A Multi-Agent System for Households Response to Dynamic Pricing

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21 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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A Multi
-
Agent System for Household
s

Response to Dynamic Pricing

J
iang

W
u
,
Member, IEEE
,
Feng Gao,
Member, IEEE
,

and
Z
hi Xi Kang
.


Abstract

Demand response
behaviors

of
retailers

are very important for dynamic pricing
mechanism

design and analysis.
This paper presents a multi
-
agent system to simulate the household response to
dynamic pricing. In each household, the best activities under real time pricing for every major electric
ity
devices
with their own
characteristics and flexibilit
ies

are formulated as mixed integrated linear
programming problem
s
. Then a Markov gaming framework is used to analysis the response behavior of
each household.

Some study cases
show

the households
response
behavior

in different situations.

Index Terms

Dynamic Pricing, Demand Response, Multi
-
agent, Game Theory
,
Q
-
learning



I.

I
NTRODUCTION

Dynamic pricing
encourages the demand side to be more active

in demand response. Some study
have shown that d
ynamic pricing would have given customers an incentive to lower loads during peak
times ,
as well as
would have reduced market
-
clearing prices
[
1
-
3
]
. But some
experiment
s

also
show
ed

that
sometimes households are not active
enough

to check prices and respo
nse to them if the
price values can only be available via telephone and the internet

[
4
]
. With the
development

of smart
gird
technology
,
Advanced
m
etering
i
nfrastructure

(AMI),
smart meter, in
-
home display and
intelligent

load control devices make
the
demand response is convenient and efficient for households.
Then i
t is
important to know what the
characteristics

and flexibility

of
residential

customers

and how much they
will response to the price
signals
.

This paper presents a multi
-
agent system to si
mulate the household r
esponse to dynamic pricing. In

each household,
the best activities under real time pricing for every major
electricity

devices are
formulated as mixed
integrated

linear programming problem. Then a Markov gaming framework is
used to analysis the response behavior
of each household.


II.

P
ROBLEM
F
ORMULATION

A.
Multi
-
Agent System Framework


Fig. 1.
Frame work for multi
-
agent system based households


demand response simulation

As shown in fig. 1, each agent
presents a household. Within each agent, the response behavior of
each major electricity devices is formulated
.

B.
Models of Electricity Devices


Response

Behavior


S
pace heating &

cooling, hot water, washer
& dryer, and lighting used most of electricity in
household, which are 45%, 12%, 10%, 7% respectively

[
5
]. Each of them has different
patterns in
response to changes in the price of electricity over time
.

Generally, residential

customers can
response to dynamic price
by reschedule
household activities

in
following three ways: firstly, they can
reduce their electricity usage during peak periods when prices
are high
with
a temporary loss of comfort

(
e.g. lighting
)
.

Secondly, cust
omers may respond to high
electricity prices by shifting some of their peak demand operations to off
-
peak periods (e.g.,
washer
and dryer
)
.

Thirdly, customers can reduce their usage as well as shift some peak demand on
pre
-
heating or pre
-
cooling

by some kinds of storages (e.g. air
-
condition

and hot water heating).

Based on the discussion above, three
types of response
behaviors

can be formulated as follows:

1)

Type 1
:
The
device
demand

profile

only depends on the situation and operating status in

current
time. T
here is
no
relationship within
neighbor times

in demand response
.

Lighting and basic load
are formulated as this type. The best response under real time pricing is:

0
min ( ) ( ) ( )( ( ) ( ))
t p t t d t d t
  


t
=1, 2, 3,

,
T
.

s.t.


( ) ( )
p t d t


0
0 ( ) ( ) ( )
d t d t D t
   


2)
Type 2
:
The
device

demand
profile depends on not only the situation and operating status in
current time, but also those in
neighbor

times
. The response
behavior

is coupled with times.

Spacing cooling and hot water heating are formulated as this type. The best response under real time
pricing is:



0
1
min ( ) ( ) ( )[ ( ) ( )]
T
t
t p t t d t d t

  


s.t.


( 1) ( ) ( ) ( ) ( )
V t p t d t v t V t
    

( )
V V t V
 

0
0 ( ) ( ) ( )
d t d t D t
   

3)
Type 3
:
The device demand profile is independent on the time of use.
Such device can be
started to use in anytime of the day or night
with uncontrollable demand profile
and
will
be shut down
after a certain time.

Washer and dryer
are formulated as this type. Th
e best response under real time
pricing is:

1
min ( ) ( ) ( )
T
t
t u t d t




s.t.


( ) 1 ( ) 1 ( 1,2,...,)
u t s if u t s
   


1
( )
T
t
u t U




Where
p
(
t
) and
d
(
t
) are electricity
consuming

and demand,
λ
(
t
) and
μ
(
t
) are real time pricing and
comfort
-
loss factor respectively.
V
(
t
) is the storage
column

of
devices
type 2. u(t) means the
state
-
up
decision

of
devices type 3

II
I
.

S
OLUTION
M
ETHODOLOGY

Under dynamic pricing framework, e
ach
agent (household)
ha
s

only the information on his/her

own
devices status, demand profile and current retail price
,

but lacks information on other participants.

Thus, the demand response process is a stochastic process.
To apply the
Q
-
Learning algorithm in the
demand response

strategy

for
households
to achieve their objectives, it is necessary

to define the st
ates,
actions, and rewards
of the game
.

1)
States
: The state of environment is represented by the

market
retail
price
s
, which is equally
divided into

2
0

intervals between
2
0 $/MWh and the market ceiling price

40

$/MWh
.

2)
Actions
: Each
type

of devices
has

his own actions under different retail prices, which is shown in
Fig. 2.

3)
Rewards
:
The reward of each agent is also decomposed into every device, which is defined as the
objective

functions in section II.


Fig.
2
.
Action sets for different types of
electricity

devices.

I
V
.

U
SE
C
ASE
S
TUDIES


Fig. 3 Lighting, cooling and hot water demand




Fig. 4 Dynamic prices in summer peak day

V
.

C
ONCLUSION

In this paper, a Multi
-
agent system is used to
simulate the households demand response to dynamic
pricing. T
h
e
character
istics and flexibilities of major
electricity

devices (air condition, hot water
heating, lighting, washer and dryer,
etc.
) are modeled as the response behaviors respectively. A
Q
-
le
arning a
lgorithm

is used to analysis the e
quilibrium

of dynamic pricing and demand response.
The study case shows that dynamic pricing
encourages the
households

to be more active

in
demand
response.

VI
.

R
EFERENCES

[1]

C. Triki and A. Violi, “Dynamic pricing
of electricity in retail markets,” 4or
-
a Quarterly Journal of Operations Research,
vol. 7, (no. 1), pp. 21
-
36, Mar 2009.

[2]

A. Faruqui and S. Sergici, “Household response to dynamic pricing of electricity: a survey of 15 experiments,” Journal of
Regulatory Ec
onomics, vol. 38, (no. 2), pp. 193
-
225, Oct 2010.

[3]

F.A. Wolak, “Do Residential Customers Respond to Hourly Prices? Evidence from a Dynamic Pricing Experiment,”
American Economic Review, vol. 101, (no. 3), pp. 83
-
87, May 2011.

[4]

A. Mohsenian
-
Red, L. Alberto
, “
Optimal Residential Load Control
w
ith

Price Prediction in Real
-
Time Electricity

Pricing
Environments,”
IEEE Trans.
o
n Smart Grid
, vol. 1, (no.
2
), pp.
120
-
133
,
Sep.

201
0
.

[5]

U.S. Department of Energy,

Buildings Energy Data Book

,
http://buildingsdatabook.eren.doe.gov
.

0
5
10
15
20
25
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time Index (h)
Demand (kWh)


Lighting
Cooling
Hot water
0
5
10
15
20
25
20
22
24
26
28
30
32
34
36
38
40
TIme Index (h)
Electricity Price ($/MWh)


Initial
Equilibrium
Confortable

First

Cost
-
saving First

Type 1

P
re
-
production

Equal to demand

Type 2

Start
-
on

Shut
-
up

Type 3

Less
production