Performance Analysis of Short-Term Electricity Demand with Meteorological ... and trading activities ... to that day. Procedure hold same for months d...

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Performance Analysis of Short-Term Electricity Demand with Meteorological Parameters Kamal Chapagain∗ , Tomonori Sato † , Somsak Kittipiyakul∗ ∗ Sirindhorn

International Institute of Technology, Thammasat University, Pathumthani, Thailand School of Environmental Science, Hokkaido University, Sapporo, Japan Corresponding author: [email protected]

† Graduate

Abstract—The quality of short term electricity demand forecasting is essential for all the energy market players for operation and trading activities. Electricity demand is significantly affected by non linear factors such as climatic condition, calendar and other seasonality have been widely reported in literature. This paper considers parsimonious forecasting models to explain the importance of meteorological parameters for the hourly electricity demand forecasting. Many researchers include only temperature as a major weather factor because it directly influences electricity demand, however other meteorological factors such as relative humidity, wind speed etc. are rarely included in literature. Therefore, the main purpose of this study is to investigate the impact of meteorological variability such as relative humidity, wind speed, solar radiation etc. for short term demand forecasting and analyzed it quantitatively. We demonstrate three different multiple linear models including auto-regressive moving average ARMA (2,6) models with and without some exogenous weather variables to compare the performances for Hokkaido Prefecture, Japan. We applied Bayesian approach to estimate the weight of each parameters with Gibbs sampling and results show overall improvement of mean absolute percentage error (MAPE) performance by 0.015%.

I. I NTRODUCTION Short term electricity demand forecasting is important for all stakeholder of electricity- such as market operator, electricity generators, electricity retailers and ultimately for general people. For market operator, forecasting is crucial for scheduling and dispatch of generators capacity. For electricity generators, strategic choice involved in bidding and re-bidding of capacity depends on demand forecast[3]. For, electricity retailer, demand forecasting affects the decisions about the balance between hedging spot acquisition of electricity, and finally these actions helps for general people due to consistent energy supplies without black out and possibly minimum cost. Various models are discussed in literature and pay attention for better performance. Electricity demand in Japan has strong time correlation with lagged dependent variable such as Ohtsuka Y. et al. [8], and therefore there are several papers that relate with ARMA time series structure. Ohtsuka Y. et al. have proposed Bayesian estimation procedures for univariate ARMA and got good performance as well. Since each model has its own strength and weakness, we have developed multiple equation model accounting correlated error as hybrid model. As distinct from previous studies, we employ two stage estimation of multiple linear regression MLR ARMA(2,6) model. First stage, we get point estimation values

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of parameters using ordinary least square (OLS) technique and refine these estimation using Bayesian technique in second stage. To develop model several factors that directly or indirectly influence on electricity demand have to take in account. For example- weather, calendar, and historical demand data. Impact of weather variables on electric power demand in England, Australia, Jordan and many more regions are found in literature, but their focus is on the affect of temperature. Failure of power supply in 1995 due to excessive hot, and corresponding increase of electricity demand in Malaysia. Such increment of demand is possible if temperature lowers significantly. Countries having cold regions have the peak demand in the summer are usually lower compared to the peak demands of winter. This indicates that human activities during winter season is higher. Various weather variables can be considered for demand forecasting: temperature and humidity are the most commonly used, but wind, radiation and cloud cover are often excluded. The affect of meteorological factors such as temperature, humidity, solar radiation, precipitation, and wind speed varies according to the season and hence varies electricity demand significantly. However, most of the paper exclude other factors and include only temperature for their analysis. Among various approaches for predicting future data, we can generalize into two types of estimates. i) point estimatesingle valued forecast, and ii) probabilistic estimate- where each parameters are treated as random variable and several possible values for the future demand is predicted. The main advantage of probabilistic forecast is that it contains additional information in terms of uncertainty. This paper employ two stage for estimation. In first stage, the point estimated values obtained from OLS is considered as prior information for Bayesian and in next stage, these parameters are used as random variable for Markov Chain Monte Carlo (MCMC) and obtained the final values in terms of distributions for probabilistic forecast. Finally, forecasting the next day demand is in terms of mean, median and 60 percentile value. II. M ETHODOLOGY A. Description of data We have played with the hourly electricity demand data from Jan 1, 2013 until December 31, 2015 for Hokkaido Prefecture provided by Hokkaido Electric Power Company

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2017 14th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON)

(HEPCO) and same period of meteorological data set from Japan Meteorological Agency (JMA). Some missing data for snowfall, and cloud are filled up with interpolation of data.

Figure 1: Trend of electricity demand profile: average data 2013-2015 (×10 MW) Figure 1 demonstrates the average electricity demand profile of past two years for each months and hours. Contour map indicates the maximum demands upto 4800MW during morning (approx. 4 to 6 AM) and evening (approx. 6 PM to 7 PM) at winter season, specially in December and January. Since, Hokkaido Prefecture suffers from very cold climate during winter season around -20◦ C, people use electricity for warming purpose such as room heating, building heating, water heating etc. Also variation on pricing and necessity of people cause excessive demand during morning and evening time. The lowest demand on the similar time period are found in summer season, specially May to September. This is exactly the opposite effect and exhibits seasonal variation. Table 1. Correlation between weather variables and electricity demand Weather variable

Winter (Jan)

Summer (Aug)

1. 2. 3. 4. 5.

-0.3495 0.0727 0.1385 -0.2321 0.1013

0.5302 -0.0078 -0.4348 0.4141 NaN

Temperature Rainfall Relative humidity Solar radiation Snowfall

Since our interest is to analyze the affect of meteorological parameter, the table above shows the variables most significantly correlated with electrical demand are temperature, solar radiation having both negative correlation during winter season while it is positive during summer. Similarly, relative humidity and precipitation shows positive correlation during winter and opposite in summer. However, Solar radiation, and relative humidity during summer shows approximately equal and opposite correlation results minimization of their individual affect and strong correlation of temperature remains dominant factor for electricity demand during summer. B. Related works In literature, many authors develop univariate time series model without any exogenous variables with competitive for-

casting performance. For example, Taylor [9] employ a double seasonal exponential smoothing for half hour data to predict very good result with mean absolute percentage error (MAPE) of 1.25 to 2%. However, only historical demand data set may not sufficiently address the cause of effect on demand because temperature variation is also an important factor that directly influence electricity demand. After 2003,climate change significantly affect the variation on demand such as modification of annual daily load curve, shifting of the peak demand occurrence from evening to morning in Jordan [7]. In Europe, extremely high temperatures during summer of 2003 creating significantly greater electricity demand. Therefore, it is worth to specifically examine the influence of each meteorological parameters for electricity demand. Some multivariate weather parameters- like temperature, precipitation, wind speed, cloud cover, humidity are employed for modeling electricity consumption load [4][5]. They also mentioned that the use of additional weather variables such as precipitation, wind speed, humidity and cloud coverage should yield even better results. That means the performance is improved and consistent due to such meteorological variables. Friedrich L. et al. [6] investigate the results for Abu Dhabi city electricity load using multiple weather variable for 24 hour to 48 hour prediction horizon and got very promising result of 1.5% MAPE for 24-hour and 48-hour horizon. Apadula et al. [1] analyze weather, and calendar variables effects on monthly electricity demand using MLR model for Italy. Including good meteorological variable estimates highly improve monthly demand forecast with MAPE around 1.3%. However, they haven’t analyzed the performance including and excluding individual meteorological parameters. Another important factor found in literature is day types. Dordonant et al. [5], Chapagain and Kittipiyakul [2], forecast the electricity load considering a normal day, and make adjustments with other dummy variable for treating as weekend or other special days which is also taken into account during modeling. But, our intention here in this paper is to analyze the improvement of performance when we include such weather variables. So far we are not getting any quantitative comparison among the weather variables, such as what is the improvement of performance if we include meteorological variables for example- wind speed, humidity, cloud coverage, precipitation. Therefore this is our interest to analyze it quantitatively. C. Prototype Modeling In this paper we compare the forecasting results based on a hour ahead prediction between three models named as model A, B, and C. These models are developed as multiple linear regression (MLR) with AR(2) model inspired by the seminal paper of Ramanathan et al. [?], multiple regression model with separate equations for each hour of the day approached for California electricity market. We estimate the demand for the first hour of the day with one equation and the second for the second hour of the day from next equation and so on. Therefore, we need 24 individual equations for the complete prediction of demand in one day and prototype model is-

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2017 14th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON)

Demandh,d = Deterministich,d + M eteorologyh,d + (1) HistDemandh,d + vh,d where h indicates the hour of the day, and d indicates the daily observations and vh,d contains the correlated error term with some order of lag data. We use some special technique to select the appropriate order of q called Bayesian Information Criteria (BIC). vh,d =

q X

ρi h,d−i + h,d

(2)

variables from Model A such as rain, snow, wind, radiation, humidity, cloud and their interactions (12 variables). Therefore, model B will consist 56 exogenous variables excluding 6 correlated coefficients, for prediction of demand. Similarly, 16 more variables having very low weight on their coefficients are removed from model B for model C. The covariates for model A, B, and C can be arranged in column vector form and are estimated using OLS. These point values are used as prior values for Bayesian rule and Markov Chain Monte Carlo (MCMC) is constructed to find the distribution of the parameters for better forecast.

i=1 2

III. R ESULTS AND DISCUSSIONS

and, h,d = N (0, σ ). Deterministich,d variables refer predictable variables such as days of week, months, and years. Daily load profile shows the higher demand during the business week (Monday to Friday) than that of weekend (Saturday and Sunday) or public holidays. Such effect can be address with dummies. For example- For the case of all days of week, we can consider Saturday as reference dummy so that other days can be compare with respect to that day. Procedure hold same for months dummies and seasons dummies. And the model Deterministich,d is modeled with 25 variables. M eteorologyh,d variables are the another factor that effect the demand of electricity. Some pre-processing of temperature is done finding some correlation between temperature and demand, which implies that 17.1◦ C as the reference point where there is no effect of temperature for demand. We include some other meteorological variables such as relative humidity, wind speed, precipitation( rain or snowfall), solar radiation are also accounted for formulations. Main objective of this paper is focused on their affects for electricity demand and model M eteorologyh,d consists 34 variables. For HistDemandh,d , we studied the variation of historical electricity demand pattern. We conduct Ljung-Box Q-test for BIC test after analyzing the pattern of residuals. Since, autoregressive (AR) component captures the pattern of load in hour h = i for any given day is a good indication that load will be higher in hour h = i on the following day(s), HistDemandh,d is modeled as-AR(2) and MA(6) representing the appropriate model of cyclicality for off-peak and peak hours with 13 variables including constant term. Therefore, model A is constructed with 74 variables including 6 correlated variables. Still demand is continuously varies due to random kind of disturbances. For example, unknown working hours of large steel mills, shutdown of industrial activities, days with extreme weather or sudden change in weather are the promising factors that affect on demand. Although, we are trying to address extreme weather or sudden weather change by inserting hourly and daily deviation terms, but unscheduled holidays (eg- 28 Dec 2014 to 3rd Jan 2015) is still a limitation in our study. As our interest is to analyze the effect of other meteorological factors on the demand forecasting, now we develop next model called model B. Where we exclude some meteorological

We have used three years of data set upto 2015 through 2012, where complete 2 years (730 days) of moving windows is used as training data set to predict the out sample demand for the year of 2015. The multiple equations modeled here is estimated for each hour with separate equations having its own covariants. Therefore, each hour of the day, they have a different weight of parameter value.

Figure 2: Hourly analysis of coefficient for week dummies To discuss day type dummies in detail, we have plot the coefficients values in figure 2. Since, we represent dummy variables Sunday to Friday, considering Saturday as a base level. The largest coefficient values are seen to occur on Monday because of previous day’s demand, which are substantially lower than Monday demand, is being used to predict Monday forecast (AR(2)ef f ect : demandh,d−1 , demandh,d−2 ). The smallest coefficient specially during morning time (exactly same time of sharply increment of demand during weekdays) significantly decreases to generate lower weekends loads. Coefficients for different weekdays are found almost similar patterns indicating similar effects though out 24 hours, but during morning and night hours, coefficients are negative indicating decrease of demand than that of day hours specially evening 18 to 20 hour. In figure 3, forecasted electricity demand for first week of January, 2015 is plotted and compared with actual demand. Since, we have implemented mean, median and 60 percentile forecast from the distribution of predicted data, which is the beauty of Bayesian estimation. For future prediction, such

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2017 14th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON)

Figure 3: Weekly demand variation for the first week of Jan 2015, and this week consists a lot of variations on demand.

information are quite helpful to express demand prediction in terms of uncertainty. This first week consists various types of day types such as scheduled public holiday, unscheduled holidays, weekends and weekdays. Overall MAPE for this week is 0.82%, but still it is over estimated on Jan 1, due to non holiday effect of 31 Dec, under estimated on Jan 5, and 7 due to significant rise of peak on that day compared with the peaks of previous day. We have forecast the electricity demand for complete year 2015, with Bayesian approach with MAPE 0.69% and 0.15% variation. In literature, MAPE, and Root Mean Squared Error (RMSE) are widely used for performance analysis purpose. Figure 4 compares the performance of model A to other models B, and C. Positive value indicates that there is some improvement on our forecasting due to the meteorological variables such as- wind speed, humidity, cloud coverage, precipitation. This was the main objective of this paper. Finally, we can clearly observe that on each months comparison, model A shows dominant MAPE improvement compare to other models B, and C through out the year except some summer months July and August. Interestingly, both model B and C provide better result. The variation of electricity demand on summer may be highly depends on temperature and both models B and C are quite enough for these two months. Because, in table 1. temperature shows the dominant correlation for demand during summer. In overall, performance can be improve by 0.015%, if we include other meteorological variables in our model formulation. IV. C ONCLUSION In this paper we developed three models based on literature about multiple equation demand forecasting model. During modeling, we pays particular attention to the weather variables that effects electricity demand and try to analyze quantitatively. We have analyzed these models based on their forecasting performance for complete one year out-sample prediction. Since, models were categorized based on all weather parameter include or not, they have a bit variation on their performances. More specifically, comparing with model B and C, model A that include all available weather parameters can improve the overall performance by at least 0.015%. Interestingly, during summer months (July and August) both model B

Figure 4: Performance improvement of model A with respect to other models

and C looks better. One complexity for prediction during summer season is due to its high variation of demand. Sudden changes of temperature due to rainfall or wind speed also cause immediate fluctuations on demand. But, model B and C are succeed to address such a variation of demand. This indicates that optimization of exogenous variable is also necessary to improve performance. ACKNOWLEDGEMENT This research work is conducted under Regional Climate System Laboratory, Hokkaido University, Japan. Authors are thankful to SIIT, Thammasat University and PARE exchange program that provide partial funding for this work. HEPCO, and JMA Japan are always thankful for providing necessary data that is used in this research. R EFERENCES [1] F. Apadula, A. Bassini, A. Elli, and S. Scapin. Relationships between meteorological variables and monthly electricity demand. Applied Energy, 98:346 – 356, 2012. [2] K. Chapagain and S. Kittipiyakul. Short-term electricity load forecasting model and Bayesian estimation for Thailand data. In 2016 Asia Conference on Power and Electrical Engineering (ACPEE 2016), volume 55, pages –, 2016. [3] A. E. Clements, A. S. Hurn, and Z. Li. Forecasting day-ahead electricity load using a multiple equation time series approach. European Journal of Operational Research, 251(2):522 – 530, 2016. [4] R. Cottet and M. S. Smith. Bayesian modeling and forecasting of intraday electricity load. Journal of the American Statistical Association, 98:839– 849, 2003. [5] V. Dordonnat, S. J. Koopman, and M. Ooms. Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling. Computational Statistics & Data Analysis, 56(11):3134–3152, November 2012. [6] L. Friedrich and A. Afshari. Short-term forecasting of the abu dhabi electricity load using multiple weather variables. Energy Procedia, 75:3014 – 3026, 2015. [7] M. A. Momani. Factors affecting electricity demand in jordan, 2013. [8] Y. Ohtsuka, T. Oga, and K. Kakamu. Forecasting electricity demand in japan: A bayesian spatial autoregressive arma approach. Computational Statistics & Data Analysis, 54(11):2721–2735, November 2010. [9] J. W. Taylor. Short-term electricity demand forecasting using double seasonal exponential smoothing. J Oper Res Soc, 54(8):799–805, 2003.

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