In this paper, a new control method for the parallel operation of inverters operating in an island grid or connected to an infinite bus is described. Frequency and voltage control, including mitigation of voltage harmonics, are achieved without the need for any common control circuitry or communication between inverters. Each inverter supplies a current that is the result of the voltage difference between a reference ac voltage source and the grid voltage across a virtual complex impedance. The reference ac voltage source is synchronized with the grid, with a phase shift, depending on the difference between rated and actual grid frequency. A detailed analysis shows that this approach has a superior behavior compared to existing methods, regarding the mitigation of voltage harmonics, short-circuit behavior and the effectiveness of the frequency and voltage control, as it takes the R to X line impedance ratio into account. Experiments show the behavior of the method for an inverter feeding a highly nonlinear load and during the connection of two parallel inverters in operation.

A Voltage and Frequency Droop Control Method for Parallel Inverters

Unlike traditional passive harmonic filters, modern active harmonic filters have the following multiple functions: harmonic filtering, damping,isolation and termination, reactive-power control for power factor correction and voltage regulation, load balancing, voltage-flicker reduction, and/or their combinations. Significant cost reductions in both power semiconductor devices and signal processing devices have inspired manufactures to put active filters on the market. This paper deals with general pure active filters for power conditioning, and specific hybrid active filters for harmonic filtering of three-phase diode rectifiers.

Active Harmonic Filters

Preface. Acknowledgments. 1 Complex Electricity Markets. 1.1 Liberalization. 1.2 The Marketplace. 1.2.1 Power Pools and Power Exchanges. 1.2.2 Nodal and Zonal Pricing. 1.2.3 Market Structure. 1.2.4 Traded Products. 1.3 Europe. 1.3.1 The England and Wales Electricity Market. 1.3.2 The Nordic Market. 1.3.3 Price Setting at Nord Pool. 1.3.4 Continental Europe 13. 1.4 North America. 1.4.1 PJM Interconnection. 1.4.2 California and the Electricity Crisis. 1.4.3 Alberta and Ontario. 1.5 Australia and New Zealand. 1.6 Summary. 1.7 Further Reading. 2 Stylized Facts of Electricity Loads and Prices. 2.1 Introduction. 2.2 Price Spikes. 2.2.1 Case Study: The June 1998 Cinergy Price Spike. 2.2.2 When Supply Meets Demand. 2.2.3 What is Causing the Spikes?. 2.2.4 The Definition. 2.3 Seasonality. 2.3.1 Measuring Serial Correlation. 2.3.2 Spectral Analysis and the Periodogram. 2.3.3 Case Study: Seasonal Behavior of Electricity Prices and Loads. 2.4 Seasonal Decomposition. 2.4.1 Differencing. 2.4.2 Mean or Median Week. 2.4.3 Moving Average Technique. 2.4.4 Annual Seasonality and Spectral Decomposition. 2.4.5 Rolling Volatility Technique. 2.4.6 Case Study: Rolling Volatility in Practice. 2.4.7 Wavelet Decomposition. 2.4.8 Case Study: Wavelet Filtering of Nord Pool Hourly System Prices. 2.5 Mean Reversion. 2.5.1 R/S Analysis. 2.5.2 Detrended Fluctuation Analysis. 2.5.3 Periodogram Regression. 2.5.4 Average Wavelet Coefficient. 2.5.5 Case Study: Anti-persistence of Electricity Prices. 2.6 Distributions of Electricity Prices. 2.6.1 Stable Distributions. 2.6.2 Hyperbolic Distributions. 2.6.3 Case Study: Distribution of EEX Spot Prices. 2.6.4 Further Empirical Evidence and Possible Applications. 2.7 Summary. 2.8 Further Reading. 3 Modeling and Forecasting Electricity Loads. 3.1 Introduction. 3.2 Factors Affecting Load Patterns. 3.2.1 Case Study: Dealing with Missing Values and Outliers. 3.2.2 Time Factors. 3.2.3 Weather Conditions. 3.2.4 Case Study: California Weather vs Load. 3.2.5 Other Factors. 3.3 Overview of Artificial Intelligence-Based Methods. 3.4 Statistical Methods. 3.4.1 Similar-Day Method. 3.4.2 Exponential Smoothing. 3.4.3 Regression Methods. 3.4.4 Autoregressive Model. 3.4.5 Autoregressive Moving Average Model. 3.4.6 ARMA Model Identification. 3.4.7 Case Study: Modeling Daily Loads in California. 3.4.8 Autoregressive Integrated Moving Average Model. 3.4.9 Time Series Models with Exogenous Variables. 3.4.10 Case Study: Modeling Daily Loads in California with Exogenous Variables. 3.5 Summary. 3.6 Further Reading. 4 Modeling and Forecasting Electricity Prices. 4.1 Introduction. 4.2 Overview of Modeling Approaches. 4.3 Statistical Methods and Price Forecasting. 4.3.1 Exogenous Factors. 4.3.2 Spike Preprocessing. 4.3.3 How to Assess the Quality of Price Forecasts. 4.3.4 ARMA-type Models. 4.3.5 Time Series Models with Exogenous Variables. 4.3.6 Autoregressive GARCH Models. 4.3.7 Case Study: Forecasting Hourly CalPX Spot Prices with Linear Models. 4.3.8 Case Study: Is Spike Preprocessing Advantageous?. 4.3.9 Regime-Switching Models. 4.3.10 Calibration of Regime-Switching Models. 4.3.11 Case Study: Forecasting Hourly CalPX Spot Prices with Regime-Switching Models. 4.3.12 Interval Forecasts. 4.4 Quantitative Models and Derivatives Valuation. 4.4.1 Jump-Diffusion Models. 4.4.2 Calibration of Jump-Diffusion Models. 4.4.3 Case Study: A Mean-Reverting Jump-Diffusion Model for Nord Pool Spot Prices. 4.4.4 Hybrid Models. 4.4.5 Case Study: Regime-Switching Models for Nord Pool Spot Prices. 4.4.6 Hedging and the Use of Derivatives. 4.4.7 Derivatives Pricing and the Market Price of Risk. 4.4.8 Case Study: Asian-Style Electricity Options. 4.5 Summary. 4.6 Further Reading. Bibliography. Index.

Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach

A review and categorization of electric load forecasting techniques is presented. A wide range of methodologies and models for forecasting are given in the literature. These techniques are classified here into nine categories: (1) multiple regression, (2) exponential smoothing, (3) iterative reweighted least-squares, (4) adaptive load forecasting, (5) stochastic time series, (6) ARMAX models based on genetic algorithms, (7) fuzzy logic, (8) neural networks and (9) expert systems. The methodology for each category is briefly described, the advantages and disadvantages discussed, and the pertinent literature reviewed. Conclusions and comments are made on future research directions.

Electric load forecasting: Literature survey and classification of methods

Conventional power distribution system is radial in nature, characterized by a single source feeding a network of downstream feeders. Protection scheme for distribution system, primarily consisting of fuses and reclosers and, in some cases, relays, has traditionally been designed assuming the system to be radial. After connecting distributed generation (DG), part of the system may no longer be radial, which means the coordination might not hold. The effect of DG on coordination will depend on size, type, and placement of DG. This paper explores the effect of high DG penetration on protective device coordination and suggests an adaptive protection scheme as a solution to the problems identified. Results of implementation of this scheme on a simulated actual distribution feeder are reported.

Development of adaptive protection scheme for distribution systems with high penetration of distributed generation

An optimal measurement scheme for tracking the harmonics in power system voltage and current waveforms is presented. The scheme does not require an integer number of samples in an integer number of cycles. It is not limited to stationary signals, but it can track harmonics with time-varying amplitudes. A review is first presented of the common frequency domain techniques for harmonics measurement. The frequency domain techniques are based on the discrete Fourier transform and the fast Fourier transform. Examples of pitfalls in the common techniques are given. The authors then introduce the concepts of the new scheme. This scheme is based on Kalman filtering theory for the optimal estimation of the parameters of time-varying harmonics. The scheme was tested on simulated and actual recorded data sets. It is concluded that the Kalman filtering algorithm is more accurate than the other techniques. >

A digital recursive measurement scheme for online tracking of power system harmonics

High-impedance faults are accompanied by variations in the 60 Hz and harmonic components. An approach that accounts for the time-varying nature of the fundamental and harmonic components is developed. This approach is based on Kalman-filtering theory to obtain the best estimation of the time variations of the fundamental and harmonic components. Four actual recorded data sets for staged arcing fault on different types of soil are investigated by the proposed Kalman-filtering technique. The time variations of fundamental and low-order harmonic components significantly contribute to high-impedance fault detection using the features presented. >

Analysis of high-impedance fault generated signals using a Kalman filtering approach

This paper presents a new time domain controlled voltage source (CVS) model for an arc furnace using the Electro Magnetic Transients Program (EMTP). The developed model is based on a piecewise linear approximation of the V-I characteristic of the arc furnace load. In addition to this, the novelty of this simulation technique lies in the fact that the active power consumed by the load is also considered in the proposed load model, thus making the proposed load model dependent on the operating conditions of the load. Dynamic variation of the arc is incorporated through sinusoidal and band limited white noise variation of the arc resistance in the V-I characteristic of the arc furnace load. Depending on the variation of the arc resistance, the developed load model accurately represents both static (deterministic) and dynamic (random) arc characteristics. While static arc models are useful for harmonic studies, dynamic models are useful for power quality studies and in particular, the study of voltage flicker. The results are compared with actual voltage measurements taken from a local utility to prove the validity of the proposed load model.

A new time domain voltage source model for an arc furnace using EMTP

This paper presents an adaptive arc furnace model. The integrated model is divided into three parts, the supply system model, the nonlinear load model and the controller model. First, the supply system is represented by a set of linear differential equations. Simulation is achieved by a numerical method and the measurements are taken as the control input. Secondly, based on the arc melting process and typical arc furnace V-I characteristic, the arc furnace load is described as a current-controlled nonlinear resistance. The pattern of nonlinear resistance is controlled by the average arc length, which reflects the arc furnace operating condition. Finally, the rectangular approximation of arc voltage is adopted by the controller to generate the arc power-arc length and the arc current-arc length curves. This information combined with the arc furnace operation and measurement information is used for the control scheme to determine the arc length and arc furnace transformer tap. Thus, the proposed adaptive arc furnace model is suitable for different operating conditions. This model is also compared prith the existing arc furnace models, which provides its validity. The effect of arc furnace load on the power system is also studied through the proposed model.

An adaptive arc furnace model

This paper presents the application of wavelet transforms in power system transient and harmonic analyses. Based on the discrete time domain approximation, the system components such as resistors, inductors and capacitor are modeled respectively in the discrete wavelet domain for the purpose of transient and steady state analyses. Since the power system is described by a set of ordinary differential equations, an initial value of the state variable is considered for the transient analysis, while a periodic condition is applied to the state variable for the steady state analysis. The wavelet domain impedance is set up, and the equivalent circuit is thus built for system simulation. This method can be implemented by any kind of orthogonal wavelet transform. Numerical results from an arc furnace system are also presented for the transient, harmonic and time-frequency analyses.

Elham B. Makram

Papers

A digital recursive measurement scheme for online tracking of power system harmonics

Analysis of high-impedance fault generated signals using a Kalman filtering approach

A new time domain voltage source model for an arc furnace using EMTP

An adaptive arc furnace model

Power system transient and harmonic studies using wavelet transform