INTEGRATION OF DEMAND RESPONSE RESOURCE PAYBACK
EFFECT IN SOCIAL COST MINIMIZATION BASED MARKET
SCHEDULING
Mahdi Behrangrad
Hideharu Sugihara
Tsuyoshi Funaki
Osaka University
Osaka, Japan,
Osaka University
Osaka University
Osaka, Japan
Osaka, Japan
Suita shi, 2-1 yamadaoka, P.O.box:565-0871
[email protected] [email protected] [email protected]
Abstract – Demand response (DR) can be defined as
changes in the load demand/energy pattern for improving
the power system economic and reliable operation in return
of receiving financial incentives. Due to low curtailment
frequency and duration of spinning reserve resources,
reserve supplying service suits the nature of DR resources
that have fast response. More DR resources are attracted to
this market. Increase in the reserve supplying demand
response (RSDR) resources necessitates integration of
payback effect of such resources in the market scheduling.
Payback characteristics of this resource can affect the market scheduling. In order to analyze the payback effect,
RSDR resources with payback effect are integrated in a
comprehensive simultaneous market-scheduling framework in this paper. The market scheduling of this paper
adopts a social cost minimization point of view. In order to
reduce the computational burden of the mixed integer
programming (MIP) based objective function of the paper
in day-ahead market, a recursive MIP based optimization
method is developed that reduces the computational burden while maintaining the ability to reach the optimal answer. IEEE RTS 1996 test system with 32 units is utilized
for numerical simulations.
Keywords: Demand response, payback effect, spinning reserve scheduling, probabilistic market scheduling, mixed integer programming
NOMENCLATURE
s
i,t
1 if outage of unit i causes loss of load at
hour t and 0 otherwise.
d
i , j ,t
1 if outage of unit i and j cause loss of
load at hour t and 0 otherwise.
pb , s
i ,t
1 if outage of unit i causes loss of load
when payback occurs at hour t and 0
otherwise.
pb , d
i , j ,t
1 if outage of unit i and j cause loss of
load when payback occurs at hour t and
0 otherwise.
ii.
Continuous variables
Cte
Total energy procurement cost at hour t
[$].
Ctr
Total reserve procurement cost at hour t
[$].
s
Ct
Total start up cost at hour t [$].
Ctint
Total expected load not supplied at hour
t [$].
p ig, t
Scheduled power output of unit i at hour
t [MW].
pir,t
Scheduled reserve contribution of unit i
at hour t [MW].
1.1 Sets
t
i,j
h
Time index with cardinality T (total time
steps).
Unit number index with cardinality NG
(total number of generation units).
DR resource number index with cardinality NH (total number of DR resources).
phdr,t
Scheduled reserve contribution of DR
ELNSt
resource h at hour t [MW].
Total expected load not supplied for
system at hour t [MW].
ELNS ts
Total expected load not supplied for
system with single outage at hour t
[MW].
ELNStd
Total expected load not supplied for
system with double outage at hour t
[MW].
1.2 Variables
i.
uige
,t
Binary variables:
1 if unit has been scheduled “on” in
energy market at hour t and 0 otherwise.
uigr
,t
ELNS t
1 if unit has been scheduled “on” in
Rt
pb
Total expected load not supplied for
system because of payback effect at hour
t [MW].
Total system reserve at hour t [MW].
reserve market at hour t and 0 otherwise.
uhdr,t
1 if DR has been scheduled “on” in
reserve market at hour t and 0 otherwise.
17th Power Systems Computation Conference
Stockholm Sweden - August 22-26, 2011
1.3 Functions
ge ge
Cige
, t (ui, t , pi , t )
Price-quantity function offered by the
i’th generation unit in energy market at
hour t [$/(MW·h)].
gr
gr
Cigr
, t (ui, t , pi , t )
Price-quantity function offered by the
i’th generation unit in reserve market at
hour t [$/MW].
Chdr,t (uhdr,t , phdr,t )
Price-quantity function offered by the
h’th DR resource in reserve market at
hour t [$/MW].
1.4 Parameters
Dt
Total system demand at hour t [MW].
VLNSt
Average value of load not supplied in
OPi
system at hour t [$/MW].
Outage probability of unit i.
SRUP
gmax, gmin
The spinning reserve utilization probability.
Minimum and maximum bound of unit
output [MW].
Pi,gt.l
The piece wise linearization approxima-
RMRi
tion separation point number l of unit i at
hour t.
Ramp up rate of unit i [MW/min].
ah , bh , ch
Payback function coefficients
1- INTRODUCTION
Increasing uncertainty in the generation side of power
system, as a result of integrating intermittent renewable
resource, and increased importance of system reliability
maintenance necessitates taking preventive actions such
as spinning reserve scheduling. The importance of the
spinning reserve optimality and its effect on the energy
and reserve market clearing schedules, has spurred extensive research [1]-[12]. Mostly the generation side has
been considered in the reserve scheduling process and
the demand side is assumed to be inactive. However, the
new concept of electrical energy system smart-grid has
promoted flexible utilization of the demand side potentials. Although the participation of the DR resources in
energy market and reserve service of ancillary service
markets is considered a promising solution, system operators express some concerns about their reliability and
side effects. One of the DR side effects that can affect
the functionality of the DR resources that attend in reserve supplying process is payback effect. The payback
effect means increase in the load energy consumption
because of curtailment in previous hours. This effect has
been observed and modeled in classic direct load control
(DLC) resources.
There are researches addressing different aspects of
the RSDR resources with focus on their economical
aspects and role in the optimal spinning reserve scheduling [1]-[5]. Although there are researches about the
RSDR effects, to the best knowledge of the authors, the
payback effect of DR resources that attend in the reserve
market is not considered and analyzed thoroughly. This
is important because the RSDR resource utilization is
17th Power Systems Computation Conference
increasing in the modern power systems [5]-[11] and one
of the best DR resource candidates for spinning reserve
supplying is air conditioning load [6] which suffers from
payback effect. Therefore it is important to analyze the
effect of DR resource that are not ideal and have payback characteristics.
In this paper the RSDR impact is analyzed with focus
on its payback effect. In order to do so the marketscheduling framework is extended to integrate the payback effect of RSDR resources. The RSDR utilization is
stochastic which makes consideration of its payback
effect different from the payback effect of the DR resources that are utilized in energy market. In case of the
RSDR, the payback effect is like a conditional increase
in the load, bind to the condition that then RSDR is actually utilized in the previous hours. Therefore the RSDR
payback effect has a probabilistic nature. This probabilistic feature is combined with the market scheduling.
However market scheduling based on social cost minimization is computationally intensive and integrating
RSDR payback effect makes it more colossal. Therefore
in this paper a recursive optimization method based on
MIP is developed that will reduce the computational
burden of the problem, while maintaining the ability to
reach to optimal solution.
The next parts of paper are as following; part 2 discusses the modeling of the adopted framework and
RSDR resources. Part 3 presents the optimization method. Part 4 presents numerical results and the part 5
draws the main conclusions of this paper.
2
MODELING
2.1 Objective function
The objective function of the adopted marketscheduling framework consists of the three following
components.
Energy procurement cost ( Cte )
This is mainly the load-generation balance cost
imposed by the price-quantity bid from generation
units and the start up cost at time t.
-
-
s
Start up cost( Ct )
This is the start-up cost at hour t
Cr
- Reserve cost ( t )
This is the reserve procurement cost of the system
that is imposed by price-quantity bidding function
generation units and DR resources.
Interruption Cost ( Ctint )
This term models the economic loss imposed on
the demand side in the case of any involuntary interruption of electrical power at time t. This term has an
opposite relation with the reserve schedule and reserve cost.
In the formulation all these costs should be formulated using unit commitment (UC) decision variables.
These variables are binary commitment and continuous
power output variables. The objective function of the UC
problem is formulated as follows. The solution of this
objective function is the optimal market clearing schedule:
-
Stockholm Sweden - August 22-26, 2011
Minimize
NG NG
pb,d
i, j,t $OP i $ OP j $ SRUP$
i"1 j &i
( pig,t # pir,t # p gj,t # p rj,t # PB(h, t) % Rt ) #
NG
pb,s
! i,t $ OPi $ SRUP$
i"1
( pig,t # pir,t # PB(h, t) % Rt )
ELNS tpb " ! !
T
Obj . func "
! (Cte # Cts # Ctr # Ctint )
(1)
t "1
Where the variables can be defined as follows:
NG
ge ge
g
Cte " ! u ige
, t $ C i , t (u i , t , p i , t )
i "1
(2)
max( 0 , sign ( p ig, t # p ir, t % R t ))
NH
s
i ,t "
h "1
g
d
i , j , t " max(0, sign( pi , t
Ctr " ! u hdr, t $ Chdr, t (u hdr, t , phdr, t ) #
NG
i "1
C
int
t
(3)
" ELNS t $ VLNS t
(4)
Equation (1) is the objective function, (2) is the total
energy procurement cost that is imposed by bids from
the gencos (generation companies) units. Equation (3)
defines the total reserve cost that is imposed by the generation and demand side. Equation (4) is the expected
loss that will be imposed on the load due to generation
unit outages and payback effect. This term is the product
of the value of load not supplied (VLNS) and the probabilistic variable, expected load not supplied (ELNS).
VLNS expresses the value that loads consider for their
continuous electrical energy usage. ELNS shows the
expected load that will not be supplied or average load
shedding in case of loss of load. Equation (5) shows the
total expected load not supplied of the system. Equations
(6) to (7) calculate the expected load shedding in single
and double outage contingencies without payback and
equation (8) calculates the expected load shedding as a
result of payback. Equation (9) shows the expected load
not supplied that unit outage, when there is payback
effect, imposes to the system. As equation (9) shows the
payback amount is addressed in spinning reserve
amount. This is because unlike the DR resources that are
used for peak reduction or load reduction, the actual
utilization of the RSDR resources is stochastic, so it
cannot be addressed in load-generation equality constraint. In other words the probabilistic payback amount
should be considered in calculation of required reserve
amount.
Rt
"
NG
NH
i "1
h "1
r
dr
! pi , t # ! p h , t
(5)
ELNSt " ELNSts # ELNStd # ELNStpb
ELNS ts
NG
"
ELNStd "
!
i "1
s
i ,t
NG NG
! !
$ OPi $( pig,t # pir,t % Rt )
d
i, j ,t
i "1 j &i
$ ( pig,t # pir,t
#
(6)
(7)
$OPi $ OPj
p gj ,t
#
p rj ,t
(10)
# pir, t # p gj , t
# p rj , t % Rt )), 'i, j, i > j
gr
gr gr
r
! ui , t $ Ci , t (ui ,t , pi , t )
(9)
pb, s
g
i , t " max(0, sign ( pi , t
# pir, t # PB (h, t ) % Rt ))
(11)
(12)
pb , d
i, j ,t "
max( 0, sign ( p ig, t # p ir, t # p gj , t # p rj , t
# PB ( h , t ) % Rt )), ' i , j , i > j
PB (h, t ) " ah $ phdr,t %1 # bh $ phdr,t % 2 # ch $ phdr,t %3
(13)
(14)
2.2 Constraints
UC problem is subject to physical, load balance and
inter-temporal coupling constraints. As mentioned
above, the adopted framework is self-contained and does
not require a security constraint for reserve scheduling.
The applied constraints are assumed as follows:
i " NG
g
! pi ,t " Dt
i "1
0(
pir, t
(15)
( gmax
gmin $ u ige
,t
$ u igr
,t
pig, t
(
Min( phdr,t ) $ uhdr,t
(
gmin $ u ige
,t
pig, t
(
(
phdr,t
#
(16)
gmax $ uige
,t
(17)
( Max( phdr,t ) $ uhdr,t
(18)
pir, t
(
gmax $ u ige
,t
(19)
Equation (15) describes the system generation-load
balance constraint. Here it should be noticed that unlike
the DR resources that are used in energy market, the
payback effect of RSDR resources cannot be addressed
in load-energy balance because payback in RSDR resources will happen if the RSDR is actually utilized that
is a stochastic event. Equations (16)-(19) are presenting
the upper and lower bound of the different commodities
of energy and reserve. The upper and lower bound will
be declared by Genco and DR service provider.
pig, t #1 % pig, t ( RMRi $ 60
(20)
pir, t ( RMT $ RMRi
(21)
ge
if (u ige
, t %1 " 1) and (u i , t " 0 )
ge
then ( u ige
, t # ... # u i , t # MinDT ) " 0
(22)
i
% Rt )
(8)
Equations (10) to (13) show the binary loss of load
variable that is 1 in case that loss of load event may
happen, in the addressed contingency with or without
payback effect, and 0 otherwise. Equation (14) shows the
payback function considered in this paper, a weighted
summation of the previous utilization of the DR resource
[5],[7],[8].
17th Power Systems Computation Conference
ge
if (uige
, t %1 " 0) and (ui, t " 1)
ge
then uige
, t to ui, t # MinOT " 1
(23)
i
Equations (20) and (21) consider the ramp up constraint of the unit and its effect on offered energy and
reserve amount. The parameter RMT is a duration that
the unit should fully deliver the reserve amount if asked.
It is usually 10 minutes [9], and this paper considers the
same amount. Equations (22) and (23) are enforcing the
Stockholm Sweden - August 22-26, 2011
minimum down time and minimum up time constraints.
Equation (24) is showing the maximum allowed utilization time for the RSDR resources. These will be declared
by the DR provider and is mostly affected by type of the
loads being involved.
! uhdr,t ( MaxOTh
(24)
t
This type of DR bids its price and capacity limitation to system operator, then based on its market clearing
framework system operator decides whether they are
accepted or not. If accepted at the contracted hour, they
should be ready for reaction if they receive dispatch
signal in short time. In this paper the same structure is
considered for the DR.
The actual spinning reserve utilization probability
SRUP, which can be calculated from UC problem, is
important in the RSDR payback characteristics analysis.
The duration and probability of RSDR actual utilization
can be assumed equal to the probability and duration of
actual spinning reserve utilization. When this probability
is higher the payback characteristics will be more important. In this paper in order to reduce the computational
burden, this parameter is selected as an external parameter instead of calculating it from UC output.
2.3 DR Resources
The proposed DR attends in day-ahead ancillary service market for supplying reserve and responds to events
that threaten the system reliability. Loads that are wellsuited to provide this kind of service include large industrial batch processes, refrigerated warehouses, electric
water heaters, dual-fuel boilers and buildings with sufficient thermal mass to retain ambient temperatures for
brief periods without air conditioning [10]-[11]. These
loads mostly have payback effect. In the current power
system large-scale customers that have relay equipment,
communication equipment and monitoring facilities are
good candidates for reserve procurement programs.
However with the progress of the AMI (advanced metering instrument), small loads can also attend in these
activities through a certified aggregator. There are some
pilot projects using the DLC and air conditioner control
in small loads for reserve procurement [10]-[11]. The
technical and institutional requirement of the loads that
want to attend in this service is dependent on the particular market. The ability to be monitored and having a fast
response to curtailment requests or signals are the most
common requirements. All loads that satisfy these requirements can attend the suitable market. The references [1]-[6],[12] are considering the DR resource as an
aggregated resource which is modeled by its quantityprice bidding function and its operational limitations of
the upper and lower utilization constraint. The same
approach is considered in this paper and the RSDR is
modeled by its quantity-price bidding function and its
operational limitations as is shown in figure 1. It is assumed that the DR resource has high reliability as is
shown in [10]-[11].
Cdri,t ($)
Pdr i,t (MW h)
Min (pdr h,t)
3 OPTIMIZATION METHOD
The optimization method developed in this paper is
presented in figure 2 and can be explained as following:
1-First, assume thresholds for effective single and
double outage contingencies in each hour.
2-The binary variables of equations (10) and (12) for the
units that have maximum capacity less than the single
outage threshold will be considered 0. In the same
manner the binary variables of equations (11) and (13)
for units that have total maximum capacity less than
the double outage threshold will be considered 0
3- Optimize the 24 hour with the assumed threshold for
the contingencies
4-Check whether at hour “t” there is any single outage
contingency that is effective but not taken into account
by checking equation (25). This condition checks
whether the single outage of any unit can be handled
by the scheduled reserve. If this equation is satisfied
then there is no single outage that can impose interruption cost.
( pig, t # pir, t ) ( Reserve t , 'i
(25)
( pig, t # pir, t ) # ( p gj , t # p rj , t ) ( Reserve t , 'i, j , i & j
(26)
5-Using equations (26) check whether there is any
double contingency that is effective but not taken into
account at hour “t”. This condition checks whether the
double outage of any two units can be handled by the
scheduled reserve. Here it should be mentioned that
the optimization method of this paper can consider
higher order of outages but because of high computational burden and the fact that considering higher order
of outages is not a practical scenario in power systems,
up to double outage is considered. In hours that any of
the equations (25) and (26) are not satisfied just fix the
binary commitment variable of units that are switched
“on” in energy and reserve market. The binary commitment variables of the units that were “off” are not
fixed. This is because if extra capacity required, they
can be switched “on” in next iteration. Afterwards the
threshold in that hour should be reduced. If the equation (25) is not satisfied, reduce the single outage threshold. If equation (26) is not satisfied, reduce the
double outage threshold.
6-In hours that the above conditions are satisfied, fix the
whole binary commitment variable of units in reserve
and energy market. No extra unit can be committed in
the next iteration. This is because the optimal reserve
is reached and there is no need to extra capacity.
Max (pdr h,t)
Figure 1: the quantity-price function of the RSDR
17th Power Systems Computation Conference
Stockholm Sweden - August 22-26, 2011
1-Applying effectiveness threshold [MW] to single and
Start
double outage Sthresholdt and Dthresholdt
2- Calculate binary loss of load variables as below:
pb, d
d
If (gmaxi+ gmaxj) < Dthresholdt Then i, j , t & i, j , t =0
pb, s
s
i, t & i , t =0
Else calculate equations (10) to (13)
If (gmaxi) < Sthresholdt Then
3-Optimize the objective function
4- Is equation
(25) satisfied at
hour t?
No
4-1 Fix the binary commitment
variables of units that are switched
“on” at hour t in energy and reserve
market
4-2 Reduce
Sthresholdt
Yes
5- Is equation
(26) satisfied at
hour t?
No
5-1 Fix the binary commitment
variables of units that are switched
“on” at hour t in energy and reserve
market
5-2 Reduce
Dthresholdt
Yes
6- Fix binary commitment variables of units (both that are switched “on” and “off”) at hour t in energy and reserve market
7- All the 24
hours checked
No
t=t+1
Go to step 4
Yes
8-Should
threshold
changed?
any
be
Yes
Go to step 2
No
9-Finish
Figure 2: Flowchart of optimization method
7-If all time steps are not checked then consider next
time step and go to step 4. If all checked, go to step 8.
8-If the threshold should be reduced in any hour, reduce
it and go to step 2. If not then go to step 9.
9- Finish, the output is the final answer
4 NUMERICAL RESULTS
In this paper the IEEE RTS 1996 with 32 units is
used as the test system. The information for the generation units is taken from [15]. In the base case the VLNS
is assumed 2000 $/MWh. Because the probability of
actual RSDR resources utilization in two continuous
hours is almost zero[9], just the parameter “ah”in eq(14)
is considered non-zero and is equal to 0.7, which is
consistent with the range reported by [5],[7], [8]. The
probability of actual utilization of RSDR in the spinning
reserve, or actual spinning reserve utilization probability, is considered 0.05 which is in consistency with reference [10].
DR resource potential ranges from 3 to 9% of a region’s summer peak demand in most USA regions [13]
so in this paper the DR capacity is selected as 5% of the
17th Power Systems Computation Conference
total capacity. The bidding price of RSDR is 20 $/MWh
which is consistent with range reported by [10], [11],
[14]. In order to analyze the RSDR payback effect from
theoretical point of view more clearly, it is assumed that
the RSDR can bid in all hours of day. In following the
impact of RSDR resource with payback on different
system aspects is analyzed.
4.1 Impact of payback effect on scheduled reserve
Figure 3 shows considering payback effect can
change the optimal scheduled reserve amount. This is
mostly because in lower load levels, considering payback will almost eliminate RSDR utilization. This is to
prevent extra interruption cost that is imposed by RSDR
payback effect. When the RSDR is eliminated the unit
commitment pattern will change. But while the load
level is very high using RSDR is inevitable. So in this
case in order to reduce the expected interruption cost the
amount of worst contingency, which will be worsened
by payback amount, should be reduced. The worst contingency is double outage of two biggest gen units, so
total dispatched amount of biggest generators will
slightly decrease. This is the reason that in higher load
levels not only the reserve amount but also the system
Stockholm Sweden - August 22-26, 2011
4.4 Impact of spinning reserve utilization probability
on effectiveness of RSDR with payback
As figure 5 shows the RSDR ability in total system
cost reduction is influenced by this parameter but the
influence is not so large. As it can be seen the RSDR
utilization can be more beneficial in systems with lower
actual reserve utilization probability. When the probability of SR utilization is increased 50 percent from the
base case, ability of RSDR in total system cost reduction is decreased around 12.5%. In other words RSDR
effect changes in different systems.
4.5 Impact of payback effect on RSDR utilization
The pattern that RSDR will be accepted is affected
by many factors. The numerical results of this paper
show when payback is considered, it can play an important role in this pattern. As figure 6 shows, total amount
of RSDR offer that will be accepted in 24 hours fall
shortly with payback coefficient increase. In order to
investigate in what hours RSDR utilization is mostly
affected by payback characteristics, the reduction in
RSDR utilization, in comparison with “no payback
RSDR” case, is presented in figure 7. As figure 7 shows
when there is a sharp increase in load in hour “t+1” the
RSDR utilization in hour “t” is reduced to decrease the
expected interruption cost. Hours “8”, “10” and “16”
exemplify this in the base case. As it can be seen the
reduction in accepted RSDR bid, in case with lower
payback coefficient, is less. But still in hours “16”and
“17” which the load level is high and followed by even
higher load level, at hour “18”, the accepted RSDR bid
will be lowered. It should be mentioned that in peak
hours the RSDR utilization cannot be ignored and that is
why there is no reduction in RSDR utilization on those
hours.
17th Power Systems Computation Conference
Reserve (MW)
4.3 Impact of payback effect on system total cost
Payback characteristics affect the ability of RSDR in
reducing total system cost and interruption cost. As
figure 4 shows, with increase in the RSDR payback
coefficient, the RSDR ability to reduce the total cost and
interruption cost will be lower. This shows the effect of
payback characteristics cannot be ignored when social
cost minimization is studied. It should be mentioned
that although the RSDR effectiveness is reduced by its
payback characteristics, but it is still effective to reduce
the system total cost comparing with no RSDR case.
800
700
600
500
400
300
200
100
0
1
3
5
7
9
11 13 15 17 19 21 23
Hour
RSDR with paybcak
RSDR no payback
Figure 3: The impact of payback effect on scheduled reserve
Total cost reduction
percent[%]
4.2 Impact of payback effect on system total cost
Payback characteristics affect the ability of RSDR in
total system cost and interruption cost reduction. As
figure 4 shows, with increase in the RSDR payback
coefficient, the RSDR ability to reduce the total cost and
interruption cost will be lower. This shows the effect of
payback characteristics cannot be ignored when social
cost minimization is studied. It should be mentioned
that although the RSDR effectiveness is reduced by its
payback characteristics, but it is still effective to reduce
the system total cost.
4.6 Impact of load reliability requirement in RSDR
utilization
One of the important factors in social cost minimization is the load reliability requirement. This reliability
requirement is reflected in VLNS, higher values of
VLNS represents system with higher reliability requirement and a lower value represents a system with
lower load reliability requirement. The system reliability requirement can affect the reserve scheduling and
RSDR utilization. When the load reliability requirement
is high the payback effect consideration becomes more
important. When the RSDR has no payback effect, with
increase in the load reliability, more of RSDR bid will
be accepted. But when there is payback effect, with
increase in load reliability requirement, less RSDR bid
will be accepted. This is to prevent the extra expected
interruption cost. This is shown in figure 8. As it can be
seen the RSDR bid is still fully accepted in the peak
hours when the reserve resources are scarce. But the
total accepted RSDR amount is reduced.
5
4
3
2
1
0
0.7
0.5
0
payback coefficient of RSDR
Figure 4: Total system cost reduction percent in different
payback scenarios
Total cost reduction
percent[%]
scheduling are changed when a RSDR with payback
effect is utilized. Impact of payback effect on system
total cost
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0.025
0.05
0.075
SRUP
Figure 5: Total system cost reduction percent in different
actual reserve utilization
Stockholm Sweden - August 22-26, 2011
Total RSDR utilization in
24 hour (MW)
REFERENCE
3000
2500
2000
1500
1000
500
0
[1]
[2]
0.7
0.5
0
[3]
Payback coefficient of RSDR
[4]
3000
20
0
20
40
60
80
100
120
140
160
[5]
2500
2000
1500
1000
Load (MW)
Reduction in RSDR utilization
in comparision with "no
payback RSDR " case
Figure 6: Total accepted RSDR bid in different payback
scenarios
500
0
[7]
1 3 5 7 9 11 13 15 17 19 21 23
Hour
payback!coef=0.7
payback!coef=0.5
Load
Figure 7: The RSDR utilization reduction in different payback scenarios
160
140
120
3000
[8]
[9]
2500
[10]
2000
100
80
60
40
1500
1000
Load (MW)
Total acceptedRSDR bid (MW)
[6]
500
20
0
[11]
[12]
0
1
3
5
7
VLNS!5000
9 11 13 15 17 19 21 23
Hour
VLNS!2000
load!
Figure 8: RSDR utilization pattern in different load reliability
requirements
[13]
[14]
5 CONCLUSION
In this paper, the payback effect of RSDR resource
was integrated in a market-scheduling framework and
its effect was analyzed. Furthermore a recursive MIP
based optimization method was developed. The numerical results show that the payback characteristics can
affect the effectiveness of the RSDR. For example contrary to the case with no payback in RSDR, when the
load reliability requirement is higher, less RSDR bid
will be accepted when the payback is considered. Although the ability of RSDR resource in reducing the
total system cost will drop, even with payback characteristics the RSDR helps the system in reducing the total
system cost and increase the reliability of the system.
This analysis shows that the non-idealistic aspects of
DR resources, like payback, cannot be ignored with
increasing utilization of these resources. The developed
optimization method also shows to be efficient in reducing the computational time and reaching to the optimal
point.
17th Power Systems Computation Conference
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