Power system planners and operators rely very heavily on the computational tools to assist them in maintaining a reliable and secure operating environment. The various computational algorithms were developed around the requirements of power system operation. The underlying principle of a power flow problem is that given the system loads, generation, and network configuration, the system bus voltages and line flows can be found by solving the nonlinear power flow equations. The basic objective of the optimal power flow is to find the values of the system state variables and/or parameters that minimize some cost function of the power system. Many power system applications, such as the power flow, offer only a snapshot of the system operation.
Book Chapter
Improving QC Relaxations of OPF Problems via Voltage Magnitude Difference Constraints and Envelopes for Trilinear Monomials
AC optimal power flow (AC~OPF) is a challenging non-convex optimization problem that plays a crucial role in power system operation and control. Recently developed convex relaxation techniques provide new insights regarding the global optimality of AC~OPF solutions. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This paper proposes two methods for tightening the QC relaxation. The first method introduces new variables that represent the voltage magnitude differences between connected buses. Using \"bound tightening\" techniques, the bounds on the voltage magnitude difference variables can be significantly smaller than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can tighten the relaxation. Second, rather than a potentially weaker \"nested McCormick\" formulation, this paper applies \"Meyer and Floudas\" envelopes that yield the convex hull of the trilinear monomials formed by the product of the voltage magnitudes and trignometric terms in the polar form of the power flow equations. Comparison to a state-of-the-art QC implementation demonstrates the advantages of these improvements via smaller optimality gaps.
Paper
Empirical Investigation of Non-Convexities in Optimal Power Flow Problems
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. These constraints can yield non-convex feasible spaces that result in significant computational challenges. Despite these non-convexities, local solution algorithms actually find the global optima of some practical OPF problems. This suggests that OPF problems have a range of difficulty: some problems appear to have convex or \"nearly convex\" feasible spaces in terms of the voltage magnitudes and power injections, while other problems can exhibit significant non-convexities. Understanding this range of problem difficulty is helpful for creating new test cases for algorithmic benchmarking purposes. Leveraging recently developed computational tools for exploring OPF feasible spaces, this paper first describes an empirical study that aims to characterize non-convexities for small OPF problems. This paper then proposes and analyzes several medium-size test cases that challenge a variety of solution algorithms.
Paper
Waveform relaxation methods for the simulation of systems of differential algebraic equations with applications to electric power systems
This thesis reports the continuing effort towards establishing a parallel numerical algorithm known as Waveform Relaxation (WR) for simulating large power system dynamics. Past work has shown the feasibility of this method for frequency studies involving the classical model generator and loads modeled as constant impedances. This work has been expanded to include voltage studies where the loads are modeled as constant power loads and the load terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical engineering, economics, and physics. The main contribution of this thesis is to define and prove conditions under which the waveform relaxation algorithm for a general system of DAEs will converge. The algorithm is then tailored for the simulation of large-scale power systems. Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the waveform relaxation algorithm. One of the main contributions in this area includes a method for determining a fault-dependent partitioning of the power system for parallel implementation. Simulation results for small, medium, and large test systems are included.
Dissertation