Energy Efficient Control of a gy
Smart Grid with Sustainable Homes b d Di ib i Ri k
based on Distributing Risk
Prof. Brian C Williams
with support from Masahiro Ono, with
support from Masahiro Ono,
and Wesley Graybill
8th CMU Electricity Conference
March 14th, 2012
Motivation: High Penetration of Renewables
Electrical grid must prepare for high penetration of renewables.
Challenge: Wind and solar are undispatchable, intermittent, and unpredictable.
d
d bl
Key Elements of Approach
1. Increase controllability on demand side through
– Flexible specifications of user needs and preferences, and
– goal‐directed optimal planning.
2. Improve robustness to uncertainty in supply and demand through
g
– risk‐constrained planning and – distributed risk markets.
distributed risk markets.
3. Reduce labor, hence adoption barriers, by automating
by automating
– Inference of expected user and environmental behavior, and
– model
d l acquisition of physical plant and customer behaviors
iii
f h i l l
d
b h i .
Architecture: Risk‐constrained, Goal‐directed Grid Control
Key Technologies
Risk allocation
Goal‐direction
Framework
Market‐based
Non‐dispatchable Resource allocation
supply
l
(solar, wind)
Dispatchable supply
(Micro‐CHP, biomass)
Demand
Micro-grid
Micro
grid
Contingent power dispatch
~24 hr time scale
Goal‐directed p
demand response (buildings & E‐cars)
Goal‐directed Demand Response p
• Today: Demand
y
is inelastic, supply adapts.
pp y
p
• Goal: introduce flexibility in meeting demand.
• Approach:
A
h
– Acquire descriptions of the consumer’s intended activities, constraints and preferences.
– Exploit flexibility in activity descriptions to reduce
p
y
y
p
• overall energy consumption,
• peak demand, and
peak demand, and
• risk of failing to support important consumer activities.
5
Testbed: Connected Sustainable Home
Federico Casalegno (PI), MIT Mobile Experience Lab
Federico Casalegno
(PI) MIT Mobile Experience Lab
•
•
•
•
Goal: Optimally control HVAC, window opacity, washer/dryer, e‐car.
Objective: Minimize energy cost.
Uncertainty: Solar input, outside temp, energy supply, occupancy.
Risk: Resident goals not satisfied; occupant uncomfortable.
6
Example Goals: Description of Resident Activities
Description of Resident Activities
“Maintain
Maintain room temperature after waking up until I go to
work. No temperature constraints while I’m at work, but
when I gget home, maintain room temperature
p
until I ggo to
sleep. Maintain a comfortable sleeping temperature while I
sleep. Cook dinner within at least an hour of arriving home,
andd at least
l
3 hours
h
before
b f
bed.
b d Also,
Al dry
d my clothes
l h before
b f
morning. I need to use my car to drive to and from work, so
make sure it is fully charged by morning.
morning It’s
It s acceptable if
my clothes aren’t ready by morning or if the house is a
p degrees
g
too cold, but myy car absolutelyy needs to be
couple
ready to use before I leave for work.”
7
Example Goals: Description of Resident Activities
Description of Resident Activities
“Maintain
Maintain room temperature after waking up until I go to
work. No temperature constraints while I’m at work, but
when I gget home, maintain room temperature
p
until I ggo to
sleep. Maintain a comfortable sleeping temperature while I
sleep. Also, dry my clothes before morning. I need to use my
car to drive
d i to andd from
f
work,
k so make
k sure it
i is
i fully
f ll
charged by morning. It’s acceptable if my clothes aren’t
ready by morning or if the house is a couple degrees too
cold, but my car absolutely needs to be ready to use before I
leave ffor work.”
8
Example Goals: Description of Resident Activities
Description of Resident Activities
“Maintain
Maintain room temperature after waking up until I go to
work. No temperature constraints while I’m at work, but
when I gget home, maintain room temperature
p
until I ggo to
sleep. Maintain a comfortable sleeping temperature while I
sleep. Also, dry my clothes before morning. I need to use my
car to drive
d i to andd from
f
work,
k so make
k sure it
i is
i fully
f ll
charged by morning. It’s acceptable if my clothes aren’t
ready by morning or if the house is a couple degrees too
cold, but my car absolutely needs to be ready to use before I
leave ffor work.”
9
Example Goals: Description of Resident Activities
Description of Resident Activities
“Maintain
Maintain room temperature after waking up until I go to
work. No temperature constraints while I’m at work, but
when I gget home, maintain room temperature
p
until I ggo to
sleep. Maintain a comfortable sleeping temperature while I
sleep. Also, dry my clothes before morning. I need to use my
car to drive
d i to andd from
f
work,
k so make
k sure it
i is
i fully
f ll
charged by morning. It’s acceptable if my clothes aren’t
ready by morning or if the house is a couple degrees too
cold, but my car absolutely needs to be ready to use before I
leave ffor work.”
10
Example Goals: Description of Resident Activities
Description of Resident Activities
“Maintain
Maintain room temperature after waking up until I go to
work. No temperature constraints while I’m at work, but
when I gget home, maintain room temperature
p
until I ggo to
sleep. Maintain a comfortable sleeping temperature while I
sleep. Also, dry my clothes before morning. I need to use my
car to drive
d i to andd from
f
work,
k so make
k sure it
i is
i fully
f ll
charged by morning. It’s acceptable if my clothes aren’t
ready by morning or if the house is a couple degrees too
cold, but my car absolutely needs to be ready to use before I
leave ffor work.”
11
Flexibility Available to Control
• When activities are performed.
p
• When to charge/discharge batteries.
g /
g
• Which activities to shed (when supply is low).
Which activities to shed (when supply is low).
12
Encoding: Qualitative State Plan (QSP)
[24 hours]
Wake
up
[1‐3 hour]
Maintain room
temperature
[7‐9 hours]
Go to
work
Home
from
work
Maintain room
temperature
“Maintain room temperature after waking
up until I go to work. No temperature
constraints while I’m at work, but when I
get home, maintain room temperature
until I go to sleep. Maintain a
comfortable
f
bl sleeping
l
temperature while
hl I
sleep.”
13
[7‐8 hours]
[6‐8 hours]
Go to
sleep
Maintain comfortable
sleeping temperature
Wake
up
Encoding: Qualitative State Plan (QSP)
[24 hours]
Wake
up
[1‐3 hour]
Maintain room
temperature
[7‐9 hours]
Go to
work
Home
from
work
[7‐8 hours]
[6‐8 hours]
Maintain room
temperature
Go to
sleep
Maintain comfortable
sleeping temperature
…
“Maintain room temperature after waking
up until I go to work. No temperature
constraints while I’m at work, but when I
get home, maintain room temperature
until I go to sleep. Maintain a
comfortable
f
bl sleeping
l
temperature while
hl I
sleep.”
…
14
Wake
up
Encode the Qualitative State Plan and Dynamics
within a Model-Predictive Controller
min J(X,U)
J(X U)  H(xT )
U
Cost function
Cos
u c o (e
(e.g.
g fuel
ue co
consumption)
su p o )
st
s.t.
Dynamics
(Discrete time)
Constraints
 xt 11  Axt  But
0  t T 1
T N M
   h xt  g
t 0 i 0 j 0
iT
t
ij
t
Mixed Logic or Integer
X  x0  xt 
T
State vector (e.g. position of vehicle)
U  u0  ut 1  Control inputs
T
15
pSulu Results
[24 hours]
Wake
up
Wake
p
up
Maintain room
temperature
16
Go to
work
Home
H
from
work
Maintain room
temperature
Go to
sleep
Maintain comfortable
sleeping temperature
Energy Savings: Optimal Control
• 42.8% savings in winter over PID
• 15.3%, 16.8%, and 4.4% in spring, summer,
autumn
Energy Savings: Flexibility
• Reduction in energy consumption by considering
resident
id t fl
flexibility.
ibilit
• 10.4%, 1.6%, 1.6%, and 0.7% in the winter,
spring, summer, and autumn.
Testbed: Connected Sustainable Home
Federico Casalegno (PI), MIT Mobile Experience Lab
Federico Casalegno
(PI) MIT Mobile Experience Lab
•
•
•
•
Goal: Optimally control HVAC, window opacity, washer/dryer, e‐car.
Objective: Minimize energy cost.
Uncertainty: Solar input, outside temp, energy supply, occupancy.
Risk: Resident goals not satisfied; occupant uncomfortable.
19
Managing Uncertainty and Risk
•
•
20% usage
rate – XeroxisPARC
Responsive
Environment must
study, 1993.
Occupancy
Uncertain
 Controller
take
Each room has a different occupancy profile.
profile
Occupancy probability
risk.
Late lunch @ 2pm
100%
Crazy night workers
Max occupancy
rate @ 5pm
0%
12am
6am
12pm
6pm
CSAIL students cannot wake up early
12am
Control Decisions Imply Risk
• When should a controller take risk?
– Risk at time t : δt
– Acceptable risk over time horizon: ∆
t  0 or pt
T

t

pt : Occupa
ancy pro
obability
δt : Risk a
allocated
d at t
t1
100%
δt= 0
δt = pt
0%
12am
6am
12pm
6pm
12am
Approach: Risk Allocation
with Masahiro Ono
Framework :
– Chance-constrained
Stochastic Optimization.
Optimization
Methods:
– Iterative
te at e Risk
s Allocation
ocat o ((IRA))
algorithm.
– Market-based
Market based Iterati
Iterative
e Risk Allocation
(MIRA) algorithm.
22
Example: Race Car Path Planning
Planned Path
Actual Path
Goal
Walls
Start
23
Example: Race Car Path Planning
Planned Path
Actual Path
Goal
Walls
• C
Cannott guarantee
t 100%
safety.
• Driver wants a probabilistic
guarantee:
P(crash) < 0.1%
Chance constraint.
Start
24
Chance‐Constrained Optimal Planning
minT J (u1:T )
u1:T U
st
s.t.
Stochastic dynamics
T 1
Convex function
Cost function (e.g. fuel consumption)
( g
p
)
 xt 1  Axt  But  wt
t 00
wt ~ N (0,  t )
x0 ~ N ( x0 ,  x , 0 )
25
Assumption: Δ < 0.5

iT
i
Pr    ht xt  g t   1  
t 1 i 1

T N
Chance constraint
Chance constraint
Risk bound
(Upper bound of the probability of failure)
probability of failure)
Example: Race Car Path Planning
Planned Path
Actual Path
Safety Margin
Walls
Safety Margin
n
Goal
• C
Cannott guarantee
t 100%
safety.
• Driver wants a probabilistic
guarantee:
P(crash) < 0.1%
Chance constraint.
Start
• Approach: design safety
margin.
26
Iterative Risk Allocation (IRA) Algorithm
• Starts from a suboptimal risk allocation.
• Improves the risk allocation through iteration.
iteration
Iteration
27
Iterative Risk Allocation Algorithm
Algorithm IRA
No gap = Constraint is active
1
2
3
G
Goal
4
Best available path
given the safety margin
5
Safety margin
Start
6
Gap = constraint is inactive
28
Initialize with arbitrary risk
allocation.
Loop
Compute
p the best ppath for
the current risk allocation.
Decrease risk where a
constraint
t i t is
i inactive.
i ti
Increase risk where a
constraint is active.
End loop
Iterative Risk Allocation Algorithm
Algorithm IRA
1
2
3
G
Goal
4
5
Safety margin
Start
6
29
Initialize with arbitrary risk
allocation.
Loop
Compute
p the best ppath for
the current risk allocation.
Decrease risk where a
constraint
t i t is
i inactive.
i ti
Increase risk where a
constraint is active.
End loop
Iterative Risk Allocation Algorithm
Algorithm IRA
1
2
3
G
Goal
4
5
Safety margin
Start
6
30
Initialize with arbitrary risk
allocation.
Loop
Compute
p the best ppath for
the current risk allocation.
Decrease risk where a
constraint
t i t is
i inactive.
i ti
Increase risk where a
constraint is active.
End loop
Robust-IRA- MPC for Dynamic Window
Solar heat input
Outside temperature
Comfortab
C
ble range
Ro
oom Temp
perature
6am
12pm
6pm
Heat the room using sunlight
sunlight…
Optimal temperature
…so
so that the temperature will stay within the comfortable
range WITHOUT using heaters in the night
31
Application: Building Control
(a) First Iteration
30°C
Active 25°C
22°C
22
C
20°C
18°C
Home
Asleep 5°C
0 am
(b) Second Iteration
Active Away Home
Home
Asleep Away Home
Inactive
8 am 12 pm
5 pm 12 pm
0 am
8 am 12 pm
5 pm
12 pm
: Safety
S f t margin
i
: Optimal plan at current iteration
: Optimal plan at previous iteration
Take risk of violating resident
constraints where largest energy
savings are possible.
Robust-IRA-MPC Results
Margin protects
against uncertainty
33
Results
Improvement in Comfort
• Deterministic control (Sulu): 30% comfort
violations.
i l ti
• Risk-sensitive control (p-Sulu): near 0%
violations.
((Sub)Urban
)
Scale Sustainability
y
• Heterogeneous
connected homes with
different energy
sources.
• Symmetric energy
exchange between
houses.
houses
• Challenge:
– How to distribute
energy optimally,
– while limiting the risk of
an energy
gy shortage,
g ,
– without centralized
control.
Allocation between Risk‐coupled Agents
p
g
Operator
I
i
i
min
J
(
U
)
1:I
1:I 
specifies
U U
System’ss risk bound: System
risk bound: 0.1%
s.t.
Risk is distributed among agents
+
0.04%
Multi‐agent i 1
 I N i iT i
i
Pr    hn X  g n   1  

i 1 n 1
0.06%
Decomposed, deterministic RA reformulation min
1:I
1:I
U U , i1::NI
s.t.
Risk is distributed among constraints

1
1
0.02%

1
2
0.01%

1
3

0.01%
0.01%
2
1

2
2
0.02%
37

2
3
0.03%
I
i
i
J
(
U
)

i 1
 
  hniT X i  g ni  mni  ni
i n
I
Ni
i

 n  
i 1 n 1
Allocation between Risk‐coupled Agents
p
g
Operator
I
i
i
min
J
(
U
)
1:I
1:I 
specifies
U U
System’ss risk bound: System
risk bound: 0.1%
Risk is distributed among agents
0.04%
+
Multi‐agent s.t.
i 1
 I N i iT i
i
Pr    hn X  g n   1  

i 1 n 1
0.06%
Decomposed, deterministic reformulation min
1:I
1:I
U U , i1::NI
•
Need to optimize risk allocation between
p
agents since they have different sensitivities to risk.

s.t.
I
i
i
J
(
U
)

i 1
i n
I
Individual
risk bounds

System’s
risk bound
38
 
  hniT X i  g ni  mni  ni
Ni
i

 n  
i 1 n 1
Market‐based Iterative Risk Allocation
Operator supplies risk
Operator
specifies
System’ss risk bound: System
risk bound: 0.1%
Risk is distributed among agents
0.04%
+
0.06%
Agents consume risk 
39
Individual
Demands
risk
for bounds
risk

System’s
Supply
risk
of bound
risk
• Treat each agent as an i d
independent
d
d
decision maker.
k
• Agents communicate through market.
g
y p
• Find a globally optimal solution through iteration.
Approach is economically
• Approach is economically inspired (tâtonnement):
– Risk
Risk is a resource
is a resource traded in a traded in a
market.
– Each agent has a demand
Each agent has a demand for risk
for risk
as a function of the price of risk. Based on Dual Decomposition
Risk taken by
Decentralized
the i’th agent Optimization
Centralized Optimization
((decomposed,
p
, deterministic form))
1:I
min
1:I
U U
s.t.
, i1::NI
I
 J (U
i
i
i’th agent:
t (Primal)
(P i l)
i
i
i
min
J
(
U
)

pD
i
i
i
)
U U ,1:N
i 1
I
T
x
i
t 1
i 1 t 1
I
N
 Ax Bu
i
i
t
i
i 1 n 1
I
N
i
i
n
i
n
 xti1  Ai xti  B i uti
t 1
 
N
 
  h X  g m 
iT
n
s.t.
i
t
Dual variable
T = Price of risk
 hniT X i  g ni  mni  ni
i
n
n 1
Ni
for risk
D i    ni Demand
from i’th agent
i
i

 n  
n 1
i 1 n 1
Market (Dual)
Convex optimization
I
*i
D
 ( p)  
i 1
40
Root finding problem
41
Market-based Contingent Power Dispatch
• Two kinds of energies are traded in a market:
Prob
bability de
ensity
– Nominal power
– Contingent power
Predicted load
Micro-grid
Load (kW)
Mean: 300kW
=Nominal
N
i l power
Standard deviation: 50kW
= Contingent power
Key Elements of Approach
1. Increase flexibility on demand side through
– flexible specifications of user needs and preferences, and
– goal‐directed optimal planning.
2. Improve robustness to uncertainty in supply and demand through
g
– risk‐constrained planning, and
– Distributed risk markets.
Distributed risk markets.
3. Reduce labor, hence adoption barriers, by automating
– Inference of expected user behavior, and
Inference of expected user behavior and
– Models of environment and plant.
Questions?