ANN based STLF of Power System


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ANN based STLF of Power System

  1. 1. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 2011 Artificial Neural Network based Short Term Load Forecasting of Power System Salman Quaiyum, Yousuf Ibrahim Khan, Saidur Rahman, Parijat Barman Department of Electrical and Electronic Engineering, American International University – Bangladesh, Banani, Dhaka – 1213.ABSTRACT forecasting applications. These algorithms are better than back- propagation in convergence and search space capability.Load forecasting is the prediction of future loads of a powersystem. It is an important component for power system energy 2. ARTIFICIAL NEURAL NETWORKmanagement. Precise load forecasting helps to make unitcommitment decisions, reduce spinning reserve capacity and An Artificial Neural Network (ANN) is a mathematical orschedule device maintenance plan properly. Besides playing a computational model based on the structure and functionalkey role in reducing the generation cost, it is also essential to the aspects of biological neural networks. It consists of anreliability of power systems. By forecasting, experts can have an interconnected group of artificial neurons, and it processesidea of the loads in the future and accordingly can make vital information using a connectionist approach to computation. Andecisions for the system. This work presents a study of short- ANN mostly is an adaptive system that changes its structureterm hourly load forecasting using different types of Artificial based on external or internal information that flows through theNeural Networks. network during the learning phase.General Terms 2.1 Recurrent Neural NetworkArtificial Intelligence, Neural Networks. A Recurrent Neural Network (RNN) is a class of neural network where connections between units form a directed cycle. Unlike feed-forward neural networks, RNNs can use their internalKeywords memory to process arbitrary sequences of inputs. A recurrentLoad Forecasting, Power System, Particle Swarm Optimization. neural network consists of at least one feedback loop. It may consist of a single layer of neurons with each neuron feeding its1. INTRODUCTION output signal back to the inputs of all the other neurons.Load forecasting is one of the central functions in powersystems operations and it is extremely important for energy In this work, Elman’s recurrent neural network has been chosensuppliers, financial institutions, and other participants involved as the model structure which has shown to perform well inin electric energy generation, transmission, distribution, and comparison to other recurrent architectures [8]. Elman’s networksupply. Load forecasts can be divided into three categories: contains recurrent connections from the hidden neurons to ashort-term forecasts, medium-term forecasts and long-term layer of context units consisting of unit delays which store theforecasts. Short-term load forecasting (STLF) is an important outputs of the hidden neurons for one time step, and then feedpart of the power generation process. Previously it was used by them back to the input layer.traditional approaches like time series, but new methods basedon artificial and computational intelligence have started toreplace the old ones in the industry, taking the process to newerheights.Artificial Neural Networks are proving their supremacy overother traditional forecasting techniques and the most popularartificial neural network architecture for load forecasting is backpropagation. This network uses continuously valued functionsand supervised learning i.e. under supervised learning, the actualnumerical weights assigned to element inputs are determined bymatching historical data (such as time and weather) to desiredoutputs (such as historical loads) in a pre-operational “trainingsession”. The model can forecast load profiles from one to sevendays.Evolutionary algorithms such as, Genetic Algorithm (GA) [1, 2],Particle Swarm Optimization (PSO) [3-5], Artificial ImmuneSystem (AIS) [6], and Ant Colony Optimization (ACO) [7] havebeen used for training neural networks in short term load Fig 1: Elman recurrent neural network topology. 1
  2. 2. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 2011Figure 1 is an Elman recurrent neural network topology where w the leader and each particle keeps track of its coordinates in thedenotes a vector of the synaptic weights, x and u are vectors of problem space. This fitness value is stored which is referred tothe inputs to the layers, m is the number of input variables, and r as pbest. Another “best” value tracked by the particle swarmis the number of neurons in the hidden layer. optimizer, is the best value obtained so far by any particle in the neighbors of the particle. This location is called lbest. When aThe weighted sums for the hidden and the output layers are: particle takes all the population as its topological neighbors, the best value is a global best and is called gbest. (1) (7) (2)where,k = [1,r], n = [1,N], and N is the number of data points (8)used for training of the model. The outputs of the neurons in thehidden layer and output layer are computed by passing the where, Vi is the current velocity, Δt defines the discrete timeweighted sum of inputs through the tan sigmoid and pure linear interval over which the particle will move, ω is the inertiatransfer functions respectively. weight, Vi-1 is the previous velocity, presLocation is the present location of the particle, prevLocation is the previous location ofMathematically, the outputs of the hidden layer and the output the particle and rand( ) is a random number between 0 and 1. c1layer can be defined as: and c2 are the learning factors, stochastic factors and acceleration constants for “gbest” and “pbest” respectively. (3) (4)where,K is a coefficient of the pure linear transfer function.Another training parameter considered is the momentum factoras an attempt to prevent the network to get stuck in a shallowlocal minimum. Equation (5) shows how the synoptic weightsare adjusted and how the network determines the value of theincrement on the basis of the previous value of theincrement (5)The other important training parameter is the learning rate whichcontrols the amount of change imposed on connection weightsduring training and to provide faster convergence.Mathematically, the weights are updated using the equation: (6)where, η is the learning rate. Fig 2: PSO-ERNN Learning Process Figure 2 shows the learning process of PSO-ERNN (Particle3. PARTICLE SWARM OPTIMIZATION Swarm Optimized – Elman Recurrent Neural Network). ThePSO as a tool that provides a population based search procedure learning is initialized with a group of random particles in step 1,in which individuals called particles change their position (state) which are assigned with random PSO positions (weight andwith time. In a PSO system, particles move around in a bias). The PSO-ERNN is trained using the initial particlesmultidimensional search space. During flight, each particle position in step 2. Then, it produces the learning error (particlecarries out position adjustment in accordance to its own fitness) based on initial weight and bias in step 3. The learningexperience, to the experience of a neighboring particle. This error at current epoch is reduced by changing the particleshelps make use of the best position of the particle encountered position, which updates the weight and bias of the network. Theby itself and its neighbor. Thus, a PSO system combines local “pbest” and “gbest” values are applied to the velocity updatesearch methods with global search methods, attempting to according to (7) to produce a value for positions adjustment tobalance exploration and exploitation. the best solution or targeted learning error in step 4. Step 5 has the new sets of positions (weight and bias) produced by addingThe basic concept is that for every time instant, the velocity of the calculated velocity value to the current position value. Then,each particle, also known as the potential solution, changes these new sets of positions are used to produce new learningbetween its pbest(personal best)and lbest(local best) locations. error in PSO-ERNN. This process is repeated until the stoppingThe particle associated with the best solution (fitness value) is 2
  3. 3. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 2011conditions of either minimum learning error or maximum 4. DATA COLLECTION ANDnumber of iterations are met which is shown in step 6. PREPROCESSING3.1 Global best PSO A simple data collection method was employed to ensureGlobal version of PSO is faster but might converge to local adequate historical samples of the load. Load Data used in thisoptimum for some problems. The Local version, though slower work were collected from the Bangladesh Power Developmentdoes not easily get trapped into a local optimum. We Board (BPDB) and ISO New England.implemented the global version to achieve a quicker result. Theposition of a particle is influenced by its best visited position 4.1 Data Scaling Methodsand the position of the best particle in its neighborhood. Data scaling is carried out in order to improve interpretability of network weights. The equation below has been adopted andParticle position, xi, was adjusted using implemented to normalize the historical load data. (9) (12)where the velocity component, vi, represents the step size. The load value is normalized into the range between 0 and 1 andFor the basic PSO, then the neural networks are trained using the suitable algorithm. Neural networks provide improved performance with the normalized data. The use of original data as input to the neural network may increase the possibility of a convergence problem. (10) 4.2 Data Storagewhere, w is the inertia weight, c1and c2 are the acceleration Data can be stored in many ways. In this work, the collectedcoefficients, r1,j, r2,j ~ U(0,1), yi is the personal best position of data was stored in Microsoft Excel worksheets. The worksheetsparticle i, and is the neighborhood best position of particle i. were then imported into MATLAB using the command “xlsread”.If a fully-connected topology is used, then ŷi refers to the bestposition found by the entire swarm. That is, 4.3 Composition of the Input Vector of the prediction models (11) The structure of the input vector specifies the selected endogenous and exogenous variables. In the work of T. Gowriwhere,s is the swarm size. Monohar et al. [9] five inputs were selected from the previous day and five each from the previous weeks on the same dayThe pseudo-code for PSO is shown below: were selected to predict the load of the next day. If data pointsfor each particle i∈ 1,...,s do were insufficient, the forecasting would be poor. If data points were useless or redundant, modeling would be difficult or evenRandomly initialize xi skewed [10]. Set vi to zero The input vector (IV) structure used here, consists of two Set yi = xi previous hours active power values, L(t-1) and L(t-2) and some homologous consumption past load values of the previous weekendfor L(t-168) and L(t-169). The inclusion of these values providesRepeat information regarding the consumption trend in the past for each particle i∈ 1,...,s do homologous periods [11]. It was found that load for 24 hours and 168 hours are highly correlated. The structure of IV is givenEvaluate the fitness of particle i, f(xi) in Figure 3. Update yi Update ŷ using equation (11)for each dimension j∈ 1,...,NddoApply velocity update using (10) endloopApply position update using (9) endloopUntil some convergence criteria is satisfied Fig 3: Composition of the input vector (IV) (non-weather and weather sensitive model) 3
  4. 4. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 2011The ISO New England historical load data was first collectedfrom their website. The load data was taken every hour for aperiod of one week. The training data was defined fromMonday, 31st March till 6th April, 2008 and the correspondingtarget was defined for the period from 7th to 13th April, 2008.The models were also evaluated for generalization capability,thus testing data set was defined from the first week of March3rd to 9th. After correlation analysis, Dry Bulb and Dew Pointtemperatures were used as the input for the Elman WeatherSensitive Model.5. SIMULATION AND RESULTSFor evaluating our proposed load forecast model, several neuralnetwork architectures were implemented in MATLAB version7.10.0.499 (R2010a). Feed Forward Network and ElmanRecurrent Network – these two networks were implanted Fig 4(a): The performance goal metaccording to their default architectures as provided inMATLAB. In addition, Jordan Recurrent Network was created Load Forecasting: Day Modelusing the custom network creation process. Before starting the 4900training of the networks, each layer was individually initialized Actual load values Predicted load valuesusing the initnw function. 4800Then each model was trained using traingdx (Gradient descentwith momentum and adaptive rule backpropagation) training 4700algorithm with the help of Neural Network Training tool. Afterthat each network was simulated and their performance was Load [MW] 4600observed. Finally, Elman Network was trained using ParticleSwarm Optimization method. Mean Square Error (MSE) 4500performance measure function was employed along with otherfunctions like MPE (Mean Percentage Error) and MAE (MeanAbsolute Error). 4400 (13) 4300 1 2 3 4 5 6 7 Day (14) Fig 4(b): Forecasting Result of the maximum demand (15) -3 x 10 Network Error 0where, Lactual (n) is the actual load, Lpredicted (n) is the forecastedvalue of the load, and N is the number of data points. -0.55.1 Daily Maximum Demand PredictionFor maximum demand prediction, the data that was collected -1from BPDB was insufficient for training of the network using Errortraingdx. Therefore, the network was trained using trainlm -1.5(Levenberg-Marquardt backpropagaton). This networkperformed better – it achieved smaller MSE than the networktrained with traingdx. -2 -2.5 1 2 3 4 5 6 7 Day Fig 4(c): Actual Network Error 4
  5. 5. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 20115.2 Forecasting with ISO New England Load 4 x 10 -3 Network ErrorData 4 3 x 10 168 hours ahead STLF using training data 1.8 Actual load values 2 1.7 Predicted load values 1.6 1 Error 1.5 0 Load [kW] 1.4 -1 1.3 -2 1.2 1.1 -3 1 0 20 40 60 80 100 120 140 160 180 -4 Time [hrs] 0 20 40 60 80 100 120 140 160 180 Time [hrs] Fig 4(d): Output of Feedforward Network Fig 4(g): Network Error (Elman) -3 x 10 Network Error 4 5.3 Particle Swarm Optimized Elman 3 Recurrent Neural Network (PSO-ERNN) -4 2 x 10 average error 1 error goal Error 0 3 -1 Performance 2 -2 -3 1 -4 0 20 40 60 80 100 120 140 160 180 Time [hrs] 0 0 0.5 1 1.5 2 2.5 3 Fig 4(e): Network Error (Feedforward) Epochs Fig 4(h): The performance goal met 4 x 10 168 hours ahead STLF using training data 4 x 10 168 hours ahead STLF using training data 1.8 1.8 Actual load values Actual load values 1.7 Predicted load values Predicted load values 1.7 1.6 1.6 1.5 1.5 Load [kW] Load [kW] 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1 1 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Time [hrs] Time [hrs] Fig 4(i): Output of PSO-ERNN Fig 4(f): Output of Elman Network 5
  6. 6. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 2011 Network Error For future works, the error in the network can be further reduced 0.02 if a larger dataset is used for network training. Also, the load forecasting model can be improved by including other weather 0.015 parameters like temperature, wind speed, rainfall etc. 0.01 7. ACKNOWLEDGMENT 0.005 We would like to thank Engr. K. M. Hassan, CSO, BPDB for 0 providing us with necessary information. Error -0.005 8. REFERENCES [1] Heng, E.T.H., Srinivasan, D., Liew, A.C., “Short term load -0.01 forecasting using genetic algorithm and neural networks”, -0.015 Energy Management and Power Delivery, 1998. Proceedings of EMPD 98. 1998 International Conference -0.02 on, Volume 2, 3-5 March 1998, Page(s):576 - 581 vol.2. -0.025 [2] Worawit, T., Wanchai, C., “Substation short term load 0 20 40 60 80 100 120 140 160 180 Time [hrs] forecasting using neural network with genetic algorithm”, TENCON 02. Proceedings. 2002 IEEE Region 10 Conference on Computers, Communications, Control and Fig 4(j): Network Error (PSO-ERNN) Power Engineering; Volume 3, 28-31 Oct. 2002, Page(s):1787 - 1790 vol.3. Table 1: Comparison between different network [3] Azzam-ul-Asar, ul Hassnain, S.R., Khan, A., “Short term performances load forecasting using particle swarm optimization based Network Training MSE MAE MPE ANN approach”, Neural Networks, 2007. IJCNN 2007. Epoch International Joint Conference on ; 12-17 Aug. 2007, Feedforward 8 2.0351e-6 0.0012 0.0011 Page(s):1476 – 1481. Jordan 3 4.6124e-6 0.0018 0.0021 [4] Wei Sun, Ying Zou, Machine Learning and Cybernetics, Elman 7 1.868e-6 0.0012 9.1269e-4 “Short term load forecasting based on BP neural network Elman (WS) 8 2.3895e-6 0.0013 1.8288e-8 trained by PSO”, 2007 International Conference on; PSO-ERNN 3 1.6296e-5 2.6042e-3 7.1934e-3 Volume 5, 19-22 Aug. 2007, Page(s):2863 – 2868. [5] Bashir, Z.A., El-Hawary, “Short-term load forecasting using artificial neural network based on particle swarmFrom the above table, it can be seen that PSO-ERNN is faster optimization algorithm”, Electrical and Computerbut slightly more prone to errors (with MSE); but this model Engineering, 2007. CCECE 2007. Canadian Conferencecould outperform others if more data sets were used. This on; 22-26 April 2007, Page(s):272 – could handle large amount of data in a short amount oftime. The Elman Weather sensitive model performs better but it [6] You Yong, Wang Sunan, Sheng Wanxing, “Short-termtakes longer time than Simple Elman network. Dry bulb and load forecasting using artificial immune network”, Powerdew point temperatures had a very weak correlation with the System Technology, 2002. Proceedings. PowerCon 2002.load, so their presence did not have any significant effect on International Conference on; Volume 4, 13-17 Oct. 2002,forecasting. Providing different weather parameters would have Page(s):2322 - 2325 vol.4.definitely increased the network performance. Overall this tableshows that there is always a trade-off between the networks and [7] Chengqun Yin, Lifeng Kang, Wei Sun, “Hybrid neuraldepends on the amount of data, quality of data, time required network model for short term load forecasting”, Thirdand most importantly design requirements and designers. International Conference on Natural Computation, 2007. [8] Almedia L.B. et al., “Parameter adaptation in stochastic6. CONCLUSION optimization”, On-line learning in neural Networks (Ed. D.Several neural network models for short-term load forecasting Saad), Cambridge University Press, 1998.were studied in this work. According to the discussion and thecomparison of model forecast accuracy shows that Particle [9] T.Gowri Monohar and V.C. Veera Reddy, “LoadSwarm Optimized Elman Recurrent Neural Network (PSO- forecasting by a novel technique using ANN”, ARPNERNN) is the best model for 168 hours ahead load forecasting. Journal of Engineering and Applied Sciences, VOL. 3, NO.This type of network can be very efficient in terms of predicting 2, April 2008.future loads. [10] Lendasse, J. Lee, V. Wertz, M. Verleysen, “Time SeriesThough the simulations seemed very promising, the models Forecasting using CCA and Kohonen Maps - Applicationdeveloped here still need to be tested on data sets from other to Electricity Consumption”, ESANN2000 proceedings -sources, so that reliability of these models can be verified for European Symposium on Artificial Neural Networksother load patterns. Bruges (Belgium), 26-28 April 2000, D-Facto public., ISBN 2-930307-00-5, pp. 329-334. 6
  7. 7. International Journal of Computer Applications (0975 – 8887) Volume 30– No.4, September 2011[11] P.J. Santos, A.G. Martins, A.J. Pires, J.F.Martins, and R.V. Illam Region”, International Journal of Electrical, Mendes, "Short Term load forecast using trend information Computer, and Systems Engineering, Volume 1, 2007, and process reconstruction”, International Journal of pp.1307-5179. Energy Research, 2006; 30:811-822. [15] T.Gowri Monohar and V.C. Veera Reddy, “Load[12] Simaneka Amakali, "Development of models for short-term forecasting by a novel technique using ANN”, ARPN load forecasting using artificial neural networks", Cape Journal of Engineering and Applied Sciences, VOL. 3, NO. Peninsula University of Technology Year, 2008. 2, April 2008.[13] Ayca Kumluca Topalli, Ismet Erkme, and Ihsan Topalli, [16] George I Evers, “An automatic regrouping mechanism to “Intelligent short-term load forecasting in Turkey”, deal with stagnation in particle swarm optimization”, International Journal of Electrical Power & Energy Graduate thesis for the degree of Master of Science, Systems, Volume 28, Issue 7, September 2006, pp. 437- University of Texas-Pan American, pp. 35-40, 2009. 447. [17] S. Sumathi, Surekha P., “Computational Intelligence[14] Mohsen Hayati and Yazdan Shirvany, “Artificial Neural Paradigm: Theory and application using MATLAB”, CRC Network Approach for ShortTerm Load Forecasting for Press, 2010. 7