Voltage Stability Monitoring using a Modified Thevenin Impedance S. Polster and H. Renner Institute of Electrical Power Systems Graz University of Technology Graz, Austria D. T. Duong and K. Uhlen Department of Electric Power Engineering Norwegian University of Science and Technology Trondheim, Norway Abstract – This paper presents a method for voltage stability monitoring based on the maximum power transfer to the load. The only required information is the system topology, the data from PMUs and the operational status of synchronous generators. With this information, the Thevenin impedance seen from a load bus can be estimated and by using the Thevenin theorem for maximum power transfer an impedance based stability index can be established. Since the Thevenin impedance is influenced by the operational conditions of the synchronous generators, it is consequently not a constant value and differs from the short circuit impedance of the bus. It is emphasized that the method requires only the information of the considered subsystem. Therefore, since the computation requirement is insignificant, the algorithm can be used for online monitoring. The validation of the approach is achieved by simulating a simple transmission system. Index Terms – PMU, Thevenin impedance, voltage stability, influence of generator capability I. INTRODUCTION The combination of increasing energy consumption and the boost of renewable energy sources requires a paradigm shift regarding operation of transmission and distribution grids in Europe. It becomes necessary to be more flexible and better informed of the system status in power system operations, especially due to the unbundling of the former vertically integrated energy supply companies into independent energy production and transmission companies. As a result no direct information link between power grid status and the control of energy production units exists anymore. Altogether, this leads to the need of a real-time identification of the transmission limits and given operation margins to be able to react fast enough to maintain a sufficient security of supply. Voltage stability becomes more and more a limiting factor, since generation and load centers are often connected with long and heavily loaded transmission lines. Most of previous research on voltage stability focused on off-line solutions such as the continuation power flow [1] or the analysis of the sensitivity of the Jacobian matrix [2]. The increasing use of phasor measurement units (PMUs) makes real-time approaches to the voltage stability monitoring possible. Most analyses concentrate on wide area monitoring of voltage stability, such as the real-time dynamics monitoring system [3] or wide area monitoring implementations [4]. A different method, more suitable for distribution grids, uses PMU-data to estimate the Thevenin impedance and based on that calculating the maximum loadability at a given node [5]. The main advantage of this application is that only the measured data of the PMUs and the topology of the examined subsystem must be known. Furthermore, due to the detailed consideration of any concerned bus, it can be enhanced to a protection system. However, there is a lack of analyses related to performance and validity of the Thevenin impedance based methods. So far, the Thevenin impedance seen from the load bus was assumed to be the equivalent impedance in short circuit calculation. This assumption is only valid, if none of the generators reach a limiting parameter. The algorithm proposed in this paper offers a solution on how to include the influence of these limits on the Thevenin impedance and therefore increase the accuracy method to monitor voltage stability. Similar to [5], this approach requires the topology of the concerned subsystem and the data of PMUs in the concerned buses. Additional information about the actual operational status and limiting parameters of the generators are required. The rest of this paper is organized as follows. Section II focuses on the basic idea of online voltage stability monitoring based on the Thevenin impedance and the required algorithm to calculate the Thevenin impedance in a general power system. The main generator parameters affecting the Thevenin impedance and the proposed method to take them into account are described in section III. Section IV shows the variation of the Thevenin impedance caused by generator limits and simulation results. The drawn conclusion is stated in section V. II. REVIEW OF ONLINE VOLTAGE STABILITY MONITORING BASED ON THE THEVENIN IMPEDANCE The basic idea of the proposed method is to use the available data of the network topology, SCADA systems and measurements from PMUs to reduce the complex voltage instability estimation to a maximum power transfer problem,