arXiv subjects

Larry Pileggi

Publications and source records attributed to Larry Pileggi.

51 records · Page 3Linked to original sources

arXiv2019

Improving Voltage Profile of the Nigerian Power Grid

Extreme voltages at the system nodes are one of the primary causes for total and partial collapse of the Nigerian grid. In this paper, we develop a framework to re-dispatch the voltage set-points of committed generators in the grid to improve the voltage profile of the system nodes thus lowering the likelihood of a grid collapse. This framework is an extension of circuit-theoretic formulation that can robustly solve general-purpose grid optimization problems. In the results section, we re-dispatch the voltage setpoints for committed generators in real-life Nigerian grid operation and planning test cases to improve the overall voltage profile of the grid. We further demonstrate that the re-dispatched grid is more resilient and secure than the base case through running contingency analyses.

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arXiv2019

A Probabilistic Approach to Power System State Estimation using a Linear Algorithm

An equivalent circuit formulation for power system analysis was demonstrated to improve robustness of Power Flow and enable more generalized modeling, including that for RTUs (Remote Terminal Units) and PMUs (Phasor Measurement Units). These measurement device models, together with an adjoint circuit based optimization framework, enable an alternative formulation to Power System State Estimation (SE) that can be solved within the equivalent circuit formulation. In this paper, we utilize a linear RTU model to create a fully linear SE algorithm that includes PMU and RTU measurements to enable a probabilistic approach to SE. Results demonstrate that this is a practical approach that is well suited for real-world applications.

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arXiv2019

Impact of Load Models on Power Flow Optimization

Aggregated load models, such as PQ and ZIP, are used to represent the approximated load demand at specific buses in grid simulation and optimization problems. In this paper we examine the impact of model choice on the optimal power flow solution and demonstrate that it is possible for different load models to represent the same amount of real and reactive power at the optimal solution yet correspond to completely different grid operating points. We introduce the metric derived from the maximum power transfer theorem to identify the behavior of an aggregated model in the OPF formulation to indicate its possible limitations. A dataset from the Carnegie Mellon campus is used to characterize three types of load models using a time-series machine learning algorithm, from which the optimal power flow results demonstrate that the choice of load model type has a significant impact on the solution set points. For example, our results show that the PQ load accurately characterizes the CMU data behavior correctly for only 16.7% of the cases.

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arXiv2019

Equivalent Circuit Programming for Estimating the State of a Power System

An Equivalent Circuit Programming (ECP) approach that expresses the optimality conditions of an optimization problem in terms of an equivalent circuit model and uses circuit simulation techniques to solve for an optimal solution, is applied to the state estimation problem for power systems. The benefits of using an equivalent circuit formulation for incorporating both Phasor Measurement Units (PMU) and Remote Terminal Units (RTU), as well as for reducing the nonlinearities of the state estimation problem was previously demonstrated. In this paper we further exploit the circuit nature of the state estimation problem to formulate not only the model but also the optimality conditions as an ECP problem. The efficiency and accuracy of our approach are demonstrated by estimating the states of large-scale power grids (80k+ buses).

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arXiv2019

Robust and Efficient Power Flow Convergence with G-min Stepping Homotopy Method

Recent advances have shown that the circuit simulation algorithms that allow for solving highly nonlinear circuits of over one billion variables can be applicable to power system simulation and optimization problems through the use of an equivalent circuit formulation. It was demonstrated that large-scale (80k+ buses) power flow simulations can be robustly solved, independent of the initial starting point. In this paper, we extend the electronic circuit-based G-min stepping homotopy method to power flow simulations. Preliminary results indicate that the proposed algorithm results in significantly better simulation runtime performance when compared to existing homotopy methods.

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arXiv2018

An Equivalent Circuit Formulation for Power System State Estimation including PMUs

In this paper, a novel formulation for the power system state estimation is proposed, based on the recently introduced equivalent split-circuit formulation of the power flow problem. The formulation models the conventional and time synchronized measurements simultaneously and contains a significantly lower level of nonlinearity compared to the available hybrid state estimators. The appropriate circuit models are derived for different types of measurements and integrated into the existing circuit framework for the power flow problem. A constrained optimization problem is then formulated to estimate the states of the system in rectangular coordinates, while satisfying the circuit equations and bounds on the measurement data. To further prove the concept and validate the accuracy of the proposed formulation, several test cases are solved and the results are presented and discussed.

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arXiv2018

Linear Power Grid State Estimation with Modeling Uncertainties

Recent advances in power system State Estimation (SE) have included equivalent circuit models for representing measurement data that allows incorporation of both PMU and RTU measurements within the state estimator. In this paper, we introduce a probabilistic framework with a new RTU model that renders the complete SE problem linear while not affecting its accuracy. It is demonstrated that the probabilistic state of a system can be efficiently and accurately estimated not only with the uncertainties from the measurement data, but also while including variations from transmission network models. To demonstrate accuracy and scalability we present probabilistic state estimation results for the 82k test case that represents the transmission level grid of the entire USA. It is shown that the estimated state distributions include the true grid state, while their mean exactly corresponds to the estimated deterministic state obtained from the nonlinear state estimator.

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arXiv2018

A Linear Formulation for Power System State Estimation including RTU and PMU Measurements

In this paper, a novel linear formulation for power system state estimation that simultaneously treats conventional and synchrophasor measurements is proposed. A linear circuit model for conventional measurements is introduced to enable a fully linear equivalent circuit representation of the power system. The estimated system state is then obtained by formulating the optimization problem to minimize the measurement errors and solving the resulting linear set of optimality conditions. To evaluate the accuracy of the proposed method, simulations are performed on several test cases of various sizes and the results are presented and discussed.

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arXiv2018

Continuously Differentiable Analytical Models for Implicit Control within Power Flow

Achieving robust and scalable convergence for simulation of realistic power flow cases can be challenging. One specific issue relates to the disconnected solution space that is created by the use of piecewise-discontinuous models of power grid devices that perform control mechanisms. These models are generally resolved by outer iteration loops around power flow, which can result in solution oscillations, increased iteration count, divergence or even convergence to a solution in an unstable operational region. This paper introduces a continuously differentiable model for device control mechanisms that is incorporated within the power flow formulation. To ensure robust power flow convergence properties, recently introduced homotopy methods are extended to include these continuous models. The scalability and efficacy of the proposed formulation is demonstrated on several large-scale test cases that represent the US Eastern Interconnect network, the Synthetic USA, and the Nigerian grid.

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arXiv2018

Unified power system analyses and models using equivalent circuit formulation

In this paper we propose and demonstrate the potential for unifying models and algorithms for the steady state and transient simulation of single-phase and three-phase power systems. At present, disparate algorithms and models are used for the different analyses, which can lead to inconsistencies such as the transient analysis as time approaches infinity not matching the steady state analysis of the same conditions. Using our equivalent circuit formulation of the power system, we propose a methodology for forming physics-based models that can facilitate transient, balanced power flow, and three-phase power flow in one simulation environment. The approach is demonstrated on a three-phase induction motor. Existing industry tools are used to validate the model and simulation results for the different analyses.

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arXiv2018

Robust Power Flow and Three-Phase Power Flow Analyses

Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid (three-phase power flow). Due to the non-linear nature of the problem, it is difficult for alternating current (AC) power flow and three-phase power flow analyses to ensure convergence to the correct physical solution, particularly from arbitrary initial conditions, or when evaluating a change (e.g. contingency) in the grid. In this paper, we describe our equivalent circuit formulation approach with current and voltage variables that models both the positive sequence network of the transmission grid and three-phase network of the distribution grid without loss of generality. The proposed circuit models and formalism enable the extension and application of circuit simulation techniques to solve for the steady-state solution with excellent robustness of convergence. Examples for positive sequence transmission and three-phase distribution systems, including actual 75k+ nodes Eastern Interconnection transmission test cases and 8k+ nodes taxonomy distribution test cases, are solved from arbitrary initial guesses to demonstrate the efficacy of our approach.

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arXiv2018

Robust Probabilistic Analysis of Transmission Power Systems based on Equivalent Circuit Formulation

Recent advances in steady-state analysis of power systems have introduced the equivalent split-circuit approach and corresponding continuation methods that can reliably find the correct physical solution of large-scale power system problems. The improvement in robustness provided by these developments are the basis for improvements in other fields of power system research. Probabilistic Power Flow studies are one of the areas of impact. This paper will describe a Simple Random Sampling Monte Carlo approach for probabilistic contingency analyses of transmission line power systems. The results are compared with those from Monte Carlo simulations using a standard power flow tool. Lastly, probabilistic contingency studies on two publicly available power system cases are presented.

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arXiv2017

Aggregated Load and Generation Equivalent Circuit Models with Semi-Empirical Data Fitting

In this paper we propose a semi-empirical modeling framework for aggregated electrical load and generation using an equivalent circuit formulation. The proposed models are based on complex rectangular voltage and current state variables that provide a generalized form for accurately representing any transmission and distribution components. The model is based on the split equivalent circuit formulation that was previously shown to unify power flow, three phase power flow, harmonic power flow, and transient analyses. Importantly, this formulation establishes variables that are analytical and are compatible with model fitting and machine learning approaches. The parameters for the proposed semi-empirical load and generation models are synthesized from measurement data and can enable real-time simulations for time varying aggregated loads and generation.

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arXiv2017

Improving Power Flow Robustness via Circuit Simulation Methods

Recent advances in power system simulation have included the use of complex rectangular current and voltage (I-V) variables for solving the power flow and three-phase power flow problems. This formulation has demonstrated superior convergence properties over conventional polar coordinate based formulations for three-phase power flow, but has failed to replicate the same advantages for power flow in general due to convergence issues with systems containing PV buses. In this paper, we demonstrate how circuit simulation techniques can provide robust convergence for any complex I-V formulation that is derived from our split equivalent circuit representation. Application to power grid test systems with up to 10000 buses demonstrates consistent global convergence to the correct physical solution from arbitrary initial conditions.

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arXiv2017

Robust Convergence of Power Flow using Tx Stepping Method with Equivalent Circuit Formulation

Robust solving of critical large power flow cases (with 50k or greater buses) forms the backbone of planning and operation of any large connected power grid. At present, reliable convergence with applications of existing power flow tools to large power systems is contingent upon a good initial guess for the system state. To enable robust convergence for large scale systems starting with an arbitrary initial guess, we extend our equivalent circuit formulation for power flow analysis to include a novel continuation method based on transmission line (Tx) stepping. While various continuation methods have been proposed for use with the traditional PQV power flow formulation, these methods have either failed to completely solve the problem or have resulted in convergence to a low voltage solution. The proposed Tx Stepping method in this paper demonstrates robust convergence to the high voltage solution from an arbitrary initial guess. Example systems, including 75k+ bus test cases representing different loading and operating conditions for Eastern Interconnection of the U.S. power grid, are solved from arbitrary initial guesses.Interconnection of the U.S. power grid, are solved from arbitrary initial guesses.

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