Study of Reduced System Models for Power System Monitoring

Author Name(s): A Kranthi Kumar, Ch. V. V. S. Bhaskara Reddy
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With increase in loads and generation the complexity and interconnection of power system are increasing. It necessitates more computational time to study the system behaviour for large power systems. During the emergency conditions like faults the computational time must be less. The network reduction techniques are useful in analysing large interconnected systems with less computational time. Some of the network reduction techniques, such as Ward reduction, Kron reduction and Dimo’s method are discussed in this paper. The effectiveness of these reduced models are analysed with their ability to follow the bus voltages of the complete system. The IEEE 14 bus and 118 bus systems are taken as the test cases.


Modern power systems have become highly interconnected to maintain the quality and reliability of the supply. These systems are being operated under heavily loaded condition to meet the growing demand for electricity with limited resources. Over the past few decades, the characteristics of the power system generation and loads have been changed rapidly due to increase in renewable energy sources, frequent usage of power electronic devices. Therefore, special attention has to be given for the modelling of power system for various types of analysis.

In a power system it is difficult or not economical to develop a detailed model although we have powerful computing capabilities available nowadays. Therefore, it is necessary to develop the reduced models that properly resemble the detailed model for steady state and dynamic characteristics. The reasons for using the reduced models are as follows: (i) it is required to monitor the system by using limited number of measurements from measuring units, such as PMU’s; (ii) in the interconnected systems they refuse to share the information with the others; (iii) practical limitations on the computational resources; (iv) as the electrical distance from the point of interest increases, the requirement of detailed model decreases.

Power systems are mostly interconnected, with several areas connected with each other by tie-lines. Usually the utilities of own system are called internal system or internal area and the rest of the system is called external system for internal area considered. For power system analysis the internal area is modelled in detail and external areas are represented by simplified models, which are referred as the external equivalent systems. The problem of network reduction is not only related to the inter-company ties but, some of the individual systems are grown to such an extent that it represents its own power system. Network reduction techniques are broadly classified as static and dynamic based on its intended use [1-2]. Static reduction techniques are used for static performance analysis only, such as load-flow analysis and system operation and planning studies. Whereas, for the analysis of system dynamics the reduced dynamic equivalents of the external system are required. In this paper, the term ‘network reduction’ implies only the static reduction.This paper compares the effectiveness of some of the commonly used network reduction methods, such as Ward reduction, Kron reduction and Dimo’s method.


Network reduction methods are found to be very useful in the analysis of very large and complex interconnected power systems. IEEE 14 and IEEE 118 bus test systems are analysed and error in voltage magnitude for each method are observed. The accuracy of the Kron method is low as compared to other two methods analysed. Ward reduction technique exhibiting close convergence for both the test systems. The complexity of ward and Kron method is less compared to the Dimo method as it involves the aggregation of nodes.

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