An Application of Genetic Programming for Power System Planning and Operation

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This work incorporates the identification of model …

This work incorporates the identification of model
in functional form using curve fitting and genetic programming
technique which can forecast present and future load
requirement. Approximating an unknown function with
sample data is an important practical problem. In order to
forecast an unknown function using a finite set of sample
data, a function is constructed to fit sample data points. This
process is called curve fitting. There are several methods of
curve fitting. Interpolation is a special case of curve fitting
where an exact fit of the existing data points is expected.
Once a model is generated, acceptability of the model must be
tested. There are several measures to test the goodness of a
model. Sum of absolute difference, mean absolute error, mean
absolute percentage error, sum of squares due to error (SSE),
mean squared error and root mean squared errors can be used
to evaluate models. Minimizing the squares of vertical distance
of the points in a curve (SSE) is one of the most widely used
method .Two of the methods has been presented namely Curve
fitting technique & Genetic Programming and they have been
compared based on (SSE)sum of squares due to error.

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  • 1. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012 An Application of Genetic Programming for Power System Planning and Operation R.Behera1, B.B.Pati2, B.P.Panigrahi2, S. Misra 1, 3 Department of Electrical Engineering I.G.I.T.Sarang, Orissa; India b_rabindra@yahoo.co.in 2, 4 Department of Electrical Engineering VSSUT Burla, Orissa, IndiaAbstract: This work incorporates the identification of model determine future fuel requirements. Thus a good forecastin functional form using curve fitting and genetic programming reflecting the present and future trend is key to all planning.technique which can forecast present and future load D.K.Chaturvedi & R.K.Mishra (1995) [3] presented therequirement. Approximating an unknown function with Genetic Algorithm approach for long term load forecasting.sample data is an important practical problem. In order to For load forecasting the results obtained through geneticforecast an unknown function using a finite set of sampledata, a function is constructed to fit sample data points. This algorithm is compared With the result given by APS(Annualprocess is called curve fitting. There are several methods of Power Survey) carried out by CEA(Central Electricitycurve fitting. Interpolation is a special case of curve fitting Authority).Genetic Algorithms claims to provide near optimalwhere an exact fit of the existing data points is expected. solution or optimal solution for computationally intensiveOnce a model is generated, acceptability of the model must be problems.tested. There are several measures to test the goodness of a Dr. Hanan Ahmad Kamal (2002) [4] focused on techniquemodel. Sum of absolute difference, mean absolute error, mean of solving curve fitting problems using genetic programmingabsolute percentage error, sum of squares due to error (SSE), Curve Fitting problems used to be solved by assuming themean squared error and root mean squared errors can be used equation shape or degree then searching for the parameterto evaluate models. Minimizing the squares of vertical distanceof the points in a curve (SSE) is one of the most widely used values as done in regression techniques. This papermethod .Two of the methods has been presented namely Curve demonstrates that Curve Fitting problems can be solved usingfitting technique & Genetic Programming and they have been GP without need to assume the equation shape. Objectcompared based on (SSE)sum of squares due to error. oriented technique has been used to design and implement a general purpose GP engine.Key words: Power System Planning, Load Forecasting, Curve M. A. Farahat and M. Talaat (2010) [6] presented a NewFitting, Genetic Algorithm, Mutation, Fitness Function. Approach for Short-Term Load Forecasting Using Curve Fitting Prediction Optimized by Genetic Algorithms Curve I. INTRODUCTION fitting prediction and time series models are used for hourly One of the primary power system planning tasks of an electric loads forecasting of the week days. It is shown that theutility is to accurately predict load requirements at all times. proposed approach provide very accurate hourly loadResults obtained from load forecasting process are used in forecast. Also it is shown that the proposed method candifferent areas such as planning and operation. Planning of provide more accurate results. The mean percent relative errorfuture investment for the constructions depends on the of the model is less than 1 %. actual data. The ANN model isaccuracy of the long term load forecasting considerably then used to forecast the annual peak demand of a Middletherefore, several estimation methods have been applied for Eastern utility up to the year 2006.short, mid and long term load forecasting. Conventional load Khaled M. EL-Naggar (2005) [2] which presents a paperforecasting techniques are based on statistical methods. which describe the comparison of three estimation techniquesStochastic time series, non-parametric regression models used for peak load forecasting in power systems. The threewere used in load forecasting. Also soft computing techniques optimum estimation techniques are, genetic algorithms (GA),were used as load estimator, such as recurrent neural net least error squares (LS) and, least absolute value filteringwork of ANN model [8]. The estimation of load in advance is (LAVF). The problem is formulated as an estimation problem.commonly known as Load Forecasting. Power system Different forecasting models are considered.expansion planning starts with a forecast of anticipated future Azadeh, S.F. Ghaderi and S. Tarverdian (2006) [7] pre-load requirement. The estimation of both demand & energy sents a genetic algorithm (GA) with variable parameters torequirement is crucial to an effective system planning. forecast electricity demand using stochastic procedures. TheDemand predictions are used for determining the generation, GA applied in this study has been tuned for all the GA param-capacity transmission and distribution system additions [3]. eters and the best coefficients with minimum error are finallyLoad forecasting is also used to establish policies for found, while all the GA parameter values are tested together.constructions, capital energy forecast which are needed to The estimation errors of genetic algorithm model are less© 2012 ACEEE 15DOI: 01.IJCSI.03.02.59
  • 2. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012than that of estimated by regression method. Finally, analy- III. GENETIC PROGRAMMINGsis of variance (ANOVA) was applied to compare genetic Genetic programming is an extension of the geneticalgorithm, regression and actual data Zargham Hayadri (2007) algorithm in which the structures in the population are not[1] presented a Time-Series Load Modeling and Load Fore- fixed-length character strings that encode candidate solutionscasting Using Neuro-Fuzzy Techniques. In this method, en- to a problem, but programs that, when executed, are theergy data of several past years is used to train an Adaptive candidate solutions to the problem. Genetic programming isNetwork based on Fuzzy Inference System (ANFIS). ANN a domain-independent method that genetically breeds astructure of ANFIS can capture the power consumption pat- population of computer programs to solve a problem.terns, while the fuzzy logic structure of ANFIS performs sig- Moreover, genetic programming transforms a population ofnal trend identification computer programs into a new generation of programs by John R. Koza et al.,(1994) [17] presented the survey of applying analogs of naturally occurring genetic operationsgenetic algorithm and genetic programming where both iteratively .This process is illustrated in Fig 3.1.method has been compared and their represented scheme ofsolutions has been deeply focused. Zhu Huan-rong et al (2010) [18] uses the geneticprogramming(GP) method to establish the mathematical modelof load forecasting to meet certain precision required underthe conditions of a particular time in the future developingtrend of the load to make estimates and assumptions ofscience. considering the meteorological factors on the impactof electricity load. Edgar Manuel Carreno (2011) [21] formulated a paperwhich forecast a spatial electric load using cellular automationapproach The most important features of this method aregood performance, few data and the simplicity of the algorithm, Fig 3.1 Main Loop of genetic programmingallowing for future scalability. The approach is tested in areal system from a mid-size city showing good performance. A. Genetic RepresentationResults are presented in future preference maps. The programs are represented in a tree form in GP, which is the most common form, and the tree is called program tree II. LONG TERM LOAD FORECASTING (or parse tree or syntax tree). Some alternative program This is done for 1-5 years in advance in order to prepare representations include finite automata (evolutionarymaintenance schedule of generating units, planning future programming) and grammars (grammatical evolution). Forgeneration capacity, entering into an agreement for energy example, the simple expression min(x/5y, x+y) is representedinterchange with neighboring utilities. There are two as shown in Figure 3.2. The tree includes nodes (which areapproaches namely, also called points) and links. The nodes indicate the instructions to execute. The links indicate the arguments forA. Peak Load approach each instruction. In the following, the internal nodes in a treeIn this simple approach is to extrapolate the trend curve, will be called functions, while the tree’s leaves will be calledwhich is obtained by plotting the past values of annual peak terminals. The trees and their expressions in geneticagainst year of operation. The following analytical function programming can be represented using prefix notation (e.g.,can be used to determine the trend curve [13]. as Lisp S-expressions). A basic idea of lisp programs is(i) Straight Line required to understand the representations and programming of genetic programming. In prefix notation, functions always(ii) Parabola precede their arguments. In this notation, it is easy to see the(iii) Polynomial curve correspondence between expressions and their syntax trees.y represents peak load and x represents time in years. The Simple recursive procedures can convert prefix-notationmost common method of finding coefficient is the expressions into infix-notation expressions and vice versa.least square curve fitting technique.B. Energy approach Another method is to forecast annual sales to differentclass of customers like residential, commercial industrial etcwhich can be converted to annual peak demand using annualload factor Fig 3.2 Basic Tree-Like Program Representation Used in Genetic Programming© 2012 ACEEE 16DOI: 01.IJCSI.03.02.59
  • 3. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012The choice of whether to use such a linear representation or programs. A run of genetic programming is a competitivean explicit tree representation is typically guided by ques- search among a diverse population of programs composedtions of convenience, efficiency, the genetic operations be- of the available functions and terminals.ing used (some may be more easily or more efficiently imple-mented in one representation), and other data one may wishto collect during runs. These tree representations are themost common in GP, e.g., numerous high-quality, freely avail-able GP implementations use them.B. Genetic Programming Methodology Genetic programming starts with a primordial ooze ofthousands of randomly created computer programs. Thispopulation of programs is progressively evolved over a seriesof generations. The evolutionary search uses the Darwinianprinciple of natural selection (survival of the fittest) andanalogs of various naturally occurring operations, includingcrossover (sexual recombination), mutation, gene duplication,gene deletion. In addition, genetic programming canautomatically create, in a single run, a general (parameterized)solution to a problem in the form of a graphical structurewhose nodes or edges represent components and where the Fig 3.4 Functionality of Genetic Programmingparameter values of the components are specified by C. Benefits Of Genetic Programmingmathematical expressions containing free variables. That is,genetic programming can automatically create a general A few advantages of genetic programming are:solution to a problem in the form of a parameterized topology. (i) Without any analytical knowledge accurate results are obtained. Preparatory Steps Of Genetic Programming: (ii) If fuzzy sets are encoded in the genotype, new and more Genetic programming starts from a high-level statement suited fuzzy sets are generated to describe precise andof the requirements of a problem and attempts to produce a individual membership functions. This can be done by meanscomputer program that solves the problem. The human user of the intersection and/or union of the existing fuzzy sets.communicates the high-level statement of the problem to the (iii) Every component of the resulting GP rule-base is relevantgenetic programming system by performing certain well- in some way for the solution of the problem. Thus nulldefined preparatory steps. The five major preparatory steps operations that will expend computational resources atfor the basic version of genetic programming require the runtime are not encoded.human user to specify. (iv) This approach does scale with the problem size. Somei. The set of terminals (e.g., the independent variables of the other approaches to the cart-centering problem use a GAproblem, zero-argument functions, and random constants) that encodes NxN matrices of parameters. These solutionsfor each branch of the to-be-evolved program, work badly as the problem grows in size (i.e., as N, increases).ii. The set of primitive functions for each branch of the to-be- (v) With GP no restrictions are imposed on how the structureevolved program, of solutions should be. Also the complexity or the number ofiii. The fitness measure (for explicitly or implicitly measuring rules of the computed solution is not boundedthe fitness of individuals in the population), D. Applications Of GPiv. Certain parameters for controlling the runv. The termination criterion and method for designating the There are numerous applications of genetic programming.result of the run. Some of them are: i. Black Art Problems ii. Programming The Unprogrammable (PTU iii. Commercially Useful New Inventions (CUNI) iv. Optimal Control Fig 3.3 Preparatory steps of Genetic Programming IV. RESULTS & DISCUSSIONThe figure below shows the five major preparatory steps forthe basic version of genetic programming. The preparatory Accurate load forecasting holds a great saving potentialsteps (shown at the top of the figure) are the human supplied for electric utility corporations since it determines its maininput to the genetic programming system. The computer source of income, particularly in the case of distributors.program (shown at the bottom) is the output of the genetic Precise load forecasting helps the electric utility to make unitprogramming system. The first two preparatory steps specify commitment decisions, reduce spinning reserve capacity andthe ingredients that are available to create the computer schedule device maintenance plan properly. It is therefore© 2012 ACEEE 17DOI: 01.IJCSI.03.02. 59
  • 4. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012necessary that the electricity generating organizations should the model for its accuracy. Here power model is selected, itshave prior knowledge of future demand with great accuracy. coefficient is calculated .The year is normalized and is takenSome data mining algorithms play the greater role to predict from numerical value one and so on. Though power model isthe load forecasting. This research work examines and nonlinear in nature, it can be converted to linear by takinganalyzes the use of Curve Fitting Techniques and Genetic logarithmic both sides .Though this model suffers from highProgramming (GPLAB) as forecasting tools for predicting error rate .This model is selected only to make suitablethe energy demand for three years ahead and comparing the comparison. While comparing table 5.3 and table 5.7 it isresults. Various case studies has been taken from specific found that SSE of polynomial model is less as compared toareas and energy consumption forecasting has been power model. Moreover RMSE of polynomial model is betterpresented using tools mentioned above. than the power model. By incorporating the values of independent variable andA. Case Study the calculated coefficient in equations the values of Energy consumption for has been taken from Turkey dependent values can be found. Hence the forecasted valuesbased power utilities started from year 1994 to 2005. Based of demand can be calculated both for the current and futureupon this future energy consumption has been forecasted years respectively.up to year 2012.In this study, power consumption data is Power Model :The equation found for power model isprocessed with both conventional regression analysis and (4.2)genetic programming techniques.. Curve fitting tool ofMATLAB (cftool) is used for conventional regression and TABLE IV.4 CALCULATED COEFFICIENTS OF POWER MODELGPLAB Toolbox for MATLAB is used for applying geneticprogramming. Curve fitting tool of MATLAB can be used tofit data using polynomial, exponential, rational, Gaussian andother equations. It also provides statistics to evaluate the TABLE IV.5 MEASURES OF G OODNESS OF FIT FOR POWER MODELgoodness of a fit produced. GPLAB is a free, highlyconfigurable and extendable genetic programming toolboxsupporting up-to-date features of the recent geneticprogramming research. Curve fitting tool is used forcomparison with the genetic programming application. Among GP Model :Using Symbolic regression both parameters &the different types of the fit, a 4th degree polynomial and a Symbolic model is found for long term energy consumptionpower equation the following form has produced the best forecasting. For this GPLAB Program has been run for 800results. Coefficients are calculated with 95% confidence generations and population size of 100. It has fitness valuebounds. Using Curve Fitting and GP techniques the model 599396247.98.The function found for symbolic regression atfound for long term demand forecasting is as follows: Generation 752 . TABLE IV.1 ENERGY CONSUMPTION DATA OF TURKEY BASED POWER UTILITYThe equation found for 4th degree polynomial model is TABLE IV.2 CALCULATED COEFFICIENTS OF A 4TH DEGREE POLYNOMIAL MODEL Fig 4.1 Output of polynomial model & it’s Residual Table IV.3 Measures of Goodness of fit for polynomial modelHere independent variable is taken as year and demand asthe dependent variable. Functional form is found which bestdescribes the data while minimizing the error. In conventionalregression a model is selected in form of polynomial equation.The above table shows the various measures of checking© 2012 ACEEE 18DOI: 01.IJCSI.03.02.59
  • 5. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012 TABLE IV.6 FORECASTING DEMAND FOR TURKEY BASED POWER UTILITY (A COMPARATIVE STUDY) Fig 4.4 Forecasting energy consumption for next year’s using power model Fig 4.5 Forecasting energy consumption using input data for GPTABLE IV.7 FORECASTING OF ENERGY CONSUMPTION FOR NEXT SEVEN YEARS USING model (A COMPARATIVE STUDY) Fig 4.6 Graph for forecasted energy consumption of next seven years using GP model DISCUSSION Annual demand data has been taken from various utility as case studies. Both conventional and symbolic regression has been successfully implemented using input data. Considering the demand data of Turkey based power utility, SSE in case of GP model is 0.00038000 which is less than Fig 4.2 Output of power model & its residuals Polynomial model which is 0.0060879 or power model which is 0.02194693.It means if SSE is low the sum of vertical distances between the desire curve and the obtained curve is small, which guarantees the best model. Here GP is run population size of 100 and 800 generations. The best fitness value is found to be 338.50 at generation 792. CONCLUSION While forecasting the future energy consumption using Fig 4.3 Forecasting energy consumption for next year’s using the data of turkey base power utilities by the method of curve polynomial model fitting and genetic programming technique .We have used polynomial model, power model and GP model to forecast the load requirements by providing time as an independent variable, it is found that output produces by power and polynomial model somewhat deviates from the actual data while output produces by GP model closely resembles the actual value and error is less in case of Genetic Programming.© 2012 ACEEE 19DOI: 01.IJCSI.03.02.59
  • 6. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012Moreover SSE nearly approaches zero in case of GP model as [7]. Edmund, T.H. Heng and Dipti Srinivasan “Short Term Loadcompared to curve fitting technique which ensures that model Forecasting Using Genetic Algorithm and Neural Networks” IEEEfound using GP closely fits the actual data. Hence forecasting Catalogue No: 98EX137 June 1998, page no.21-26. [8]. Tawfiq Al-Saba and Ibrahim El-Amin (1999) “Artificial neuralof annual energy consumption must be done based upon networks as applied to long-term demand forecasting” ArtificialGenetic Programming which uses symbolic regression Intelligence in Engineering volume no.13, page no.189–197.technique. This is the advantages of symbolic regression [9]. T. Rashid and T. Kechadi (2005) “A Practical Approach forover conventional regression technique .In symbolic Electricity Load Forecasting” World Academy of Science,regression both model and its coefficients can be found which Engineering and Technology, volume no.5.minimizes the chance of selecting a inbuilt function which [10]. A.Azadeh, R. Tavakkoli-Moghaddam,and S.Tarverdian ( 2010)may not be a better model as in case of curve fitting technique. “Electrical Energy Consumption estimation by Genetic AlgorithmTo test the model RMSE has been calculated and compared and Analysis of Variance..It is been found to be nearly one in case of GP model while [11]. Sanjib Misra & S.K.Patra (2008) “ Short Term Load Forecastingits value deviates from one in case of power model or using Neural Network trained with Genetic Algorithm & Particlepolynomial model Swarm Optimization” First International Conference on Emerging Trends in Engineering and Technology,IEEE computer society. [12]. Quinlan et.al (1990) “genetic programming” paradigm which FUTURE SCOPE OF THE WORK genetically breeds populations of computer programs to solve In the present work Genetic programming is used to problems” Computer Science Department Stanford University.forecast the future load requirements which incorporate time [13]. K.Timma Reddy 2004 “Forecasting using Neural networkas an independent variable and energy consumption as a and genetic algorithm”. [14]. P.K. Sarangi & R.K.Chauan (2005-2009) “short term loaddependant variable. Practically it may be possible to include forecasting using neuro genetic hybrid approach”.weather information, temperature, GDP, Number of consumers [15]. R John Koza et.al (1990) “genetic programming techniqueas independent variables. We can apply genetic algorithm, based on Darwinism & natural selection for formulating and solvingANN, Fuzzy Logic to long term energy forecasting so as to problems”.get desired form of accuracy. We can also use GA-ANN and [16]. John R. Koza (1994) “Survey of Genetic Algorithm and Geneticother hybrid optimization technique to forecast the future progrmming”.load requirements. [17]. Zhu Huan-rong (2010) “genetic programming(GP) method to establish the mathematical model of load forecasting” International REFERENCES Conference On Computer Design And Appliations [18]. Limin Huo (2007) “Short-Term Load Forecasting Based on[1]. Zargham Haydari and F. Kavehnia (2006) “ Time-Series Load Improved Genetic Programming” IEEE proceeding.Modeling and Load Forecasting Using Neuro-Fuzzy Techniques”,9th [19]. D. K. Chaturvedi, Sinha Anand Premdayal,and Ashishinternational conference, electrical power quality and utilization Chandiok (2010) “Short-Term Load forecasting Using Soft,page no.9-11. Computing Techniques” Int. J. Communications, Network and[2]. Khaled M. EL-Naggar, and Khaled (2005) “Electric Load System Sciences, volume no.3, page no.273-279.Forecasting Using Genetic Based Algorithm, Optimal Filter [20]. Edgar Manuel Carreno 2011 “A Cellular Automaton ApproachEstimator and Least Error Squares Technique: Comparative Study” to Spatial Electric Load Forecasting” IEEE Transactions on powerWorld Academy of Science, Engineering and Technology ,volume system, vol.26, No. 2.no. 6. [21]. Nima Amjady 2011 “Midterm Demand Prediction of Electrical[3]. D. K. Chaturvedi, R. K. Mishra, and A. Agarwal. (1995) “Load Power Systems Using a New Hybrid Forecast Technique” IEEEForecasting Using Genetic Algorithms” Journal of The Institution Transactions on power system, vol.28, No. 4.of Engineers (India), EL 76.3, page no.161-165. [22]. Nima Amjady 2011 “Midterm Demand Prediction of Electrical[4]. Dr. Hanan Ahmad Kamal (2002) “Solving Curve Fitting Power Systems Using a New Hybrid Forecast Technique” IEEEproblems using Genetic Programming” IEEE MELECON May page Transactions on power system, vol.28, No. 4.no.7-9. [23]. Yang Wang 2011" Secondary Forecasting Based on Deviation[5]. M. A. Farahat and M. Talaat “A New Approach for Short- Analysis for Short-Term Load Forecasting” IEEE Transactions onTerm Load Forecasting Using Curve Fitting Prediction Optimized power system, vol.30, No. 7.by Genetic Algorithms (2010) “Proceedings of the 14th International [24]. Alaa F. Sheta (2001) “Forecasting Using GeneticMiddle East Power Systems Conference (MEPCON’10), Cairo Programming”IEEE proceeding.University, Egypt Volume No.125 December page no.19-21. [25]. Yusak Tanoto and Weerakorn Ongsakul (2010) “Long-term[6]. A. Azadeh, S.F. Ghaderi and S. Tarverdian (2006) “Electrical Peak Load Forecasting Using LMFeedforward Neural Network forEnergy Consumption Estimation by Genetic Algorithm “IEEE ISIE Java-Madura-Bali Interconnection, Indonesia” page no.2-4page, no.9-12.© 2012 ACEEE 20DOI: 01.IJCSI.03.02. 59