Research Journal of Applied Sciences, Engineering and Technology 4(7): 764-767, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: September 29, 2011
Accepted: October 23, 2011
Published: April 01, 2012
Real-Time Pricing DR Programs Evaluation Based on Power Model
in Electricity Markets
Shoorangiz Shams Shamsabad Farahani, Mohammad Bigdeli Tabar,
Hossein Tourang, Behrang Yousefpour and Mojtaba Kabirian
Department of Electrical Engineering, Islamshahr Branch, Islamic Azad University, Tehran, Iran
Abstract: Along with developing Demand Response Programs (DRPs), suitable chances have been created to
take part the demand-side in electricity markets. The results of such programs are improvement of some
technical and economical characteristic of power system. DRPs are divided into two categories which are
priced-based and incentive-based demand response programs. This paper presents the application of power
modeling for Real-Time Pricing programs (RTP) as most prevalent priced-based DRPs. the nonlinear
behavioral characteristic of elastic loads is considered which causes to more realistic modeling of demand
response to RTP rates. In order to evaluation of proposed model, the impact of running RTP programs using
proposed power model on load profile of the peak day of the Iranian power system in 2007 is investigated.
Key words: Demand response programs, elasticity, real-time pricing programs
2010; Schweppe et al., 1988; Schweppe et al., 1985). This
simple and widely used model is based on an assumption
in which demand will change linearly in respect to the
elasticity. The outstanding researches considering the use
of linear model of responsive demand have been
presented and analyzed in Schweppe et al. (1988) and
Schweppe et al. (1985). However, those models do not
consider nonlinear behavior of the demand which is of
great importance in analyzing and yielding the results.
In this study, a power model to describe price
dependent loads is developed such that the characteristics
of RTP programs can be imitated.
INTRODUCTION
According to the U.S. Department of Energy (DOE)
repor t, t The definition of Demand Response (DR) is:
"Changes in electric usage by end-use customers from
their normal consumption patterns in response to changes
in the price of electricity over time, or to incentive
payments designed to induce lower electricity use at times
of high wholesale market prices or when system
reliability is jeopardized" (Department of Energy, 2006).
According to DOE classification, demand response
programs (DRPs) are divided into two categories as
shown in Fig. 1.
Real-time Pricing (RTP) rates vary continuously
during the day, directly reflecting the wholesale price of
electricity, as opposed to rate designs such as Real-time
Pricing (RTP) or critical peak pricing that are largely
based on preset prices. RTP links hourly prices to hourly
changes in the day-of (real-time) or day-ahead cost of
power. The direct connection between wholesale prices
and retail rates introduces price responsiveness into the
retail market, and serves to provide important linkages
between wholesale and retail markets. There are several
RTP variants in place across the United States – day-of
versus day ahead pricing, one-part versus two-part
pricing, and mandatory versus voluntary (FERC report,
2006, 2008).
In considerable research works, a linear economic
model for DRPs have been used (Goel et al., 2008;
Faruqui et al., 2005; Aalami et al., 2009; Aalami et al.,
ELASTICITY DEFINITION
Generally, electricity consumption like most other
commodities, to some extent, is price sensitive. This
means when the total rate of electricity decreases, the
consumers will have more incentives to increase the
demand. This concept is shown in Fig. 2, as the demand
curve.
Hachured area in fact shows the customer marginal
benefit from the use of d MWh of electrical energy. This
is represented mathematically by:
d
B(d ) = ∫ ρ (d ).∂d
(1)
0
Based on economics theory, the demand-price elasticity
can be defined as follows:
Corresponding Author: Shoorangiz Shams Shamsabad Farahani, Department of Electrical Engineering, Islamic Azad University,
Islamshahr Branch, Tehran, Iran, P.O. Box 3135-369, Tel.: +989122261946; Fax: +982188043167
764
Res. J. App. Sci. Eng. Technol., 4(7): 764-767, 2012
Time-of-use
Real-time pricing*
Price-base programs
options
Critical peak pricing
Demand response
programs
Direct load control
Interruptible/curtailable (l/C)
service
Insentive-base
programs
Demand bidding/buybavk
programs
Emergency demand
response programs
Capacity market programs
Ancillary services market
programs
Fig.1: Demand response programs, *Highlighted program has been considered in this study
ρ
changes during time period t are defined by following
relations:
Price [S/MWh]
B (d)
Demand (MWH)
∆d / d
∆ ρ / ρ0
∂ dt / dt
∂ ρt / ρt
(3)
ett ′ =
∂ dt / dt
∂ ρ t′ / ρ t′
(4)
Power modeling of elastic loads: The proper offered
rates can motivate the participated customers to revise
their consumption pattern from the initial value dt0 to a
modified level dt in period t.
Fig. 2: Demand curve
e
ett =
(2)
∆ dt = dt − dt0
For time varying loads, for which the electricity
consumptions vary during different periods, cross-time
elasticity should also be considered. Cross-time elasticity,
which is represented by cross-time coefficients, relates the
effect of price change at one point in time to
consumptions at other time periods. The self-elasticity
coefficient, ett!, (with negative value), which shows the
effect of price change in time period t on load of the same
time period and the cross-elasticity coefficient, etÙ ,(wisth
positive value) which relates relative changes in
consumption during time period t! to the price relative
(5)
It is reasonable to assume that customers will always
choose a level of demand dt to maximize their total
benefits which are difference between incomes from
consuming electricity and incurred costs; i.e., to maximize
the cost function given below:
B [dt ] − dt . ρt
(6)
The necessary condition to realize the mentioned
objective is to have:
765
Res. J. App. Sci. Eng. Technol., 4(7): 764-767, 2012
∂ B [ dt ]
− ρt = 0
∂ dt
4
X10
3.4
(7)
do
3.2
3.0
MW
Thus moving the last term to the right side of the
equality:
2.8
2.6
∂ B [dt ]
= ρt
∂ dt
2.4
(8)
2.2
0
Substituting (8) to (3) and (4), a general relation
based on self and cross elasticity coefficients is obtained
for each time period t as follows:
∂dt
∂ρ
= ett ′ t ′
dt
ρt ′
∫
∂d t
0
dt
dt
⎧⎪ ⎡ ∂ρ ⎤ ⎫⎪
= ∑ ⎨ ett ′ ⎢ ∫ t ′ ⎥ ⎬
o ρ
t =1 ⎪
⎩ ⎢⎣ ρ t t ′ ⎥⎦ ⎪⎭
dt =
ρ t′⎞
⎟
ρt0′ ⎠
6
8
Peak
10 12 14 16 18 20 22 24
Hour
Off-peak
0.010
- 0.100
0.016
Peak
0.012
0.016
- 0.100
SIMULATION RESULTS
In this section numerical study for evaluation of
proposed model of RTP programs are presented. For this
purpose the peak load curve of the Iranian power grid on
28/08/2007 (annual peak load), has been used for our
simulation studies (Ministry of Energy of IRAN, 2007).
Also the electricity price in Iran in 2007 was 150 Rialsss.
This load curve, shown in Fig. 3, divided into three
different periods, namely valley period (00:00 am-9:00
am), off-peak period (9:00 am-7:00 pm) and peak period
(7:00 pm-12:00 pm).
(10)
Combining the costumer optimum behavior that leads
to (8), (9) with (10) yields the power model of elastic
loads, as follows:
NT ⎛
d t0 ∏ ⎜
t =1 ⎝
4
Table 1: Self and cross elasticities
Low
Low
- 0.10
Off-peak
0.010
Peak
0.012
(9)
ρt
NT
2
Fig. 3: Initial load profile
By assuming constant elasticity for NT-hours period,
etÙ = 1 Constant for t, t’ , NT integration of each term, we
obtain the following relationship:
dt
Off-peak
Valely
2.0
ett ′
38000
(11)
Scenario 1
Scenario 2
Base case
33000
MW
Parameter 0 is demand response potential which can be
entered to model as follows:
28000
23000
⎫⎪
− 1⎬
⎪⎭
(12)
18000
13000
1
2
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
24
22
23
24
⎧⎪ NT ⎛ ρ ⎞
d t = d t0 + ηd t0 ⎨ ∏ ⎜ t0′ ⎟
⎪⎩ t =1⎝ ρt ′ ⎠
ett ′
The larger value of 0 means the more customers'
tendency to reduce or shift consumption from peak hours
to the other hours.
Hours
Fig. 4: The impact of adopting scenarios 1 and 2 on load profile
Table 2: The considered scenarios
Scenario no.
RTP rates (rials/MWh)
1
40, 40, 40, 40, 20, 20, 20, 20, 80, 80, 80, 80,110, 110, 110, 110, 160,
160, 160, 500, 500, 500, 160, 160 at 1-24 h, respectively
2
40, 40, 40, 40, 20, 20, 20, 20, 80, 80, 80, 80,110, 110, 110, 110, 160,
160, 160, 500, 500, 500, 160, 160 at 1-24 h, respectively
766
Demand response potential (%)
5
10
Res. J. App. Sci. Eng. Technol., 4(7): 764-767, 2012
Table 3: Technical characteristics of the load profile in scenarios 1 and 2 in comparison with the base case
Energy
Energy
Peak
Peak reduction
Load
(Mwh)
change(%)
(MW)
(%)
factor
Base Case
662268
0.0
33286.0
0.0
0.8290
Scenario 1
687943.6178
3.9
32776.6
1.5
0.8745
Scenario 2
707200.3311
6.8
32394.5
2.7
0.9096
Table 4: Economical characteristics of the load profile in scenarios 1
and 2 in comparison with the base case.
Bill in scenario
Bill reduction
1(Rials/Day)
(Profit) (%)
Base case
99340200.0
0
Scenario 1
89881873.5
9.5
Scenario 2
89576064.8
9.8
ACKNOWLEDGMENT
The authors gratefully acknowledge the financial and
other support of this research, provided by Islamic Azad
University, Islamshahr Branch, Tehran, Iran.
REFERENCES
Aalami, H.A., G.R. Yousefi and M.P. Moghaddam, 2009.
Modeling and prioritizing demand response programs
in power markets. Electr. Power Syst. Res., 80(4):
426-435.
Aalami, H.A., M.P. Moghaddam and G.R. Yousefi, 2010.
Demand response modeling considering Interruptible
/Curtailable loads and capacity market programs.
Appl. Energ. 87(1): 243-250.
Department of Energy, U.S., 2006. Benefits of Demand
Response in Electricity Markets and
Recommendations for Achieving Them.
Faruqui, A. and S. George, 2005. Quantifying customer
response to dynamic pricing. Electri. J., 18(4): 53-63.
FERC Report, 2006, 2008 Regulatory Commission
Survey on Demand Response and Time Based Rate
Programs/Tariffs, Retrieved from: www.ferc.gov.
Goel, L., W., Qiuwei and W. Peng, 2008. Nodal price
volatility reduction and reliability enhancement of
restructured power systems considering demandprice elasticity. Electric Power Syst. Res., 78:
1655-1663.
Ministry of Energy, I.R., 2007. Statistical Information on
Energy Balance. Retrieved from: http://www.
iranenergy.org.ir.
Schweppe, F., M. Caramanis and R. Tabors, 1985.
Evaluation of spot price based electricity rates. IEEE
Trans. Power Apparatus Syst., 104(7): 1644-1655.
Schweppe, F., M. Caramanis, R. Tabors and R. Bohn,
1988. Spot Pricing of Electricity. Kluwer Academic
Publishers, Norwell MA.
NOMENCLATURE
ett
etÙ
0
Peak to
valley (MW)
11318
8125.5
5731.2
model could imitate customers' response to RTP program
as prevalent DRPs. This model can help sponsor's RTP
programs to simulate the behavior of customers for the
purpose of improvement of load profile characteristics as
well as satisfaction of customers. Simulation results on
Iranian power system revealed the feasibility of the
proposed model.
The selected values for the self and cross elasticities
have been shown in Table 1. Two scenarios are
considered as Table 2. The impact of adopting scenarios
1 and 2 on load profiles have been shown all together in
Fig. 4. As seen, the load of peak periods is reduced and
shifted to other periods. Hence, the load of low periods is
increased. By increasing the value of demand response
potential according to scenario 1 and 2, the peak reduction
and load shifting are increased.
Technical characteristics of the load profile in
scenario 1 and 2 have been given in Table 3. It is seen that
the technical characteristics such as peak reduction, load
factor have been improved by adopting scenario 1 and
more in scenario 2 while daily energy change is positive.
Also the values of peak to valley are improved.
According to data reported in Table 4 which are
economical characteristics of the load profile in scenario
1 and 2, running RTP program is profitable for
participated customers. Also by increasing demand
response potential customers' profit is increased and it
leads to more satisfaction of customers to participate in
RTP program.
0
t,t!
NT
)d
)D
)d
)D
Load factor
improvement (%)
0.0
5.5
9.7
Initial state index (superscript)
Time period indices (subscript)
Number of hours within period of study
Load (MW)
Price (Rials/MWh)
Demand change (MW)
Price change (Rials/MWh)
B[dt]Benefit of consumer at time period t by
consuming dt
Self elasticity
Cross elasticity
Demand response potential (%)
CONCLUSION
Study of demand-side modeling on demand response
program is investigated. It is demonstrated that that this
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