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Praveen A. Rosario University of New Brunswick, Fredericton, NB, Canada
Walid G. Morsi University of Ontario Institute of Technology, Oshawa, ON, Canada
Liuchen Chang University of New Brunswick, Fredericton, NB, Canada
EPEC 2011
Worldwide average energy consumption: steadily increasing over past few decades
Fig. 1: World marketed energy consumption 2007-2035 (quadrillion Btu) [1]
Fig. 2: World marketed energy use by fuel type 1990-2035 (quadrillion Btu) [1]
2 [1] Energy Information Administration, "International Energy Outlook 2010," U.S. Department of Energy, Jul. 2010.
Additional system
resources required
High cost of providing Ancillary
Services (AS)
Rising fuel prices
Scarcity of resources
Rising greenhouse gas
emissions
Fig. 3: Challenges associated with increased power demand and generation
3
Proposed solution: A DSM program that employs DLC to provide some Synchronous Reserve (SR) capacity from users’ loads
DSM Programs
Direct Load Control (DLC)
Utility intervenes with consent of customers
Indirect Load Management (ILM)
Customers alter their usage patterns
Fig. 4: Types of DSM programs
4
In many North American states/provinces, DWHs: ◦ Are mainly electric
◦ Contribute to about 30% of average household energy consumption [2]
Useful properties of DWHs: • Thermostatically Controlled
Loads (TCLs) [3] • Energy storage capability • Similar usage profile as total
household Using aggregated DWHs for load
control: • Reduce total household load
demand [4] • Provide AS, like SR [5]
Fig. 5: Relationship between total power demand and DWH demand [4]
5
[2] M. H. Nehrir, B. J. LaMeres and V. Gerez, "A customer-interactive electric water heater demand-side management strategy using fuzzy logic," IEEE Power Engineering Society 1999 Winter Meeting, vol. 1, pp. 433-436, Jan.31 - Feb.4 1999. [3] D. S. Callaway, "Tapping the energy storage potential in electric loads to deliver load following and regulation, with application to wind energy," Energy Conversion and Management, vol. 50, no. 5, pp. 1389-1400, May 2009. [4] M. H. Nehrir, R. Jia, D. A. Pierre and D. J. Hammerstrom, "Power management of aggregate electric water heater loads by voltage control," in Proc. of IEEE Power Eng. Soc. 2007 General Meeting, Tampa, Florida, Jun. 2007, pp. 1-6.[ [5] K. Huang and Y. Huang, "Integrating direct load control with interruptible load management to provide instantaneous reserves for ancillary services," IEEE Transactions on Power Systems, vol. 19, no. 3, pp. 1626-1634, Aug. 2004.
Power rating of DWHs ◦ Small-scale with respect to power capacity values in the power system
Necessary to control DWHs on an aggregate scale, to provide AS on a large-scale ◦ Intermediate system called an aggregator will ensure this is done
Fig. 6: Power system structure with the aggregator [6]
Aggregator will turn on/off several DWHs to maximize reserve coming from demand side, ensuring: ◦ Customer usage is not
affected ◦ Customer comfort is not
compromised
6 [6] L. Chang, “Aggregated Load Control Using Electric Domestic Water Heaters and Smart Meters”, Project Proposal, Sept. 2007
Development + Testing of
DSM Program
Maximize SR from aggregate DWHs, without affecting user
comfort
Compute benefits of
providing AS from demand-
side
Reduced reserve
requirements from
generators
Less overall peak power demand
Monetary savings for
ISO
Less power generation required at peak times
Reduced rate of CO2
emissions
Fig. 7: Flowchart demonstrating the significance of the proposed work
7
Need to quantify benefits of thesis objectives
Compute operational savings: integrate DLC with UC and ED
Translates into constrained optimization problem
Maximize SR from DWHs
Consumer comfort not aversely affected Less SR is required from generators
SR requirement from ISO
Day-ahead or Hour-ahead % of largest possible contingency % of peak demand every hour
8 Fig. 8: Flowchart illustrating the importance of UC and ED in the DSM program
Main objective function:
Constraint:
Necessary condition: To provide SR, DWH must be ‘off ’
Final objective function:
9
Diff. between reserve requested by ISO and provided by DWHs
Temp. in DWHs must remain at comfortable levels
Binary state variable xd indicates operating state of DWHs
Substituting eq. (3) into eq. (1)
Main objective function [7]:
Constraints: 1. Power balance constraints 2. Spinning reserve constraints 3. Generator output constraints 4. Minimum up/down time constrain
Fuel-cost function
Start-up cost
10
[7] T. O. Ting, M. V. C. Rao and C. K. Loo, "A novel approach for unit commitment problem via an effective hybrid particle swarm optimization," IEEE Transactions on Power Systems, vol. 21, no. 1, pp. 411-418, Feb. 2006.
1. Power balance constraints
2. Spinning reserve constraints
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Total power generation must equal total power demand
Uih : binary variable status of generator Pih : continuous variable power output of generator
At least a certain amount of reserve must come from generating units
This amount is set to a % of the hourly demand
3. Generator output constraints
4. Minimum up-time constraint
5. Minimum down-time constraint
12
Power output levels of units must be within practical operating limits
Unit must stay on for a certain period after being turned on
Unit must stay off for a certain period after being turned off
• Discrete binary variable xd • Linear Aggregator
• Discrete binary variable Uih
• Continuous variable Pih
• MINLP
UC + ED
Fig. 9: Factors influencing choice of optimization technique
13
Population based
method
Global optimization
technique
Discrete & continuous variables
Applicable to power system optimization
Easy to implement
High quality solutions
Robust control
parameters
Stable convergence characteristic
Fig. 10: Characteristics of PSO
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2 0
11 5
35
49 43
98
130
175
105
0
20
40
60
80
100
120
140
160
180
200
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
No.
of P
SO p
ublic
atio
ns o
n IE
EE T
rans
acti
ons
Year
Fig. 11: Number of PSO publications on IEEE Transactions over the years
15
Flight of particle i governed by: ◦ Velocity:
◦ Position:
◦ Inertia weight factor:
16
Pbest personal best experience Gbest global best experience
Position update rule vector addition
ω dictates balance between local and global discoveries
Fig. 12: Flowchart demonstrating basic PSO algorithm [8]
Fig. 13: Modification of current searching point for PSO [8]
17 [8] K. Y. Lee and M. A. El-Sharkawi, Modern Heuristic Optimization Techniques: Theory and Applications to Power Systems. New Jersey, United States of America: John Wiley & Sons, Inc., 2008.
Xi, Pbesti and Gbest 0 or 1
Velocity still computed using eq. (13) ◦ Applied to sigmoid function:
Position discretized using: If rand() < s(Vi) Then Xi = 1; Else
Xi = 0; 18
Squashes the input, making it applicable for use as a probability threshold
rand() is a random number generated between 0 and 1
Basic binary PSO algorithm used for aggregator
Inequality constraint is enforced at each iteration ◦ If Temperature violation occurs Switch state of DWH Proceed with algorithm
19
Penalty function approach to handle constraints ◦ Penalty factor ‘s’ added to objective function
where
Power output levels
Min. up-time constraint
Min. down-time constraint
Checked at each iteration for violations
20
C1 = 1 if power balance constraint is violated, and C1 = 0 otherwise.
Similarly, C2 = 1 if spinning reserve constraint is violated, and C2 = 0 otherwise.
Thermal model of DWH [9]
21
τ Initial time (hours) T Current time (hours) TH(t) Water temp. in DWH at time t (°F) TH(τ) Water temp. in DWH at time τ (°F) Tin Incoming water temp. (°F) Tout Ambient air temp. outside DWH (°F) Q Energy input rate as a function of t (W) R DWH thermal resistance (m2. °F/W)
SA Surface area of DWH (m2) G SA/R (W/°F) WD Water demand (L/hr) Cp Specific heat of water (W/(°F.kg)) D Density of water = 1kg/L B D* WD * Cp (W/°F) C Vol. of tank*D*Cp (W/°F) R’ /(B + G) (W/°F)
[9] L. Paull, D. MacKay, H. Li and L. Chang, "A water heater model for increased power system efficiency," in Proc. of Canadian Conf. on Elec. and Comp. Engineering 2009, St. Johns, NL, 2009, pp. 731-734.
Fig. 14: Proposed method to supply reserve from DWHs and evaluate benefits
22
Difference between operating costs before and after load control quantify benefits to ISO
Aggregator will turn off/on DWHs to obtain max. SR without impacting users
Pmax (MW)
Pmin (MW)
α ($/h)
β ($/MWh)
γ ($/MWh2)
Min Up-‐Time (h)
Min Down-‐Time (h)
Hot start cost ($)
Cold start cost ($)
Cold start hours (h)
IniEal status (h)
Table 1: System Operator Data Parameters
23
Table 1 operating parameters of the ten generating units the proposed algorithm is applied to
Practical output bounds
Fuel cost coefficients
Switching constraints
Start-up parameters
Initial state (on/off)
Parameter Value # particles 20
itermax 1000
Vmax 4
ω 1.0
c1, c2 2.0
s0 100
Table 2: PSO Parameters
Parameter Value Unit
G 7 Btu/(hour°F)
D 8.25 lb/gallon
Cp 1.0 Btu/(lb°F)
C 500 Btu/°F
WD 0 gallon/hour
B 0 Btu/(hour°F)
Tout 70 °F
Tin 50 °F
Q
0, if xd = 0 10235, if xd = 1 Btu/hour
θmin 131 °F
θmax 144 °F
Table 3: DWH Parameters
24
Total Operating Cost, TOCH ($)
Best Case Average Case Worst Case Standard Deviation
Before Load Control $574,603.45 $575,597.05 $577,545.25 $918.97
After Load Control $571,013.58 $572,384.62 $573,487.25 $946.73
Cost Savings $3,589.87 $3,212.43 $4,058.00
Table 4: Comparison of Total Operating Costs for Case I over 24 hours
25
Results are indicative of: 10 runs of the proposed algorithm A group of 100 DWHs from 10 different user classification profiles 10 generator system
Hour
Total Demand
before Load Control (MW)
Total Demand
after Load Control (MW)
1 700 695.8
2 750 747.6
3 850 837.1
4 950 940.1
5 1000 989.5
6 1100 1094
7 1150 1150.3
8 1200 1197.6
9 1300 1294.9
10 1400 1397.9
11 1450 1448.8
12 1500 1496.7
1 700 695.8
Hour
Total Demand
before Load Control (MW)
Total Demand
after Load Control (MW)
13 1400 1397.3
14 1300 1296.1
15 1200 1200.6
16 1050 1046.1
17 1000 1000.6
18 1100 1104.5
19 1200 1192.5
20 1400 1397.6
21 1300 1301.5
22 1100 1093.4
23 900 893.1
24 800 792.8
13 1400 1397.3
Table 5: Change in Hourly Demand Due to Load Control for Case I
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~ 95 MW Reduction
Fig. 15: Synchronous reserve available from DWHs for Case 1
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Best case scenario: 28MW of SR available from DWHs Worst case scenario: 12.6MW of SR available from DWHs
Fig. 16: Synchronous reserve required from generating units for Case 1
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Total Operating Cost, TOCH ($)
Best Case Average Case Worst Case Standard
Deviation
Before Load Control $ 574,603.45 $575,597.05 $577,545.25 $918.97
After Load Control $556,412.71 $557,564.48 $558,985.24 $720.38
Cost Savings $18,190.74 $18,032.57 $18,560.01
Table 6: Comparison of Total Operating Costs for Case 2 over 24 hours
29
Fig. 17: Hourly demand in system both before and after load control for Case 2
30
Fig. 18: Synchronous reserve available from DWHs for Case 2
31
Best case scenario: 185MW of SR available from DWHs Worst case scenario: 84MW of SR available from DWHs
Fig. 19: Synchronous reserve required from generating units for Case 2
32
33
◦ 100 DWHs Each one randomly assigned to one of 10 user
classification groups
◦ After the DSM program is applied: DWH temperatures are still within the acceptable
bounds for consumer comfort
DSM program developed: ◦ Allows consumers to become system providers ◦ Allows controllable loads to provide AS like SR ◦ Demonstrates significant savings in terms of
operating costs TOC on average reduces by $3,212.43 for Case 1 and
by $18,032.57 for Case 2 Algorithm is more valuable when applied to a larger
scale
◦ Consumer comfort is not altered significantly
34
Include loss coefficients with respect to power system
Design a specialized controller to work in tandem with aggregator ◦ Send out control signals ◦ Feedback info Actual DWH temperature, power and water
consumption
35
Praveen A. Rosario M.ASc. Student in Electrical and Computer Engineering
University of New Brunswick, Fredericton, NB, Canada E3B 5A3 [email protected], [email protected]
Walid G. Morsi Assistant Professor in Electrical Computer and Software Engineering
University of Ontario Institute of Technology (UOIT), Oshawa, ON, Canada L1H7K4
Liuchen Chang Professor in Electrical and Computer Engineering
University of New Brunswick, Fredericton, NB Canada E3B 5A3
