Demand Response
Management in Power
Systems Using Particle
Swarm Optimization
Pedro Faria, Zita Vale, João Soares, and Judite Ferreira
Competitive electricity markets have arisen as a result of power- sector restructuration and power-system
deregulation. The players participating in competitive electricity markets must define strategies and make
decisions using all the available information and business opportunities.
1–3
Demand response (DR) has proven an
effective approach for allocating electri-
cal loads, gaining a competitive advantage,
and providing significant benefits for elec-
tricity market performance. DR programs
can increase power consumption efficiency
through active consumer participation,
showing the value that each consumer attri-
butes to his or her individualized additional
demands.
Recent efforts aim to improve wholesale
markets with more intensive use of DR. This
includes, for example, the acceptance of de-
mand bids and offers for ancillary services;
the specification by the DR resources of the
frequency, duration, and level of participa-
tion in consumption reduction; and the exis-
tence of aggregators that bid into the market
on behalf of customers.
4
Fully leveraging all of the advantages of
active consumer participation requires an
infrastructure able to accommodate all cen-
tralized and distributed energy resources.
This approach corresponds to the practical
implementation of smart grids,
5
which are
currently the focus of significant research
efforts. In practice, DR programs imple-
mentation is in an initial stage, using tech-
nologies close to smart metering.
The available DR opportunities should be
used in the best way to attain the involved
agents’ goals. This entails time-consuming
and complex optimization problems, requir-
ing huge computational means. Traditional
optimization methodologies are usually not
able to cope with this type of problem for
realistic cases. Researchers have used arti-
ficial intelligence techniques to address sev-
eral problems in the scope of power systems
and electricity markets.
6–7
Particle swarm
optimization (PSO)
8–9
has been successfully
applied to power systems
10
and is proposed
in this work to address DR management.
T
hi
s
a
r
t
icl
e
p
r
ese
nt
s
a
DR
si
mula
t
o
r
(
call
e
d
D
e
mSi
)
t
ha
t
w
e
d
e
v
e
l
o
p
e
d
t
o
s
imu-
la
t
e
t
h
e
u
se
o
f
DR
p
r
o
g
r
am
s
.
D
e
mSi u
ses
P
o
w
e
r
S
y
s
t
e
m
s
C
A
D
(
P
S
C
A
D
;
see
h
tt
p
s:
//
h
v
dc
.
ca
/
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s
cad
)
f
o
r
n
e
t
w
o
r
k
si
mula
t
i
o
n
a
n
d
provides users with optimized DR
action management. The proposed
methodology considers DR in terms
of electricity price variation imposed
by the distribution network operator
in the presence of a reduction need
for any reason, such as lack of gener-
ation or high market prices. The pro-
posed method is based on the use of
real-time pricing. This price-responsive
approach would help address the dif-
ficulties in monthly fixed-remuner-
ation programs, such as direct load
control, and when the smart grid is at
an initial implementation stage.
Demand Response Concepts
and Programs
DR includes all intentional electricity-
consumption pattern modifications
by end users that alter timing, in-
stantaneous-demand level, or total
electricity consumption
11
in response
to changes in electricity’s price over
time. Further, we can also define DR
as incentive payments designed to in-
duce lower electricity use at times of
high wholesale market prices or when
system reliability is jeopardized.
12
their electricity consumption during
times of especially high demand
13
and
usually occur through utility-load-
management programs aiming es-
sentially at obtaining peak reduction.
Competitive electricity markets enable
a wide set of new opportunities for
more strategic consumer behavior and
new models of DR.
Several studies have shown that
loads aren’t rigid, exhibiting elasticity
that can be used for the mutual ben-
efit of power systems and consum-
ers. Changes in electricity prices over
time and incentive payments increase
demand flexibility as users intention-
ally modify their electricity consump-
tion patterns in response to exterior
stimulus. DR can be contracted over
longer or shorter periods, either as
a result of its inclusion in capacity
markets or directly through bilateral
contracts.
DR, including real-time pricing,
can be used to optimize distribution-
network operation, reduce incident
consequences, and reduce wind cur-
tailment.
14
DR programs can be used
to both increase and decrease load
consumption in these periods helps to
overcome this problem.
Measures and Programs
Price elasticity is a measure used in
economics to evaluate the respon-
siveness of the demanded quantity of
a good or service to a change in its
price, or the percentage change in
quantity demanded in response to a
one percent price change.
15
In electric
loads, price elasticity is a normalized
measure of the intensity of how usage
of electricity changes when its price
changes by one percent. In the oppo-
site way, demand elasticity is a mea-
sure of how price changes when usage
of electricity changes.
Demand price elasticity can be
evaluated using Equation 1, where
Quantity is the quantity of the us-
age of the good or service and Price
is the price of this good or service.
16
Quantity and Price refer to the
quantity of usage and price variations
between the periods before and after
the implementation of DR programs.
DR Benefits
An important advantage of DR im-
demand. The use of DR to reduce
load consumption in peak, congested,
and/or incident periods helps distri-
(1)
plementation is the postponement of
investments in generation resources
and transmission and distribution
lines. This is highly important when
the generation is near its maximum
capacity with exponentially increas-
ing generation costs. In these condi-
tions, a small reduction in load will
cause a big reduction in generation
costs and, therefore, a significant re-
duction in the price of electricity.
Usually the actions that result from
demand-side behavior or those in-
tended to manage consumer behavior
are referred to as DR, load manage-
ment, and demand-side management.
Traditionally, these measures are taken
to encourage consumers to reduce
bution network operators by relieving
the network components. In this way,
important benefits can be achieved in
terms of reliability and service qual-
ity, cost minimization, and savings
on network investments. In the case
of incidents, the contracted load cur-
tailment is expected to minimize the
nonsupplied load’s monetary global
value. Increases of wind-based elec-
tricity generation systems and the
wind’s intermittent nature often lead
to periods of excess generated energy.
This imposes relevant losses in wind
curtailment, making wind farms less
efficient and the corresponding in-
vestment payback period higher. The
use of DR programs to increase load
We can divide DR programs into
two general groups: price and incen-
tive based.
17
Price-based DR is related
to changes in energy consumption by
customers in response to variation in
the prices they pay. This group in-
cludes three key pricing rates:
•
Time-of-use pricing includes differ-
ent prices for usage during different
periods, usually defined for periods
of 24 hours. This rate reflects the
average cost of generating and de-
livering power during each period.
•
Real-time pricing defines the price
of electricity for shorter time pe-
riods, usually one hour, reflecting
changes in the wholesale price of
Qu
an
tity
Qu
an
tity
Pr
ic
e
Pr
ic
e
electricity. Customers usually have
the information of prices one day
or one hour beforehand.
•
Critical-peak pricing is a hybrid of
the other two pricing programs.
The base program is time-of-use,
with a much higher peak pricing
applied under specified conditions
(for example, when system reliabil-
ity is compromised or supply costs
are high).
For different hours or time periods,
if the price varies significantly, cus-
tomers can respond with changes in
energy use. Response to price-based
DR programs is entirely voluntary.
I
n
c
e
nt
i
v
e
-ba
se
d
DR
i
n
clud
es
p
r
o
-
g
r
am
s
t
ha
t
gi
v
e
cu
s
t
o
m
e
r
s
fi
x
e
d
o
r
t
im
e
-
v
a
r
y
i
n
g i
n
c
e
nt
i
v
es
a
n
d
t
ha
t
c
o
m-
pl
e
m
e
nt
t
h
e
i
r
e
l
e
c
t
r
ici
ty
r
a
t
e
.
U
t
ili
ty
c
o
mpa
n
i
es
,
lo
ad-
se
r
v
i
n
g
e
nt
i
t
i
es
,
o
r
a
r
e
gi
o
n
al g
r
id
o
p
e
r
a
t
o
r
ca
n
es
t
abli
s
h
t
h
ese
app
r
o
ach
es
.
S
o
m
e
o
f
t
h
ese
p
r
o
-
g
r
am
s
p
e
n
ali
z
e
cu
s
t
o
m
e
r
s
wh
o
f
ail
t
h
e
c
o
nt
r
ac
t
ual
r
es
p
o
n
se
wh
e
n
a p
r
i-
o
r
i
s
p
e
ci
fi
e
d
e
v
e
nt
s
a
r
e
d
e
cla
r
e
d
.
T
hi
s
g
r
o
up i
n
clud
es
p
r
o
g
r
am
s
s
uch a
s
di-
r
e
c
t
lo
ad c
o
nt
r
o
l
,
i
nt
e
rr
up
t
ibl
e
/
cu
r
t
ail-
abl
e
se
r
v
ic
e
,
d
e
ma
n
d biddi
n
g
/
buybac
k
,
e
m
e
r
g
e
n
c
y
DR
,
capaci
ty
ma
r
k
e
t
,
a
n
d
ancilla
r
y
s
er
v
ic
es
ma
r
k
e
t
.
In other work, Lorna Greening ex-
poses the expected responsibilities
and functions of each player in a de-
regulated electricity market.
18
Green-
ing states that larger participation is
required for DR to be viable in the
scope of electricity markets, and that
this requires a more intensive collab-
oration between regulators, market
participants, and market and system
operators.
Katherine Hamilton and Neel Gul-
har propose a complex-bid, market-
clearing mechanism that considers
price-sensitive bids made by consum-
ers.
19
This work quantifies the effect
of the increasing participation of the
demand-side on various categories
of market participants. The authors
conclude that the increase of demand
shifting causes the reduction of market-
clearing prices, benefiting all bidders
even if they don’t participate in the
shifting activities.
Direct load control is a DR model
for which the utility is able to control
customer equipment. This control has
shown positive results, avoiding the
use of additional generation. Imple-
mented models have been applied to
air conditioners and water heaters.
However, some problems related to
the functioning of switches installed
by the utility have been reported. In
the future, with further implementa-
tion of the smart grid concept with
two-way communication ability, it’s
expected that utilities will have bet-
ter control over the target equipment.
This is important because incentive
payments are usually paid monthly to
customers as fixed rates.
20
Although
this concept isn’t presently considered
useful, utilities are planning to of-
fer programs in which they give cus-
tomers price signals through smart
pricing programs. These signals are
expected to give incentives to custom-
ers to make their own investments in
DR equipment.
20
Problem Formulation and
Resolution
The DR problem that we consider
here is motivated by a need to reduce
the energy supply to a set of con-
sumers by a specified amount. This
event is managed by a consumer ag-
gregator, aiming at minimizing the
global value paid by the consumers.
To achieve this goal, the aggregator
considers the individual consumers’
price elasticity, which relates demand
reduction with price increase. Indi-
vidual load reduction and price in-
creases that minimize the consumers’
global cost are determined for each
consumer.
Problem Formulation
The problem we aim to solve consists
of the optimal minimization of the
global costs from the point of view
of electricity consumers, regarding
loads managed by a load aggregator.
The problem’s characteristics lead to
a nonlinear model.
In practice, when a reduction in
electricity consumption is needed,
the aggregator, based on its knowl-
edge about the consumers, raises the
price of electricity with the expecta-
tion that consumers will reduce their
electricity use. The objective function
can be expressed as shown in Equa-
tion 2 and is subjected to several
constraints.
Min Cost
nc
E
Lo
ad
(
c
)
E
LoadRed
(
c
)
c
1
Pr
ic
e
En
ergyIni
ti
al
(
c
)
Pr
ic
e
En
ergyVar
(
c
)
(2)
Here,
Cost
is the total load
consumption cost,
nc
is the number
of consumers,
E
Load(c)
is initial energy
consumption of consumer
c
,
E
LoadRed(c)
is energy consumption reduction of
consumer
c
,
Price
EnergyInitial(c)
is ini-
tial electricity price for consumer
c
,
and
Price
EnergyVar(c)
is variation in con-
sumer
c
electricity price. The objec-
tive function in Equation 2 aims to
minimize costs associated with elec-
tricity consumption (that is, the to-
tal amount consumers pay) when an
overall demand reduction is required.
We can calculate these costs based on
the final load demand (initial load
demand minus demand reduction
value) and on the final price (initial
price plus the price increment used
to obtain the required consumption
reduction).
Limitations are imposed on each
customer’s power (see Equation 3)
and price (Equation 4) variations
according to the extent in which they
can and/or want to participate in the
DR program and to their price elas-
ticity. Power system operation re-
quires the balance between load and
generation to be guaranteed at all
times (see Equation 5).
P
LoadRed(c)
MaxP
LoadRed(c)
(3)
Price
EnergyVar(c)
MaxPrice
EnergyVar(c)
(4)
nc
nc
P
Main
P
Re
serv
e
P
L
oad
(
c
)
P
LoadRe
d
(
c
)
,
Particle swarm Optimization
The optimization of the formulated
nonlinear problem consists of the
minimization of a multimodal func-
tion with many local minima and a
global optimum. This is considered
an NP-hard problem because the
computational complexity is high
even in simple cases.
In past decades, AI techniques
have deployed a set of effective and
efficient methods to mitigate the dif-
ficulties of solving complex com-
putational time problems. These
Simulator
DemSi is a DR simulator that we de-
veloped to simulate the use of DR
programs. We used PSCAD as the
base platform for the network simu-
lation, enabling the use of detailed
models of electrical equipment and
the consideration of transient phe-
nomena. These abilities are relevant
to analyze the technical viability of
the DR proposed solutions, both for
steady state and transients (although
we don’t present network response to
load changes here).
c
1
c
1
(5)
algorithms explore a given search
space and return the best solution
found. PSO belongs to the category
DemSi considers the players in-
volved in the DR actions and allows
result analysis from each specific
where MaxP
LoadRed(c)
is the maxi-
mum permitted variation in power
for consumer c; MaxPrice
EnergyVar(c)
is the maximum permitted variation
in energy price for consumer c; P
Main
is power received from the main grid;
P
Reserve
is reserve power; P
Load(c)
is ini-
tial power consumption of consumer c;
and P
LoadRed(c)
is power consumption
reduction of consumer c.
The consideration of load response
is formulated based on elasticity val-
ues (see Equation 6). Because the
elasticity is a fixed and constant value
for each load, the optimal relation
between load and price variation is
determined in the optimization. The
present study considers the obliga-
tion of having the same price varia-
tion for the loads of the same type as
expressed in Equation 7.
Elasticity
(
c
)
P
LoadRed
(
c
)
Price
EnergyInitial
(
c
)
of swarm intelligence methods, and
we use it in this work to solve the DR
problem because it’s effective in dif-
ficult optimization tasks such as non-
linear problems.
21
We describe the
algorithm as follows:
1. START
2. Initialization of param-
eters (maximum veloci-
ties, minimum velocities,
position limits, maximum
iterations)
3. Random generation of ini-
tial values (swarm)
4. REPEAT
5. Reproduction: Each particle
generates 1 new descendent
(movement, new position)
6. Evaluation: Each particle
has its fitness value, ac-
cording to its current po-
sition in search space
7. Store the best solution of
swarm
8. UNTIL termination criteria
(Number of generations)
player’s viewpoint. This includes four
types of players: electricity consum-
ers, consumer aggregators, electricity
retailers (suppliers), and the distri-
bution network operator. Here, we
analyze the case study from the view-
point of a consumers’ aggregator.
Consumers can be characterized
on an individual or aggregated basis.
Based on their profiles, some clients
can establish flexible supply contracts
with their suppliers. DemSi considers
the information concerning the quan-
tity of load that can be cut or reduced
and the corresponding compensa-
tions for each client.
DemSi classifies the loads as five
main types based on function of peak
power consumption, energy destina-
tion, and load diagram:
•
domestic,
•
small commerce,
•
medium commerce,
P
Load(c)
Price
EnergyVar(c)
(6)
9. END PSO
We then compared the results and
•
large commerce, and
•
industrial.
Price
EnergyVar
(
c
)
Price
EnergyVar
(
T
)
,
c
T,
(7)
where Elasticity
(c)
is price elasticity
for consumer c, and T is consumer
type.
performance of this technique with
those obtained with conventional
techniques using the professional op-
timization tool, General Algebraic
Modeling System (GAMS; see www.
gams.com).
Figure 1 shows DemSi’s general
architecture.
To fully attain our goals, PSCAD
is linked with Matlab (see www.
mathworks.com) and GAMS. These
links let us use programmed modules
to model the relevant
players’ behavior and re-
lationships, focusing on
the contracts between
each client and each
supplier. The formulated
optimization problem’s
solution is found using
Matlab and/or GAMS.
Using diverse approaches
for solving the optimiza-
tion problems, it’s pos-
sible to derive the best
approach for each type of
situation.
Once the simulation is
started, a simulation time-
line feeds DemSi with time-
tagged events. PSCAD
simulates all physical phe-
nomena related to the
power system. The man-
agement of DR programs
is undertaken by a module
Figure 1. The DemSi architecture. A simulation timeline is used
to feed DemSi with time-tagged events. Power Systems CAD
(PSCAD) simulates the physical phenomena related to the power
system; the simulation’s end is determined by the end of the
simulation timeline.
0.12, 0.20, 0.28, and
0.38, respectively, for do-
mestic, small commerce,
medium commerce, large
commerce, and indus-
trial consumer types.
The corresponding val-
ues for electricity price,
which correspond to re-
tailer’s flat-rate tariff val-
ues, are 0.18, 0.19, 0.20,
1.16
, and 0.12 euros per
kW hour.
As a restriction on the
proposed formulation, we
consider a price and
power cap; we can pa-
rameterize these cap val-
ues for each case study.
For this case study, the
price cap is equal to 150
percent of the energy
price value and the power
cap is 15 percent of the
developed in Matlab. The simulation’s
end is determined by the end of the sim-
ulation timeline.
Every time the simulator is initi-
ated, an initial state (for example,
load value, breaker state, and so on)
is considered as the departing simu-
lation point. Once the simulation is
launched, the supply information and
the consumer knowledge base have
the required information that allows
optimizing DR program use over
time, allowing the simulation to con-
tinue. The DR program-management
module optimizes the use of DR op-
portunities for each situation.
Case Studies
Here, we illustrate the use of the pro-
posed methodology in the developed
DR simulator DemSi. The case study
considers a distribution network with
32 buses from Mesut Baran and Felix
Wu,
22
which we evolved in a scenario
to the year 2,040 in terms of load
characterization.
23
All the results
presented in this article are obtained
for two scenarios, with 32 and 320
consumers, respectively.
Case Characterization
Table 1 shows the load demand in
the first scenario, with 32 consum-
ers. The second scenario had 10 con-
sumers in each bus, corresponding to
a total of 320 consumers. In this sce-
nario, the 10 loads connected to each
bus have the total power presented
in Table 1 and are of the same load
type. Table 1 also shows each con-
sumer’s type.
In both scenarios, we considered
that all loads of the same type have
the same price variation during the
DR program application. We solved
each scenario and reduction need
with two approaches: with the devel-
oped PSO module and with nonlinear
programming (NLP) implemented in
GAMS. We compared results in terms
of time of execution and solution val-
ues. The values of elasticity are 0.14,
power consumption value for every
customer.
DR program use is triggered by a
load reduction required by the sup-
plier. We consider a set of seven re-
duction values for each scenario. For
each reduction requirement, the en-
ergy price for each consumer type
and the load reduction for each con-
sumer are obtained as a result of the
optimization problem.
Particle swarm Optimization
application Details
The problem described here has five
variables that are the price variation
upper limits for the five load types.
In PSO, these variables are easily
coded—that is, each particle has a di-
mension space of five. Table 2 shows
the results of the performance and
parameters sensitivity analysis of the
method for 1,000 runs.
Given our results, we adopted con-
figuration A for this case study. The
maximum position of each particle’s
Start
Network
data
Supply
information
Consumer
knowledge
base
Network
simulation
(PSCAD)
Simulation
timeline
events
End
Ye
s
Simulation
timeline
end?
No
Demand
response
program
management
