Blackouts in electric power transmission systems KARAMITSOS IOANNIS and ORFANIDIS KONSTAΝΤINOS Athens 16342 GREECE Abstract: - In this paper an analysis of blackouts in electric power transmission systems is implemented and studied in simple networks with a regular structure. The proposed model describes load demand and network improvements evolving on a slow timescale as well as the fast dynamics of cascading overloads and outages. The model dynamics are demonstrated on the simple power system networks. Key-Words: - Blackout, Generator, Load, Power load 1 Introduction Electrical power transmission systems are complex engineering systems with many static or dynamic components. Their complete dynamical description involves detailed knowledge of each component and its coupling to the rest of the system. The power system can be modeled using two possible approaches. The most commonly used approach is a deterministic calculation that models all the components in detail. Because all of the components and the physical laws that govern their interactions are known, it is possible to develop software that simulates particular blackouts. These codes may be complicated and time-consuming, but they are feasible. This approach has proven to be effective in helping to manage the power system. However, a different perspective can be taken. Blackouts in power systems happen quite frequently. These blackouts have a multiplicity of causes such as equipment failure, weather conditions, vandalism, and human error [1]. The dominant causes triggering blackouts cannot be written in the equations of a software code. Therefore, if we want to understand the global dynamics of power system blackouts, we need to emphasize the random character of the events that trigger them and the overall response of the system to such events. This is the approach taken in this paper. The two approaches are necessary and complement each other. They may converge in the future when the second approach is further developed. In following the second approach, it is sensible to start from a global, top-down methology with simple models that capture the main effects only. A recent analysis of blackouts in the North American power grid [2, 3] has shown that measures of such blackouts such as megawatt hours unserved or number of customers affected show the existence of long-range dependencies. Furthermore, the probability distribution function (PDF) of the size of the blackouts has a power law scaling. This behavior of the power transmission system is suggestive of a dynamical system close to a critical point. One possible governing principle for its dynamics is self- organized criticality [6]. We have considered a sequence of models that may reflect the dynamical properties of a self organized critical system. The simplest model was employed in reference [3]. In [3] we used a sand-pile model [7] as a black box to generate a 2 self-organized critical time series that could be compared to the time series of historical data for power grid blackouts. The sandpile was not a model for the dynamics of the power grid, but merely a means of testing the self-organized critical properties of the data. The next step was taken by constructing a power transmission model [4] based on a cellular automaton similar to the sandpile model. This model allowed studying properties of network power transmission, but it did not solve the network power flow equations. The interesting result is that these two models produce PDFs of blackout sizes that are quite similar and are also similar to the PDF determined from the historical data for North American power grid blackouts. Here we describe the implementation and results of a model [5] that takes it a step further by solving the network power flow equations. This model still remains simple, and in this paper we consider the power networks of homogeneous structure. In this way, we can vary a minimum number of parameters to explore the dynamics. However, extensions of the model are possible and easy to implement. These extensions will allow us to consider more realistic power system networks, incorporate the reliability of each component, and to vary the methods of responding to increasing power demand and improving the system. Many researches and studies should be paid to issues of voltage and reactive power control and load behavior. This paper is organized as follows: Following the introduction, an analysis of the proposed model is Proceedings of the 5th WSEAS International Conference on Applications of Electrical Engineering, Prague, Czech Republic, March 12-14, 2006 (pp44-47)