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

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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

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