Adaptive Quadrant Filter Based Phase Locked Loop System

Phase-Locked-Loop (PLL) is one of the key technologies extensively used in grid connected power electronics system. A good PLL system can detect the grid phase angle and frequency fast and accurately, and additionally it can extract the positive sequence (or fundamental component for single phase system) exactly. In real applications, source signal (voltage or current) sensed for PLL usually includes harmonic distortion, unbalanced components, noises and frequency variations. Conventional PLL strategy cannot solve all the problems, especially the unbalanced and harmonic distortion. There is a trade-off between the dynamic response and phase angle tracking accuracy. Different PLL solutions are proposed in literature in recent years. The general considerations for these different approaches are to design positive sequence estimator to eliminate the negative sequence components and use filters to filter out the higher order harmonic distortions from the PLLs. In this paper, an adaptive quadrature filter based synchronous reference frame PLL (SRF-PLL) with positive sequence estimation feature is presented. The proposed PLL has good performances in filtering harmonic, eliminating unbalanced components and auto-adjusting frequency change. The simulation model is built in Matlab/simulink and the simulation results are given to verify the mathematical analysis

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.Comment: 8 pages, 1 figur

Retention of Female Faculty Members

The recruitment and the retention of female undergraduate and graduate students into engineering courses is discussed. A similar challenge lies in recruiting female faculty member from the limited pool of candidates in several fields at most universities. It is found that about half the females who were hired did not stay at the university. It is suggested that programs should be introduced to encourage mentoring and career development as such improvements would benefit all faculty members both female and male

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

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

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

Comparison of Matrix Pencil and Prony Methods for Power System Modal Analysis of Noisy Signals

Modal information extracted from the dynamic response of power systems can be applied to detect low frequency oscillations and assess stability margins for monitoring and preventive control. This paper examines two techniques for modal identification based on their ability to accurately identify system modes in the presence of noisy signals. The methods investigated include Prony analysis, which has commonly been used in power system studies, and the Matrix Pencil method, which is more common in electromagnetic analysis. Prony analysis has been shown to have difficulties extracting the modes of noisy signals, so the examples presented explore these shortcomings and compare them to the capabilities of the Matrix Pencil method

Voltage collapse

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