INTERRUPTIBLE LOAD MANAGEMENT USING ... - IEEE Xplore

IEEE Transactions on Power Systems, Vol. 11, No.2, May 1996

715

INTERRUPTIBLE LOAD MANAGEMENT USING OPTIMAL POWER FLOW ANALYSIS S.Majumdar D.Chat topadhyay Jyoti Parikh Indira Gandhi Institute of Development Research Gen.Vaidya Marg, Goregaon (East), Bombay-400 065, India

e-mail: [email protected] Abstract- An interruptible load management (ILM) scheme is proposed using dynamk Optimal Power Flow analysis. It enables real-time selection of interruptible loads incorporating network constraints and dynamic restriction on generation v i z ramp-rate limits. The model provides an analytical framework for addressing several important issues associated with optimal selection of load curtailment e.g. advance notification for load curtailment, short-term price discounts and long-term discounts on demandcharges, power factor of the load and customer-cost associated with the load to be curtailed, and system security. A six-bus example illustrates the proposed methodology. Keywords: Interruptible Lood management, Optimal Power Flow, Discount on Spot-Price,Discount on Demand-Charge

1. INTRODUCTION 1.1Background: Utilities are increasingly taking recourse to rate incentives for effective management of customer loads. The most common among these are interruptible tariffs as a means to relieve part of the power demand during peak hours by involving customer participation. The objective is to device a rate structure which is incentive compatible to both the utility and customers i.e it minimizes utility cost of generation and maximizes the economic benefits of the customers simultaneously. Implementation of interruptible tariff structure involves unbundling electric service and offer the cusbmers a range of rate reliability choices. The customers sign an interruptible load contract with the utility to reduce their demand as and when requested by the utility. The load reduction can be achieved by demand limiter which is installed by the customers and the utility sends control signals to interrupt the contract amount, if such need arises. 95 SM 501-7 PWRS A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering society for presentation at the 1995 IEEE/PES Summer Meeting, July 23-27, 1995, Portland, OR. Manuscript submitted December 28, 1994; made available for printing June 7, 1995.

The need for integrating load management programs in utility long-term planning has been indicated in [l]. Supply planning in shorter run requires the utility to make short term and medium term adjustments typically carried out in an Optimum Power Flow (OPE) analysis. But, customer short and long term cost are not adequately included partly due to the lack of availability of data. Thus they are not adequately included in setting up of real time tariffs. Smith [2], has developed a comprehensive model of real-time pricing scheme, that balances supply and demand under various operating scenarios while addressing utility capacity commitment decisions and customer subscription decisions in terms of customer curtailment costs. Chen [31 describes the interruptible load program by the Taiwan Power Company in 1987 and compms different strategies therein. It also calculates the avoided cost in terms of less requirements of capacity build-up, and consequently design a better incentive rate structure for interruptible load program. It is justifiably argued in [3], that devising an interruptible load program is similar to finding the equilibrium point in the economic analysis to determine the market price and quantity. There exists some oscillations to reach the equilibrium point. These oscillations depend on the qualitative and the quantitative response of the suppliers and the customers and estimation of these responses are crucial. Questioneering or a survey to estimate potential of the load interruptible program is essential to reach to the equilibrium point. Updating of the rate design with respect to the potential estimates is the crux of devising an interruptible load management program. There is also the need to post menus in advance and thereby provide users with a non-binding forecast of the probabilities associated with different day types being operative, so that users have sufficient information to facilitate longer term planning decisions related to electricity generation. Thus the challenge lies to determine in each situation the minimum set of real time parameters necessary to enhance economic efficiency just up to the point of diminishing returns e.g a load reduction forecasting system is proposed to assist direct load control program by cycling residential air-conditioning load, for Pacific Gas & Electric [4]. There is another important aspect of designing interruptible rates which has been widely discussed in the literature on elctricity pricing viz. static vis-a-vis dynamic.

0885-8950/96/$05.00 0 1995 IEEE

716

The static Time-of-Use tariffs are based on some estimates of key stochastic variables of a particular state. But if the real condition turn out to be different then these static tariff are likely to convey incorrect price signals which may even foster counter productive customer response. Dynamic tatiff schemes,therefore, could be essential for reflecting the correct marginal costs of generation incurred by the utility [51. Finally, interruptible rate design can vary widely in terms of the controlling agent and these span the entire spectrum from utility to centralized control to customer choice. The utility can exercise full controt in certain cases e.g domestic customers where the customers subscribepart of its demand and must respond to utility requests, else pay p e ~ l t i eOn ~ . the other hand the utility rates may be such that the penalty or the over-ride option offers the customers to purchase power at utility's marginal cost [SI. Some of the existing interruptibletariff schemes [5,6] are cited here to illustrate the different types of inyntives or disincentives offered by the utilities in practice: 1. Interruptible tariff in Sweden in which suuulv is guaranteed for 8000 hours/annum on average over 5 year contract period while in another tariff scheme it guarantees only 15,000 hours of supplies in 5 years. 2. Ontario Hydro (Canada) Interruptible Power tariff service is available for a minimum of 1,500 hours per year in a continuous segment of thm hours or more at a time. In US, San Diego Gas and Electric company offers 3. an interruptible tariff with an over-ride urovision at a cost of $8.25/kWh on ne&. In exchange the company provides substantial discounts on enerm during off-Deak Deriods. 1.2 Some Issues in ILM Which Merit Attention: In order to be an effective means of managing peak load by the utility, Interruptible Load Management (ILM) must adequately address the following issues: 1. What are the short-term discounts in prices (in $/kWh) to be offered to the customers participating in the ILM program?

2.

3.

(a) (b)

(c)

What are the longer-term benefits to be given to the customers in terms of reduction in demand charges (in $bW)for the part of the demand subscribed to ILM?

ultural load for example), high ost of switching to altemative (d)

(e)

generation and network characteristics - spatial demand and generating sources, limits on generation output (MW and MvAr), ramp rate, voltage, line flow etc. system secwity - to ensure that the system can "survive" a specified list of contingencies viz. the emergency limits on voltage and line flow limits are not exceeded for certain line, bus or generator outage combinations.

1.3 OPF as LE tool in ILM ' optimal power flow (OPF) this p a p e r to address these issues. incoprate the features mentio t h m would amount to either setection of interruptible load se account for the factor of the loa

the &a&-off between dr with a notice of one for several hours wi merits attention in an

load curtailment

must be taken into interruptible load selection. Se1 guided by system safeguarding the sy ineorporats most o constraints and contingen in the present work. Th hourly/half-hourly time generation schedule that sam

1.

a range of interruptible loads available at load buses of differentpower factor

How does the utility go about selecting different of interruptible loads in real-time taking into

account the following considerations: advance notificationfor load curtailment - 1-hour, 1day etc. duration of curtailment - curtailment limited to peak hour only, longer period curtailment by shifting load to Off-peak hours nature of load and cost associated with load curtailment - low power factor load with lower cost

2.

day in

1.

2.

The modified-OPF model is used for the hours of the which loads can be curtailed determine the following: optimize the selection of interruptible loads at different buses of various nature and duration. calculate the discount in the spot prices to be offered

717 to the customers.

3.

calculate the aggregate benefit from the interruptible load program.

Evaluating Discounts on Demand-Charges due to Long-Term Benefits: Once the optimal selection of interruptible loads and the price discounts are resolved, the next step is to decide the longer-term benefits to be offered which arises due to the reduction of capacity addition by the utility in the long run. Following OPF, the modified load curve for the hours under consideration is obtained and the capacity response ratio (CRR) [7] of the interruptible load program is calculated. CRR is an indicator of the effective capacity reduction from the interruptible load program selected using OPF. CRR is utilized to enumerate the discounts to be given on the demand charges ($/kW) for the interruptible part of the load by the customers. Such incentives could also be given in altemative ways of giving discounts on the equipment needed for participating the interruptible had program e.g the Swedish utilities offer bonuses for installing dual-fired systems [8], or in terms of "demand-chargefree days in a week followed by Pennsylvania Power & Light [5]. 1.4

2. THE MODEL

Nomenclature: time-period ( k l ,...,") in which load curtailment may t take place k types of curtailable load by customer class e.g agricultural, industrial etc. (based on power factor and curtailment cost of customers) Z Objective function (mal power generation cost and curtailment cost of customers for the hours of the day in which loads can be curtailed, $) Ci(.) Generator i cost characteristic MCPi Marginal cost of real-power generation at bus i in t t$/p.u.Mwh) LSF Load scaling factor N Total number of buses NG Number of generating buses NL Number of load buses i, j Index for buses Real power generation at bus i at t (p.u.MW) F"? Qgi Reactive power generation at bus i at t (p.u.MVAr) Pdi Real power demand at bus i at t @.u.MW) Qdi Reactive power demand at bus i at t (p.u.MVAr) Vi Voltage at bus i at t @.u.) Yii Element of network admittance matrix @.u.) €3, Phase angle of Yii (radian) Si Voltage angle at bus i (radian) Pii Power transfer on line i-j at t (P.u.) PTmx Maximum power transfer limit (P.u.) CCk Curtailment cost of customer type k ($/p.u.MW) XI,' Max. curtailable M W at 1-hour notice of type k at t at bus i @.u.MW) QCl$ Max. curtailable MVAr at 1-hour notice of type k at

t at bus i (p.u.MVAr) Max.curtailable M W at 1-day notice of type k at t at bus i (p.u.MW) QC2,l Max. curtailable MVAr at 1-day notice of type k at t at bus i @.u.MVAr) Level of curtailable load selection of type k at t at Xk bus i at 1-hour notice (0 to 1). It is assumed that, with 1-hour notice, the load curtailment duration is shorter and is limited to time-period t. Level of curtailable load selection of type k at t at Utfi bus i at 1-day notice (0 to 1). It is assumed that with 1-day advance notice, the customers can shift their load for longer duration and it would give a MW and MVAr reduction for a fixed number of hours S . ramp-rate limit on generator bus i in % of generator Rgi output that can be changed in a time-step Limits on bus voltage levels (P.u.) V"'", vReal power generation limits at bus i P8?, P," (P.u.Mw) Reactive power generation limits at bus i Qgi-3 Qgi(p.u.MVAr) X2,L

2.1 Dynamic Optimal Power Flow Model: The modified formulation of the OPF problem is described below: Obiective Function:

The system operating constraints are the following: a. Load Flow Equations: [PCI', XI, + PC2', * Ul,I PI8' - PI, +

-

k N

lv,l Iyl

tyJ

(2)

.cos(eij + sj - si)

j-1

Q8, - Qd,+z) [QCI

*

XI,

+

QC2 ,'

*

U ,'I

k

N

(3) b. Generating Limits: I PI8, I (1+R8J ' Pt-1& (1-Rg]

(4)

Q , - I el8, Q,-

(5)

for i = 1,...,NG If the MW-limits exceed the actual limits i.e. Pgi""", P,,-, these are reset to the actual limits. c. Voltage Limits: IV'E = Constant IF4 I rV'J 5 W--l

for i

=

1,...8 G

for i

=

1,......JVL

(6)

718

d. Transmission Limits: p, V ij; i#j

(7)

e. Longer-duration curtailment: u tk, = Uf+Ik, .....= UtiS k,

(81

-

3. AN EXA

The objective function (1) is minimized subject to the constraints (2)-(9). It should be noted that the number of decision variables and constraints increases marginally in the modified OPF model as compared to the standard version and accordingly the computational resource requirement would be similar even for a large scale real-life system.

shown in Appendix-1. load curtailment in the program is simulated w advance times for notification.

Type

Advance

Load

2.2 Discount on Hourly Spot-Prices: The hourly spot-prices can be obtained from the dynamic OPF model described above using the following relation: MCP, = pi, - XJJOW 4- If,*

(93

where, dual or shadow price associated with the real-power ptl= flow equation (2). = dual or shadow price associated with the lower limit on generator output in constraint (4) (either the actual lower limit, or due to the ramp-rate limit which ever is higher). hf,,upp = dual or shadow price associated with the upper limit on generator output in constraint (4) (either the actual upper limit, or due to the ramp-rate limit which ever is lower). The discount on spot-price due to interruptible load is calculated as the difference between the spot-price without he interruptible load program (Le with the original load level] and with interruptible load.

2.3 Discount on Demand-Charge: To calculate the CRR of &e interruptible load program, an hourly loss of load probability COLP) is calculated using the convolution method [9] for the hours under study using the original load level i.e without my interruptible load. The aggregate LOLP for the entire period is calculated. Next, the selected interruptible loads are deducted from the original load to arrive at the modified load for each hour and the modified LOLP. A reduction in the load due to optimal K M would improve the reliability index i.e modified LOLP would be lower than the original level. The next step is to incrementally raise the entire modified load pattern till the modified LOLP reaches the original level. The difference between the original peak load and the peak load thus obtained. The difference of this new peak load at the original LOLP level and the modified peak load due to ILM is divided by the actual peak load reduction due to EM. The product of CRR and marginal capacity cosi ($lkW) determines the discount on demand-charge to be offered for the part of the demand subscribed to ILM. A CRR value of less than one would reduce the actual benefiucost ratio and a value greater than one would improve it [73.

rate constraints EM-2: Interruptible lo

ramprate limits. The generator outputs ( are shown in Table-2. Table-2 Generator OutDut (in t=l

t=2

t=3

t=4

t=5

t=6

62

80

135

45

80

53

BASE

I

ILM- 1

I

Total Cos

45

46

63

42

Total Cost = $23,323

ILM-2 I

45

54

72

r[

40

46

59

39

46

37

719

The cheaper generator delivers higher share of the total load in all scenarios and in all time periods. In case of ILM-1 and ILM-2, the generation level of both generators drops as part of the load can now be interrupted during peak hours. The total cost, which include generation cost and customer costs, falls in LM-1 and ILM-2 as a result of incorporating the interruptible load program. However, in ILM-2, the binding ramp-rate limits have led to different generation schedule from ILM-1 and has higher costs associated with it. The selection of interruptible loads in ILM-1 and ILM-2 are shown in Table-3 and Table4 The f i t row gives the load scaling factors for each hour used in the example. The fist column refers to the bus number and type of curtailable load respectively as Bus.Type. The level of curtailable load selection i.e optimal values of X and U described in section 2, are shown for each hour. The inclusion of mhp-rate eliminates the selection of Type4 curtailable loads and also modifies the selection of other types during the fourth time-period. This is because of the ramp-rate limits which restricts the variation of generator loads beyond a certain limit. Table-3: ;optimal Selection of Interruptible Loads in EM-1 Bus.Type

t=l

t=2

t=3

t=4

t=5

t=6

0.8 1.0 LSF 1.3 0.6 1.0 0.7 .......................................... 3.1

0.98

1

1

0

1

0

3.2

1

1

1

0

1

1

6.1

1

0

1

0

1

1

0

1

1

1

1

1

1

1

0.24

1

6.2

1

6.3

1

6.4

0

1

1

1

1

0

Following the optimal selection of curtailable loads, the short-term price discounts can be obtained as the difference between the spot prices across BASE and ILM-1 (both these cases do not consider ramprate limits), as shown in Table-5. It is to be noted that the discount to be offered varies across space and time depending upon several factors viz. network configuration, power factor of curtailable load and advance notification time, demand, customer costs in load curtailment. In order to calculate the CRR of the interruptible load program in ILM-1, the original and modified LOLP levels are obtained for the system assuming a 10%forced outage rate of both the generators. The modified load levels are obtained by

Table-5: Discount in Spot-Prices in $MWh Bus#

t=l

t=2

t=3

t=4

t=5

t=6

5

50

50

69

36

50

46

5

17

38

158

13

38

12

6

19

40

186

14

40

13

reducing the original load by the curtailed amount given in Table-3. The original peak demand is 175 MW and the modified peak demand is 105 MW. The original LOLP is 0.14 hourdday and modified LOW level is 0.06 hours/day for the test system. As the modified load curve is scaled up, the LOW reaches the original level when the new modified peak demand is 150 MW (Fig.1). Hence, the CRR is calculated as,

-

CRR = (150 105)/(175

- 105) = 0.64

The discount on demand-charge for the part of the demand subscribed to ILM program is obtained as $5 x 0.64 = $3.2/kW, where the marginal capacity charge is valued at $5 per installed kW.

720 management program l a d reductionforecas

1989, pp.463-471.

J"u"LB-

IEEE-PES WInr

I-CRKWALWW-ll.14) P - h % X l m o L p - Q M ) m - NBW MCDIPIBD (mrw.l.4)

Fig.1: Load Curve With and Without Intenuptible Loctd Program 6. APPENDIX-1

4. CONCLUDING REMARKS An OPF-based model is developed to support interruptible load management (EM)by elecmc utilities. It encompasses several important features which need to be incorporated in ILM: distinguishing interruptible loads by

power factor, advance notification and customer costs involved in load curtailment. It also enables satisfying network constraints and dynamic restriction on generators viz. ramp-rate limits. Short-term discounts on spot-prices may be obtained as the difference in spot-prices with and without E M , while the long-term benefits may be calcuIated using the capacity response ratio (CRR)of the ILM options. Modelling these features lead to optimal selection of interruptible load taking into account netwwk configurations, power factor of load to be curtailed, period of curtailment etc., and also accurate calculation of dynamic interruptible tariffs and discounts to be offered on demand-charges.The model codcl be extended to make decision on participation of non-utility generators and other types of demand-side management options.

University in 1990. Currently, he is working towards his Ph.D. at the Indira Gandhi Institute. of Development Research, Bombay, India. His research interestsinclude electricitypricing. power systemplanning, environmentaland demand-side management aspects.

D.Chattopadhyay obtamed his B.E.

5. REFERENCES [l]

C.W.Gellings,"Integratinglmd management into utility planning" IEEE Trans. on Power Systems, Vol.PAS-104, N0.8, 1985, pp.2079-2085.

PI

S.A.Smith,"A h e a r programming model for real-time pricing of electric power service" Operations Research, Vo1.41, No.3, 1993, pp.470-483.

[31

C.S.Chen and J.T.Leu,"Intemptible load control for TaiwanPower Company" IEEE Trans. on Power Systems, Vo1.5,No.2, 1990, pp.460-465.

[41

M.R.Mcrae,

R.M.Schmr

and

B.A.Smith,"Integrating

load

interests include environmental and