Spatial Short-Term Load Forecasting using Grey Dynamic Model Specific in Tropical Area

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1 E5-0 International Conference on Electrical Engineering and Informatics 7-9 July 0, Bandung, Indonesia Spatial Short-Term Load Forecasting using Grey Dynamic Model Specific in Tropical Area Yusra Sari #, anang Hariyanto #, Fitriana * # Power System and Electricity Distriution Laoratory School of Electrical Engineering and Informatics, Institute of Technology Bandung Gedung Kerma PL-ITB Lt. Jalan Ganesha o.0 Bandung 40 Indonesia yusra@power.ee.it.ac.id radi@power.ee.it.ac.id fitrisalsa@gmail.com Astract - Grey systems theory is the one of the most important research of uncertainty system, developed into a set of address information is not a complete systems. This theory realizes the correct description and effective supervision in operation action and evolution law of system, mainly through generating, exploring and extracting valuale information from a little part known information to predict the unknown information value. Dynamic forecasting model is needed due to the uncertain nature of the load predicting process specifically when load changes is correlated to the tropical temperature effect in Indonesia. A grey predicting approach is implemented in this paper to solve dynamic short term load forecasting in local sustations of the Indonesian high voltage grid, as provided y Jawa Bali Load Control and Operator Center (PL PB Gandul. Traditional GM(, model is presented to compare with the GM(, for weekday and weekend load conditions refer to the temperature variation pattern during the year 009. GM(, model denotes the relationship of hourly load demand affected to the tropical climate change variale, i.e. local amient temperature. The daily load curve for Cawang and Ciatu sustations, as representing Jakarta area, was used to validate the models. Typical comination Grey model specified in tropical climates was implemented to capture the load changes correlated to the temperature effect in each particular season, The model adequacy and weekly forecasting result had indiced a good grade in error diagnostic checking (MAPE in each location. Keywords - grey dynamic forecasting model, amient temperature records, local load profiles, short-term spatial load forecasting. I. ITRODUCTIO Rapid formation and development of new theories of systems science have ecome an important part of modern science and technology, especially in research of uncertainty system. There are several theories how to handle uncertain data: fuzzy logic, system identification, dimension analysis. A new one may e added: the Grey System Theory (GST. GST is also one of such systems theories that appeared initially in early 980 y J. Deng []. So its theory and successful application is now well known in China, almost all the journal and conference papers have een pulished y eastern authors, and there are only two ooks in English which are also written y Chinesse scientists. In grey systems, the information have partially known and partially unknown parameters especially useful, when the complete set of factors involved in the system s ehavior is unclear, ( when the relationships of system factors to the system s ehavior and inter-relationships among factors are uncertain, ( when the system ehavior is too complex to determine completely, or (4 when only limited information or time series data on system ehavior is availale. The essential scopes of GST encompass in research methods aout: grey relational space, grey generating space, grey forecasting, grey decision making, grey control, grey mathematics and grey theory as ase []. In short-term load forecasting (STLF, daily load requirement would change in real time due tue uncertainty electric power systems. ational Electric Company in Indonesia (PL have developed STLF ased on the coefficient method to support its operation and control planning []. But it have een implemented only for a high scale data in Jawa Bali load systems using -5 years past data. Unfortunatelly, its method cannot improve the real relationship etween daily loads and many weather components such as amient temperature, relative humidity, wind speed, etc. that suggested as one of essential factors in load variance incident lately, e.g. loading fail on inter-us transformer of Cawang sustasion and more. Whereas the future loading on the Jawa Bali grid systems will e affected y potential impacts of changing climate and rising extreme weather, specific for tropical area such as Indonesia. Therefore, their electricity demand currently must e predicted y extrapolating a predetermined relationship etween the load and its influential variales - namely, time and/or weather-sensitive, toward short-term nor long-term load forecasting. In this study, determining this relationship is a two stage process that requires identifying the relationship etween the load and amient temperature data information and quantifying this relationship through the use of a suitale parameter estimation technique otained from Grey Forecasting Method (GFM. However, due having only a little temperature data and smaller case coverage, only two main schemes of the GFM as grey dynamic models, areviated as //$ IEEE

2 GM (, dan GM (,, will e implemented []. It was used to predict of future electric demand that includes location (where as one of its chief elements, in addition to load magnitude (how much and seasonal or temporal (when characteristics, as a condition called Spatial Short-Term Load Forecasting (SSTLF. As study cases, (two local sustations in a metropolitan area such Jakarta in Indonesia had een chosen to improve the grey predicting approach in power/energy systems. As main references in this study were application GM(, model considering the influencing factor of load to forecast a day-ahead electricity prices in China comined with Particle Swarm Optimization (PSO [6]. Genetic Algorithm (GA s also can e adopted to otain optimal coefficient with GM(, to replace the GM(, for enhancing the forecasting validation index [4],[5]. However, the new contriution in this paper was grey model implementation in spatial load forecasting analysis with incomplete data covering a local sustation as part of Jawa- Bali high grid area, where known the specific condition in one sustation area cannot e equated with another, inclusive weather effects, power consumption pattern of its customer, sudden network maneuver in load control operation, etc. II. GREY FORECASTIG METHODS Theory, techniques, notions, and ideas for analysing nonlinier systems in GST provide a differential model,so called as Grey Model (GM y using the least 4 (four data to replace difference modelling in vast quantities of data. A. GM(, Model The series processed is ordered to e the GM (, modeling sequence, denote the original data sequence as follows: {, (, (..., ( n The AGO formation of ( k 0, k,,,..., n is generated to the first order series { ( k {, ( k is defined as follows: {, (, (,..., ( n ( The aove two series meet the following relationship as follows:, and k ( k m ( x ( m, k,,,..., n The GM(, model can e constructed y estalishing a first order differential equation for ( k as follows: d ( k + a (4 dt where, a and are the parameters to e determined, (4 is scattered availale as follows: ( [ ( k + + ( k ], ( k,,,..., ( k + + a n (5 Then, (5 can e expressed y using the matrix form as follows:, where Y n Ba B [ + (] [ ( + (] [ ( n + ( n ] Y n ( ( ( n a T ( a, (6 In (5, the unknown variale is only a and, ut there are n- numers of equations, it is oviously no solution, ut the least square method can e used to derive least square solution. The matrix equation can e rewritten as follows: Y n Baˆ +ε,ε is the error terms, min Y Baˆ min( Y T Baˆ ( Y Baˆ n n n the derivation is ordered y using the matrix, it is availale as follows: a ( B B T a B Yn T ˆ (7 (7 is into (4, the time response function can e solved as follows: ˆ (0 ( t e at + a (8 The scattered type as the time response sequence of grey differential equation is given y ˆ (0 ( k + e ak + a (9 ˆ ˆ ( ( ˆ ( k + k + ( k (0 (0 is the asic model of the gray forecasting GM (,, it is the specific formula of the GM (, model of grey prediction. Then the meaning of the symol GM(, is given as follows [] G M (, Grey Model st Order and so on for other models. a a OneVariale

3 With GM (, model for demand forecasting, the accuracy of forecasting model is also need to e checked so that the future value predicted have a higher crediility using residual test as follows: ( ( ˆ ε k k ( k then asolute error in percentage (MAPE, Δ ε ( k/ ( k B. GM(, Model One of the grey relationship model in GST is GM(,, where the data can e separated into two sequences, i.e. one major sequence factor, which is the sequence that masters the systems represent such as equation ; and influencing sequence factors, which are the sequences that influence the systems, as follows:, (, (,..., ( n { {, (, (,..., ( n {, (, (,..., ( n where is defined as the original sequence numer. T T T [ a,,,..., ] ( B B B Y [ + (] ( [ ( + (] ( ( After this sequences are sujected to the Accumulating Generation Operation (AGO, refer to equation (, the following sequences otained. The grey differential equation of GM(, model is [] d ( k + a ( k i i ( k dt i ( where a is the develop factor and i as the driving terms which is the relationship weighting factors. So, the parameter vector define in (6 can e solved where: aˆ B ( ( [ ( + ( ] ( ( n n n n ( (4 Then the approximate time response sequence of GM(, equation is written as ˆ ak ( ( ( k + k + e + ( k + (5 i i i i a i a i where is taken to e. Then the restoration of Inverse AGO using equation (0. Summarizing the aove GM(, model, the grey system model can e illustrated as Fig., where the system input is influencing sequences and the system output is major sequence. By utilizing relational factors and GM(, model, we can construct the function of the input and output sequences to furthermore understand the relationship. Relational factor Relational factor... Relational factor... GM(, Fig. Block diagram of the grey relationship analysis input-output Major factor In the aove mentioned GM(, model, we used GM(, to correlate the relationship etween the two sequences derived in prolem statement i.e. load and amient temperature data samples in certain location. III. UMERICAL STUDY The sample data in this study were ased on the historical load dan amient temperature informations in (two local High Voltage Sustations (HVST in Jakarta area, i.e: Cawang sustation in 009, only data until Septemer 8, 009 when IBT fail loading in there, and Ciatu sustation with 009 data records from January until Decemer, 009. Through this informations, we divide the data into weekday, weekend, and separated holiday data for determining GM (, model. This data is managed refering to the threshold values scheme using appoint technique [4]. In our data, we find that daily load curve of each day in Cawang HVST in a week not e similar, as well Ciatu HVST. But weekly amient temperature patterns always similar tendency in the same season. As we know, there are two main tropical season in Indonesia, dry and rain season. Climate changes effects have distracted existing period of each season, hence for similarity the data schemes of Cawang and Ciatu HVSTs have een adapted in accordance with weather tendencies. A. SPATIAL GREY ESTIMATIO I TROPICAL CLIMATE In this paper, daily day-ahead load in MW distriuted in Cawang and Ciatu HVST are selected to forecast and validate the performance of the common Grey estimation model. i.e. GM(, and GM(,. Each model was applied to the same hours and the same days matched with the particular season to find the output parameters or coefficients therein. In general, variales that act upon the system of interest should e external or predefined. The GM(, model is a single sequence modeling, which makes use of only the system s ehavioral sequence, represented y output sequence or ackground values, without considering any external acting sequences represented y some input sequences or driving quantities as well as in GM(, model []. The parameters (-a and ( mentioned in (9 are called the development coefficient and grey action quantity, respectively.

4 The parameter (-a reflects development states of ˆ and ˆ, and the grey action quantity in GM(, is a value derived from the ackground values contained in column of matrix B in (6. Interestingly in GM(, model, (-a still represent the development coefficient of the system, ut i i ( k is called the driving term which ( i reflect the driving coefficients. It would e different among ( in GM(, with ( in GM(, which had een used in this paper. We had collected all parameters derived from simulation in each season. It used to compare the impact correlations of daily weather trend and daily load curve in different sustations, where shown in Tale I. TABLE I CORRELATIO COEFFICIET COMPARISO I CAWAG HVST SEASO Driving Parameter or Model Control Variale ( MO TUE WED THU FRI SAT SU DRY RAI In the item of Monday until Sunday as shown in Tale I aove, it can e seen the average correlation coefficients aggregated for 4 hours in all days of week. The average driving coefficient in all Saturday and Sunday (weekend period throughout the dry season had indicated lower value rather than Monday until Thursday (workday period, as shown in Fig.. Whereas daily temperature had the similar distriution in all days of week during the dry season, y looking at Fig.. Likewise in period of the rain season, as shown in Fig. 4, temperature tendency of each day in a week may similar too, ut it had lower value compared than temperature tendency during dry season. The same trend also occurred y comparing the driving coefficient during dry season (Fig. with rain season (Fig.5. TABLE II CORRELATIO COEFFICIET COMPARISO I CIBATU HVST SEASO Driving Parameter or Model Control Variale ( MO TUE WED THU FRI SAT SU DRY RAI Fig. Amient Temperature Distriution through Dry Season Fig.4 Amient Temperature Distriution through Rain Season Fig. Correlation Coefficient in GM(, for All Days of Week through Dry Season Fig.5 Correlation Coefficient in GM(, for All Days of Week in through Rain Season We can conclude that the correlation etween load distriution and temperature in weekend period did not corresponded with

5 their daily temperature distriution spatially. However, the driving coefficient derived in Ciatu HVST had given similar results, as shown in Tale II. Meaning that in order to conform each correlation factors spatially, it is necessary to comine grey model appropriate with the daily temperature patterns in certain location which has a tropical climate. Also the model should not ignore the power consumption pattern at the location. Hence, the hyrid grey model developed y [8] could not e applied in tropical climate condition at all, so the GM(, method schemes proposed as in [4] did not appropriated to all of our cases. For our cases in Jakarta area, which are a capital and usiness city, GM(, would e applicale to forecast the power demand in workday period, and GM(, just applicale for forecast implementation in weekday period. The proposed scheme would e implemented throughout the year in Jakarta area, oth in dry season and rain season, spatially. In Jakarta area, the special holiday with a long period which gives a significant effect on daily load curve are only in Hari Raya Learan (HRL. From historical data known that HRL holiday period until nearly a week continuously with lower demand than other holiday usually. Because lack of data, we cannot estimate the grey model of HRL period for Cawang HVST, even the Ciatu HVST had a adequate data in 009. Caused y the temperature data otained only a year, in 009, estimation model could not een executed to the other types of holiday had one day off, called ational holiday such as Hari Waisak, Chinese ew Year, Christmas Day, Independence Day, etc. in which almost totally 5 types in a year. included good grade in model adequacy, as defined in []. Meanwhile, limit of the justified grade adequacy is 0%. For Jakarta area spatially, the proposed grey comination model was used to predict one-hour ahead load value in each location during the same season. From equation (5 and (9, there were 4 hours x 7 days x 4 variael values that would produce 4 sequence sets which are capale for estalishing 4 GM(, models to predict one-workday ahead daily loads and 4 GM(, models to predict one-weekday ahead daily load, respectively in a week. In workday forecasting, one temperature value must e included to incease the last numer of AGO simulated, ( k as initial value, (5. Due to space limitations in this paper. It is practical to present only a representative suset of the load forecasting results. During dry season, oth the forecasted daily load curve were drawn, as shown in Fig.6 and Fig.7, on Sunday August, 009 (representing weekend and on Monday August 4, 009 (representing workday for Cawang and Ciatu HVST, respectively. Likewise in Fig.8 to represent daily load curve during rain season. From these figures, it can e seen that the predicted load agree with the oserved value quite well, and still had forecasting error value (MAPE under the limit of adequacy. B. TEST VALIDATIO Accordance with the proposed scheme, the MAPE of the proposed comination Grey model in tropical climate were showed in Tale III. TABLE III ERROR COMPARISO FOR SPATIAL GREY MODEL I TROPIC CLIMATE MAPE (% DRY SEASO RAI SEASO CAWAG CIBATU CAWAG CIBATU MODAY TUESDAY WEDESDAY THURSDAY FRIDAY SATURDAY SUDAY AVERAGE ERROR Fig.6 CAWAG Daily Load Curve during Dry Season The items of presented tale can compare the implementation of model estimation in particular season for each sustation in Jakarta area. It can e seen that the estimation precision for Cawang HVST has etter accuracy compared to the Ciatu. The adequacy of the Cawang Grey models were tested through the diagnostic checking of residuals, with MAPE values were elow 5%, which were also

6 Fig.7 CIBATU Daily Load Curve during Dry Season (ote: UBAH GAMBAR LAGI IV. COCLUSIOS This paper had proposed the comination grey model ased on GM(, and GM(, to predict one-workday ahead and one-weekend loading distriuted to a local sustation, with specific location in tropical area. GM(, more appropriately used ecause load demand was correlated with temperature rise only in Monday until Friday, whilst not in Saturday and Sunday. We also concluded that the load prediction model in Jakarta area more influenced y energy consumption pattern and the most dominant type of consumer. Oviously, the adequacy of the models had indiced a good grade when their error diagnostic were checked, with average error level still under 0%. If there are incidence of anormal distriution from load control center, i.e. sudden maneuver operations, these forecasting models will not e feasile numerically. The proposed scheme was not also applicale to any holiday factor. Hence in the next study it may e possile that the model y adding a factor, will affect the holiday factor added to the final prediction results. ACKOWLEDGMET This study is one part of thesis, which conducting after UI and ITB link project in 00, i.e. study of the amient temperature effect to the 500/50 kv IBT loading and 500 kv transmission in four local sustations. The authors thankful to Jawa Bali Load Control and Operator Center (PT. PL PB Gandul and all of the project team. Fig.8 CAWAG Daily Load Curve during Rain Season Finally, we had listed one-week ahead load forecasting error of the spatial comination grey method from August to August 9, 009 throughout dry season as descried in TABLE IV for each location, respectively. Likewise the weekly load forecasting error had een conducted from Feruary until Feruari 8 during rain season in 009, as listed in TABLE V. HVST Location TABLE IIV WEEKLY LOAD FORECASTIG ERROR DURIG DRY SEASO Forecasting Validation Error (% Mean Error SU MO TUE WED THU FRI SAT Cawang Ciatu REFERECES [] J. Deng, Introduction to Grey System Theory, The Journal of Grey System, Vol., o., pp. -4, 989. [] E. Wahyudi. Pementukan Model Bean dalam Satu Tahun, PL PB Gandul, 00. [] S. Liu, Y. Lin. Grey Information Theory and Practical Applications. ser. Advanced Information and Knowledge Processing. Verlag, London: Springer, 006. [4] Z. L. Gaing, R. C. Leou. Optimal Grey Topological Predicting Approach to Short-term Load Forecasting in Power System, IEEE Trans. on Power Systems, 00. [5] W. Li, Z. H. Han. Application of Improved Grey Prediction Model for Power Load Forecasting, IEEE Trans. on Power Systems, 008. [6] R. Wang, GM(, Forecasting Method for Day-ahead Electricity Price Based on Moving Average and Particle Swarm Optimization, in Proc.6th International Conf. on atural Computation, ICC, 00. [7] E. Kayacan, B. Ulutas, O. Kaynak, Grey system theory-ased models in time series prediction, Elsevier Journal in Expert Systems with Applications, vol. 7 p , 00. [8] H. T. Yang, T. C. Liang, K. R. Shih, C. L. Huang. Power System Yearly Peak Load Forecasting: A Grey System Modeling Approach, IEEE Catalogue o. 95TH80, 995. TABLE V WEEKLY LOAD FORECASTIG ERROR A WEEK DURIG RAI SEASO HVST Location Forecasting Validation Error (% Mean Error MO TUE WED THU FRI SAT SU Cawang Ciatu