ENTECH’15 III. Energy Technologies Conference 21-22 December 2015, Istanbul, Turkey
Demand Elasticity Estimation Based on Piecewise Linear Demand Response Modeling of Smart Grid Energy Market Murat Akcin, B. Baykant Alagoz, Asim Kaygusuz Murat Akcin, Inonu University, Electrical-Electronics Engineering, Turkey B. Baykant Alagoz, Dr,Inonu University, Electrical-Electronics Engineering, Turkey Asim Kaygusuz, Assoc. Prof, Inonu University, Electrical-Electronics Engineering, Turkey
Abstract: Demand side load management based on dynamic electricity pricing provides significant demand elasticity. This flexible electricity demand in smart grid facilitates utilization of intermittent renewable energy sources. This study presents a demand elasticity analysis method for smart grid energy markets. For pricedemand response modeling, a piecewise linear function is used to consider maximum and minimum demand points with respect to market price and demand profiles. It is anticipated that automated demand side load management via domestic agents can make price-demand response of energy market more linear in characteristic and predictable. This allows the demand elasticity analysis based on piecewise linear pricedemand modeling more relevant for the characterization of demand elasticity of real electricity markets. Keywords: Smart Grid, Energy Market, Demand, Energy Price.
Introduction: Due to increasing environmental impacts and diminishing resources, it is necessary to increase energy efficiency in consumption and increase portion of renewable energy sources in electricity generation [1-6]. However, for the utilization of renewable energy sources, there is need for smart energy management since generation of renewable energy sources such as wind and solar energy depends on the meteorological condition. Hence, energy generations of these sources are intermittent character and presents irregular fluctuations in a day. Therefore smart grids should provide flexibility in demand and generation to manage energy balance in electricity networks. Increasing use of smart meters and domestic load management applications provides demand flexibility. Recent works, focused on control of consumer demand via dynamic electricity pricing, indicated to demand elasticity [7-9]. The domestic load management applications can gain significant demand elasticity for future smarty grids. For this reason, analysis of demand elasticity and price-demand response modeling of energy markets is gaining importance for simulation, planning and smart management of energy markets. For the effectively control of demand and generation by dynamic pricing, characterization of behaviors of grid participants under variable price conditions are needed. This study presents a method for the piece-wise linear characterization of price-demand response of energy markets from time-dependent demand and dynamic price profiles. In literature, modeling efforts of price-demand response was based on potential, logarithmic, exponential and linear models [9, 10]. Since these models contain lots of parameters, they are very complex and not useful to characterize demand response of real markets by using only price and demand data taken from energy markets. On the other hand, they do not clearly emphasize maximum and minimum demand points, which are important to express demand elasticity rate of energy market. The current study presents a methodology for estimation of price-demand response by using price and demand profiles from markets. Piece-wise linear characterization of market data allows to indicate the price range where market exhibiting
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demand elasticity, and it is used to calculate demand elasticity rate of markets, easily. To demonstrate utilization of the method for an hourly market price and demand date, a demand elasticity analysis example is presented and results are discussed. Theoretical Background: (a) Modeling demand elasticity by dynamic electricity pricing in smart grids Figure 1 depicts an illustration of domestic load management method based on dynamic electricity pricing in smart grids. Direct load control agent can work in smart meters and automatically adjust demand of house by applying load shifting or load shedding [7] according to instant price signal coming from dynamic price server. One of the advantages of such automated load management is that total demand of grid can be predictable and price-demand response of system can be characterized properly.
Dynamic Price Server Domestic Load Management
Communication Link
Smart Meter
Socket
Socket
Grid
Figure 1. An illustration of Domestic load management based on dynamic electricity pricing in smart house [7]
Figure 2 shows general characteristics and important parameters of price-demand response model based on piece-wise linear function [8]. This model is based on the following assumptions: (i) Total demand of consumers is not infinite due to limited consumers. It reaches a maximum level ( DH ) at a possible low energy price point ( PL ). The point ( PL , DH ) of the characteristic is important saturation point where demand elasticity removes. (ii) Total demand of consumers never goes to zero due to critical loads and system losses. It reaches a minimum level ( DL ) at a possible high energy price point ( PH ).The point ( PH , DL ) is also another important saturation point where demand elasticity removes. (ii) Between low energy price point ( PL ) and high energy price point ( PH ), there is elastic demand region depending on energy price. In this study, relation of price and demand is assumed to change linearly due to automation of demand side load management of smart grids. The demand elasticity rate of the market was written [8] as, D Te = L (1) DH Here, demand elasticity rate takes values of 1 ≥ Te ≥ 0 . For Te = 1 , it means there is not any elasticity in consumer’s demand. It is constant for any price in this region, that is, the demand is firm. For Te = 0 , it means that the demand is fully elastic in this price range. In practice, the fully elastic demand is not applicable because of critical loads that must be always supplied.
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D
Price-Demand Elasticity
DH
DL pL
pH
p
Figure 2. General characteristics of price-demand response model and important parameters and points [8]
By considering to Figure (2), piece-wise linear price-demand response can be expressed as, DH ( DH − DL ) D( p) = ( p − p L ) + DH ( pL − pH ) Te DH
p < pL pL ≤ p ≤ pH
(2)
p > pH
It is useful to obtain piece-wise linear price-demand response model of real markets for simulation and resource management. (b) Price-demand elasticity analysis from price and demand profiles This section introduces a methodology to estimate the piece-wise linear price-demand response from demand and price profiles of energy markets. Since price-demand data set depends on numerous definite and uncertain factors (time, meteorological parameters and physiological, social, political and economical conditions) in traditional energy markets, it may not effective to use curve fitting methods directly to extract a relevant pricedemand function. Instead of curve fitting, we used extreme point selection method to estimate the pricedemand response model from price and demand data set, which is summarized below: Step 1: Form time-independent price-demand data set by combining price and demand profiles with respect to sampling time. The price is represented in x-axis and demand presented in y-axis as shown in Figure 3. Step 2: Select a maximum demand point from low price region and consider it as the point ( PL , DH ) Step 3: Select a maximum price point from lower demand region and consider it as the point ( PH , DL ) Step 4: By using these extreme points ( PL , DH ) and ( PH , DL ) , write equation (2) to obtain piece-wise linear price-demand response model and use equation (1) to calculate overall demand elasticity rate in price and demand profiles of the market. One of the main advantages of this method is that extreme point selection can neglect data that can not represent price-demand relation properly. These data is not strongly related with proper price-demand characteristic, which is defined as dD ( p) < 0 . Figure 2 shows an illustration of extreme point selection and dp
data related with proper price-demand characteristic. Removed data is related with other factor effecting demand.
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D
High Demand ( PL , DH ) Point
Low Demand Region
D
DH
( PH , DL ) High Price Point
Low Price Region
( PL , DH )
( PH , DL )
DL
pL
p
pH
p
Figure 3. Two extreme point selection from price and demand data and the data related to proper pricedemand characteristics An Example Demand Elasticity Analysis This section presents an illustrative example for estimation of demand elasticity rate and piece-wise linear price-demand response model from market data. Hourly dynamic price and demand profiles were taken from the study of Niknam et al. [9]. Figure 4 shows these dynamic price and demand profile for 24 hours.
Energy Price (Ect)
4
3
2
1
5
10
15
20
Hours
Total Load Demand (Kw)
90 80 70 60 50 5
10
15
20
Hours
Figure 4. Hourly energy price and total demand profiles from electricity market [9] Figure 5 shows relevant extreme points selection from time-independent price-demand data set. Selected points for extreme points ( PL , DH ) = (0.35, 90) and ( PH , DL ) = (4, 72) and linear price-demand characteristic are indicated by dashed line connecting selected points. The 7-8 data points around the dashed line are related
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to proper price-demand characteristic. Figure 6 shows piece-wise linear price-demand response model which is expressed as, 90 p < 0.35 D( p ) = − 4.93 p + 91.72 0.35 ≤ p ≤ 4 72 p>4
(3)
The demand elasticity rate of the market data is obtained as Te = 0.8 . It means demand can reduce to 80% percent of maximum demand depending on price changes. This system shows this flexible demand in the price ranges of [0.35,4] . (PL , DH )
90
Total Load Demand (Kw)
85 80 75
(PL , DH )
70 65
Data group that is not related with proper pricedemand relation
60 55 50
0
1
2 Energy Price (Ect)
3
4
Figure 5. Time-independent data set of price and demand profiles in Figure 4 and appropriate extreme points {( PL , DH ), ( PH , DL )} selection for proper price-demand relation 90 88 Total Load Demand (Kw)
86 84 82 80 78 76 74 0
1
2 3 Energy Price (Ect)
4
Figure 6. The piece-wise linear price-demand response model estimation
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In order to discuss the result of curve fitting to time-independent price-demand data set, Figure 6 is illustrated. Resulting linear curve D( p ) = 3.13 p + 66.82 is not a proper price-demand relation so that the increase of price results in the increase of demand. In other words, a proper price-demand line requires negative slope. Therefore, results of curve fitting is not convenient to estimate relevant price-demand elasticity from the data set. 90
Total Load Demand (Kw)
85 80 75 70 65 60 55 50
0
1
2 3 Energy Price (Ect)
4
5
Figure 7. Result of linear curve fitting to time-independent data set of price and demand profiles in Figure 4. Resulting linear curve D( p ) = 3.13 p + 66.82 is not a proper price-demand relation. Discussions and Conclusions As summary, this study demonstrates demand elasticity analysis based on piece-wise linear price-demand response model from price and demand profiles of market. Since many definite and uncertain factors affect conventional market demand and price data, estimation of proper price-demand response model and demand elasticity may not be effective by using curve fitting method. Conventional curve fitting strategies cannot give satisfactory results for the estimation of demand elasticity rate. To deal with this complication, this study suggests a data analysis method based on two extreme point selections in order to extract a proper pricedemand relation from the complicated price-demand data set. Results of the illustrative example showed that the method can deal with the complicated data sets. When utilization of automated demand side load management system increases in future smart grid, price and demand data will be more deterministic and predictable and the piece-wise linear price-demand response can well characterize the demand response of smart energy markets. References: [1] Amin, S.M., Wollenberg, B.F., 2005. Toward a smart grid: power delivery for the 21st century. IEEE Power and Energy Magazine; 3(5), pp.34-41. [2] Molderink, A., Baker, V., Bosman, B.G., Hurink, J.L., Smit, G.J., 2009. Domestic energy management methodology for optimizing efficiency in Smart Grids. IEEE Bucharest PowerTech, pp.1-7.
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[3] Ayompe, L.M., Duffy, A., McCormack, S.J., Conlon, M., 2010. Validated real-time energy models for smallscale grid-connected PV-systems. Energy, 35(10), pp.4086-91. [4] Prasad, A.R., Natarajan, E., 2006. Optimization of integrated photovoltaic-wind power generation systems with battery storage. Energy, 31(12), pp.1943-54. [5] Lund, H., 2005. Large-scale integration of wind power into different energy systems. Energy, 30(13), pp.2402-12. [6] Alagoz, B.B., Kaygusuz, A., Karabiber, A. 2012. A User-Mode Distributed Energy Management Architecture for Smart Grid Applications. Energy, 44(1), pp.167-177. [7] Keles, C., Karabiber, A., Akcin, M., Kaygusuz, A., Alagoz, B.B., Gul, O., 2015. A smart building power management concept: Smart socket applications with DC distribution, Electrical Power and Energy Systems, 64, pp.679-688. [8] Alagoz B.B., 2015. Energy balancing in smart grids under varying generation and demand conditions, Inonu University, Department of Electric-Electronics Engineering, pp.81-87. [9] Niknam, T., Golestaneh, F., Malekpour, A., 2012.Probabilistic energy and operation management of a microgrid containing wind/photovoltaic/fuel cell generation and energy storage devices based on point estimate method and self-adaptive gravitational search algorithm, Energy, 43(1), pp.427-437. [10] Zarnikau, J., 2003. Functional forms in energy demand modeling, Energy Economics, 25(6), pp.603-613.
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