Cooperative methods for security planning

This paper develops a new approach to an old important and difficult problem: security planning in power system operations. The complexity of the problem is due primarily to two factors: (i) the large number of contingencies that need to be analyzed make it computationally intractable for real-time operations, and (ii) the problem has many solutions, and the global optimum is likely to be much better than the many local optima. We believe the problem is too big and difficult to be solved by any single, monolithic agent. Instead, we have developed a team of co-operative agents, called an A-Team, that is well-suited to solve this problem. The agents are autonomous, work in parallel, and communicate asynchronously. The paper describes the organizational structure of the team and presents results obtained both for the security-planning problem and for some other difficult global optimization problems. Key-words: power systems security, parallel processing, distributed artificial intelligence, global optimization 1. PROBLEM FORMULATION 1.1 Background and Terminology Think of a power system as a network containing m switches, each of which can be either open or closed. Thus, the system can adopt M = 2 different configurations, denoted by Co, C-|,... C M , where Co is the current configuration. Let Xn be a vector whose elements are the bus voltages and bus power injections of Cn. Though Xn contains both state and control variables, we will, for the purposes of brevity, call it a state vector. The concerns in operating a power system can be divided into two broad categories: cost and quality. Cost is usually represented by a function: f(Xn, D(t)), where t is time and D is a vector of exogenous, timevarying quantities, such as customer demands for electric energy. Quality concerns are usually expressed as a set of nonlinear relations (sometimes, called load and operating constraints) that are configuration-specific, and have the general form: Gn(Xn,D(t)) = 0 Hn(Xn,D(t)) < 0 Xn is said to be a normal state if it satisfies these constraints. S n , the set of all normal states for configuration Cn , is called the normal set of Cn . Configurations for which Sn is empty are said to be uncorrectable; all other configurations are said to be correctable. Two sorts of events can cause a system state to become abnormal: gradual changes in the exogenous variables, D, and sudden disturbances that result in random configuration changes. The latter can cause far larger excursions, and hence, are much more dangerous. This paper is largely concerned with control actions that can be used to counter the effects of sudden disturbances. These actions can be discrete (switching operations) or continuous (changes in the independently controllable components of the state vector). We will concentrate on the latter. Let in (Xna. Xnb) b e t h e l e a s t t i m e r e c l u i r e d t 0 change the state of Cn from Xna to Xnb through a sequence of control actions. We will call xn a transition delay. Note that xn is non-zero because many control actions are rate limited. The output of a typical generator can, for instance, be increased at most by a few megawatts per minute. 1.2 Optimum Power Flows (OPFs) One of the simplest operating philosophies is to attempt to minimize instantaneous costs while keeping the state normal. In other words: (OPF): Min f(X0) s.t. Go(Xo,D) = 0 Ho(Xo,D) < 0 Since the dimensions of Xo, Go. a n d Ho are often of the order of 1000, this is a large problem; available techniques are barely able to solve it fast enough for the results to be useful in real-time operations. 1.3 Adding Contingency Constraints How can one limit the ill effects of the random configurational changes that result from sudden disturbances? By far the most common practice involves two steps. First, a set of critical configurational changes (called contingencies) is identified. Second, plans are made to reestablish a normal state within some short period after each contingency. The identification of critical contingencies requires system-specific knowledge, much of which can be encoded in expert systems [1]. In other words, much if not all of the identification process can be automated with existing techniques. The same is not true for planning responses to these contingencies. To understand why, suppose that the n-th contingency would cause the system's state to change from Xo to XncIf Xnc is a b n o r m a l ' t h e planning problem is to find a normal state, Xn, that can be achieved within an acceptably short time, say Tn . There are two different ways to formulate this problem: the first treats correction times as hard constraints, the second, in a softer way, specifically, as terms of an objective function. The modifications that result to (OPF) from these two treatments are indicated below: contingency to be corrected, wn is a weight assigned to the n-th contingency; and it has been assumed that xn(Xn Xn c ) can be approximated by