Short-Term System Marginal Price Forecasting Using System-Type Neural Network Architecture

Transcription

1 Short-Term System Marginal Price ing Using System-Type eural etwork Architecture Byounghee Kim, John P. Velas, Jeongkyu Lee, Jongbae Park, Member, IEEE, Joongrin Shin, and Kwang Y. Lee, Fellow, IEEE Abstract eural networks have been applied in various new ways to the problem of short-term load and electricity price ing for power systems. Virtually all of these methods are based on using statistical patterns, which are perceived between the yearly load and system marginal price (SMP) histories of the system to predict the ed year s power demand and SMP. The SMP ing is a very important element in an electricity market for the optimal biddings of market participants as well as for market stabilization of regulatory bodies. The proposed method introduces a system type neural network architecture to perform electricity price ing. Specifically, the proposed approach begins with the premise that the electricity price for a given year can be given a structure which can then be related to the structure of the year, in such a way that a transformation can be found from the year s structure to the ing year s structure. The transformation depends upon how parameters, which influenced the SMP but can not be measured, move from the year to the ing year. I. ITRODUCTIO CCURATE system marginal price (SMP) or locational Amarginal price (LMP) ing is a crucial issue for all market participants in a power market. The SMP is the market price that is determined to consider the characteristics of generators in bidding, under a given power system condition and demand. In many countries, the electric power industry has been undergoing deregulation and privatization through the introduction of competition [1], [2]. The LMP is a localized form of the SMP [3], [4]. In order to supply high quality electric energy to the customer in a secure and economic manner, an electric company faces many economical and technical problems in operation, planning, and control of an electric energy system []. SMP ing helps an electric utility to make important decisions including decisions on purchasing and generating electric power, load switching, and infrastructure development. SMP ing is also important for energy suppliers, financial institutions, and other participants in electric energy generation, transmission, distribution, and markets [6]. The goal of power system planning and operation for the previously vertically integrated industry was to minimize This work was supported in part by the U.S. ational Science Foundation under Grant ECS-13. B. H. Kim, J. P. Velas, and K. Y. Lee are with the Electrical Engineering Department, the Pennsylvania State University, University Park, PA 1682 USA (phone: ; bxk232@psu.edu; jpv1@psu.edu; kwanglee@ psu.edu) J. K. Lee, J. B. Park, and J. R. Shin are with the Electrical Engineering Department, the Konkuk University, Seoul, , Korea ( aikk@konkuk.ac.kr; jbpark@konkuk.ac.kr; jrshin@konkuk.ac.kr). production and operation cost. However, the goal is now changed into maximizing the profit or return to the market participants since the introduction of competition in the electricity market. Indeed, it may become possible to use certain strategies in order to maximize the profit. Every market participant has to invest in their facilities, such as generators, transmission lines and distribution networks, etc., to maximize their profit. Generation expansion, transmission expansion and distribution planning cannot be completed in short-term, such as in one or two years, and must be considered under long-term market conditions. That is to say, market participants should have appropriate facilities in accordance with the electricity price ing in the future. In this competitive market environment, participants bid at a specific time period to trade the electric power. In this bidding, each participant can maximize their profit though a bidding strategy that is considered under several power system conditions, primarily the electric power demand at each time period. Therefore, the energy trading levels between market participants is highly dependent on the short-term price [1], [2], [7]. Most ing methods use statistical techniques or artificial intelligence algorithms such as regression, neural networks, fuzzy logic, and expert systems [6]. A variety of methods, which include various regression models, time series, neural networks, statistical learning algorithms, fuzzy logic, and expert systems, have been developed for short-term ing. ing has been mentioned as one of the most promising application areas of artificial neural networks (As). Several authors have attempted to apply the backpropagation learning algorithm to train As for ing time series. There once was also a negative opinion that the ing ability of the backpropagation algorithm was inferior to simple linear regression. The ational Science Foundation organized a workshop to address the importance of As in power system engineering [6]. The success of a ing technique depends on the quality of input data that could contain proper patterns representing the system dynamics. In this paper, a system-type neural network architecture is proposed to perform short-term SMP ing using the historical data from Korea Power Exchange (KPX). In Section II, the general background of ing will be presented and the newly proposed approach will be presented in Section III. In Section IV, the proposed approach will be simulated on empirical data. Finally, we make some conclusions in Section V X/6/$2. 26 IEEE 173 PSCE 26 Authorized licensed use limited to: Baylor University. 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2 II. GEERAL BACKGROUD Price ing techniques in power systems are relatively recent procedures. Several techniques have been in use to prices, such as time-series, jump diffusion/mean reversion models, neural networks, agents based simulations, generalized autoregressive conditional heteroskedastic (GARCH) model, wavelet transform and autoregressive integrated moving average (ARIMA) models [8]. Many ing methods can be divided into two broad categories: parametric methods and artificial intelligence based methods. The parametric methods formulate a mathematical or statistical model by examining qualitative relationships between the SMP and the factors affecting the SMP. The assumed model parameters are then estimated from historical data and the adequacy of the model is verified by analysis of errors. Artificial intelligence based methods use artificial neural network as load or SMP models. For either of these methods, to perform short-term load or SMP ing, several factors should be considered, such as the time factor, weather data, and possible customers classes [9]. However, due to the complicated factors affecting electricity prices, accurate price ing turns out to be very difficult. As is known, power plant construction requires large investment and a relatively long period, which leads to power-market entry barriers. Therefore the electricity markets are apt to be oligopolistic, in which power suppliers make strategic bidding and/or withhold capacities to raise the price so as to maximize their own profits. In addition, various factors such as transmission congestion, maintenance of generation units, variations of fuel costs or water supply and load fluctuation, etc., will also affect the electricity price noticeably and increase the complexity of accurate price ing [1], [2]. A. Parametric ing Methods There are a variety of statistical techniques that have been developed for short-term load and price ing. One of the most widely used techniques is the regression method. For electric load and price ing, regression methods are usually used to model the relationship of load consumption and other factors such as weather, dry type, and customer class. Another approach uses the time series method, which is based on the assumption that the data have an internal structure, such as autocorrelation. In addition, state variable models and ARIMA models have also been developed to describe the load and electricity price behavior [7], []-[11]. B. Artificial Intelligence ing Methods The use of artificial neural networks has been a widely studied electric load and price ing technique. An application of a neural network reduced some of the burden associated with the parametric approach. The main advantage of using neural networks lies in their abilities to learn the mentioned dependencies directly from the historical data without necessity of selecting an appropriate model. There are a few types of neural network that have been applied for load and price ing. A multi-layered feedforward network with one hidden neuron layer is most commonly used [6], [12]. A recursive neural network uses a ing error as one of its input variables, which increases its adaptability although it may also lead to stability problems. A radial basis function (RBF) network has the ability of computing reliability measures. Expert systems have also been applied to ing, where the system learns the rules and procedures used by human experts to automatically make s without human assistance. Fuzzy logic and support vector machine techniques have also been applied to load and price ing [6], [13]-[1]. III. PROPOSED METHOD A. Failures/Shortcomings of Conventional s. Recently, a shift has occurred in the overall architecture of neural networks from simple or component-type networks to system-type architectures. The most popular architecture seems to be the one advocated by Jacobs and Jordan [16], called the Modular Connectionist Architecture. The most serious flaw in the design of system-type neural networks is the lack of a cohesive discipline in the architectural design and in the design of the learning algorithm. Virtually, the entire design is done on an intuitive basis. To illustrate the lack of a cohesive discipline, in [17], the partitioning of components corresponds to separation of variables, which works if the variables are separated and does not work if the variables are not separated [18]-[2]. B. System Type eural etwork Method In previous papers [18]-[2], a system type neural network was proposed which implemented extrapolation. In this method, the surface determined by a given data set was expanded along one axis. In the current method, a similar system type approach will be used but its purpose is to implement a form of correlation, where the ed surface will be generated from a surface by a transform, dependent upon parameters which are difficult to measure. Short term load ing is mainly affected by weather parameters. However, in short term price ing, the main variable that drives the price is the power demand. Therefore, the SMP can be thought as SMP f ( load) f ( day, hour). If we consider all possible factors that affect the SMP, ing will be more accurate, however, it is very difficult to do in the real market. Therefore, this paper considers only the past power demand and SMP to future SMP. The data can be defined on a point (d,h) in the two dimensional space, with the day (d) and hour (h) as the coordinates. The current SMP is affected by the past SMPs and the pattern in which the current SMP is included. In addition to the past SMPs, the SMP is also influenced by the power demand. In order to, similar days approach is considered since the main variable of SMP is power demand and it is a well known fact that the pattern of power demand is similar along same days. The motivation for this approach stems from a particular interpretation of the influence that the parameters play in determining a load function. That is, rather then thinking of the load as, for example, SMP = f(day, hour,weather,customer classes, etc.), this approach considers 174 Authorized licensed use limited to: Baylor University. Downloaded on January 26, 21 at 2:1 from IEEE Xplore. Restrictions apply.

3 the SMP f ( day, hour), parameterized primarily by the load demand and additionally by other parameters, such as population growth and special events like the Olympics. That is, the role of the parameters is that they determine the transformation form one SMP surface to another surface. In the next section, it will be shown that the SMP (P) for any year can be represented in the following form: P( day, hour) C( day) E( hour) (1) This entire method hinges on the assumption that the basis vector set remains very similar from year to year. Because P T(, l pg, etc.) P and since P C E and also, P C E, this implies that C T(, l pg, etc.) C, where l is load, pg is population growth, and T is a transformation. The year SMP is chosen as that one which provides the best fit between itself and the ing year load when the transformation is applied. The proposed method can be applied directly to LMP ing. C. Proposed eural etwork Method. Unlike conventional neural network architectures that would attempt to achieve the mapping SMP( day, hour ) with one neural network, the proposed architecture reflects a system-type approach using a combination of an RBF neural network together with a comparator, in an adaptation of the connectionist architecture [18]-[2]. The proposed method uses artificial neural networks with three significant features. One, the influence of the day of the week and of the season of the year are combined into one variable. Further, the recognized influence of weekdays versus weekends must be expanded to a day-by-day influence. Therefore, the approach begins by introducing a new variable for each day of the week and each week of the year. For example, Mondays are grouped into one variable, number of Mondays, which ranges from 1 to 2. The SMP for a Monday is then represented as a function of the hour of the day and the Monday number. The second significant feature of the approach is that this SMP must be able to be represented as the product of a coefficient vector and a basis set. This, in its general form, has been established [18]-[2]. Therefore, one of the assumptions in this paper is that the general SMP can be represented in the form given by (1). E( hour) is the orthonormal basis set and Cdaydetermines ( ) the coefficient for a given day [18]-[2]. In this case, Ehour ( ) is a -dimensional set, where each member represents the SMP for an entire 24 hour (Monday) period. For example, the load for the 32 nd Monday of the year is given by SMP( Monday 32, hour) C( Monday 32) E( hour) (2) The third significant feature of the approach is that the coefficient vector for the ing year is related to the coefficient vector from the year. The year Choose day is chosen by comparison of the year with all previous available years. Mon. # Tue. # Wed. # Thr. # Fri. # Sat. # Sun. # 26 week of year Mon_RBFs Tue_RBFs Wed_RBFs Thu_RBFs Fri_RBFs Sat_RBFs Sun_RBFs Comparator C i, 26 week of year Fig. 1. Overall structure of the er. C i, SMP_Mon. = C(Monday)E(hour) C ( day) T (, ) C ( day) (3) Once the year is selected, the parameters and are chosen to provide the best correlation between the ing year coefficient vector and the year coefficient vector. The overall structure is shown in Fig. 1. There are seven ers and one comparator. The ers have a Radial Basis Function (RBF) architecture [21]. Each er consists of n RBF networks, each one of which implements one orthonormal vector of an n-dimensional basis set of vectors. The outputs of the orthonormal vectors are (internally) linearly summed so that the er spans an n-dimensional function space [9], [18]-[2]. The coefficients which determine the linear sum and thereby define the specific function being implemented is supplied by the comparator. Up to this point, the operation of the RBF channel parallels the idea used by Phan and Frueh [22]. One of the essential differences between their approach and the present proposed approach is that the former requires prior engineering knowledge for selecting the basis vectors, and the latter approach requires no such knowledge. One advantage that RBF networks have over other architectures is that their functionality can be given an explicit mathematical expression in which the neuron activation functions act as Green s functions [23]. This makes these networks amenable to design rather than training. Another advantage is that they function as universal approximators [21]. To start with, s are made on a weekly basis; for example, from a given Monday, the following Monday SMP is ed. For clarity, the point at which the is to be made is referred to as the point of ing. For each day of the week, there is a -dimensional RBF neural network. For ing purposes, the comparator correlates a 17 Authorized licensed use limited to: Baylor University. Downloaded on January 26, 21 at 2:1 from IEEE Xplore. Restrictions apply.

4 26-week window from the ing year with the corresponding 26- week window from the year and determines, which then transforms the year coefficient vector to the ing year coefficient vector. This latter coefficient vector is then applied to the basis set of vectors to determine the hourly profile for that day. The 26-week windows begin at the point of ing and extend backward 26 weeks. The relationship between the coefficient vectors for the ing year and for the year is as follows: i ( day) i i i C Previous year C mon, Point of 2 ing Correlate C mon, and C mon, Reference year weeks C mon, 26 weeks year Reference year Fig. 2. Conceptual transformation of to coefficient vectors. [ C ( day)], i 1,, n. where n is the dimensionality of the SMP surface and is determined as explained above. As time progresses the windows move forward. To define the windows the following perspective must be adopted, which is shown in Fig. 2 for a Monday for illustration purposes. If the point of ing is greater than or equal to 26, the ing window consists of the ing year s data and the window consists of the year s data. However, if the point of ing is less than 26, the ing window consists partly of the ing year s data, and partly of the previous year s data; likewise, the window consists partly of the year s data and partly of the year-1 data. D. ing Procedure Assume the ing year is 24. First, the year SMP must be selected on the basis of providing the best fit between itself and the ing year. However, to illustrate the proposed approach, the previous year was arbitrarily chosen as the year. At this point, the basis set is determined. This in turn determines the Monday RBF network. This procedure must be repeated for all other days of the week. Then the procedure defined above can be applied. (4) IV. SIMULATIO RESULTS The proposed ing procedure was tested using the past SMP data (22 ~ 24) obtained from the Korea Power Exchange (KPX). The proposed method can be applied to any year, provided a suitable corresponding year can be found. The quality of the results is tied to the closeness of the fit between the year and the year. That is, if a suitable year can not be found, the performance will be degraded. The data as presented does not contain noise; however, if noise would be added, it would simply accentuate the roughness feature (the same method would be applied). For the simulation, 24 SMP data was chosen as a year. Also the year was arbitrarily chosen as the previous year (23). Furthermore, as explained above, the last half of the 22 SMP data must be used any time the point of ing is less than 26. The dimensionality of the SMP profile is chosen as n=. In addition, no attempt was made to sort the holidays from the non-holidays and weekdays and weekend days were not grouped. The results were analyzed by the following formulas: i) Standard deviation 1 ˆ 2 [ Pdh (, ) Pdh (, )] () d 1 Pdhis (, ) empirical SMP data for a given day (d) and hour (h), Pdhis ˆ(, ) SMP data for a given day (d) and hour (h). is number of weeks = 2. ii) Percent error 1 (, ) ˆ Error Pdh Pdh (, ) / Pdh (, ) 1 (6) d 1 Fig. 3 illustrates actual and SMP on May 24. Fig. 4 and Fig. show the comparison between the actual SMP and ed SMP, for Monday only. Fig. 6 shows the error between actual and ed SMP for Monday only. Table I shows the day of week ing results. For each day, the percent error is obtained as the average of 2 days for each day of the week (over the entire year). Also, the unit of standard deviation is Cent/kW. Among the daily ing, Tuesday shows the best ing results and Sunday shows the worst ing results. For Tuesday, the average error is 3.21% and the highest error is 4.6% at 12: and the lowest error is 2.24% at 16:. For Sunday, the average error is 4.44% and the highest error is.8% at 2: and the lowest error is 3.1% at 1:. From these results, we know that the Tuesday SMP has less variation than other days in 24. The total average error for daily ing is 3.61% and average standard deviation is 2.71 Cent/kW. Monday and Sunday errors are above the total average with respective errors 3.97%, and 4.44% and Tuesday, Wednesday, Thursday, Friday, and Saturday errors are below the total average with respective errors 3.21%, 3.2%, 3.43%, 3.3%, and 3.48%. 176 Authorized licensed use limited to: Baylor University. Downloaded on January 26, 21 at 2:1 from IEEE Xplore. Restrictions apply.

5 7 1st week of May (May 1 ~ May 8) Monday SMP nd week of May (May 9 ~ May 1) rd week of May (May 16 ~ May 22) Fig. 4. Monday 24 SMP. 8 2 Monday SMP th week of May (May 23 ~ May 31) Fig. 3. and ed SMP on May 24. For the time axis, the lowest error is 2.74% at 14: and the highest error is.6% at 24:. Among the monthly ing results, ovember shows the lowest error (3.17%) and September shows the highest error (4.67%). For ovember, the highest error is 4.99% at 8: and the lowest error is 1.71% at 14:. For September, the highest error is 11.6% at 3: and the lowest error is 2.92% at 11:. The total average error for monthly ing is also 3.61%. January, February, March, April, May, ovember, and December errors are lower than the total average error with respective errors 3.28%, 3.4%, 3.42%, 3.9%, 3.27%, 3.17%, and 3.18%. V. COCLUSIOS In this paper, we introduced a new neural network approach to perform SMP ing, based on the following ideas. First, virtually all SMP ing techniques are based on the idea that the three primary variables are: hour of the day, day of the week, and season of the year. As a contrast, the proposed approach combines the last two variables into one variable. Second, the weekday/weekend influence is expanded to a seven day influence. Third, the conventional connectionist architecture is adapted to reflect a system-type approach using a combination of an RBF neural network together with a comparator. The SMP data obtained from the KPX are used. For this paper, the dimensionality of the load profile is arbitrarily chosen as. By increasing the 7 Fig.. ed Monday 24 SMP dimensionality, improved accuracy is expected. Additionally, improved accuracy can be expected by choosing the year optimally. This connectionist approach was used in other papers to perform extrapolation; in this paper, it is used to perform a transformation, based upon the best correlation. For example, the SMP function for Monday is explicitly a function of and hour. The function itself is derived as a transformation from a year. The major advantage of the proposed approach is that other methods are primarily subjective while this method is objective, intending to emulate the extrapolation aspect of human learning. 1 Error between and Monday SMP 4 1 Fig. 6. Error between actual and Monday SMP Authorized licensed use limited to: Baylor University. Downloaded on January 26, 21 at 2:1 from IEEE Xplore. Restrictions apply.

6 TABLE I STATISTICS OF DAILY FORECASTIG RESULTS Mon Tue Wed Thu Fri Sat Sun avg REFERECES [1] J. K. Lee, J. B. Park, J. R. Shin, and K. Y. Lee, A system marginal price ing method based on an artificial neural network using time and day information, Proceedings of the IFAC 26, accepted. [2] J. K. Lee, J. B. Park, J. R. Shin, and K. Y. Lee, A system marginal price ing based on an artificial neural network adapted with rough set theory, IEEE Power Engineering Society General Meeting, pp , 2. [3] Y. Ma, P. B. Luh, and K. Kasiviswanathan, A neural network-based method for ing zonal locational marginal prices, IEEE Power Engineering Society General Meeting, vol 1., pp , 24. [4] J. Bastian, J. Zhu, V. Banunarayanan, and R. Mukerji, ing energy prices in a competitive market, IEEE Computer Applications in Power, vol 12., pp. 4, [] J. H. Chow, Applied Mathematics for Restructured Electric Power Systems: Optimization, Control, and Computational Intelligence. ew York: Spinger-Verlag, 2, ch. 12. [6] K. Y. Lee, Y. T. Cha, and J. H. Park, Short-term load ing using an artificial neural network, IEEE Trans. on Power Systems, vol. 7, pp , Feb [7] M. Zhou, Z. Yan, Y. X. i, G. Li, and Y. ie, Electricity price ing with confidence-interval estimation through an extended ARIMA approach, Proceedings of IEE Generation, Transmission, and Distribution, vol. 13, o. 2, pp , Mar. 26. [8] P. Mandal, T. Senjyu, and T. Funabashi, eural network models to predict short-term electricity prices and loads, IEEE International Conference on Industrial Technology, pp , Dec. 2. [9] B. H. Kim, J. P. Velas, and K. Y. Lee, Short-term load ing using system-type neural network architecture, WCCI 26, accepted. [1] K. Y. Lee, Y. T. Cha, and J. H. Park, Artificial neural network methodology for short-term load ing, SF Workshop on Artificial eural etwork Methodology in Power System Engineering, Clemson University, SC, Apr. 9-1, 199. [11] J. H. Park, Y. M. Park, and K. Y. Lee, Composite modeling for adaptive short-term load ing, IEEE Trans. on Power Systems, vol. 6, pp. 4-47, May [12] D. Park, M. El-Sharkawi, R. Marks, A, Atlas, and M. Damborg, Electric load ing using an artificial neural network, IEEE Trans. on Power Systems, vol. 6, pp , May, [13] W. Charytoniuk, M. S. Chen, and P. Van Olinda, onparametric regression based short-term load ing, IEEE Trans. on Power Systems, vol. 13, pp , Aug [14] K. Y. Lee, Y. T. Cha, and C. C. Ku, A study on neural networks for short-term load ing, Proceedings of the First International Forum on Applications of eural networks to Power Systems, pp. 26-3, [1] D. K. Ranaweera,. F. Hubele, and A. D. Papalexopoulos, Application of radial basis function neural network model for short-term load ing, IEE Proceedings of Generation, Transmission and Distribution, vol. 142, pp. 4-, Jan., 199. [16] R. Jacobs and M. Jordan, A competitive modular connectionist architecture, Advances in eural Information Processing Systems, Vol. 3, p , [17] A. Atiya, R. Aiyad, and S. Shaheen, A Practical Gated Expert System eural etwork, IEEE International Joint Conference on eural etworks, Vol. 1, pp , [18] K. Y. Lee, J. P. Velas, and B. H. Kim, Development of an Intelligent Monitoring System with High Temperature Distributed Fiberoptic Sensor for Fossil-Fuel Power Plants, IEEE Power Engineering Society General Meeting, pp , Jun 6-1, 24. [19] B. H. Kim, J. P. Velas, and K. Y. Lee, Development of intelligent monitoring system for fossil-fuel power plants using system-type neural networks and semigroup theory, IEEE Power Engineering Society General Meeting, pp , 2. [2] B. H. Kim, J. P. Velas, and K. Y. Lee, Semigroup based neural network architecture for extrapolation of enthalpy in a power plant, Proceedings of the ISAP, pp , 2. [21] S. Haykin, eural etworks, 2nd ed., Prentice Hall:.J., [22] M. Q. Phan and J. A. Frueh, Learning control for trajectory tracking using basis functions, Proceedings of the 3th IEEE Conference on Decision and Control, pp , Dec [23] A.. Tikhonov, On regularization of ill-posed problems, Doklady Akademii auk USSR, vol. 13, Authorized licensed use limited to: Baylor University. Downloaded on January 26, 21 at 2:1 from IEEE Xplore. Restrictions apply.