Prioritizing Demand Response Programs from Reliability Aspect

Mehdi Nikzad Department of Electrical Engineering, Islamshahr Branch,

Islamic Azad University, Tehran, Iran. mehdi.nikzad@yahoo.com

Mahdi Bashirvand Department of Electrical and Computer Engineering,

Science and Research Branch, Islamic Azad University, Tehran, Iran.

mahdibashirvand@yahoo.com

Babak Mozafari Department of Electrical and Computer Engineering, Science and

Research Branch, Islamic Azad University, Tehran, Iran. mozafari@srbiau.ac.ir

Ali Mohamad Ranjbar

Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran.

amranjbar@sharif.edu

Abstract— In this paper, the impact of demand response programs (DRPs) on reliability improvement of the restructured power systems is quantified. In this regard, the demand response (DR) model which treats consistently the main characteristics of the demand curve is developed for modeling. In proposed model, some penalties for customers in case of no responding to load reduction and incentives for customers who respond to reducing their loads are considered. In order to make analytical evaluation of the reliability, a mixed integer DCOPF is proposed by which load curtailments and generation re-dispatches for each contingency state are determined. Both transmission and generation failures are considered in contingency enumeration. The proposed technique is modeled in the GAMS software and solved using CPLEX. Reliability indices for generation-side, transmission network and whole system are calculated using this technique. Different DRPs based on the DR model are implemented over the IEEE RTS 24-bus test system, and reliability indices for different parties are calculated. Afterward, using proposed performance index, the priority of the considered programs is determined from view point of different market participants.

Keywords-demand response programs; analytical reliability evaluation techniques; mixed integer linear programming; expected energy not supplied; expected interruption cost.

I. INTRODUCTION According to DOE classification, demand response

programs (DRPs) are divided into two categories as priced-based and incentive-based. Price-based demand response programs are Time-Of-Use (TOU) rates, Real-Time Pricing (RTP) and Critical Peak Pricing (CPP). Incentive-based demand response programs consist of Direct Load Control (DLC) programs, Interruptible/Curtailable (I/C) programs, Demand Buyback or Bidding (DB) programs, Emergency Demand Response Programs (EDRP), Capacity Market Programs (CAP) and Ancillary Services market programs (A/S). More detailed explanations can be found in [1].

The use of DR lowers undesirable effects of failures that usually impose financial costs and inconveniences to the

customers. Also, not only customers gain benefits but the system operator will have more options and flexibility for providing systems security [2]. One challenge for independent system operators (ISOs) and regional transmission organizations (RTOs) is to how quantify and measure the effect of DRPs on improvement of reliability in restructured environment. In this paper, our endeavors have been focused to address such a challenging problem.

The pioneer researches about DR modeling have been reported in [3]. Linear economic model of DRPs as a simple model has been developed and used in [4, 5] which is based on an assumption in which demand will change linearly in respect to the elasticity. However, those models do not consider nonlinear behavior of the demand which is of great importance in analyzing and yielding the results.

Considerable efforts have been done to develop analytical techniques for bulk power system reliability assessment in traditional vertically integrated and restructured power systems [6-10]. In recent methods known as OPF-based methods, it has been concentrated on improving the contingency analysis performance by integrating remedial/corrective actions into an optimization model to reach minimum load shedding values [8, 9]. The OPF is often used to determine the expected energy not supplied or amounts of loads to be curtailed. By considering some practical constraints of generating units such as nonzero minimum power output and ramp rate limits, due to some contingency some generation units must be inevitably decommited. Also in some other cases, it is required that non-economical units be decommited, instead of operation in minimum output level. Most of the existing OPF-based methods have no mechanism to deal with such circumstances. Hence we propose a straightforward unit decommitment method based on linear mixed integer technique for analyzing the problem. The proposed method considers the operation costs of generating units and value of loss load. It also considers some technical constraints for safe operation of the power network and generating units operation. The proposed

978-1-4577-1829-8/12/$26.00 ©2012 IEEE

method is formulated by GAMS programming language and solved using the CPLEX as a powerful solver in mixed integer linear programming (MILP). Also in this paper, demands are treated by their nonlinear characteristics to the electricity price alteration by assuming constant elasticity for demand curves. In this regard, a model to describe price dependent loads is developed such that the characteristics of different types of DR program can be imitated by introducing some incentive or penalty factors into the formulation.

The remaining parts of the paper are organized as following: Modeling DR is developed in section 2. The proposed reliability evaluation method is introduced in section 3. In this section the used method for computation of reliability indices from view of system, generation-side and transmission network are introduced. Also a performance index is defined to prioritize DRPs from views of different market participants. In section 4, the simulation results over the IEEE 24-bus reliability test system are given. In our simulation, both transmission and generation failures are included for contingency enumeration. Finally, the paper is concluded in section 5.

II. DEMAND RESPONSE MODELING

A. Customer Benefit Defenition Generally, when electricity rate increases, the consumers

will have more motivation to decrease their electricity demand. This concept is shown in Fig.1, as the demand curve.

Figure 1. demand curve

Hachured area in fact shows the customer marginal benefit from the use of d MWh of electrical energy [4]. This is represented mathematically by:

(1) dddBd

∂= ∫0 ).()( ρ

Where ρ is the total rate of electricity for customers.

B. Modeling of Elastic Loads The value of tariffs, incentives and penalties considered in

different DRPs could motivate the participated customers to revise their consumption pattern from the initial value id0 to a modified level id in period i.

iii ddd 0−=Δ (2) In this case, the total revenue for the customers who

participate in the DRPs will be calculated as follows based on

the hourly incentive rate, iinc , given for load reduction encouragement in period i.

)()( 0 iiii ddincdINC −⋅=Δ (3) Some programs are included penalty payments for those

enrolled customers who do not respond or satisfy their contract obligations. In such condition, considering the level of contract, iL , and penalty factor, ipen , for period i, the total penalty charge could be accounted as follows:

[ ]{ }iiiii ddLpendPEN −−⋅=Δ 0)( (4) It is reasonable to assume that customers will always choose

a level of demand id to maximize their total benefits which are difference between incomes from consuming electricity and incurred costs; i.e. to maximize the cost function given below:

( ) )()( iiiii dPENdINCdpdB Δ−Δ+⋅− (5) Where ip is the electricity price in period i. The necessary condition to realize the mentioned objective is

to have: ( ) ( ) ( )

0=∂

Δ∂−

∂Δ∂

+−∂

∂

i

i

i

ii

i

i

ddPEN

ddINC

pddB

(6)

Thus moving the last three terms to the right side of the equality,

( )iii

i

i penincpddB ++=

∂∂ (7)

Combining (1) and (7), it could be seen that the total electricity rate in any period i will compose of three terms as given in (8)

iiii penincp ++=ρ (8) Based on economics theory, the price elasticity of demand between two time periods is defined as the ratio of the relative change in demand within a time period to the relative change in price within other time period:

j

j

ii

ijd

d

E

ρρ∂

∂

= (9)

Where ijE is the price elasticity of demand between periods i and j.

Substituting (8) to (9), a general relation based on elasticity coefficients is obtained for each time period i as follows:

jjj

jjjij

i

i

penincppenincp

Edd

++∂+∂+∂

=∂ (10)

By assuming constant elasticity for 24 hours of a day, { }24,...,2,1,: ∈ji for constantEij , separation of the equation

(10) and integration of each term over a 24 hour period we obtain the following relationship.

⎪⎭

⎪⎬⎫

⎥⎥⎦

⎤

++∂

+++

∂

+⎪⎩

⎪⎨⎧

⎢⎢⎣

⎡

++∂

=∂

∫∫

∑ ∫∫=

jj

j

j

i

i

pen

jjj

jinc

jjj

j

j

p

p jjj

jij

d

d i

i

penincppen

penincpinc

penincpp

Edd

00

24

1 00

(11)

Where jp0 is the initial electricity price in period j. We have:

⎪⎭

⎪⎬⎫

⎥⎥⎦

⎤⎟⎟⎠

⎞⎜⎜⎝

⎛

+++

+⎟⎟⎠

⎞⎜⎜⎝

⎛

+++

+

⎪⎩

⎪⎨⎧

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

++++

=⎟⎟⎠

⎞⎜⎜⎝

⎛ ∑=

jj

jjj

jj

jjj

j jjj

jjjij

i

i

incppenincp

Lnpenp

penincpLn

penincppenincp

LnEddLn

24

1 00

(12)

And then,

( )( ) ( ) ( )∏

=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+⋅+⋅++++

=24

1 0

3

0j

E

jjjjjjj

jjjii

ij

incppenppenincppenincp

dd

(13) The costumer optimum behavior as equation (6) leads the

model of elastic loads as equation (13).

III. RELIABILITY ASSESSMENT Reliability assessment of a power system relies on the

selection of contingency at the first step. This is simply done by enumeration methods or Monte-Carlo simulation approach. Once the set of critical contingencies are determined, focus must be placed on analyzing them in the next step.

For contingency state c, the objective function is then defined as:

( )∑ ∑= = ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

×+N

k

NG

g

ckk

cgk

cgk

cgk

k

LCVOLLuPGCMin1 1

, (14)

Where N is the number of buses, kNG is the number of

units connected to bus k, cgkGC is the generation cost of unit g

in bus k under contingency c in k$/h, cgkP is the real power

dispatched from unit g in bus k due to contingency c in MW,

kVOLL is the value of loss load in bus k in k$/MWh, ckLC is

the real power capacity not delivered in bus k due to contingency c in MW and c

gku is the binary variable, which is 1 if the unit is committed and 0 otherwise.

The production cost of generating units in each hour is assumed to be a quadratic function of active power generation, as follow:

( ) ( ) cgkgk

cgkgk

cgkgk

cgk

cgk

cgk ucPbPauPGC ⋅+⋅+⋅= 0

2, (15)

Where gk

cba gkgk 0,, are the generation cost function

coefficients.

Equation (15) can be well approximated by a set of line segments.

There should be considered some technical constraints in conjunction with the objective function for representing the system operational restrictions as well. Below are the major constraints introduced in the proposed model for analyzing each contingency c:

• Power balance constraint:

( ) ( )∑∑≠==

−=−−N

kll

clk

cl

ckc

kdk

NG

g

cgk X

LCPPk

1

0

1

θθ (16)

Where 0dkP is the real power load of bus k in MW, c

kθ and clθ

are the bus angels under contingency c and clkX line reactance

between buses k and l with considering contingency c. • Upper and lower limits on generation:

( ) ( ) cgkgkgk

cgk

cgkgkgk uPPPuPP ⋅−≤≤⋅− 0maxmin0 (17)

Where 0gkP is the initial real power dispatched from unit g in

bus k (in normal state), maxgkP and min

gkP are the maximum and minimum real power generation of unit g in bus k in MW, respectively.

• Ramp rate limits: ( ) ( ) c

gkupgkgk

cgk

cgk

downgkgk uRampPPuRampP ⋅⋅+≤≤⋅⋅− ττ 00 (18)

Where upgkRamp and down

gkRamp are up and down the ramp rate limits of unit g in bus k in MW/min, respectively, and τ is the reserve lead time in minute.

• Load curtailment upper and lower limits : 00 dk

ck PLC ≤≤ (19)

• Thermal line flow constraints : max

lkclk SS ≤ (20)

Where clkS is the magnitude of apparent power flow from bus

i to k under contingency c in MVA, and maxlkS is the apparent

power limit of line in MVA.

IV. RELIABILITY INDICES In a system with NN independent components, if s element

failures occur in contingency c, the relations among the probability of the occurrence, departure rate, contingency duration and frequency of contingency c are what defined in (21) (22), (23) and (24), respectively.

∏∏+==

−×=NN

snn

s

nn

c FORFORprob11

)1( (21)

∑∑ +==+=

NN

sn ns

n ncdep

11λμ ⎟

⎠⎞⎜

⎝⎛ yearoccurance (22)

cc

depdur 1= ⎟

⎠⎞⎜

⎝⎛ occurance

year (23)

ccc depprobf ⋅= ⎟⎠⎞⎜

⎝⎛ yearoccurance (24)

Where nFOR is the force outage rate of element n, nμ is the repair rate of element n in repairs/year and nλ is the failure rate of element n in failures/year.

A. System reliability indices The Expected Energy Not Supplied ( sEENS ) and Expected

Interruption Cost ( sECOST ) of system within the period of study are two wide applicable indices for reliability evaluation indices used for system reliability assessment and are defined by:

∑∑= =

⎟⎠⎞⎜

⎝⎛⋅⋅⋅=

N

k

NC

c

cccks day

MWhdurfLCEENS1 1

24 (25)

(26) ∑∑= =

⎟⎠⎞⎜

⎝⎛⋅⋅⋅=

N

k

NC

c

ckk

ccs day

KLCVOLLdurfECOST1 1

$.24

Where NC is the number of contingencies.

B. Generation-side reliability indices In this section, the expected energy not supplied ( GEENS )

and the expected interruption cost ( GECOST ) for generation-side is calculated. GEENS and GECOST indicate the contribution of generation-side in sEENS and sECOST , respectively. In order to calculate these two indices, the real power capacity not delivered from generaton-side for each contingency has to be determined in the load shedding process. For contingency c in system, if the summation of power output of generation units, in normal state, is more than the summation of their maximum available capacity, it can be concluded that generation-side doesn’t have enough capacity to supply demand. It should be noted that the maximum available capacity of a unit is determined using inequalities defined in (17) and (18). In this case, the capacity not delivered c

GCD for generation-side due to contingency c is calculated according to the following equations:

(27)

It can be easily seen, when generation-side doesn't have enough capacity to supply system demand during contingency c, c

GCD becomes greater than zero.

In case of load curtailment, the energy not supplied cGENS

caused by generation-side for contingency c can be calculated as:

( )0,max cG

ccG CDdurENS ×= (29)

Where, ( )0,max cGCD is the capacity shortage caused by

inadequate generation system capacity that leads to load

curtailment. Considering all the contingencies within the period of the study, GEENS and GECOST caused by

generation-side based on the departure rate cdep and

probability cprob for contingency c are as follows:

∑=

⎟⎠⎞⎜

⎝⎛⋅⋅⋅=

NC

c

cg

ccG day

MWhENSprobdepEENS1

24 (30)

∑=

⎟⎠⎞⎜

⎝⎛⋅⋅⋅=

NC

c

ckk

ccG day

KLCVOLLprobdepECOST1

$.24 (31)

C. Transmission network indices Once a contingency occurs, load may be curtailed because of

either generation system shortage or transmission network congestion. Thus TEENS and TECOST for transmission network can be calculated as below:

∑=

−=NG

GGST EENSEENSEENS

1

(32)

∑=

−=NG

GGST ECOSTECOSTECOST

1

(33)

D. Analyzing DRP performance It is necessary to compare results of implementing DRPs

with each other and prioritize from views of different market participants. It should be noted that the priority of implementing DRPs might be different for each market participant. To prioritize DPRs, a performance index (PI) is defined using the following equations:

0

0

0

0

ECOSTECOSTECOST

EENSEENSEENSPI

DRPDRP −+−=

(34)

Where, from a market participant, the values of EENS and ECOST in the case of no DRP are 0EENS and 0ECOST , respectively, and in the case of employing a DRP they are given by DRPEENS and DRPECOST , respectively. The positivity of the first term indicates per unit reduction of EENS index when a specific DRP is executed. The second term demonstrates per unit change of ECOST index. Briefly, the higher the PI index, the better the performance of the executed DRP. In order to compare different DRPs, the PPI coefficient can be normalized as follows:

max(%)PI

PIPPI = (35)

V. SIMULATION RESULTS The proposed reliability evaluation approach in this paper is

formulated as a linear mixed integer DCOPF which can be modeled in GAMS and solved using CPLEX as a MILP solver [11]. The proposed algorithm is tested over the IEEE 24-bus test system [12]. Values of parameters 0, c andba in equation (15) are chosen from [13] and the curve is approximated by 3 tangent lines. And all other data of the system, ramp rates,

power production constraints of units, reliability parameters, etc., are extracted from [12]. It is supposed that the amounts of VOLL in all buses are the same and equal to 2 k$/MWh.

The hourly load corresponds to a weekend in winter while the peak load of the day is assumed to be 2850 MW. The load curve is divided into three intervals: Low load period (from 24:00 p.m. to 8:00 a.m.), peak period (17:00 p.m. to 24:00 p.m.) and other times which are defined as off-peak periods. The selected values for the self and cross elasticities are shown in Table I.

TABLE I. SELF AND CROSS ELASTICITIES

Low Off-peak Peak Low -0.10 0.014 0.016

Off-peak 0.014 -0. 10 0.012 Peak 0.016 0.012 -0. 10

In the first step, active power outputs of units in normal state (without considering contingency) are determined by solving the conventional DCOPF for each hour. Afterward the N-2 contingency analysis, which include the failure of a generating unit or a transmission line, and the failure of two units or two lines or the combination of one unit and one line, are considered and then for each contingency scenario, the amount of load shedding and generation re-dispatch are computed using the proposed mixed integer DCOPF technique. In the next step the corresponding reliability indices are calculated. The lead time for the spinning reserve market which is used in the equation (18), is assumed to be 10 minutes.

Several DRPs are considered and described as follows: Program #0 (Base case): flat rate contract. Program #1 (TOU): Electricity tariffs are 0.9, 1 and 1.2

times of the flat rate value for low, off-peak and peak load periods, respectively

Program #2 (CPP): Electricity tariffs are same as TOU rates for low and off-peak period but 1.5 times of the flat rate value for peak periods

Program #3 (RTP): Electricity tariffs are [0.93 0.87 0.82 0.80 0.78 0.79 0.80 0.84 0.95 1.03 1.06 1.07 1.06 1.03 1.02 1.02 1.08 1.29 1.26 1.20 1.12 1.09 1.02 0.96] times of the flat rate value for hours 1 to 24, respectively

Program #4 (DLC): Electricity tariffs are equal to flat rate value and incentive rate is 15% of flat rate value in peak load periods

Program #5 (EDRP): Electricity tariffs are equal to flat rate value and incentive rate is 40% of flat rate value in peak load periods

Program #6 (CAP): Electricity tariffs are equal to flat rate value. Incentive and penalty rates are 25% and 5% of flat rate value in peak load periods, respectively. The contract level is 70% of load in peak periods of the base case.

Program #7 (I/C): Electricity tariffs are equal to flat rate value. Incentive and penalty rates are 40% and 20% of flat rate value in peak load periods, respectively. The contract level is 70% of load in peak periods of the base case.

It should be mentioned that the flat rate value is characterized by the average price of electricity over a 24-hour horizon which is calculated base on DC OPF and is equal to

78 $/MWh. In program number 0 as the base case, it is assumed that all customers face with the flat rate contract.

A. Analysis of the results In this section, the results obtained before and after

implementing DRPs are discussed.

TABLE II. RELIABILITY INDICES FOR DIFFERENT PARTIES IN DIFFERENT PROGRAMS

Program no.

System indices Generation-side indices

Transmission network

EE

NS

(MW

h/da

y)

EC

OST

(K

$/da

y)

EE

NS

(MW

h/da

y)

EC

OST

(K

$/da

y)

EE

NS

(MW

h/da

y)

EC

OST

(K

$/da

y)

0 4073.8 200071.4 3871.7 190523.3 202.1 9548.1

1 1488.8 73347.3 1308.4 64950.9 180.4 8396.3

2 1850.7 88855.4 1622.8 77625.9 227.9 11229.5

3 1391.6 70727.2 1201 61249.1 190.6 9478.1

4 1923.6 91997.9 1700.9 81706.5 222.7 10291.4

5 1912.7 91828.1 1696 80974 216.7 10854.1

6 1810.6 87205.6 1590.5 76281.4 220.2 10924.2

7 2138.1 102426.4 1931.9 92282.6 206.2 10143.8

According to Table II, from view of the system, program number 3 has the lowest values of reliability indices. EENS and ECOST values for program number 0 are 4073.8 MWh/day and 200071.4 K$/day which are reduced to 1391.6 MWh/day (equal to 65% reduction) and 70727.2 K$/day (equal to 71% reduction) after the implementation of program number 3.

From view of the generation-side, it is clear that the reliability indices are improved by any DRP implementation. Generally, the implementation of program number 3 leads to the lowest reliability indices values from the view of generation-side. According to the calculated results of EENS and ECOST for transmission network given in Table II, programs number 1 and 2 have the lowest and the highest values of the reliability indices, respectively. The values of EENS and ECOST for program number 1 are 180.4 MWh/day and 8396.3 K$/day and for program number 2 are 227.9 MWh/day and 11229.5 K$/day, respectively. However, these values for program number 0 are 202.1 MWh/day and 9548.1 K$/day. It should be noted that EENS and ECOST values caused by the transmission network are very small compared to the others due to strong connectivity of the grid.

B. Prioritizing of considered DRPs In this section, using the introduced performance index

defined by equations (34) and (35), PPI, considered DRPs are prioritized from different view.

TABLE III. PROGRAM PRIORITIZING BASED ON DIFFERENT POINT OF VIEW

Program no.

System Generation-side

Transmission network

PPI(%) Priority PPI(%) Priority PPI(%) Priority 0 0 8 0 8 0 3

1 97.2 2 94.5 2 100 1

2 84.4 4 81.5 4 -133.2 8

3 100 1 100 1 28.2 2

4 81.8 6 81.4 5 -78.8 5

5 82.1 5 78.3 6 -91.7 6

6 85.8 3 82.5 3 -102.5 7

7 73.8 7 70.7 7 -36.3 4

Programs priority from view point of system is represented in Table III using the results of Tables II. It can be seen that all DRPs have positive PPI and program number 3 is of the highest priority and has the maximum effect on system reliability improvement. Also program number 0, base case, is of the lowest priority. Also in Table III, the prioritized programs from generation system point of view are reported. All DRPs have positive PPI values and programs number 3 and 0 are considered as the highest and lowest priority. The values of PPI show that the considered DRPs have effective performance on reliability improvement from generation-side point of view while in case of not using DRPs (i.e program number 0) generation units should be more responsible for customer interruptions and should purchase more additional reserve to improve their reliabilities.

Figure 2. Priority of programs from different point of view

The prioritized programs from the transmission network point of view are reported in Table III. It can be observed that the PPI of programs number 1 and 3 has positive value and other program have PPI with negative values which means that implementation of these programs increase EENS and ECOST caused by transmission network. However, according to Table II, the reliability indices values caused by the transmission network are very small. From Table III, it can be seen that program number 0 is located in the third position.

The sorted priorities from market participant point of view are depicted in Figs. 2. These figures reveal that for different participants, priorities of program depend on different decision factors as the trend of electricity price, incentive and the penalty values determined for DRPs.

VI. CONCLUSION In this paper a DR model with considering incentive and

penalty mechanisms has been developed, so that behavior of customers under different types of DRPs could be thoroughly modeled. In order to do analytical reliability evaluation, a mixed integer DC OPF to determine load curtailment and generation re-dispatch for each contingency state has been proposed and reliability indices for system, generation-side and transmission network have been calculated accordingly.

Different DRPs have been implemented over the IEEE RTS 24-bus test system and the reliability indices have been calculated for each of them with considering N-2 criterion.

The achieved results reveal that implementation of DRPs lead to an improvement of reliability at system. The considered DRPs have been prioritized based on the proposed PPI index from view points of different parties including the ISO, generation-side and transmission network.

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