Long-term electric load forecasting using a dynamic neural network architecture

Abstract

The use of tlie recurrent inultilaycr perceptron network, a hybrid feedforward antl feedback arcliiteclure, as a inode1 structiire for empirical modeling in electric power system planning is investigated. In particular, tlie long-term forecasting of total energy usage by the U.S. inanufacturing sector is addressed. Forecasting results for the period 19791984 indicate that during and followiiig significant structural clianges, tlie proposed model structure appears to offer improved prediction accuracy. Comparative forecasting results with a conventio~ial approach are presented, deinonstratiiig tlie potential benefits of empirical modeling using Llie recurrent multilayer pcrceptron as a nonlinear state-space model structure. INTRO DUCTI0 N Electric power systems are cliaracterized by increasingly more coniplex and more sophisticated daily 011erations arid resource planning activities. Furtliermore, iii view of world events in the last twenty years, tlie safe, reliable, and cconomically eficient production and delivery of electric energy lias become of vital importance. Tlius, the elficiciit and optimurn economic operation antl planning of electric power systems has occupied an increasingly more important position in the electric power industry. Prior to 1973, electric utilities in the U S . spent approxiniatrly 20 % of their tola1 revenues on fuel for electricity production. That numher increased to 40 % of tlie total revenues by 1980. ‘l’lie amounts involved just for annual fuel expenditures i n a large utility company can be on the order of a few billion dollars. Thus, even small pcrceiitagc savings, resulting fioin iinprovctl oper a t ion aii tl p1 mi 11 i ng , coil Id 11 avc sig ni li can t ecou oin i c impact 0 1 1 both the supplier ant1 tiir co~isiiiiirr of clectiic energy. Paper APT 213-25-13 accepted for pieseiitation at the IEEEBTUA Athens Power Tech Conference: “Planning, Operation and Control of Today’s Electlic Power Systeiils“, Athens, Gieece, Sept. 54, 1Y93. Load forecasting lias beconie one of the most important aspects of electric utility planning. The economic consequences of improved load forecasting approaches have kept development of alternate, more accurate algorithms at the forefront of electric power research. From short-term load forecasts used in the daily unit allocations [I], to mid-term load forecasts used for fuel budgeting, aid to tlie long-term load forecasts used for resource planning and utility expansion, numerous different techniques have been proposed and are currently in use [2]. These methods can be classified into two major categories: (I) time series approaches, treating the load pattern as a time series signa3 and predicting tlie future load using some time series aiialysis tool, and, (2) regression approaches, which recognize the strong effects of weather on electric load use, for example, and attempt to find a (usually static) functional relationship between the two. Tlie major sliortconiing of these approaches is their limited accuracy partially resulting from use of linear model structures for the former (nonlinear time series using conventional methods have been proposed, but they have not yet proven practical), and the predominant use of static nonlinear functional relationships for the latter. In both of these approaches, however, the fundamental problem being atldressed is that of empirical inodeling or system identification. More recently, however, as a result of tlie renewed interest in Artificial Neural Networks (RNNs), a nuniber of authors have attempted tlieir utilization for the nonlinear identification of dynamic sys tcms [ 11 ,[3] ,pi]. Tlic ANN teclinology, attenipting to emulate tlie iiiforrnation processing iiietliods of living neural syst e m , can address coiiiplex problems, sucli as forecasting, einpiiical modcliiig and data reconciliation, encountered in power system planning and oper a t‘ 1011s. The ANN teclinology provides the computational capability to “learn by example”, and thereafter perform complex tasks, such as forecasting future trends. Based on the inforniation processing approaches used by living organisms, this emerging technology has proven successful in a number of significant engineering applications, some of wliich are of interest to the 1) oiver en gi nccri ng community. This paper presents a recently developed empirical state-space model structure based on the technology of ANNs, ant1 its preliminary application to a longterm electric load forecasting problem. A brief discrissioii of the utilized empirical model structure is presented along with the learning algoritlim used i n tlie training pliase of the network. This is followed by tlic preliminary results for a case study of long-term electric load forecasting. Comparative results with a conventional long-term forecasting approach are presented, demonstrating the potential benefits of the proposed forecasting method. The paper ends with a brief summary and conclusions. RECENT DEVELOPMENTS IN NONLINEAR SYSTEM IDENTIFICATION Identification is the use of sensed informakion to complete part of or all of an unknown system model (ettlier physical or empirical). Because of the complexity of the processes involved in electric power system operation and planning, it has been widely believed that identification using empirical models could provide more useful results than identification using first principle models. Model structure selection is an important stcp in tlie overall identification cycle, because it places sonic inherent limitations on tlie accuracy of the identified model and it also dictates the nature of the parameter estimation algoritlirri to be uscd. A review of the relevant literature indic;ltes that even though a number of processes of Interest 111 power engineering are nonlinear, linear modei structures have been almost exclusively used to represent them [5]. Nonlinear model structures have been examined by a few researchers, for various classes of nonlinear dynamic systems. In nonlinear system identification, two major problems have been investjgated: (1) the traditional parameter estimation of an assumed nonlinear structure, and, (2) the structure idcntification of nonlinear dynamic systems. Some results have been reported for the first problem, however, poor coiiver cncc properties of parameter estimation acceptance of such approaches. Recently, a number of results have been reported in the literature on the use of RNNs, particularly of singlelayer and multilayer feedforward perceptrons, for identification of static and dynamic systems. The majority o l these approaches are based on the premise that tlie deterministic part of a process can be adequately approximated by a Nonlinear Auto ltegressive with eXogcnous input (NARX) model structure, as follows: algorithms B or nonlinear structures have limited the (1) where y ( k ) , u(k), and e ( k ) are the system output, input, and white noise disturbance signals a t the discrete time characterized by the index k , respectively. As a result of specific p's and q's used in this approach, the order of the system to be identified is assumed known. Identification is performed by approximating the nonlinear function f(.) using a feedforward network trained by the standard backpropagation (BY) algorithm or by any of its variants [8]. During training, the inputs to tlie network are y(k), ..., y ( k p ) , u(k), ...) u(k q ) , and the target is y ( k + 1). Therefore, in the identification of a predosninantly deterministic system, that is when the noise term e ( k ) is negligible, no distinction is made between a teacher forced (series-parallel) and a recurrent (parallel) architecture. Such a procedure has been considered by a number of investigators [3],[6]. Reccurent Links