Title Hybrid dynamical system as model for cascading outage in apower system

This paper uses hybrid dynamical systems as a mathematical model for cascading outages in a power system. Hybrid dynamical systems can combine families of flows describing swing dynamics of generators with switching rules describing protection control mechanisms. We refer to data observed in a cascading outage in the September 2003 blackout in Italy and show a hybrid dynamical system by which propagation of outages reproduced is consistent with the data. I. I NTRODUCTION Complex dynamics have recently emerged as a major issue in electric power systems [1], [2]. Cascading outage is one important example of complex dynamics and is the generic mechanism by which outages propagate to cause widespread blackouts of power systems [3], for example, the August 2003 blackout in North America [4]. Understanding such complex dynamics is required for preventing them, in particular, mi nimizing damage caused by blackouts, and for making a robust infrastructure with electricity supply. Transient stability of power systems is closely related to o ccurrence of cascading outages. Transient stability is conc erned with the ability of power system to maintain synchronism when subjected to a severe disturbance [5], [6]. The stabili y is mainly governed by swing dynamics of synchronous machines. The swing dynamics usually cause overcurrents and heavy power flows. This often results in outages of transmission and generation facilities by relay operation to protec t them. This cascading trend continues in the worst cases. The interaction between swing dynamics governing transien t stability and protection operation is hence one mechanism o f cascading outages, for example, the September 2003 blackou t in Italy [7], [4]. As indicated by [8], [9], [10], cascading o utage contains hybrid nature, implying that it is modeled with bot h continuousand discrete-valued variables. The purpose of this paper is to report a mathematical model for cascading outage in a power system. Following the importance of transient stability, we treat the interac tion between swing dynamics and protection operation. The model reported here is a hybrid dynamical system [11], [12], [13] and consists of families of flows describing swing dynamics and their switching rules that are based on protection contr ol mechanisms. We refer to data on a cascading outage in the September 2003 blackout in Italy [7] and show a hybrid dynamical model by which propagation of outages reproduced is consistent with the data. Note that the contents of this pa per have been submitted to archival journal [14]. II. CASCADING OUTAGE IN THE SEPTEMBER2003 BLACKOUT IN ITALY Before model development in Secs. III and IV, this section reviews data observed in a cascading outage in the September 2003 Blackout in Italy. The following review is based on [7]. The Italian power system experienced a large blackout on September 28, 2003. The blackout affected an area with an estimated 60 million people and load variation in the continental grid from about 24000MW at the early hours of the day, up to50000MW in the mid-day. This is regarded as the largest blackout ever to happen in Italy. Figure 1 shows (a)400 kV and (b) 220 kV power transmission networks interconnecting Italy (ITALIE therein) w ith France and Switzerland (SUISSE). A cascading outage or trip of transmission lines is indicated according to the time the y tripped, starting from #1 at 3:01.42 up to #9 at 3:25.33. The cascading trip resulted in the separation of Italian networ k from Switzerland and French ones and, after further cascadi ng trips of generators in Italy, finally led to the blackout. Figure 1(c) shows frequency traces in North Italy at Piossasco, S. Rocco, and Musignano EHV substations from 3:25.12 up to 3:26.12. Three pulsing behaviors are observed in Fig. 1(c) during the period from line trip #2 at 3:25.21 up t o #5 at 3:25.27. It is indicated in [7] that the observed behavi ors are caused by the interaction between transient stability g overned by swing dynamics and protection operation. The swing dynamics cause heavy power flows that trigger the protection operation. The operation is normally based on overcurrent o r distance relaying. We treat the swing dynamics related to th e cascading trip of transmission lines. It should be noted that various frequency dynamics are observed in Fig. 1(c). For example, the line trip # 8 at 3:25.33 in Figs. 1(a) and (b) triggered continuous decrease of frequency below48.5Hz in Fig. 1(c). The associated dynamics result in the isolation of Italian network and the blackout. Here, from phenomenological point of view, they are modeled through an interacting system with swing dynamics, voltage dynamics, and protection operation. However, this modelin g and analytical study are not easy. As a first step of analytica study on cascading outage, in this paper we focus on the relatively simple cascading outage, and the detailed model ing is in future work. 3:25.32 3:25.33 3:25.21