New Particle Swarm Neural Networks Model Based Long Term Electrical Load Forecasting in Slovakia

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1 New Particle Swarm Neural Networks Model Based Log Term Electrical Load Forecastig i Slovakia S.H. OUDJANA 1, A. HELLAL 2 1, 2 Uiversity of Laghouat, Departmet of Electrical Egieerig, Laboratory of Aalysis ad Cotrol of Eergy Systems ad Electrical Systems, LACoSERE, Laghouat 03000, ALGERIA samirehamid@yahoo.fr Abstract: - Log-term load forecastig accuracy is very importat for electrical power systems. This paper explores the applicatio of ew model usig eural etworks (NN) ad Particle Swarm Optimizatio (PSO) to study the desig of load forecastig systems for may years ahead usig historical loads databases of Slovakia power systems. I this study, istead of the method of back-propagatio of the gradiet, the optimizatio techique by swarms of particles is well tested for traiig eural etwork that optimizes the forecast error. Simulatios were ru ad the results are discussed showig that New Hybrid Techique (PSO-NN) is capable to decrease the load forecastig error. Key-Words: - Load Forecastig, Neural Networks, Particle Swarm Optimizatio 1 Itroductio The load forecastig is a importat costituet for the maagemet power system utility. It helps the electricity producer to make the right decisio to uit commitmet ad reduce the use of reserves. Thus it plays a key role i reducig the cost of electric geeratio ad remais essetial for the reliability of the power system. It is therefore extremely importat for the geeratio trasmissio ad distributio of electric eergy ad the eergy market [1]. Sice the profile of eergy productio of the ext day must be iteded for every day, the Load Forecastig of the ext day is a daily task dispatchig ceter. The forecast error affects a lot of ecoomic operatios ad the profitability of the power system. For example, a icrease of predictio error of 1% i Britai causes the icreased cost of 10 millio pouds per year [2]. The results obtaied from load forecastig process are used i plaig ad operatio. Logterm load forecastig, oe to te years ahead mothly ad yearly values, is applied i expasio plaig, iter-tie tariff settig ad log-term capital ivestmet retur problems [3]. Electricity cosumptio varies depedig o several parameters, the mai oes is seasoality climate ad electricity prices. Other explaatory variables are: exceptioal evets ca disrupt the patter of cosumptio (eg. witer storms, fial world cup of football), but their impact is impossible to predict. The methods used to solve the load forecastig problem ca be maily divided ito two categories: statistical methods ad artificial itelligece methods. The artificial itelligece methods are flexible i fidig the relatioship betwee the load ad its related factors, particularly for load forecastig of aomalous days. The artificial eural etworks (ANN) do ot require huma experiece ad are ot iteded to establish a relatioship betwee the iput ad output observed. The priciple of NNs is to establish the load profile from the traiig based o historical data, amog the differet methods of traiig. The most widely used for the load forecastig is the method of backpropagatio of error based o the gradiet method [4.8], except that sometimes the back propagatio method falls ito the local miima of the squared errors. It is therefore ecessary to fid a optimizatio techique capable of reachig the global miimum of the forecast error, istead of the back-propagatio method. The techique of particle swarm optimizatio (PSO) is tested for traiig the eural etwork that optimizes the forecast error [1,2] [9,10]. Our paper cotributio is applied ad validates the performace of hybrid techique PSO-NN of ew models usig historical data of yearly electricity cosumptio from Slovakia power systems utility, these data provided by Europea Network of Trasmissio System Operators for Electricity (ENTSOE) [11]. E-ISSN: Volume 15, 2018

2 2 Neural Networks From the begiig of ieties, ew techiques appear to study the electrical load forecastig such as artificial eural etworks. These recet techiques quickly became widely used i shortterm load forecastig. The mathematical model of a artificial euro (Fig.1) cosists essetially of a itegrator that performs a weighted sum of its iputs. The result of this sum is the trasformed by a trasfer fuctio f which produces the output of a euro. The R iput euros correspod to the vector P = [p 1. p 2.. p R ] T. Whereas W = [w 11. w 12.. w 1R ] T represets the vector of the weights of the euro, ad b is a bias. The output of the itegrator is give by the followig equatio: R 1, j j (1) j 1 w p b To formalize this movemet i more detail, we ca put it that way for each particle: v i k+1 = wv i k + c 1 rad 1 pbest x i k + c 2 rad 2 (gbest x i k ) (3) x i k+1 = x i k + v i k+1 K: Number of iteratio x : Particle positio v : Particle velocity pbest: Best positio of the particle gbest: Global best of all the particles of Swarm w: Weightig fuctio c 1. c 2 : Weightig factor rad : Radom umbers. uiform distributio o [0. 1] Weightig fuctio is give by: (4) w = w max w m ax w m i k m ax k (5) w mi : Iitial weight w max : Fial weight k max : Maximum umber of iteratios Fig. 1 Model of a artificial euro 3 Particle Swarm Optimizatio Particle swarm optimizatio is a metaheuristic based o the model developed by C. REYNOLDS i the late 1980's to simulate the movemets of a group of bird ideed i some aimal groups like group of fish. We ca observe the dyamics of relatively complex movemets while the idividual themselves have access to oly limited iformatio, such as positio ad velocity from their earest eighbors, we ca observe such a group of fish is able to avoid a predator. A swarm is composed of may particles. The size ca be dyamic: if o particle of the swarm improves the solutio. We ca geerate other ad ca also remove them. Each particle i is characterized by its positio x i ad a velocity vector v i. At each iteratio. The particle moves as followig: x i (t) = x i t 1 + v i (t 1) (2) 4 Load Forecastig by Usig PSO-NN The traiig of artificial eural etworks is a importat phase which is used to adjust the bias ad the syaptic weights so that the square error betwee the desired value (target) ad forecastig value is miimum as possible. Amog the differet methods of traiig, the most widely used for the load forecastig is the method of back-propagatio based o the gradiet method, except that sometimes the back-propagatio method falls i local miima of squared errors. It is therefore ecessary to fid a optimizatio techique capable of reachig the global miimum of the forecast error. Istead of the method of backpropagatio of the gradiet, the optimizatio techique by swarms of particles is well tested for traiig eural etwork that optimizes the forecast error. The database of this model depeds o historical load data frome 1998 util 2005, so the load of the previous year is used to forecast the actuel load, this model ca be used to forecast six yearly loads ahead. E-ISSN: Volume 15, 2018

3 4.1 Algorithm of the method The procedure of the techique is preseted as follows: iitialize swarm with radom v ad positio x iitialize w. c 1. c 2 k : umber of iteratio begi x k i : Positio of a particle pbest i : Persoal best positio of i th particle v k i : velocity of i th particle gbest: global best of all the particles of swarm Calculate the value of the load Calculate the mea square error MSE for each particle i the swarm as follows: MSE = 1 (L d i L i ) 2 (6) i=1 Where is the umber of examples of the traiig set. L d i is the desired load. ad L i is the expected load For each particle i i the swarm: If (x k i < pbest i ) The k pbest i = x i If (pbest i < gbest) The gbest = pbest i Positio ad velocity are the updated as per the followig equatios: v k+1 i = wv k k i + c 1 rad 1 pbest x i + c 2 rad 2 (gbest x k i ) x k+1 i = x k k+1 i + v i best idividual from swarm is chose as the output Ed Parameters chose for the PSO optimizatio techique: 5 Simulatios To validate the hybrid techique PSO-NN i terms of the mea relative error, we must test multiple databases ad techiques. To do this, we used databases based o historical data of yearly electricity cosumptio from 1998, the we compare betwee NN techique, ad proposed hybrid techique PSO-NN. The performace of techique is verified by the mea absolute relative error MAPE. Table 1 ad 2 represet the desired ad forecast load, ad the values of the mea absolute relative error, usig two differet techiques. Fig. 2 illustrate the aual load profile of Slovakia electrical power system. The NN ad PSO-NN models are preseted i Fig. 3 ad 4 respectively. Due to the idustriel developmet, ad ecoomic growth i Slovakia, the request eergy is icreased. We get forecastig error less tha 10%, witch be acceptable i log-term load forecastig. The PSO- NN model is better tha NN model, i term of forecastig error, the forecastig error usig PSO-NN model is 5,04% (Table 2). So the correlatio betwee the curret ad previous yearly loads is stregth, ad the perfermaces of hybridatio techique PSO-NN are satisfaisat. The hybrid techique of the eural etwork with particle swarm optimizatio applied to log-term load forecastig give the acceptable values of forecastig error. These values iflueced by the impact factor o load such as temperature ad the historic loads, furthermore the parameters of the PSO techique ad the activatio fuctio of eural etwork ca be chage the forecastig error. MSE: Objective fuctio wmax = 0.9: Iitial weight. wmi = 0.4: Fial weight. imax = 100: Maximum umber of iteratios c1 = c2 = 2: Weightig factor. id = 10: Swarm size. To verify the performace of this forecastig techique, we ca calculate the mea absolute percetage error: MAPE = 100 t=1 L t L t L t (7) L t : Desired load L t : Forecast load : Number of patters Fig. 2 Slovakia Aual Load Curve E-ISSN: Volume 15, 2018

4 Table 1. Load forecastig usig NN Year Actual (GWh) Forecast (GWh) MAPE (%) 5,43 Table 2. Load forecastig usig PSO-NN Year Actual (GWh) Forecast (GWh) MAPE (%) 5,04 6 Coclusio The load forecastig i electrical power system is a essetial task for decisio makig by the dispatch ceter that is cocered to esure etwork security by meetig the balace betwee supply ad demad of electricity while havig a maagemet reliable ad cost effective productio system. Before validatig the performace of ay model, the eural etwork must be traied by the learig phase. Amog the methods of traiig, the method of back-propagatio of error based o the gradiet method, which adapts the weights ad biases so that the square error betwee the desired ad expected output must be small, except that this method fall i the local miimum of error, ad to this raiso, we replaced this method by the techique of particle swarm optimizatio PSO able to fid the global miimum error durig the traiig phase. The work iitiated i this article aimed to apply the hybridizatio method of eural etwork techique with the techique of particle swarm optimizatio PSO-NN to may years ahead predictio of electricity cosumptio i Slovakia. The PSO-NN forecastig model deped oly o prévious loads ad it is better ad more accurately tha NN model, so the electricity cosumptio is ot oly affected by the temperature, but also it chage by historical loads. This techique is useful for solvig the problem of load forecastig. Refereces: Fig. 3 Actual ad forecast load usig NN model Fig. 4 Actual ad forecast load usig PSO-NN model [1] Sadjib, M. Short term load forecastig usig computatioal itelligece methods, Master Thesis. Natioal Istitute of Techology of Rourkela, [2] Vicet, L. Modèles semi-paramétriques appliqués à la prévisio des séries temporelles Cas de la cosommatio d électricité, PhD Thesis, Uiversité Rees 2, [3] AlRashidi, M.R.- EL-Naggar, K.M. Log term electric load forecastig based o particle swarm optimizatio, Applied Eergy, 87, No. 1, 2010, pp [4] Park, D.C - El-Sharkawi, M.A. Marks, R.J.- Atlas, L.E- Damborg, M.J. Electric load forecastig usig a artificial eural etwork, IEEE Tras. o Power Systems, Vol. 6, 1991, pp [5] Lee, K..Y.- Tae, C. - Chao, C.K. Jue, H.P. Neural etwork architectures for short-term E-ISSN: Volume 15, 2018

5 load forecastig, Neural Networks. IEEE World Cogress o Computatioal Itelligece, Vol. 7, 27 Jue -2 July,1994, pp [6] Bakirtzis, A.G. - Petridis, V. - Kiartzis, S.J. - Alexiadis, M.C. - Maissis, A.H. - A eural etwork short term load forecastig model for the Greek power system., IEEE Tras. o Power Systems, Vol. 11. No. 2, 2012, pp [7] Hogbi, W. - Wei, l.c. Load Forecastig for Electrical Power System Based o BP Neural Network, First Iteratioal Workshop o Educatio Techology ad Computer Sciece, 2009, pp [8] Maoj, K. Short-term load forecastig usig artificial eural etwork techiques, Bachelor of techology, Natioal Istitute of Techology of Rourkela, [9] Zhag, C. Li, M. Tag, M. BP Neural Network Optimized with PSO Algorithm for Daily Load Forecastig, Iteratioal Coferece o Iformatio Maagemet, Iovatio Maagemet ad Idustrial Egieerig. Vol. 3, (19-21Dec 2008), pp [10] Vicet, G. Optimisatio par Essaim Particulaire, Mémoire Adaptative et Recherche Tabou. PhD Thesis, Uiversité Rees 2, 2008 [11] E-ISSN: Volume 15, 2018