Mathematical Modelling of Contemporary Electricity Markets

Mathematical Modelling of Contemporary Electricity Markets reviews major methodologies and tools to accurately analyze and forecast contemporary electricity markets in a ways that is ideal for practitioner and academic audiences. Approaches include optimization, neural networks, genetic algorithms, co-optimization, econometrics, E3 models and energy system models. The work examines how new challenges affect power market modeling, including discussions of stochastic renewables, price volatility, dynamic participation of demand, integration of storage and electric vehicles, interdependence with other commodity markets and the evolution of policy developments (market coupling processes, security of supply). Coverage addresses all major forms of electricity markets: day-ahead, forward, intraday, balancing, and capacity.

• Provides a diverse body of established techniques suitable for modeling any major aspect of electricity markets
• Familiarizes energy experts with the quantitative skills needed in competitive electricity markets
• Reviews market risk for energy investment decisions by stressing the multi-dimensionality of electricity markets

• Language: English
• Publisher: Academic Press
• Release date: Jan 30, 2021
• ISBN: 9780128218396

Book preview

https://www.elsevier.com/books/evolution-of-global-electricity-markets/sioshansi/978-0-12-397891-2.

Part I

Modelling market fundamentals of electricity markets

Chapter 1: Forecasting energy demand with econometrics

Theodosios Perifanis    Energy and Environmental Policy Laboratory, Department of International and European Studies, School of Economics, Business and International Studies, University of Piraeus, Piraeus, Greece

Abstract

Demand forecasting is of crucial importance in the liberalized electricity markets. Many electricity markets have been under considerable regulatory transformations like unbundling. Further, issues like energy transition, electronic vehicles, distributed energy sources, environmental regulation and energy storage will alter the nature of the electricity demand in the future. Since supply capacity is almost constant in the short-term, it is important to derive a sharp forecast on demand. However, this is difficult since demand forecasting in the short-term is dependable on many variables (hour, season, working or public holiday day). Further, market stakeholders must decide on future investment. Future capacity is dependable on future demand. Long-term forecasting is difficult and subject to different drivers. We apply econometrics to investigate the relationship between economic (price and GDP), and weather conditions (number of heating and cooling degrees) in three European markets. We investigate the demand’s reactions both in the long- and short-term. Our results differ even if we researched countries with common energy regulations. European Energy Union aims at a fully integrated market. Market stakeholders should take this kind of convergence into consideration but also the still markets’ regionality.

Keywords

Electricity demand forecasting; VAR; Cointegration; VECM; Johansen; Denmark; France; Spain

Acronyms

ANFIS 

adaptive network-based fuzzy inference system

ANN 

artificial neural networks

AR 

autoregressive

ARIMA 

autoregressive integrated moving average

ARMA 

autoregressive moving average

ARTV 

autoregressive based time varying

BEMD 

bivariate empirical mode decomposition

BP 

back propagation

EEU 

European Energy Union

EFUNN 

evolving fuzzy neural network

EMD 

empirical mode decomposition

FFNN 

feedforward neural network

FID 

final investment decision

GARCH 

generalized autoregressive conditional heteroskedasticity

GDP 

gross domestic product

GP 

Gaussian processes

IRF 

impulse response functions

LEAP 

Long-Range Energy Alternative Planning system

MAPE 

mean absolute percentage error

MARS 

multivariate adaptive regression spline

MLR 

multiple linear regression

NNM 

neural network models

NPV 

net present value

PI 

prediction intervals

SARIMA 

seasonal autoregressive integrated moving average

SVR 

support vector regression

1: Introduction

Electricity is now conceived as an energy commodity. To be perceived as that a lot have changed. Many countries have taken the initiative for energy unbundling. This opened the market for several stakeholders. Further, market coupling brought the possibility of regional trading. An excellent example of this is European Energy Union which aims at a fully integrated and efficient market. As thus European countries share a regulatory framework. Trading in country or regional markets requires high quality information. Decision making based on not so accurate information, let alone misinformation, will turn into severe losses for power companies, traders, and market stakeholders. Moreover, final investment decisions (FIDs) are taken on the grounds of future fundamentals (demand and supply). Sharp forecasting is a challenge for all market stakeholders.

What is crucial for price discovery is demand forecasting both in long- and short-term horizon, since supply capacity is constant at least in the short-term. This is difficult in electricity markets as apart from the horizon (day, month, and year etc.), or the hour itself (day or night), or the season (winter, summer, etc.), there are weather, economic, or other conditions. Forecasting horizons should be discriminated accordingly. Additionally, electricity demand is subject to high volatility. Suppliers must have a transparent view of the demand side. Econometrics come to supply an objective forecasting toolbox for this challenge. However, econometrics is not the single toolbox for demand forecasting. Many use it as a component of their forecasting methodology. Econometrics use past data to forecast future values. This is a disadvantage since many challenges like distributed energy sources, energy transition or environmental regulations lay ahead. Therefore, it is difficult to forecast electricity demand since it is in a phase of transition. We try to present the most representative literature review on demand forecasting. For most of the cases, econometrics are one of the applied methods in combination with others in the forecasting procedure. Further, these methodologies vary depending on available data, sequence and the market. Long-term forecasting is mostly based on economic, demographic and weather factors. Instead, short-term forecasting is focused on more specific data like the aggregated demand per household, the number of households, hourly trends, and types of day i.e. public holiday or working day. We start the literature review with short-term forecasting to end with long-term forecasting.

An et al. (2013) use MFES methodology which integrates multi-output FFNN (feedforward neural network) with empirical mode decomposition (EMD) based signal filtering and seasonal adjustment. This removes the seasonal components and interference of noise signals from demand series. Last, demand series are modeled by FFNN approach. Vu et al. (2017) suggest an autoregressive based time varying (ARTV) model for forecasting short-term electricity demand. Their model allows coefficients to be updated at pre-set time intervals. This, in turn, updates coefficients to enhance the relationship between electricity demand and historical data. Further, data collection and usage are improved by an adjustment procedure including a similar-day-replacement technique and a data shifting algorithm. Their results are better than those of AR, ARMA, PARMA and neural network models (NNM). Son and Kim (2017) improve data selection with the support vector regression (SVR) and fuzzy-rough feature with particle swarm optimization algorithms. This methodology identified 10 variables out of 19 as most appropriate for electricity demand forecasting. In turn the SVR algorithm was applied for the forecasting model using electricity demand data and 10 variables. The SVR model performed better in forecasting the rise and fluctuation of residential electricity demand with less variables. Again, the model was compared against standard models like ARIMA, multiple linear regression (MLR) and artificial neural network ANN models. Morita et al. (2017) suggest an upscaling model which projects a small number of representative households’ electricity demand to the aggregated electricity demand of several hundred households. In addition, they use a simple 1 h forecasting model to modify a day-ahead forecasted demand. This method is favorable during summer and winter. Lebotsa et al. (2018) use a complex forecasting model with the application of partially linear additive quantile regression models for forecasting short-term electricity demand during peak hours. After that, a bounded variable mixed integer linear programming technique is applied to discover the optimal number of power generation units to switch on or off. Their results for the South African market are that gas fired generation units are too costly, while coal fired units are favorable. Laouafi et al. (2017) propose that since load demand is too complex and influenced by a variety of factors, then there is not a single forecasting method which could satisfactorily perform through all periods. As a result, they apply an adaptive exponential smoothing method in combination with forecasts of other five individual models. To improve the forecasting accuracy of the combination of the primary models, they apply a data filter and the trimmed mean. Last, their methodology does not require ample resources. Elamin and Fukushige (2018) propose a seasonal autoregressive integrated moving average (SARIMAX) model with exogenous variables as main effects and interaction variables (cross effects) to predict hourly load demand data. The model with the interactions had better predictive ability than that without interactions. Exogenous variables and their interactions should be included. Al-Musaylh et al. (2019) apply an artificial neural network model with climatic variables for 6-h and daily electricity demand forecasting. Their model was better than other standard models like multivariate adaptive regression spline (MARS), multiple linear regression (MLR), and autoregressive integrated moving average (ARIMA) model. When they integrated their model with MARS and MLR models, then they had even better results by the hybrid ANN. Al-Musaylh et al. (2018) propose that the MARS and SVR models are better in forecasting electricity demand in the short-run. Xiong et al. (2014) propose an interval forecasting method i.e. they do not predict a single value but rather a range. They also propose a hybrid method integrating bivariate empirical mode decomposition (BEMD) and support vector regression (SVR) with the extension of empirical mode decomposition (EMD). However, their research is restricted to one-step-ahead forecasting. Adeoye and Spataru (2019) take into consideration nine categories of household appliances occupancy patterns of household members, weather conditions, type of day and day-light hours to model electricity demand. They separate electricity demand in residential and rural components. Their hybrid model derived by bottom-up and top-down methodologies only had deviations due to the sudden power generation shutdowns. Yang et al. (2016) take the forecasts by back propagation (BP) neural networks, adaptive network-based fuzzy inference system (ANFIS) and difference seasonal autoregressive integrated moving average (diff-SARIMA) models, then the forecasts are multiplied by optimal weights and later summed up for the final forecast. BP and ANFIS can account for nonlinear effects, while diff-ARIMA can account for linearity and seasonality. Van der Meer et al. (2018) utilize Gaussian processes (GPs) for probabilistic forecasting. They tested various combinations of covariance functions. Their results suggest that the dynamic GPs bring out better results with sharper prediction intervals (PIs) than the static GP. Last, they examined the forecasting ability between direct and indirect strategies to suggest that the former produce sharper PIs. Chang et al. (2011) use an evolving fuzzy neural network framework (EFUNN) with weighted factors to forecast monthly demand. Their results are better than those of MAPE for the Taiwanese market. Wang et al. (2012) apply a PSO optimal Fourier methodology, seasonal ARIMA (S-ARIMA), and combinations between the aforementioned models. The combination of the models has more accurate forecasts. De Felice et al. (2015) use both linear and non-linear (based on support vector machine) regression methodologies to propose the relationship between summer average temperature patterns over Europe and Italian electricity demand. Further, their analysis is supplemented by a probabilistic approach. Li et al. (2020) also use a hybrid method. They start with Fourier decomposition to derive fluctuation characteristics. Then the conditions of linearity and stationarity sequences are satisfied to mute seasonal patterns. Further, the sine cosine optimization algorithm is used to choose the penalty and kernel parameters of support vector machine.

Zhu et al. (2011) propose a hybrid model including a moving average procedure, a combined method and an adaptive particle swarm optimization algorithm or else (MA-C-WH) model. This is developed for time series with trend and seasonality. Further, the introduced model can adjust trend and seasonality, while the APSO algorithm searches for its weighted coefficients. Their model performs well in trend forecasting as well as in seasonal forecasting. Yukseltan et al. (2017) used past data to develop a linear regression model in terms of the harmonics of the daily, weekly and seasonal variations and a modulation by seasonal harmonics was developed. Their contribution is that no weather information is needed since they incorporate the modulation of diurnal variations by seasonal harmonics. Pessanha and Leon (2015) use decomposition methodology to forecast energy consumption. The components are the average consumption per consumer unit, electrification rate and the number of households. The suggested model combines macroeconomic scenarios, demographic projection, and assumptions for ownership and efficiency of electric appliances. Oh et al. (2016) use both top-down and bottom-up approaches. Further, they put their proposals like an innovative absorbent-based dehumidifier and an indirect evaporative cooling under two scenarios. The business as usual and the high conservative scenario. This is how they forecasted future energy demand. Mirjat et al. (2018) apply a Long-Range Energy Alternatives Planning System (LEAP) to forecast Pakistan’s 2015–50 demand. Then they propose their suggestions under different supply scenarios. After that they evaluate different outcomes with NPV methodology. He et al. (2017) use classical econometric methods in combination with system dynamics. Econometrics were used for factor screening and quantitative relationships, while the systems dynamics method for demand forecasting. It is a hybrid methodology as well, whose performance is enhanced due to integration. Their results show that power consumption shifts from energy-intensive industries to tertiary industry and residents. Angelopoulos et al. (2019) suggest an ordinal regression method for power demand forecasting and they find that economic development, and energy efficiency have the greatest influence. Weather conditions are also a driver. Günay (2016) use both multiple and artificial neural networks (ANN) to forecast electricity demand. His methodology considers population, gross domestic product (GDP) per capita, inflation and average summer temperature. On the contrary, winter temperatures and unemployment were insignificant. The hybrid methodology continues with forecasting the value of statistically significant drivers by ANN models, and these are simulated in a multilayer perception ANN model forecasting demand. The forecasted demand in 2028 is double that of 2013. Pérez-García and Moral-Carcedo (2016) find that economic growth, average consumption per household, non-residential intensity and demographic components can well forecast electricity demand in Spain. Shao et al. (2015) use again a hybrid model which is a combination of the semi-parametric model with fluctuation feature decomposition technology. Their model is tested in two different Chinese regions and has satisfactory results against standard forecasting methodologies (SVM, ARIMA, and BP). Its results are probability forecasts of the total power consumption. Last, Khalifa et al. (2019) use scenario analysis for the Qatari electricity consumption. They use GDP and population growth as the main drivers. In addition, they include electricity efficiency as the muter of long-run elasticity of consumption. They conclude that efficiency is crucial for future electricity consumption.

Through the literature review, we can suggest that no applied method as a stand-alone forecasting method is considered as optimal. Most of the researchers use hybrid methodologies which include the merits of different methodologies while their disadvantages are smoothed. Econometrics play a crucial role in variable selection, future values, and relationship investigation. However, they use past data to make their projections, while they are susceptible to aggregation. Further, most of the researchers consider economic development, demographics and weather conditions as the main factors which can forecast electricity demand. We develop an econometric model by using economic variables and weather conditions to account for long- and short-run elasticities. We develop our methodology in the following