Marko Jereminov

An equivalent circuit formulation of the power flow problem with current and voltage state variables

Steady state analysis of power grids is typically performed using power flow analysis, where nonlinear balance equations of real and reactive power are solved to calculate the voltage magnitude, phase, and power at every bus. Transient analysis of the same power grids are performed using circuit simulation methods. We propose a novel approach to modeling the nonlinear steady state behavior of power grids in terms of equivalent circuits with currents and voltages as the state variables that is a step toward unifying transient and steady state models. A graph theoretic formulation approach is used to solve the circuits that enables incorporation of switch models for contingency analyses. Superior nonlinear steady state convergence is demonstrated by use of current as a state variable and application of circuit simulation methods. Furthermore, current and voltage state variables will offer greater compatibility with future smart grid components and monitors.

An equivalent circuit formulation for three-phase power flow analysis of distribution systems

In this paper, we describe a power flow formulation for 3-phase distribution systems that is based on an equivalent circuit model. It is shown that this physical model based solution is able to accommodate a wide range of complex and unbalanced loads without loss of generality. The approach is an extension of the single phase formulation in [1] that uses current and voltage as the state variables. This formulation is shown to provide excellent modeling efficiency for distribution system components, such as induction motors that can be modeled as linear circuit elements. The formulation is further capable of incorporating complex nonlinear models to capture more details or represent future bus models. A challenging IEEE 4-bus test case is used as a proof of concept to demonstrate the efficacy of this approach.

PowerCast: Mining and Forecasting Power Grid Sequences

What will be the power consumption of our institution at 8am for the upcoming days? What will happen to the power consumption of a small factory, if it wants to double (or half) its production? Technologies associated with the smart electrical grid are needed. Central to this process are algorithms that accurately model electrical load behavior, and forecast future electric power demand. However, existing power load models fail to accurately represent electrical load behavior in the grid. In this paper, we propose PowerCast, a novel domain-aware approach for forecasting the electrical power demand, by carefully incorporating domain knowledge. Our contributions are as follows: 1. Infusion of domain expert knowledge: We represent the time sequences using an equivalent circuit model, the “BIG” model, which allows for an intuitive interpretation of the power load, as the BIG model is derived from physics-based first principles. 2. Forecasting of the power load: Our PowerCast uses the BIG model, and provides (a) accurate prediction in multi-step-ahead forecasting, and (b) extrapolations, under what-if scenarios, such as variation in the demand (say, due to increase in the count of people on campus, or a decision to half the production in our factory etc.) 3. Anomaly detection: PowerCast can spot and, even explain, anomalies in the given time sequences. The experimental results based on two real world datasets of up to three weeks duration, demonstrate that PowerCast is able to forecast several steps ahead, with 59% error reduction, compared to the competitors. Moreover, it is fast, and scales linearly with the duration of the sequences.

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 104 buses demonstrates consistent global convergence to the correct physical solution from arbitrary initial conditions.

Improving robustness and modeling generality for power flow analysis

In this paper we present an equivalent circuit model for power system networks that facilitates robust and efficient AC power flow simulation and enables the incorporation of more generalized bus and line models. The circuit equations are formulated in terms of voltages and currents in rectangular coordinates using a graph theoretic algorithm that provides for optimal numerical conditioning. A current-source based generator model is introduced that provides for more robust and efficient convergence as compared to our original approach. We show that the proposed framework supports nonlinear models with insensitivity to the initial guess and converges in few iterations. We illustrate the capabilities of generalized modeling by deriving a model for a grid-connected solar panel system that includes AC, DC and semiconductor components.

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.

Steady-state analysis of power system harmonics using equivalent split-circuit models

In this paper we introduce a novel algorithm for harmonic steady-state analysis of power systems that is based on the equivalent split-circuit models recently introduced for power flow analysis. By using an equivalent circuit with current and voltage as the state variables, we extend the harmonic balance method that is used for nonlinear circuit simulation in the frequency domain to capture the frequency harmonics and inter-harmonics induced into a power grid due to nonlinear components. This enables the direct incorporation of physics-based steady-state models of power electronics and smart grid devices directly within the power-system simulation framework. For demonstration, steady-state models of a diode and a nonlinear core saturation inductor are derived and incorporated into the steady-state models of a three-phase full bridge rectifier and a magnetic core saturation transformer. These components are simulated within the proposed power flow analysis framework for a multi-bus power system.

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.

ChangeDAR: Online Localized Change Detection for Sensor Data on a Graph

Given electrical sensors placed on the power grid, how can we automatically determine when electrical components (e.g. power lines) fail? Or, given traffic sensors which measure the speed of vehicles passing over them, how can we determine when traffic accidents occur? Both these problems involve detecting change points in a set of sensors on the nodes or edges of a graph. To this end, we propose ChangeDAR (Change Detection And Resolution), which detects changes in an online manner, and reports when and where the change occurred in the graph. Our contributions are: 1) Algorithm : we propose novel information-theoretic optimization objectives for scoring and detecting localized changes, and propose two algorithms, ChangeDAR-S and ChangeDAR-D respectively, to optimize them. 2) Theoretical Guarantees : we show that both methods provide constant-factor approximation guarantees (Theorems 5.2 and 6.2). 3) Effectiveness : in experiments, ChangeDAR detects traffic accidents and power line failures with 75% higher F-measure than comparable baselines. 4) Scalability : ChangeDAR is online and near-linear in the graph size and the number of time ticks.