Load Forecasting and Dynamic Pricing based Energy ...

Load Forecasting and Dynamic Pricing based Energy Management in Smart Grid- A Review Ahsan Raza Khan1, Anzar Mahmood*,1, Awais Safdar1, Zafar A. Khan2, Syed Bilal Javaid1, Naveed Ahmed Khan1 1

EE, COMSATS Institute of Information Technology, Islamabad 2 EPE, Mirpur University of Science and Technology

Abstract. Load Forecasting (LF) plays important role in planning and operation of power systems. It is envisioned that future smart grids will utilize LF and dynamic pricing based techniques for effective Demand Side Management (DSM). This paper presents a comprehensive and comparative review of the LF and dynamic pricing schemes in smart grid environment. Real time pricing, time of use and critical peak pricing are discussed in detail. Two major categories of LF: mathematical and artificial intelligence based computational models are elaborated with sub categories. Mathematical models including auto recursive, moving average, auto recursive moving average, auto recursive integrated moving average, exponential smoothing, iterative reweighted mean square, multiple regression, etc. used for effective DSM are discussed. Neural networks, fuzzy logic, expert systems of the second major category of LF models are also covered.

1

Introduction

Energy plays a vital role in the progress and socioeconomic development of a country. Various studies and surveys directly related the energy consumption with the economic, technological and social growth of country [1, 2]. Demand of energy is increasing exponentially and the available resources are depleting at an alarming rate. So it is necessary to manage the energy sources properly to optimize its usage and minimize the production cost and environmental hazards. Demand Side Management (DSM) is an important tool which can be used to ensure power systems’ stability and reliability in context of environmental concerns. Dynamic DSM has been ignored due to complex dynamics of consumption, random behavior of consumers and lack of computational abilities. The advancement in Information Communication Technologies (ICT) has revolutionized the power sectors and it will help utilities to realize smart grids. It also assists the utilities to implement the DSM strategies on the consumer’s side. Various types of DSM based on different techniques have been depicted in Figure 1. Load Forecasting (LF) along with dynamic

1,*Corresponding

Author: Anzar Mahmood Email: [email protected], [email protected] Web: http://www.njavaid.com/anzar.aspx Ph: +9203315079549

Figure 1. Various Types of DSM Techniques pricing schemes is providing the promising solutions in DSM applications. This paper presents a comprehensive review of LF based DSM techniques in smart grids. Rest of the paper is organized as follows: Dynamic pricing scheme are discussed in Section 2. Brief introduction of LF is presented in Section 3. Section 4 covers the mathematical based LF techniques. Artificial intelligences based forecasting models are discussed in Section 5. Conclusions are drawn in Section 6.

2

Dynamic/Time Varying Electricity Pricing Schemes

Generation, transmission and distribution of electricity costs a certain amount for each Kilo Watt hour (KWhr) of energy consumed. There are mainly two types of costs involved in this process running/operational costs and fixed costs. To recover these costs every consumer of the electricity is charged with certain amount per KWhr of electricity and this cost is known as tariff. The types of tariff conventionally used for pricing of electricity are simple tariff, flat rate tariff, block rate tariff, two part tariff, maximum demand tariff and power factor tariff [41]. But with the advancement of technology and particularly with smart grids, these conventional tariffs are deficient in fulfilling the requirements of fair pricing for electricity. With the introduction of distributed generation in the grid system, it has become very complex for these old tariff methods to comply with the requirements of smart grids and intelligent electronic devices (IEDs). In response of such needs, smart pricing schemes have been devised to fulfill the requirements of modern systems. These pricing schemes include Real Time Pricing (RTP), Time of Use (TOU) and Critical Peak Pricing (CPP) which are efficient time based pricing schemes. The smart pricing plays a key role in DSM so that the system works efficiently [42]. Demand

response (DR) is the response of consumers to the changing electricity prices and helps the system to work reliably and efficiently. A successful DR for different countries depends on the time based pricing model formulated by keeping in view the structure of the power industry of that country [43].DSM is accomplished using two types of programs. First one is incentive based program which is usually offered in whole sale electricity market in the form of contract. The incentive based DSM program include direct load control, interruptible/ curtail able service, demand bidding/ buy back, emergency demand response program, capacity market program and ancillary service markets. The second kind of DSM program is time based program. The time based DSM program will make the users to choose the time of usage of electricity keeping in view the prices of electricity [43]. The time based DSM program involves the smart pricing schemes mentioned above. Detailed analysis of the effects of different pricing schemes on DSM is discussed below; 2.1.

Time of Use

This type of smart pricing scheme offers different prices at peak time and off-peak time. During the peak time, the prices are relatively higher than off-peak time. Some utilities divide the TOU pricing scheme into three parts i.e. peak time, mid-peak time and off-peak time [6]. At the peak time, rates are kept higher because of higher demand of energy, this higher demand will result in utilization of power from more plants. Such power plants which are brought in the system to meet the peak load are called peaking power plants and usually include plants which are based on less efficient and expensive fuels such as diesel, petrol or natural gas as compared to the base load or mid load plants which are hydroelectric, solar thermal, geothermal, nuclear etc. Furthermore, to meet the peak demand, expansion of existing facilities like installation of new power plants, expansion of transmission and distribution networks will be required. Once the supply of electricity increases, the system technical losses will also increase. So to curtail the electricity usage during peak hours TOU pricing scheme introduces higher prices during the peak hours. With higher price during the peak hours, users will be tempted to reduce their electricity consumption during the peak hours [5].The smart pricing schemes are required to be such that they are fair for utilities and consumers. Consumers can benefit from their own distributed generation such as a solar or wind generation system installed in their houses. They can defer the load to the off-peak time and sell the electricity to the grid at a higher price and use electricity during off-peak time at cheaper rates along with their own generation [7].Further complex forms of TOU involve seasonal variations. Also peak and off-peak time can vary according to the dynamic requirements of the system and weather conditions [8]. Prices in TOU scheme for peak and off-peak hours are decided months earlier and hence provide consumers a good time to plan their electricity consumption schedule.

2.2.

Critical Peaking Price

CPP is a modified form of TOU. This involves some time of year where the energy demand is very high as compared to the rest of peak time during the year. TOU is

unable to discriminate the time of year when the cost of energy generated exceeds the peak value set by in the TOU pricing scheme. Sometimes it costs the utility a very high whole sale energy price which is out of range of TOU peak price and consumer is charged with every day price. To keep the pricing system fair, during normal days, the peak price charged to the consumer is same as TOU peak price [6]. To rectify this economic problem and for peak shaving, CPP is declared. CPP is declared only when the load forecast shows the load being very high i.e. making the day a critical day. Usually the CPP day is announced a day ahead of the CPP. The CPP can be declared for a certain number of days during a year, 15 as given by [7] and the pricing can be 15:1 for peak to off-peak time [7]. Present situation when nuclear power plants are being taken out of service after the Fukushima Nuclear Power Plant accident, installation of new power generating facilities can be avoided by using CPP [9]. CPP plays a very critical role in stability of the system because the price of electricity during the CPP peak duration is exorbitantly high and naturally electricity consumer will prefer to reduce the load during this period. This will reduce the peak load and system will be able to operate more flexibly. Also extension of existing and installation of new facilities will be avoided which would have been inevitable without CPP. 2.3.

Real Time Pricing

RTP is considered to be the scheme that best reflects the cost incurred by the utility for the electricity utilized by the consumer. In RTP scheme consumer is charged with a price nearest to the real price of generation at that particular interval of time. The RTP scheme can be of two types, hourly pricing and day ahead pricing. For hourly pricing, the price of electricity for an hour is announced every single hour for the next hour. While for day ahead pricing of RTP, the price of electricity for next 24 hours is announced beforehand which is selected by predicting the load demand and viz-a-viz the generation cost. RTP requires the involvement of consumers so that they can be provided the cheap electricity when it is produced at a lower cost [5], [6]. Day ahead pricing can be more effective because consumers can get sufficient time to plan their electricity consumption schedule, while hourly pricing can be tedious for consumers. RTP can be made affective only with the active participation of consumers and the technological advancement achieved with IEDs can make it possible. Furthermore as discussed in [10], load control schemes can be devised to benefit utilities and consumers. RTP signals combined with automation at consumer level will benefit not only the consumer by reducing load but it will help utility by system peak shaving and by reducing load through DSM in case of capacity limitation of generation or distribution system. So a properly designed RTP scheme increases the reliability of system, reduces the generation cost and lowers consumer’s electricity bill [11], [12]. The RTP can prove to be the most efficient pricing scheme, benefiting every stake holder involved and optimized by using the automated control system for load.

3

Load Forecasting

LF is a tool to predict future energy requirements of a system on the basis of previous load data, weather condition and availability of renewable energy sources. It is recognized as the initial building block of utility planning efforts. It ensures the balance between demand and supply of energy. LF is mostly used for predication of future load on a given system for a specific period of time. These predications may be for the fraction of an hour for operation process; and may be for 20-50 years for planning purposes. LF can be classified into three main areas i.e.  Short term LF used to predict load on hourly basis up to 1 week for daily running and cost minimization.  Medium term LF usually predicts load on weekly, monthly and yearly basis for efficient operational planning.  Long term LF is used to predict load up 50 year ahead to facilitate the expansion planning [13]. Demand forecasting is a key parameter for operation and planning of a power system and had a great saving potential for utility provider [14]. Error in forecasting model causes the increase in operational cost [15] so an accurate mathematical model is required which is used to formed a relationship between load and influential variables such as time, weather and economic factor etc. Numerous forecasting methods are proposed but some of the most commonly used forecasting techniques are: (i) multiple linear regressions, (ii) Stochastic time series (iii) General exponential smoothing (iv) State space and Kalman fitter and (v) Knowledge-based system approach [16]. These models can be classified into two categories i.e. statistical based model and artificial intelligence (AI) based modeling [17].

4

Statistical based modeling

In statistical based techniques forecasting models are represented in the form mathematical equation. Some of the traditional used mathematical techniques for LF are multiple regressions, exponential smoothing, iterative reweighted least-squares, adaptive LF and stochastic time series. 4.1. Multiple Regression This LF model uses the weighted least square estimation technique to develop a relationship between load, weather condition, day timing and consumer class etc. This model is used by Mbamalu and El-Hawary for the analysis of measured load [18]. 𝒀 𝒕 = 𝒗𝒕 𝒂 𝒕 + 𝒆 𝒕

(1)

Where t= sampling time 𝑌𝑡 = Measured Load 𝑣𝑡 =vector of adapted variable such as weather, temperature, day type etc. 𝑒𝑡 = model error at time t. Researcher of modern time used this model according to their requirement i.e. 24-h load forecast is compared with other models by Moghram and Rahman [16]. Seasonal variation using regression model is evaluated by Barakat [19]. Hyde and Hodnett developed a regression based weather-load model to predict load demand for Irish electricity; later they modified it as adaptable regression model to predict day a head load [20]. A regression based model is developed by Al-Garni to predict energy consumption as function of historic weather data, solar radiation, population of area, and consumer class [21]. 4.2. Exponential Smoothing Exponential smoothing is a classical forecasting model which uses the previous load data to predict the future load. Moghran and Rahman modeled load Y (t) as fitting function and mathematically represented below [16]. Y (t) = β (𝒕)𝑻 *f (t) + e (t) (2) Where Y (t) = load at time t f (t) = fitting function vector of the process β (t) = coefficient vector e (t) = white noise T = transpose operator A hybrid model in which exponential smoothing is augmented with power spectrum and adaptive autoregressive modeling was presented by El-Keib [22]. Infield and Hills studied an optimal smoothing for trend removal technique for short term LF. This model facilitates in reducing error in demand predication up 12% as compared to traditional forecasting model [23]. 4.3. Iterative reweighted least-squares The iterative reweighted least-squares is used to identify the order and parameters of the LF model. This method controls only one variable at a time and also it helps in definition the optimal starting point of the model. Mbamalu and El-Hawary used auto correlation and partial autocorrelation function to determine suboptimal model for load dynamics using differenced past load data [18]. The linear measurement equation is shown as: Y = Xβ + e (3) Where Y= n x 1 observation vector X=n x p matrix of known co-efficient (previous load data) β=p x1 vector of unknown parameters e= n x 1 random error vector.

The unknown vector β can be found by iterative method presented in [18]. If β is known then newton or Beaton-Turkey iterative reweighted least-squares (IRLS) algorithms can be used. 4.4. Stochastic Time Series Stochastic time series model is one of the commonly used forecasting technique for short term LF. In stochastic model it is assumed that load data has internal structure i.e. autocorrelation, trend or seasonal variation. Some of the most commonly used stochastic time series forecasting models are Auto Regressive (AR), Moving Average (MA), Auto Regressive Moving Average (ARMA), and Auto Regressive Integrated Moving Average (ARIMA). The mathematics of these models is discussed in [16].

4.4.1

Autoregressive (AR)

Autoregressive is a stochastic time series LF model. In this model load is represented as the linear combination of previous load data. Mathematically it is represented by Liu [24]. 𝑳𝒌 =− ∑𝒎 (4) 𝒊=𝟏 𝒂𝒊𝒌 𝑳𝒌−𝟏 + 𝑾𝒌 𝐿𝑘 = predicted load at time k munities. 𝑊𝑘 = random load disturbance 𝑎𝑖 = i=1, 2, 3………., m are unknown coefficients. Least mean square (LMS) algorithm is used to tune the unknown coefficients of the model. This algorithm is presented by Mbamalu and El-Hawary in [18]. The adaptive autoregressive modeling enhanced with partial autocorrelation analysis is presented in [22]. The autoregressive model with optimal threshold is presented in [25]. The algorithm requires minimum number of parameters to represent random components and improve forecast accuracy. Periodical autoregressive (PAR) for hourly based LF is presented by Zhao [26]. 4.4.2

Moving average (MA)

In moving average forecast modeling the current value of time series Y (t) is expressed in terms of linear combination of current and previous values of white noise series [16]. Mathematically it is expressed as: Y (t) = a (t) 𝜱𝟏 𝒂(𝒕 − 𝟏) − 𝜱𝟐 𝒂(𝒕 − 𝟐) − … … … … − 𝜱𝒒 𝒂(𝒕 − 𝒒) (𝟓) The backshift operator on white noise modifies the equation (5) as: Y (t) = Φ (B) a (t) Where 𝜱(B)=1- 𝜱𝟏 𝑩 − 𝜱𝟐 𝑩𝟐 -…………….𝜱𝒒 𝑩𝒒

4.4.3 Autoregressive moving average (ARMA) In this model the current values of time series Y (t) expressed linearly in terms of previous period (y (t-1), y (t-2)…..) and current and previous values of white noise (a(t), a(t-1), (a(t-2)……..) [16]. Mathematical model is represented as below: Y (t) = 𝜱𝟏 y (t-1) +………………+𝜱𝒑 y (p-t) +a (t)…………𝜱𝟏 𝒂 (𝒕 − 𝟏) +………..+𝜱𝒒 𝒂(𝒕 − 𝒒). (6) A new time-temperature based forecast model is presented in [27]. In this model time series of monthly peak load is decomposed into deterministic and stochastic component, later determined by ARMA model. To update the parameters of adaptive ARMA model, Weighted Regressive Least-Square (WRLS) algorithm is presented in [28]. Adaptive ARMA model for LF uses available forecast error to update the model parameters [29]. Minimum mean square error is used to update the error learning coefficient and adaptive scheme outperformed conventional ARMA model. 4.4.4

Autoregressive integrated moving average (ARIMA)

Previously defined time series models i.e. AR, MA and ARMA were the stationary processes while the ARIMA model is the extension of ARMA for non-stationary process. To make ARIMA a stationary process differencing process is performed by introducing 𝛁 operator in the equation of ARMA. Mathematically the ARIMA (p, d, and q) the model is written as: Φ (B)𝜵𝒅 *y (t) = (B) a (t) (7) This model uses trend components to predict growth in system’s load, weather component to forecast weather sensitive load and ARIMA model is used to produce cyclic non-weather component of weekly peak load [30]. Seasonal ARIMA model uses historical data to forecast the seasonal variation in load [27].

5

Artificial intelligence based modeling

Some of the artificial intelligence based forecasting models are Expert System, Grey System, Artificial Neural Network (ANN), and fussy logic. 5.1. Artificial Neural Network (ANN) Artificial neural network (ANN) is computational model inspired by animal or human central nervous system. This system is the interconnection of “neurons” that can compute values from inputs feeding information through network. The comprehensive study of neural networks is presented in [31, 32]. Most of the review paper proposed that ANNs are classified into two groups. First group consists of only output node to predict next hour, next day peak load and other have several output node to forecast hourly load [33]. In 1998 a software based neural network technology was used by 30 US electric utilities [34]. Some of the other neural forecasting models are: radial basis function network [35], self-organizing maps [36], for clustering and recurrent neural network [37]. Srinivasan and Lee proposed hybrid

fuzzy neural approaches to predict the future load [38]. An algorithm using an unsupervised/supervised learning concept to build a relationship between load and temperature, it is used to predict 24 hours load [39]. LF model using ANNs with error correction is proposed in [17]. This model uses real time data as input of error correction mode and simulation results shows that Mean Average Percentage Error (MAPE) of 0.72% which is better than traditional system. 5.2. Expert System

It is a new field which is emerged as result of advancement in the field of artificial intelligence. Expert system is a computer based program which is built by export engineers. They extract LF knowledge from an export in field and called as knowledge based export system. The expert system with combine features of knowledge based and statistical technique is presented in [40]. The knowledge based forecasting model which combines the features of existing system knowledge, load growth in system, time horizon is proposed by Brown [41]. Several hybrid methods have been reported in literature which are used to combine the expert system with other LF models to predict load. For example Fuzzy logic and expert system is combined by dash [42]. Artificial neural network with fuzzy export system is used to predict load for Korean electric power company [43]. An hourly prediction model is formed with the combination of neural network an export system to forecast load for Egypt Electric Corporation [44]. 5.3. Fuzzy Logic Fuzzy logic is a centralized defuzzification system that can identify and approximate any unknown dynamic system i.e. loads on the compact set of arbitrary accuracy. Lui studied that fuzzy logic has a great ability to draw similarities from huge data [45]. It is represented mathematically as: 𝑽𝒌 = (𝑳𝒌 − 𝑳𝒌−𝟏 )/𝑻, 𝑨𝒌 = (𝑽𝒌 − 𝑽𝒌−𝟏 )/𝑻 (𝟖) Where (𝐿−𝑖 − 𝐿0 ) Similar input data can be identified as 𝑉𝑘 First difference 𝐴𝑘 Second difference. Fuzzy logic system works in two stages i.e. training and on-line forecasting. Training stages uses historic data from meters to train 2m input. 2n output fuzzy-logic based pattern is generated fuzzy rule by using first and second difference of given data. After training stage it is linked with controller to predict load. Centroid defuzzifier generates output pattern by matching the highest probability function. Several fuzzy models are used for load prediction. An export system with fuzzy logic set theory is used to forecast load for Taiwan power system [46]. A fuzzy linear programming model that represents the uncertainties in forecasting and input data using fuzzy set notation is proposed in [47]. To minimize the model error a fuzzy inference methods is used to develop a non-linear optimization model for short term LF is presented in [48]. A highly hybrid STLF model combines three techniques i.e.

fuzzy logic, neural network and export system with unsupervised learning is studied by Srinivason [49]. 5.4. Comparative Study of forecasting Techniques Many researchers empirically compared the techniques used for LF. Willis and Northcote compared 14 forecasting techniques which are the earliest and most comprehensive comparison ever made [50]. Lie compared three forecasting techniques i.e. Fuzzy Logic (FL), Neural Network (NN), and Autoregressive (AR) and concluded that FL and NN is much accurate then AR model [45]. Girgis uses actual load data to compare the estimation error of 1-hour and day ahead forecast with three forecasting techniques i.e. adaptive Kalman filter, neural network and expert system [50]. Many researchers also compare the model with previously proposed models and show their superiority like LF model using ANN with error correction author demonstrate that Mean Average Percentage Error (MAPE) of 0.72% which was previously 2.96% for ANN and 1.90% Wavelet transformation (WT-ANN) [17].

6

Conclusions

LF and dynamic pricing schemes helps the electric utilities in the implementation of DSM strategies in smart grid environment. These DSM techniques help the utilities in the future planning and operation of power system. Dynamic pricing schemes ensure the variable prices for consumers according to their requirements. In this work, we have reviewed LF techniques and dynamic pricing schemes. Each DSM technique is discussed separately with their merits and demerits. The above work concluded that artificial intelligence based forecasting models are much more accurate the statistical models. The best results have been achieved using artificial neural network based models [17]. These computational models help the researcher towards hybrid models by combining multiple techniques.

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