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A Generalized Formulation of Demand Response under Market Environments

  • Minh Y Nguyen EMAIL logo and Duc M. Nguyen
Published/Copyright: February 17, 2015
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International Journal of Emerging Electric Power Systems
From the journal International Journal of Emerging Electric Power Systems Volume 16 Issue 3

Abstract

This paper presents a generalized formulation of Demand Response (DR) under deregulated electricity markets. The problem is scheduling and controls the consumption of electrical loads according to the market price to minimize the energy cost over a day. Taking into account the modeling of customers’ comfort (i.e., preference), the formulation can be applied to various types of loads including what was traditionally classified as critical loads (e.g., air conditioning, lights). The proposed DR scheme is based on Dynamic Programming (DP) framework and solved by DP backward algorithm in which the stochastic optimization is used to treat the uncertainty, if any occurred in the problem. The proposed formulation is examined with the DR problem of different loads, including Heat Ventilation and Air Conditioning (HVAC), Electric Vehicles (EVs) and a newly DR on the water supply systems of commercial buildings. The result of simulation shows significant saving can be achieved in comparison with their traditional (On/Off) scheme.

Keywords: demand response; heat ventilation air conditioning; electric vehicle; water supply systems; dynamic programming; real-time markets; Smartgrid

Appendix

A.1 Heat ventilation and air conditioning

The mathematical formulation of DR problem for HVAC is as follows.

(15)minqkhvack=0,1...N−1ETkk=0,1...N−1{∑k=0N−1ρkqkhvac}

Subject to

(16)tk+1=tk+αqkhvac+βTk−tkortk+1=1−βtk+αqkhvac+βTk,k=0,1...N−1
(17)qminhvac≤qkhvac≤qmaxhvac,k=0,1...N−1
(18)tmin≤tk≤tmax,k=1,2...N

where qkhvac is the energy consumption of HVAC during state k, [kWh]; tk is the indoor temperature at the beginning of stage k, [°C]; Tk is the ambient temperature during stage k, [°C]; α is the equivalent thermal resistance of HVAC, [°C/kWh]; β is the coefficient represents the heat losses between the indoor and outdoor space, [p.u.]; qminhvac,qmaxhvac are the capacity limits of HVAC, [kWh]; and tmin, tmax are the lower and upper temperature of human comforts, [°C], e.g. human fells comfortable if the temperature is between 20 and 24°C at night time and 22 and 26°C at daytime.

The traditional operation scheme of HVAC is that it is on/off until the indoor temperature reaches the upper/lower bound of preference, respectively.

(19)qk+1hvac=qmaxhvaciftk≤tmin8qkhvaciftmin<tk<tmax80 iftk≥tmax

A.2 Electric vehicles

The mathematical formulation of DR problem for EVs is as follows:

(20)minqkevk=0,1…N−1∑k=0N−1ρkqkev

Subject to

(21)sock+1={sock+ηqkevsock−1ηqkevif chargingif discharging,k=0,1...N−1
(22)qminev≤qkev≤qmaxev,k=0,1...N−1
(23)socmin≤sock≤socmax,k=1,2...N
(24)socN=socmax

where qkev is the energy charging/discharging of the EV during stage k, [kWh]; sock is the battery SOC at the beginning of stage k, [kWh]; η is the charging/discharging efficiency, [p.u.]; qminev,qmaxev are the charging/discharging rate limits, [kW]; and socmin, socmax are the capability limits of the tank, [kWh]. It is noted that the number of stage, N, just covers a portion of day when the EV is plugged in, 06:00 pm–08:00 am in this paper. The customers’ preference is that the EV is full of charge at the end of charging duration (eq. (24)).

The traditional charging scheme of EVs is that the battery is charged with a fixed rate until full.

(25)qkev={qratedevif sock<socmax0otherwise

A.3 Water supply systems

The mathematical formulation of DR problem for water supply systems is as follows.

(26)minqkpsk=0,1...N−1Edkk=0,1...N−1∑k=0N−1ρkqkps

Subject to

(27)vk+1=vk+ηqkpsH−dk,k=0,1...N−1
(28)qminps≤qkps≤qmaxps,k=0,1...N−1
(29)vmin≤vk≤vmax,k=1,2...N

where ρk is the electricity price in stage k, [$/kWh]; qkps is the energy consumption of pumping system during state k, [kWh]; vk is the water volume in the tank at the beginning of stage k, [m3]; dk is the water demand during stage k, [m3/h]; η is the efficiency of the pump, [p.u.]; H is the height pressure of the tank, [kPa]; qminps,qmaxps are the capacity limits of pumping system, [kW]; vmin, vmax are the capability limits of the tank, [m3]; ∆T is the time basis of the electricity market, [hour]. It is obvious that the users’ comfort is always preserved by the problem constraints (eqs (27)–(29)).

The traditional pumping scheme of water supply systems is that the pump is on/off until the water level reaches the upper/lower level of the tank, respectively.

(30)qk+1ps={qmaxps if vk≤vminqkps   if vmin<vk<vmax0     if vk≥vmax
Table 2:

The parameters used in the simulation of the case study.

System parametersCustomer preference
HVACα (°C/kWh)0.05tmin (°C) at night20
β (p.u.)0.15tmax (°C) at night24
qminhvac (kWh)0tmin (°C) at day22
qmaxhvac (kWh)50tmax (°C) at day26
EVsη (p.u.)0.85The car needs to be full of charge at the end of the charging period.

socN = socmax
socmax (kWh)50
socmin (kWh)10
qminev (kWh)0
qmaxev (kWh)5
Water supply systemsη (p.u.)0.75The water of the tank needs to be maintained at adequate levels for usage, dk (m3).
vmax (m3)150
vmin (m3)10
qminps (kWh)0
qmaxps (kWh)12.5

Nomenclature

x(t)

the state of the system, i.e., state variable, at time t

u(t)

the control of the system, i.e., control variable, at time t

w(t)

the uncertainty of the system. i.e., random variable, at time t

umin,umax

the input capacity limits

xmin,xmax

the physical limits of the system

T

the terminal time

N

the number of stages

xk

the state variable at the beginning of stage k

uk

the control variable during stage k

wk

the uncertainty incurred during stage k

f(∙)

the state transition function

g(∙)

the cost function

h(∙)

the customers’ preference function

References

1. BalijepalliVS, PradhanV, KhapardeSA, ShereefRM. Review of demand response under smart grid paradigm, in Proc. Innovative Smart Grid Technologies, Kerala, India, Dec. 1–3, 2011.Search in Google Scholar

2. BrooksA, LuE, ReicherD, SpirakisC, WeihlB. Demand dispatch: using real-time control of demand to help balance generation and load. IEEE Power Energy Mag2010;5:20–9.Search in Google Scholar

3. MajumdarS, ChattopadhyayD, ParikhJ. Interruptible load management using optimal power flow analysis. IEEE Trans Power Syst1996;11:715–20.10.1109/59.496144Search in Google Scholar

4. PedrasaMA, SpoonerTD, MacGillIF. Scheduling of demand side resources using binary particle swarm optimization. IEEE Trans Power Syst2006;24:1173–81.10.1109/TPWRS.2009.2021219Search in Google Scholar

5. RuizN, CobeloI, OyazabalJ. A direct load control model for virtual power plant managements. IEEE Trans Power Syst2009;24:959–66.10.1109/TPWRS.2009.2016607Search in Google Scholar

6. FanZ. A distributed demand response algorithm and its application to PHEV charging in smart grid. IEEE Trans Smart Grid2012;3:1280–91.10.1109/TSG.2012.2185075Search in Google Scholar

7. ZhouS, WuZ, LiJ, ZhangXP. Real-time energy control approach for smart home energy management system. Elect Power Compon Syst2014;42:315–26.10.1080/15325008.2013.862322Search in Google Scholar

8. LuiP, FuY, MarvastiAK. Multi-stage stochastic optimal operation of energy-efficiency building with combined heat and power system. Elect Power Compon Syst2014;42:327–38.10.1080/15325008.2013.862324Search in Google Scholar

9. LiS, BaoK, FuX, ZhengH. Energy management and control of electric vehicle charging stations. Elect Power Compon Syst2014;42:339–47.10.1080/15325008.2013.837120Search in Google Scholar

10. YoonJH, BaldichR, NovoselacA. Dynamic demand response controller based on real-time retail price for residential buildings. IEEE Trans Smart Grid2014;5:121–9.10.1109/TSG.2013.2264970Search in Google Scholar

11. BertsekasDP. Dynamic programming and optimal control. Belmont, MA: Athena Scientific, 1995.Search in Google Scholar

12. PJM Electricity market. Available at: http://www.pjm.com. Accessed 5 Sep 2014.Search in Google Scholar

13. NguyenMY, NguyenVT, YoonYT. A new battery energy storage charging/discharging scheme for wind power producers in real-time markets. Energies2012;5:5439–52.10.3390/en5125439Search in Google Scholar

14. OtaY, TaniguchiH, NakajimaT, LiyanageK, BabaJ, YokoyamaA. Autonomous distributed V2G (vehicle-to-grid) satisfying scheduled charging. IEEE Trans Smart Grid2014;3:559–65.10.1109/TSG.2011.2167993Search in Google Scholar

15. NguyenMY, NguyenDH, YoonYT. A new battery approach to wind generation system in frequency control markets. J. Elect Eng Tech2012;8:742–9.Search in Google Scholar

16. NguyenMY, YoonYT. Optimal scheduling and operation of combined battery wind generation systems in response to real-time prices. IEEJ Trans Elect Electron Eng2013;9:129–35.10.1002/tee.21947Search in Google Scholar

17. NørgaaardJ, NielsenA. Water supply in tall buildings: Energy efficiency of roof tanks vs. pressurized systems. Grundfos Water Boosting, 2007. Available at: http://www.cbs.grundfos.com.‎ Accessed 1 Apr 2014.Search in Google Scholar

Published Online: 2015-2-17
Published in Print: 2015-6-1

©2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  3. Detection and Classification of Transformer Winding Mechanical Faults Using UWB Sensors and Bayesian Classifier
  4. A Generalized Formulation of Demand Response under Market Environments
  5. A Novel Fault Location Method for Radial Distribution Systems
  6. Counterpoise Mutual Voltage and Its Impacts on the HV Transmission UGOH Pole Earth Potential Rise
  7. Harmonic Mitigation in a Coreless Double-Wound Flywheel Machine: Experimental Verification
  8. Optimal Dispatch of Unreliable Electric Grid-Connected Diesel Generator-Battery Power Systems
  9. Comprehensive Smart Grid Planning in a Regulated Utility Environment
  10. AGC System after Deregulation Considering TCPS in Series with the Tie-Line
https://doi.org/10.1515/ijeeps-2014-0147
Keywords for this article
demand response; heat ventilation air conditioning; electric vehicle; water supply systems; dynamic programming; real-time markets; Smartgrid

Articles in the same Issue

  1. Frontmatter
  3. Detection and Classification of Transformer Winding Mechanical Faults Using UWB Sensors and Bayesian Classifier
  4. A Generalized Formulation of Demand Response under Market Environments
  5. A Novel Fault Location Method for Radial Distribution Systems
  6. Counterpoise Mutual Voltage and Its Impacts on the HV Transmission UGOH Pole Earth Potential Rise
  7. Harmonic Mitigation in a Coreless Double-Wound Flywheel Machine: Experimental Verification
  8. Optimal Dispatch of Unreliable Electric Grid-Connected Diesel Generator-Battery Power Systems
  9. Comprehensive Smart Grid Planning in a Regulated Utility Environment
  10. AGC System after Deregulation Considering TCPS in Series with the Tie-Line
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