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Modeling and Stability Analysis of Distributed Generation

Ehsan Nasr Azadani, Student Member, Claudio Canizares, Fellow, IEEE, Kankar Bhattacharya, Senior Member, IEEE

Abstract— There are many technical aspects and challenges at DG that are still not properly understood and addressed. Since most of these studies have to be carried out based on simulations, adequate static and dynamic models for DG units are required. The objective of this paper is the dynamic and static modeling of various DG technologies for stability analysis. These models allow studying systems with DGs both in the long- and short- term; thus, differential and algebraic equations of various DGs are formulated and discussed in order to integrate the models into a system model. The presented and discussed models are generally based on well-known dynamic models of different DGs for stability studies considering the dynamics of the primary governor, generators and their interfaces and controls. The results of applying these models for voltage and angle stability studies of a realistic distribution system are presented and compared, demonstrating the typical application of the presented units.

Index Terms— Modeling, distributed generation, voltage stability, angle stability.


The demand for energy is expected to increase due to a variety of reasons. Such significant increase will lead to local and regional environmental issues; therefore, international movements are pushing for the utilization of “green” energy sources instead of fossil fuels. One of the consequences of competitive electricity markets, and of international commitments to green energy (e.g., Kyoto Protocol), is the fast development and increase in the amount of decentralized or distributed generation (DG).

Currently, DG penetration can be considered to be relatively low, and this has led to existing standards requiring that DGs should not participate in voltage and frequency control, thus tripping during voltage and frequency transients to reconnect later when normal operating conditions are restored [1]. However, DG penetration is certainly increasing and is expected to attain levels that would likely impact the system operation and performance. Hence, studies are starting to concentrate on analyzing the cumulative effect of more DGs on the power network, at the local and global system levels. In this context, there are many issues that are not yet well

The authors are with the Department of Electrical and Computer Engineering the University of Waterloo, Waterloo, N2L 3G1, Canada.

This work is supported by ABB Corporate Research USA and MITACS Canada.

understood [2].

Although DG may have some benefits for the system such

as improvements in power quality and system efficiency, there are many technical aspects and challenges that are still to be properly understood and addressed. For example, there is a lack of suitable control strategies for networks with significant penetration of DG, while considering the interactions between the transmission and distributions systems. Since most of these studies have to be carried out based on simulations, adequate static and dynamic models for DG units and related interfaces and controls are required. These models should meet certain requirements to allow investigating relevant system stability and control issues, from both local and global system perspectives.

DG has been studied from the local/micro-grid point of view or the overall/global system point of view, since as the level of penetration increases, the impact of DG is no longer restricted to the local load or distribution network where these units are connected, but may also have an impact on the transmission system [3]. Thus, large DG penetration has been studied with respect to system control and stability in, for example, [4], [5] and [6]; however, these studies do not fully consider the various kinds of DGs, and mainly concentrate on studying stability and control issues from mainly the transmission system point of view. Thus, in [4] and [6], the impacts of DG penetration levels on power system transient stability are studied for different scenarios, and in [5], the impact of selected DG units, i.e. fuel cells (FCs) and micro turbines (MTs), on power system stability for various penetration levels are investigated. On the other hand, some studies have concentrated on the effect of DG units on the distribution network [7]-[10]. For example, in [10], the stability analysis of a distribution network with selected DG units, i.e. wind generators, and MTs, is presented.

The present paper concentrates on studying both static and dynamic DG models for voltage, and angle stability studies. Different types of DG technologies including small wind turbines, photovoltaic arrays, FCs, MTs, and conventional diesel generators are modeled. In these models, both transient and slow dynamics are taken into account. Based on these models, voltage, angle, and transient stability studies are carried out. Voltage stability studies are performed based on P-V curves; small perturbation stability studies are carried out based on eigenvalue analyses of the linearized system models; and transient stability studies are performed based on time


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