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

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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

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Modeling of building energy system

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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

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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

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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)

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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

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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

= =

= =

⋅ − ⋅ + ⋅ + + ⋅ − ⋅ + ⋅ +∑ ∑

+ ⋅ − ⋅ + ⋅ +∑ ∑

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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

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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