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## ABSTRACT

Cover Page i Declaration ii Certification iii Dedication iv Acknowledgement v Abstract vii List of Figures xii List of Plates xv List of Tables xvi List of Abbreviation xvii CHAPTER ONE: INTRODUCTION
1.1 Background of the study 1
1.2 Motivation 5
1.3 Significance of Research 6
1.4 Statement of Research Problem 6
1.5 Aim and Objectives 7
1.6 Methodology 8
1.7 Dissertation Organization 10
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction 11
2.2 Review of Fundamental Concepts 11
2.2.1 Electrical Power System Planning & Operations 11
2.2.2 Application and Need for Power System Planning 12
2.2.3 Electric Power Peak demand 12
2.2.4 Factors Affecting the Load Profile Patterns 13
2.2.6 Nonlinear dynamics and Chaos and Its Application in Electric Power System 16
2.3 Autoregressive Integrated Moving Average (ARIMA) Modeling 24
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2.3.1 Seasonal Autoregressive Integrated Moving Average Model (SARIMA) 26
2.4 Artificial Neural Network (ANN) 28
2.4.1 The Multilayer Perceptron (MLP) Neural Network 30
2.4.2 Nonlinear Autoregressive neural network with Exogenous inputs (NARX) 34
2.4.3 How to Build a NARX Neural Network 36
2.4.4 Concatenation of Seasonal ARIMA and NARX Model 42
2.4.5 Cubic spline interpolation 43
2.4.6 Correlation coefficient 44
2.5 Review of Existing Similar Works 45
CHAPTER THREE: MATERIALS AND METHOD
3.1 Introduction 55
3.2 Materials and Equipment Required for the study 55
3.2.1 Materials Required 55
3.2.2 Equipment Required 55
3.2.3 Data Sources 56
3.3 The Study Area 56
3.4 Data Pre-processing 56
3.5 Methodology 59
3.5.1 Characterization of Peak Load Data Using Nonlinear Dynamic Analysis
Approach 59
3.5.2 Development of an Improved SARIMA Based on NARX Neural Network Optimized with Chaos Theory Approach for Days Ahead Prediction 61
3.5.3 Evaluation of the Proposed Model Forecast Performance 69
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Introduction 72
4.2 Results of the Characterization of Peak Load Data Using Nonlinear Analysis 72
4.2.1 The Data Descriptive Analysis Results 72
4.2.2 Results of the Analysis of the Peak Load Demand Data using Time series
plot and power spectrum (visualization of variables) 73
4.2.3 Result of Phase Portrait Analysis 77
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4.2.4 Results of the Phase space reconstruction and computation of Lyapunov
exponent 78
4.3 Simulation Results for Proposed Improve SARIMA Based NARX Network Model 82
4.3.1 Simulation Results for Multiplicative SARIMA Model 83
4.3.2 Simulation Results for Proposed NARX Network for Daily Peak Load Demand
of Nigeria Power System Grid 89
4.3.3 Comparison of the Models Performance Evaluation Results 97
4.4 Results of Forecasting the Daily Peak Load Demand for Year 2017 and 2018
Using the Proposed Model 100 CHAPTER FIVE: CONCLUSION AND RECOMMENDATION
5.1 Conclusion 102
5.2 Significant Contribution 103
5.3 Limitation 103
5.4 Recommendations for Future Research 104
REFRENCES 105 APPENDICES 112 Appendix A: M -file MATLAB Program Codes for the Proposed Model 112 Appendix A1: Data smoothening using cubic spline interpolation, power spectrum and time series plot 112 Appendix A2: Correlation Analysis of the Input Variables 113 Appendix A3: Determination of time delay using the method of average mutual information (AMI) 113 Appendix A4: Determination of optimal embedding dimension using the method of false nearest neighbors (FNN) 115 Appendix A5: Computation of Largest Lyapunov exponents using Rosenstein‟s algorithm 116 Appendix B1: SARIMA model Identification selection 118
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Appendix B2: Multiplicative seasonal ARIMA model for the forecast of daily peak load demand 119
Appendix B3:Algorithm for STLF of Daily Peak Load Demand of Nigeria Power System Grid based on an improved SARIMA and NARX Neural Network model. 120 Appendix B4: Forecasting peak load demand for Nigeria power system grid in 2017 122 Appendix C: Simulation and Analysis Results of the Proposed Model 127

## CHAPTER ONE

Forecasting refers to the prediction of the load behavior for the future planning and decision making (Seifi & Sepasian, 2011). The outcomes obtained from load forecasting (LF) plays an
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important role in many decisions making by power system operators, both in the engineering side and financial perspective as they feed into their downstream components most especiallyin resources management (Banda & Folly, 2015; As‟ad, 2012). Economically, the accurate load forecasting allows utilities, generators and other stakeholder in the to operate at the least cost (Mansour & Najmeh 2011; Afshin & Sadeghian, 2007) i.e., for every small decrease in forecast error, amount to significant savings in operation cost. It is however estimated that for every 1% decrease in loads forecast error committed, a 10 GW electric utility can save up to 1.6% million annually (Dwijayanti, 2013).Contrariwise, for any increase in load forecast errorswill make electric utility to over schedule (increase operating costs) or under schedule which risky (Bozkurt & Biricik, 2017; Popoola & Ibrahim, 2014; Mansour et al., 2011). Bunn & Famer in 1985 pointed out that in the UK, a 1% increase in forecasting error implied a £10 million increasein operating costs. If the predicted electric load is higher than the actual demand, the operating cost will increase significantly, and it wastes scarce resources (Dwijayanti, 2013; Soliman & Al-Kandari 2010). On the other hand, if the predicted electric load is less than the actual demand, it can cause brownouts and blackouts, which can be costly, especially to large industrial customers. In addition, reliable load forecasting can reduce energy consumption and decrease environmental pollution.
Load forecasting (LF) is categorized into four (Luiz et al., 2015) which includes: long term load forecasting (LTLF), mid-term load forecasting (MTLF), short term load forecasting (STLF) and very short-term load forecasting (VSTLF). Each category is done at different time horizons according to requirements but the thresholds for this time interval varies (Rafal, 2006).Long term load forecasting covers one to several years (1 to 50 years) for plant and infrastructure investment decisions; such as economical location, type and size of future power plants and transmission system expansion etc., (Luiz et al., 2015; Sanjib, 2008). Mid-term load
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forecasting is prediction that covers a period of one week to one year, and is used for spinning reserve capacity, fuel allocation, maintenance scheduling and negotiation of forward contracts (Bozkurt & Biricik, 2017;Musa et al., 2014). Short term load forecasting (STLF) covers one hour to a week ahead i.e. 1 – 168 hours), and is mainly used for generation scheduling purposes such as unit commitment, hydro-thermal co-ordination, power interchange and electricity sport price market evaluation, security assessment analysis (Banda & Folly, 2015; Luiz et al., 2015). Very short-term load forecasting (VSTLF) is for few minutes to an hour ahead and is used for automatic generation monitoring and control among other functions (Mansour et al., 2011; Harun et al., 2009; Mohammed et al., 2002).
The scope and the application of this research work is focus on STLF, this is done for nationwide, regional and can also be used for micro-grids operation for daily real-time generation control, security analysis and energy transaction planning in power utility so as to reduce cost. Demand is shaped hourly and it is impossible to start or stop production instantaneously in a huge power plant; therefore, production planning is mostly done in daily basis. Thus, STLF plays a crucial role for managing operations in electricity grid (Bozkurt & Biricik, 2017;Musa et al., 2014). STLF is an old area of research in power system planning and operation. Despite the long history of active research in this area, a universal accurate load forecasting model is still a difficult task. With the deregulation of electricity markets, a variety of STLF models are developed. These models include econometric/statistical (pragmatic) models such as trend extrapolation (Chaoming et al., 2005), linear and multi-linear regression (Kandananond, 2011), Box-Jenkins methodology which includes autoregressive integrated moving average models (ARIMA), seasonal ARIMA, ARIMA with exogeneous input (ARIMAX), etc. However, these methods always fail to avoid the influence of observation noise in the forecasting which amounts to greater losses in real terms (As‟ad, 2012).
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On the other hand, many research scholars have applied various numbers of state of the art artificial intelligent techniques (AI) to improve the forecasting performance in a short and long-term basis to address the drawback of econometric models. These methods include artificial neural networks(ANNs) and fuzzy logic systems (Amjady, 2006; Santos et al., 2007; Cai, et al., 2011), expert system model (Heiko et al., 2009); Kalman Filter models (Al-Hamadi & Soliman 2010); Data mining method and machine learning; grey theory method (Niu et al., 2010)and hybrid models (Li Li et al., 2011; Banda & Folly, 2015). A support vector machine (SVMs) was also successfully employed to solve nonlinear regression problems (Jingmin et al., 2006; Wei-Chiang, 2009). Support vector regression (SVR) was proposed to correct the error deviation in statistical techniques prediction. Relationship between external factors and electrical load is not only quite complex but also nonlinear. This nature of load makes it difficult to predict future values with parametric modeling methods such as time series and linear regression analysis. Statistical and parametric methods require making assumptions on the rules of underlying system (Bozkurt & Biricik, 2017; Aqeel et al., 2012; Harun, et al., 2009). On the other hand, AI method (ANNs) require minimum number of assumptions to find out the relation between input and the output. For non-linear multivariate problems with large datasets, ANN is known to exhibit a much higher performance and therefore, seems to be appropriate for STLF. Contrariwise, autoregressive models sometimes outperform ANN based models‟ due to seasonality effect (Bozkurt & Biricik, 2017). Nevertheless, in spite of all the above techniques, there is yet notable prediction error due to the nonlinear, sophisticated and chaotic behavior of the load data.
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1.2 Motivation
The motivation for this research is gotten from the fact that,accurate forecasts can avoid energy wastageas well as preventing system failure. Therefore, it is crucial to produce forecasts with low error in order to relieve the conflictbetween supply and need. The studies of Nigerian deregulated electricity market to improve the systems operational planning for future generation scheduling of resources without compromising on the reliability requirements for capacity expansion using load forecasting information are inadequate. This can be attributed to frequent fluctuation in power generation capacity and limited access of data to date. In addition, many STLF model developed for electricity market in Nigeria are outdated and span the period before the full deregulation which may not fit into the structure of the current market. Nonetheless as liberalization is yet to be completed in present Nigeria electricity market and it is difficult for industrial, commercial and residential consumers to choose their distributing company to enjoy low prices. However, soon when market becomes fully deregulated, correct moves in the market on energy purchases, bulk power wheeling, fuel purchases, generation scheduling and units‟ commitment will depend on the accuracy of the expected electricity to minimize cost. The focus of this research work is to fill this gap by building an improved and more accurate STLF model that can run in real-time and cope with the dynamic nature of deregulated market. The initiative is to improve on the operation of the utilities and generator operators,Nigerian Bulk Electricity Trader (NBET) as well as guide Nigerian Electricity Regulatory Commission (NERC) in calculating the changes in electricity tariffs.
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1.3 Significance of Research
The importance of liberalization in electricity market is to allow more investment into power sector with the hope of boosting economy drive. The amount of risk borne by electric utilities, power producers and marketers has increased substantially. And every player that signed a short to long-term contract cannot be certain that the future delivery of power at the specified price will earn them profit. Demand frequently differ from expectations at the time the contract was signed and the actual volume traded are not be enough to cover the costs incurred, this is attributed to the forecast error during planning and decision making. Therefore, this has made building more accurate and reliable model that can effectively forecast the load demand for generation scheduling and timely dispatch of power within a short period very necessary for all active market players in Nigeria power sector most especially in the monitoring and control of grid network operation activities by the Transmission Company of Nigeria (TCN). The significance of this research is that if this model is adopted and properly implemented by every stakeholder in Nigeria power sector, many business areas in engineering and financial aspect of power system utilities, system operator and generators will be enhanced and equipped greatly with ability to project their load demand and priceaccurately for better operation and decision making.Economically, this will also save time and cost. Most importantly effective utilization of resources and forecasts days ahead demand for real time application will becomes easy for becomes utilitiesand system operators.
1.4 Statement of Research Problem
The earlier STLF studies on Nigeria electricity grid operation are very limited and few of these research works are done on regional base while many are in the periods before the full deregulation and privatization of the power sector which has low significant impact on present
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1.5 Aim and Objectives
The research work aimis todevelop an improveshort-term daily peak load forecasting model based on seasonal autoregressive integrated moving average (SARIMA) and nonlinear autoregressive neural network (NARX) for Nigeria power system grid. The objectives of this research are as follows:
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I. To characterize the signature of chaos in the daily peak loads demand time series data collected for 120 months (2006 – 2015) using nonlinear dynamics analysis approach;
II. To develop an improved local STLF model to forecast daily peak load demand of Nigeria power system grid based on SARIMA and NARX neural network implemented in MATLAB 2015a Environment with its structures optimized with the tenets of chaos theory.
III. To validate the accuracy of the proposed model by comparison of the simulated results obtained with the actualdaily peak load data of 2015 collected from TCNusing Mean absolute percentage error (MAPE) performance metrics.
1.6 Methodology
The methodologies adopted for this research towards development of multivariate STLF model using concatenation of SARIMA and ANN optimized with chaos theory approach for Nigeria power system grid in MATLAB 2015a Environment are as follows:
I. To characterize and quantify the degree of chaos in the daily loads demand time series data collected for 120 months (January 1st, 2006 – December 31st, 2015) using nonlinear dynamics analysis approach requires the following steps:
1. Collect 10 years data (peak load demand in MW and weather records data)from Transmission Company of Nigeria (TCN) and Nigerian metrological Agency (NiMet);
2. Data pre-processing usingcubic spline interpolation and moving average for smoothening and fixing missing data.
3. Adopting the algorithms for nonlinear dynamics analysisto characterize and quantify the signature of chaos in peak load data using flow chart in Figure 3.1 (Echi et al., 2015) to
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determinethe metrics such as time series plot (visualization of variables), phase space reconstruction and phase portraits, and Lyapunov exponent;
II. Development of an improved SARIMA based on NARX model optimized with chaos theory approach for a STLF in MATLAB 2015a Environment for daily and weekly ahead peak load prediction. To achieve this objective requires concatenation of the two models‟ A and B.
A. Adopt Multiplicative Seasonal ARIMA Model from the work of in Yiet al., 2013 and Maged & Elsayed, 2017. And replication of the model involves the following Box-Jenkin methodology steps (identification, estimation, diagnostic checking and forecasting).
1. Identification of t model structure:
(i) Carryout time series data preprocessing to detect dependencies between data using:
a) Time series plots for observation analysis;
b) Apply unit root and stationarity teststo the data series using Kwiatkowski, Phillips, Shmidt, Shin (KPSS) test. If the observed series in is not stationary, applied differencing process to stationaries the data (Kwiatkowski et al., 1992). Repeat the process until the data series is stationary.
c) Compute the model identification parameter to determine usingfit statistic considers the goodness-of-fit and parsimony; i.e. the simplest model with the least assumptions/variables, minimumSchwarz-Bayesian Information Criterion (SBIC) method
2. Estimate the model unknown parameters ( using the maximum likelihood estimator and conditional least square method;
3. Carryout the diagnostic checking of the estimated residuals resultsin (iii) using goodness-of fittest statistics to confirm if the estimated models‟ assumption are satisfied, else repeat step above;
4. Use the model to forecastahead base on time lag (i.e. time horizon) selected.
a) Plot the forecasted output and actual data for comparison
b) Evaluate the model performance using MAPE
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B. Developnon-linear autoregressive neural networks with exogenous input (NARX) model architecture using the following steps:
(i) Data selection and inputting,
(ii) Create and configure the network;
(iii) Initialize the weight and biases;
(iv) Training the network, using Levenberg Marquardt and Bayesian regularization training algorithms
(v) Validate and test the performance of the network.
(vi) Use the network for prediction and forecasting
C. Concatenate step II (A) and II (B) to form the proposed model as shown in Figure 3.4 and applied it on data obtained from TCN and NiMET for daily and weekly ahead STLF
(i) The proposed model was used for daily and weekly prediction of peak load demand of year 2015 and the forecast results obtained were validated using
a) Comparison between actual data and forecast output plot of SARIMA and NARX using algorithm
b) Comparison between actual data and forecast output plot of SARIMA and NARX using algorithm
c) Evaluation of the model results performance usingMAPE.
d) Residual results evaluation using regression plot, performance function Vs epochs, error autocorrelation plots etc.
e) Forecasting of daily peak generation for Nigeria power system grid in year2017 and 2018.
Finally, the implementation of the item A, B, C, D and flow charts in Figure 3.4 are converted into codes using MATLAB software (R2015a i.e. version 8.3.0.532) environment.
1.7 Dissertation Organization Outline
The general introduction has been presented in chapter one. The rest of chapters in this dissertation is organized as follows: Details of the Review of literatures comprises of the review of fundamental concepts and similar works is presented in chapter two. Chapter three contains the research materials and methods, while chapter four gives details of the results
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obtained and followed by discussion of such results. Finally, chapter five presents the conclusion and recommendations which gives the summary and provide guidelines for future work. Quoted references and Appendices are also provided at the end of the dissertation

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