stochastic energy management of energy-efficient...
TRANSCRIPT
Stochastic Energy Management of Energy-Efficient Building under the Risk of Uncertain Solar Power Supply Ping Liu MISSISSIPPI STATE UNIVERSITY U.S.A
November 4, 2014 1
November 4, 2014 2
Smart building energy systems
Smart grid The goal of smart grid is to make the next generation power
grid a green, reliable, and intelligent system.
Solar powered house (www.energy.gov)
November 4, 2014 3
CHP efficiency comparison
Benefits of CHP Improve power reliability by reducing or eliminating a building's dependence
on the electric power grid. Meet not only the electricity demand of the new buildings but also to provide
for their cooling and heating requirements.
Combined Heat and Power system
Source: T. Hubert, S. Grijalva, realizing smart grid benefits requires energy optimization algorithms at residential level
Categories of building appliances
Smart meter is introduced in smart grid to increase operation efficiency, reliability and flexibility.
Solar power Battery
Building system
CHP with Boiler
Electric grid
Washing Machine
Air Conditioner
Microwave Oven
Outdoor Ceiling Fan
Refrigerator
PC TV
November 4, 2014 4
Input Fuel
Power Generation Unit
Heat Recovery System
Boiler
Heating Coil
Waste Heat
Input Fuel
Building
Electric Grid
+ Electric Loads
Heat Loads+
Solar
Battery
Energy flow diagram of energy-efficient building
November 4, 2014 5
Modeling of building energy system
November 4, 2014 6
Electric grid
Energy sources
Solar power
CHP with boiler
Battery
Electricity purchasing price
Electricity selling price Natural gas price
Building optimization
Non-controllable (NC)electric load
Non-controllable (NC)thermal load
Controllable electric load
Controllable thermal load
Scheduling decisions
Price data
Load data
Electric grid
• how many of electricity purchased or sold
• status of electricity to or from the grid
Battery
• status of charging or discharging
• power generation
CHP with boiler
• operation status• power output
Controllable load
• ON/OFF status
Problem statement
Stochastic optimal operation
November 4, 2014 17
Properties of stochastic programming Explicitly incorporates a probability distribution of the uncertainty;
Relies on pre-sampling discrete scenarios of the uncertainty realizations;
Provides probabilistic guarantees to the system reliability with stochastic
solutions;
Provides the optimal strategy (policy) for the realization of uncertainty.
November 4, 2014 8
Multi-stage stochastic linear programming
( ){ } MinxqMinExqMinExcxF xx →+⋅+⋅+⋅= ...))(()( 32211 32
,11121 hxTxW ≤⋅+⋅ ,...,22232 hxTxW ≤⋅+⋅
,12
mRx +∈ 23 , ...mx R+∈
,, 11 XxbAx ∈=
The multi-stage stochastic programming is a promising approach to account for the impact of the uncertainties in the energy consumption and renewable energy generation on power dispatch decisions of energy-efficient buildings.
Intra-period constraints
Inter-period constraints
Where X(k) = forecast error in forecast hour k Z(k) = random Gaussian variable with standard deviation σZ in forecast hour k ∈ N α, β = parameter of the ARMA-series.
Uncertainty modeling
November 4, 2014 9
ARMA (1,1)—Auto regressive moving average series
0 2 4 6 8 10 12 14 16 18 20 22 24250
50
100
150
200
hour
unce
rtain
dat
a(kW
)
electric loadthermal load
solar power
Scenarios generated for each uncertainty with ARMA model (100 groups)
November 4, 2014 10
ω1(1)
ω2(1)
ω3(1)
p11
p13
p12
A scenario is defined as a sequence of nodes of the tree:
Determine the scenario to be deleted
Change the probability of the scenario that is the nearest to the deleted one
Change the number of scenarios
Andy Philpott, Stochastic Optimization in Electricity Systems, SPXI Tutorial, August 26, 2007
Scenarios Reduction
, , , , , , , , ,gf tj gt tj chp tj bd tj bc tj sol tj nc tj cntr t ele tjP P P P P P P P x− + + − + = + ⋅
, , , , , ,( )j j j jhc chp t boi t nc t cntr t heat t exh tjH H H H x Hη + = + ⋅ +
, ,0 gf tj gf gf tjP M x≤ ≤ ⋅
, ,0 gt tj gt gt tjP M x≤ ≤ ⋅
max, 1, , , 1, , 1,( )bat t j bat tj bc bc t j bd t j bd d batS S P P T Cη η+ + += + ⋅ − ⋅
min max, , ,bc bc tj bc tj bc bc tjP x P P x⋅ ≤ ≤ ⋅
min max, , ,bd bd tj bd tj bd bd tjP x P P x⋅ ≤ ≤ ⋅
, , 1bc tj bd tjx x+ ≤
, , ,chp tj chp tj chp tjF P xα β= ⋅ + ⋅
, , ,( )chp tj hre chp tj chp tjH F Pη= −min max
, , ,chp chp tj chp tj chp chp tjP x P P x⋅ ≤ ≤ ⋅
, ,.boi tj boi boi tjH Fη=min max
, , ,boi boi tj boi tj boi boi tjH x H H x⋅ ≤ ≤ ⋅
Electric balance
Thermal balance
, , 1gf tj gt tjx x+ ≤
Stochastic formulation
November 4, 2014 11
grid
battery
CHP
Boiler
6 3,1 ,1 ,1 ,1 ,1 ,1 ,1 , , , , , , ,
2 124 9
, , , , , , ,7 1
[ ( )] [ ( )]
[ ( )]
gf gf gt gt gas chp boi tj gf t gf tj gt t gt tj gas t chp tj boi tjt j
tj gf t gf tj gt t gt tj gas tj chp tj boi tjt j
Min C P C P C F F C P C P C F F
C P C P C F F
ρ
ρ
= =
= =
⋅ − ⋅ + ⋅ + + ⋅ − ⋅ + ⋅ +∑ ∑
+ ⋅ − ⋅ + ⋅ +∑ ∑
November 4, 2014 12
0 20 40 60 80
100 120 140 160 180
1 3 5 7 9 11 13 15 17 19 21 23
pow
er d
eman
d(kW
)
hour
non-interruptible interruptible
non-controllable total
Power demand with controllable electric load (S4)
-20
-15
-10
-5
0
5
10
15
20
1 3 5 7 9 11 13 15 17 19 21 23
batt
ery
pow
er (k
W)
hour
w/ controllable electric load w/o controllable electric load
Impact of controllable electric load on battery power supply (S4)
-40
-20
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23
grid
pow
er(k
W)
hour
w/o controllable electric load w/ controllable electric load
Impact of controllable electric load on grid power supply (S4)
Scheduling of controllable electric load: The consideration of interruptible electric
load increases the expected daily operation cost by 5.6% compared with the case without interruptible electric load.
Power supply from CHP system is not changed.
Both the power output from electric grid and battery would be changed accordingly in order to meet the extra operation requirement for interruptible electric load.
Results
November 4, 2014 13
0
50
100
150
200
1 3 5 7 9 11 13 15 17 19 21 23
ther
mal
dem
and(
kW)
hour
non-interruptible interruptible
non-controllable total
Thermal demand with controllable thermal load (S4)
0
10
20
30
40
50
60
70
80
1 3 5 7 9 11 13 15 17 19 21 23
CH
P th
erm
al o
utpu
t(kW
)
hour
w/o controllable thermal load w/ controllable thermal load Impact of controllable thermal load on CHP thermal supply (S4)
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23
boil
er th
erm
al o
utpu
t(kW
)
hour
w/o controllable thermal load w/ controllable thermal load Impact of controllable thermal load on boiler thermal supply (S4)
Scheduling of controllable thermal load: The expected daily operation cost
increases by 3.2% The scheduling of interruptible thermal
load is influenced by both electricity price and natural gas price
The maximum thermal output from the CHP unit decreases from 74.1 kW per hour to 70.8 kW per hour
The boiler unit increases its maximum thermal output from under 50 kW per hour to above 100 kW per hour
Results