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IEEE

Transactions on Power

Systems, Vo1.6,

No.1,

February

1991

23

REAL-TIME

PRICING OF REACTIVE POWER: THEORY AND CASE STUDY RESULTS

by

Martin L. Baughman

Senior Member Student Member

Professor Graduate Research Assistant

Department of Electrical and Computer Engineering

The University of Texas at Austin

Austin, Texas 78712

ShamsN Siddiqi

ABSTRACT

An analysis is made of real-time pricing policies of reactive

power using a modification of the OPF model. The theory of real-

time pricing of reactive power is presented, followed by a case study

illustrating the magnitudes and ranges that real-time prices of

reactive power might take

on

under different circumstances. The

efficiency implications of real-time pricing of reactive power are

compared with traditional power factor penalties. It is concluded

that real-time pricing of reactive power should develop

simultaneously with that of active power for maximum economic

efficiency and smooth operation of the electricity marketplace.

KEY

WORDS

;

Reactive Power, Real-Time Pricing, Optimal Power

Flow

I

NTRODUCTIO

N

Real-time pricing of electrical energy is an area of intense

research at present. Real-time pricing of reactive power is closely

related to that of active

or

eal) power.

The development of spot pricing theory and the analysis of

the practice of spot pricing for real power have been carried out by

Caramanis, Bohn and Schweppe [1],[2], among others. Schweppe,

et. al. [3]

see

spot pricing becoming more attractive n a competitive

electricity market, especially at the generation stage where

independent power producers would adjust their generation levels

according to the spot prices paid to the producers for their power

production.

An extensive discussion

on

the implementation and

functioning of a spot price based energy marketplace is made in [4].

It includes topics ranging from spot price based rates and revenue

reconciliation to optimal investment conditions. a summary

of

existing rates that are related to real-time prices and load

management schemes that reflect real-time pricing policies is

provided in [5].

A

utility perspective on spot pricing is given in [6].

Most discussions on spot pricing of real power are equally relevant

to real-time pricing of reactive power.

Unfortunately, the pricing of reactive power has received

very little attention. A reason for this negligence is the inherent

difficulty in understanding the concept, especially by economists.

Berg, et. al. [7] point out the inconsistency and inadequacy of the

present pricing policies based

on

power factor penalties. They

suggest that, given the present high cost of additional investments

by electric utilities, prices should be derived from economic

principles, which support a pricing approach that has price equal

marginal costs, that would also reflect today's technological

constraints.

As power system margins

are

reduced because of emphasis

on the greater use of generation and transmission, power systems

dispatchers must operate their systems much closer to their technical

limits. Real-time prices for react ive power provide information to

both users and dispatchers of electricity about the cost and value of

reactive power usage, flows, and sources.

90 SM

466-3

PWRS

A

paper recommended

and

approved

by the IEEE Power System Engineering Committee of the

IEEE Power Engineering Society for p re se n ta t i on a t t h e

IEEE/PES 1990 Summer Meet ing, Minn eapol is, Min nesot a,

July

15-19, 1990.

1990; made available

f o r

p r in t i n g A p r i l

24

1990.

Manuscript submitted February 1,

Ray and Alvarado [8] use a modification of the Optimal

Power Flow

(OPF)

model which allows for the price

responsiveness of real power demand to analyze the effects of spot

pricing policies. A similar model, but one which also allows for the

price responsiveness of reactive power demand, will be used here

to

analyze the impact of real-time pricing of real

In this paper, an analysis is made of real-time pricing of

reactive power using a modification of the OPF model. In the next

section the theory of real-time pricing of reactive power is presented.

In Section 111, a case study illustrating he magnitudes and ranges

that real-time prices of reactive power might take on under different

circumstances is presented. The next section then discusses the

efficiency implications of real-time pricing of reactive power when

compared with traditional power factor penalties. The last section

concludes that real-time pricing of reactive power should develop

simultaneously with that of active power for maximum economic

efficiency and smooth operation of the electricity marketplace.

II

THEORY OF REAL-TIME PRIC NG

OF

REAC'I?VE POWER

A theory of real-time pricing of reactive power that

accurately reflects the underlying physical and engineering

properties of electricity is presented below.

The following notationwll be used in the derivation:

C = total system operating cost

Ci(.)= cost function of generating plant at Bus i

Pgi

=

active power generation at Bus i

Qgi

=

reactive power generation at Bus

i

Pdi

=

active power demand at Bus

i

Qdi

=

reactive power demand at Bus i

Vi

= voltage at Bus i

6i =

voltage angle at Bus i

YBUS= Yij] = admittance matrix of the transmission network.

8ij = phase angle of Yij

Pi, = active power flow from Bus

i

to Bus j

N

= set of all buses in the system

G = set of all buses having generating capacity

MCpi= Lagrange multiplier on the active power equation at Bus i

M Q =

Lagrange multiplier on the reactive power equation at Bus i

, i n =

Lagrange multiplier on the minimum active power

hi,m=

=

Lagrange multiplier

on

the maximum active power

pi,min= Lagrange multiplier on the minimum reactive power

pi, =Lagrange multiplier

on

the maximum reactive power

qi,

=

Lagrange multiplier

on

the active power flow limit from Bus i

reactive power.

generation limit at Bus

i

generation limit at Bus i

generation at Bus

i

generation at Bus

i

to Bus j

Vimh=

Lagrange multiplier on the minimum voltage level at Bus i

Vim==

Lagrange multiplier

on

the

maximum

voltage level at Bus

i

Epi

=

price elasticity of demand of active power at Bus i

Q =

price elasticity of demand of reactive power at Bus

i

Epqi = cross-price elasticity of demand for active power with

respect to a change in price of reactive power at Bus i

Espi

=

cross-price elasticity of demand for reactive power with

respect to a change in price of active power at Bus i

Dpi

=

demand for active power at Bus

i

for active power and

reactive power prices equal to unity

Dqj =

demand for reactive power at

Bus

i for active power

and reactive power prices equal to unity.

0885-8950/91/0200-0023$01.00

1991

EEE

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24

It is assumed that a single welfare-maximizingpublic utility

owns and operates the generating plants and transmission network

of the electric power system under consideration and it sells active

and reactive power to independent customers. The utility is assumed

to be able to set and communicate prices instantly, and can set a

different price for each customer location at each moment. The

customer responses to these prices are assumed to be known and

are

given by the demand functions. It is also assumed that demands are

independent of past and future prices and, correspondingly, for

generating costs. Therefore, the model can be solved as a single

period model.

Objective:

The objective of the pricing policy is to maximize social

welfare, that is, to maximize consumers' plus producers' surplus,

subject to the operational constraints. This is accomplished by

setting prices of real and reactive power at each bus at a particular

time equal to the marginal costs of supplying real and reactive

power, respectively, at that bus and that time, where the marginal

costs are determined on the basis of an optimal load dispatch, that is,

real and reactive power dispatch so

as

to minimize total operating

costs of the utility, subject to the operational constraints. The pattern

of

optimal load dispatch is dependent on the real and reactive power

demands, and, on the other hand, real and reactive power demands

are dependent on the prices, that is, marginal costs determined from

the optimal load dispatch. Thus, this is a bi-level problem consisting

of an upper and a lower part. The upper level problem is that of

satisfying the demand functions, where the prices are implicitly

determined by the lower level problem, which is that of minimizing

total operating costs subject

to

he operational constraints.

Demand Functions:

The demand functions are assumed to be of log-linear form

exhibiting constant price elasticity and cross-price elasticity.The

demand functions may be mathematically expressed in the following

equation forms:

Pd;= Dpi MCp;)Epi MCqi)Ep9'

wi

%i (MQi)E4ph(MCqi)'1 2)

(1)

which give the demand of real and reactive power at Bus i as a

function of prices of real and reactive power at that bus, for all i E N.

The parameters of the equations, which are Dpi, Dqi, Epi,

Eqi,. Epqi, and Ew i, vary with customer classes, time under

consideration, and other exogenous factors. For example, they may

differ for residential and commercial customers, the time of day, the

season, weather conditions, etc.

The prices of real and reactive power, which are equal to

marginal costs MCpi and MCqi, respectively, when load is

dispatched optimally, are implicitly defined by the following lower

level problem.

Lower-level Objective Function:

The lower level problem is basically the optimal power flow

problem which has the objective of minimizing the total cost of

operating the spatially separated generating units subject

to

he set of

equations that characterize the flow of power throughout the system

and all operational constraints. Since the operating cost of producing

reactive power is much less than that of real power where the

capacity exists, the operating cost of generating reactive power is

assumed to be negligible compared to that of real power in the

analysis to follow. Thus, the objective function may be expressed in

the following form:

Minimize

C

=

Ci ( Pgi)

(3)

i e G

where

Ci

Pgi ) is the operating cost of producing Pgi units of real

power at the generating plant atBus i.

There are several constraints to the lower level problem.

Load Flow Equations:

The set of equations, determined by Kirchoffs laws, that

characterize the flow of power throughout the system are given

below:

(4)

gi

-

Pdi

- c

Vi IVj 1YijI COS( iJ+6j-6i ) = 0

j E N

Qg; - Qdi

+

c Vi IV,

j e N

which are the active and

respectively, for all i E

N.

lYij

eaci

Sin( Bij+6,-6i

) =

0

( 5 )

ve power flow equations,

The Lagrange multipliers of the above constraints, MQi and

MCqi respectively, give the marginal costs of supplying real and

reactive power a t Bus i and thus determine the prices of real and

reactive power, respectively, at that bus.

Generation Limits:

The generating plants of the utility have a maximum

generating capacity, above which it is not feasible to generate due to

technical or economic reasons. Generation limits are important in

determining the operating points and marginal costs of generation.

Generating limits are usually expressed as maximum and minimum

active power and reactive power outputs,

Pgi,min Pgi Pgi,max

6)

Qgi,max Qgi Qgi,max

(7)

where Pgi,min and Pgi,max are the minimum and maximum active

power output and Qgi,min and Qgi,max

are

the minimum and

maximum reactive power output, respectively, of the generating

plant at

Bus

i, for all i

E

G

If the plant at Bus

i

has only reactive power generating

capability, for example, capacitor banks or synchronous

condensers, then Pgi

min

= 0, Pgi,max = 0, Qgi,min = 0, nd the set

of constraints effectivkly reduce to

0

2

Qgi Qgi,max (8)

Transmission Limits:

Transmission limits refer to the maximum power or current

that a given transmission line is capable of transmitting under given

conditions. These limits can be based on thermal considerations or

on stability considerations. Thermal limits usually dominate for

shorter lines. Dynamic stabilitylimitsdominate longer line behavior.

These limits affect the marginal costs of operation. Transmission

limits

are

expressed here in terms of the maximum active power

flow through the lines,

9)

where Pij = IVi I IVj IYi, COS(8ij+6,-6i ) - IVi l2 IYij I Coseij,

assuming that shunt admittance is negligible, where Pij,min and

Pij,max are the minimum and maximum active power flow,

respectlvely, through the line connecting Bus i to Bus j , or i j,

and all i, j EN .

Voltage Limits:

Voltage limits refer to the requirement for the system bus

voltages to remain within a narrow range of levels. Since voltages

are affected primarily by reactive power flows, the marginal cost of

supplying reactive power to a bus is directly dependent in the

voltage level requirement at that bus. The voltage limits can be

expressed by the following constraints,

10)

where Vi,min and Vi, are the minimum and maximum voltage

levels, respectively, hat are acceptable atBus i, for all i E

N.

Model Solution:

A method of solution for the bi-level nonlinear programming

problem is presented below.

The Lagrangian to be minimized over all active power

generation levels Pg, reactive power generation levelsQg, voltage

levels V, and voltage angles 6, is:

Pij,min Pij Pij,max

Vi,min IViI I ViDa

L

Pg, Qg, V, 6 )

=

c

Ci(Pgi)

[

operating costs

I

E G

- ( M Q i ) [ P gi

-

Pdi

-

N~INjITY~~ICos(8i 6J-6i)]

i

E N j e N

[

active power flow equations ]

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25

-

M C ~ ~

i

wi

I V ~w j wi j Sin(

eij+6j--6i

i EN

j E N

[

reactive power flow equations

]

-

C hi,min(pgi-Pgi,min)

i e G

[

min. active power generation limit

]

[ max. active power generation limit ]

[min. reactive power generation limit ]

[max.reactive power generation limit]

C hi,max Pg i- Pgi,max)

i E G

-

C

Fi,min Qgi - Qi,min)

i E G

C Wi,max Qi - Qi,max)

i E G

+ c 'f qij lpijl Pij,max)

i E N J E N

I ransmission line constraints 1

- C Vi,min

-

Vi,min)

[ minimum voltage levels ]

[ maximum voltage levels ]

i E N

+ C Vi ,max

I - Vi,max)

(1 1)

with the additional condition that the demand functions must be

satisfied, that is,

(12)

i E N

Pdi= Dpi MC P~ )~ ( Cqi)ER'

Qdi=

mi

(MCPi)Egp'(MCqi)'g' (13)

for all i E

N.

The Kuhn-Tucker conditions for the minimization problem

along with the demand functions can be solved simultaneously to

obtain the real-time prices of active and reactive power at each bus

that maximizes overall social welfare along with the generation,

demand, voltage magnitude and angle at each bus and the power

flow in each line.

Definition of Real-time Prices:

Bus i and at a particular time is given by,

pi

=

total cost of providing electricity to

l

customers subject

to the operational constraints ]

The real-time price of real power based on marginal cost at

6

6Pd

6L

6Pd

-

-

= MCpi

Similarly, the real-time price of reactive power based on

6

marginal cost at Bus i and at a particular time is given by:

q , = total cost of providing electricity to

all

customers subject

to the operational constraints ]

SQdi

6L

-

-

6Qdi

=

MCqi

111. CASE STUDY

A simple, four-bus test power system, shown in Fig.1, is

used to gain insights into the effects of real-time pricing.The buses

are interconnected by high voltage transmission lines. At buses 1

and

2,

there are util ity-controlled generating plants. The two

generating units each have a unique operating cost function derived

from data on fuel costs of the generating units. A controllable

reactive power source is available at Bus 3. Customer loads exist at

every bus and each load is assumed to be price sensitive and

expressible by demand functions for active power and reactive

power that have constant price elasticity and cross-price elasticity.

The units of all quantities

are

given in per unit on a basis of 100

MVA and 138 kV. Voltage angles are in radians.

W

eneratingUnit e m

Figure 1 The Four-bus Test Power System

Model Formulation:

The modified OPF model used to solve the bi-level problem

can be formulated as the optimization problem of minimizing the

total cost of operating the spatially separated generating units subject

to the load flow equations that characterize the flow of real and

reactive power throughout the system, the operational constraints

such as generation limits, transmission limits and voltage limits, and

the demand functions for real and reactive power at every bus.

Objective Function:

Minimize C = C1( Pgl ) C2 Pg2 )

Load Flow Equations:

The formulation of the model is described below.

=

33251+1622 Pg1+169.5 Pg12+ 2098.9 Pg2+ 441.9 Pg22

4

Pgi

-

Pdi - ~ N i I N j I N i , i C ~ ~ 8 i j + 6 j - 6 i )

a i

a i

C N , I N ~ I N ~ ~ I S ~ ~ ( ~ ~ , +

  o

for i

=

1,2,3,4.

0.0

Pgl 6.3

0.0 5 Pg2

I

2.0

j = l

4

j = 1

Generation Limits:

-1.0

Qgl 3.5

-0.8 I

Qg2 S 3.0

0.05

Qg3 2 0.2

Transmission Limits:

Pij 1.8

for all i

=

1,2,3,4, j = 1,2,3,4 and i

j.

Voltage Limits:

v1

=

1.0

v2 = 1.0

0.95 I V3 1.05

0.95

I

V41 2 1.05

Pd,

=

Dpl MCpl)-0'2(MCql)o'a

Pd2

=

Dp2 M Q J ~ ) - ~MCq2)O.O

Demand Functions:

-0.0001

Pd3 = DP3 MCP3 MCq3

1

Pd4

=

Dp4 MCp4)-'.05 MCq4 )-0 04

Qd, = Dql MCpl )-o.2(MCql

Q d 2 = D q 2 MCp2

Qd3

=

Dq3 MCp3

) - 0 0 5

MCq3

Qd4 = Dq4 MCp4 )-0.02 MCq4 - O l

where Dpi and Dqi vary with time of use and are determined

from load curves. The values at the time of system peak are:

Dpl

=

5.677 Dql = 2.962

Dp2

=

1.444 Dq2 = 0.667

Dp3

=

1.889

Dq3 =

0.8175

Dp4 = 1.184 Dq4 = 0.6434

MCq2 )O

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27

Figures

6

and 7 show the effects of decreasing the reactive

generating capacity of the generating unit at Bus

3

on the real-time

prices of active and reactive power. Figures

8.9,

and 10 show the

effects on active power de,mand. reactive power demand, and the

revenue, costs and profits of the utility, respectively. Figure

11

shows that the revenue, and hence profit, of the reactive power

generating plant alone initially increases due to increasing prices but

then falls as the quantity produced is reduced more than the

corresponding rise in prices.

(b) Transmission Limits:

Transmission limits affect real-time prices of reactive power

much

in

the same way as it does real power prices. When the power

flow constraint

on

a line ismade increasingly tight, the prices of real

and reactive power on the receiving end of the line also increase.

This is because the line flow constraint forces the use of a higher

loss path to satisfy the demand requirements of the bus at the

receiving end of the line, and may also require the reallocation of

generation which would increase

total

operating costs.

(c) Voltage limit:

The greatest impact on the real-time prices of reactive power

as well as the generation and consumption pattem of reactive power

by the utility and customers is due to vol tage constraints. This is

because voltages are affected mainly by reactive power flows and

voltage constraints are usually relieved by adding sources of reactive

power.

b

Busl

Bus2

9 Bus3

Bus4

z 321 ----

3 1 :

.

I .

. 1

0 10 20 30

40

ReactivePowerGenerationat

Bus 3

Fig.6 Real-time Price of Active Power vs.Reactive Power

Generation at Bus

3

1

f

z

0.8

0.6

0.4

P,

Bus3

Bus4

Bus3

Bus4

0.2

+

0

1 0 2 0 30 4 0

ReactivePower Oeneration

t

Bus 3

MVAR)

Fig.7 Real-time Price of Reactive Power vs. Reactive Power

Generation at Bus 3

s

-0.0

-0.2

-0.4

-0.6

4

Busl

B us 2

Bus3

Bus4

-0.8

0

1 0 20

30

4 0

ReactivePowerGenerationatBus

3 (MVAR)

Fig.8 Change in Active Power Demand vs. Reactive Power

Generation

at

Bus

3

-

t

Busl

+-

Bus2

9 Bus3

Bus4

-5

10 20 30

4 0

ReactivePowerGenerationat

Bus

3 (MVAR)

Fig9 Change in Reactive Power Demand vs. Reactive Power

Generation at Bus

3

+ Profit

cost

Rev.

- l o

I

.

I

* 1 i

0 10 20 30 4 0

ReactivePower eneration t Bus 3 MVAR)

Fig.

10

Change

in

Revenue, Cost, and Profit vs. Reactive Power

Generation at Bus

3

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The effect of tightening the voltage constraint atBus 4 under

real-time pricing of active and reactive power are shown in Figures

12and 13. Figure 12 shows that the real-time price of active power

rises at Bus 4 and changes very little at other buses with the

increasingly tight constraint on Bus

4

voltage. On the other hand,

the real-time price of reactive power at Bus 4 r ises very rapidly with

the tightening of the constraint, as shown in Figure 13. Without

real-time pricing of reactive power and the corresponding price

responsiveness of reactive power demand, the tightening of the

voltage constraint at Bus 4 could lead to skyrocketing costs of

supplying reactive power

to

Bus

4

and consequent load intemption

in order to maintain the

desired

voltage level.

IV. COMPARISON

WITH

POWER F A O R PENALTIES

Reactive power pricing based on power factor penalties is

unable to provide accurate

price

signals to customers under voltage

constraints. In the case in question, the marginal cost of reactive

power at

Bus

4 is 693.52 per MVARHr when the voltage limit is

0.966 PA., but the price of reactive power would be zero under

power factor penalties since the power factor of the customer atBus

4 is greater than 85 percent. Under real-time pricing of reactive

power, the price of reactive power at Bus

4

would be

693.52

per

MVARHr, equal to the marginal cost. Such a high price would

provide a strong incentive for the customer to reduce eactive power

demand.Thus, power factor penalties are unable to give accurate

price signals to customers, while real-time prices provide such

signals.

Consider the case of two customers connected

to

Bus 4, one

large customer having a demand of 200 MW and 113 MVAR and

another smaller customer having a demand of

20

MW and

19

MVAR at the time of system peak, when the marginal cost of

reactive power

is

0.56 per

MV RHr

t Bus 4. In order to calculate

the bill for reactive power consumption under power factor penalty,

the following billing algorithm is used for customers having power

factors below 85 percent: The totalKWh for the month is multiplied

by 85 percent and divided by the average power factor for that

month for adjustment purpose. Under this penalty policy, the larger

customer who demands 113 MVAR of reactive power will not be

penalized, that is. his monthly bill for real power consumption-will

not increase due to his reactive power consumption since the

cugtomer's power factor is greater than 85 percent, namely 87

percent. On the other hand, the smaller customer would be penalized

for his demand of

19

MVAR and,

if

a load factor of one is assumed,

the customer's monthly bill would be

1.1724

times his bill for real

power consumption alone. This represents an increase in the

monthly bill of 17.24percent for the smaller customer, while the

larger customer's bill does not increase. The smaller customer

effectively pays 7.26per MVARHrwhile the larger customer pays

$0.00 per MVARHr, even though the larger customer is the major

consumer of reactive power. Thus, the cost burden is inequitably

shared by the customers under reactive power pricing based on

power factor penalties.

Under real-time pricing of reactive power, both customers

would pay the same real-time price of 0.56 per MVARHr. Thus,

each customer would pay

in

the exact proportion

as

the amount of

reactive power consumed by each, which results in an equitable

sharing of the cost burden. The cost imposed on a utility due to the

reactive power demand at a bus depends on the amount of reactive

power consumed and not on the power factors of the individual

customers. Hence, reactive power pricing based on power factor

penalties does not result in equitable sharing of the cost burdens

while real-time pricing of reactive power based on marginal costs

does result in equitable sharing of cost burdens.

V.

CONCLUSION

The importance of an efficient reactive power pricing policy

is beginning to

be

recognized by the utility industry. Accurate price

signalsare essential for proper investment planning by the utility and

the customerssoas to

maximize

overallsocialwelfare.

Real-time pricing of active and reactive power are necessary

ingredients for a successful marketplace of electricity. Such a market

would treat VARs like other market mc di ti es , thus providing a

market mechanism for buving and selling VARs. This would

facilitate marketplace transactions of reactive power including

buying and selling of VARs to neighboring utilities, large industries

and independent power producers as well as to cletermine wheeling

charges for VARs.

5 1

-15

0

10

2 0

30

40

Reactive owa

GenerationatBus3

MVAR)

Fig.

11

Change in Revenue from VAR Sales atBus 3 vs. Reactive

Power Generation at

Bus 3

3oo 1

100

0 1

0.90 0.92 0.94 0.96 0.98

Voltage

at

Bus

4

@er

unit)

Fig.12 Real-time Price of Active.Power vs. Voltage at Bus 4

M O 1

P

a

f

-200

0.90 0.92 0.94 0.96 0.98

Voltage

at

Bus4 @er unit)

Fig.13Real-time Price of Reactive Power at Bus

4

vs. Voltage

at

Bus

4

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29

APPENDIX: TRANSMISSION

LINE

IMPEDGNCE DATA

Line, Length

bus to R X R X Charging

bus km

mi

R R perunit perunit MVAR

1-2 64.4

40

8

32 0.042

0.168 4.1

1-4 48.3 30

6

24

0.031

0.126 3.1

2-3 48.3 30

6

24 

0.031

0.126 3.1

2-4 128.7

80

16 64

0.084 0.336

8.2

3-4

80.5

50

10 40

0.053

0.210 5.1

REFERENCES

1 )

Caramanis, M. C., R. E. Bohn, and F. C. Schweppe, Spot

Pricing of Electricity: Practice and Theory , IEEE

Transactions

on

Power Apparatus and Systems

Vol.

PAS-101,

No.

9,

September

1982,

pp.

3234 - 3245.

2)

Bohn, R. E., M. C. Caramanis, and F.

C.

Schweppe, Optimal

Pricing in Electrical Networks Over Space and Time ,The

Rand

Journal of Economics

Vol.

15,

No.

3

(Autumn

1984),

pp.

360

3)

Schweppe,

F.,

et al, Homeostatic Control for Electric Power

Usage ,

IEEE Spectrum

July

1982,

pp.

44

-

48.

4) Schweppe, F. C., Caramanis, M. C., Tabors, R.

D.,

and Bohn,

R. E.,

Spot Pricing

of

Electricity

Kluwer Academic Publishers,

Boston, MA,

1988.

5)

Tabors, R.

D.,

F. C. Schweppe, and M. C. Caramanis, Utility

Experience with Real Time Rates , IEEE Summer Power

Meeting,

1988.6)

Garcia, E. V., and J. E. Runnels, The Utility Perspective of

Spot Pricing , IEEE

1984

Summer Power Meeting, Seattle,

Washington, July

15 - 20, 1984.

Paper

84-SM-:54-2.

7)

Berg, Sanford V., J. Adams and B. Niekum, Power Factors

and the Efficient Pricing and Production of Reactive Power ,

The Energy Journal Vol. 4, Special Electricity Issue, pp. 93

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102.

8)

Ray,

D.,

and F. Alvarado, Use of an Engineering Model for

Economic Analyses in the Electric Utility Industry , Department

of Electrical and Computer Engineering, University of

Wisconsin-Madison,

1988,

presented at the Advanced

Workshop on Regulation and Public Utility Economics, Rutgers

University, May

25-27, 1988.

9)

Lasdon, L.S. and Waren, A.D., Generalized Reduced Gradient

Software for Linearly and Nonlinearly Constrained Problems ,

in

Design and Implementation

of

Optimization Software

H.

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- 376.

Martin L. Baughman

(S,

72)

was

bom

on February

18,1946

in

Paulding,

Ohio.

He received

his

BS

in Electrical Engineering from Ohio

Northem University in

1968

and his

MSEE ndPhD degrees in electrical

engineering at

MIT

in

1970

and

1972,

respectively.

Dr.

Baughman was

a

Research

Associate at Massachusetts Institute of

Technology from

1972

to

1975,

at

which time he joined the University

of Texas at Austin as a Senior

Research Associate. In

1976

he

joined the faculty of the Department of Electrical and Computer

Engineering as an Assistant Professor. In

1979

he coauthored a

book with Paul Joskow on electricity supply planning entitled

Electricitv in the U n i w s : Models and Policv Analv&. From

1984

to

1986

he chaired the National Research Council Committee

on Electricity

in

Economic Growth. He

has

served

as a consultant

to several agencies, including Edison Electric Institute, the MIT

Energy Laboratory, the Economic Councilof Canada, and the

Ministry of Planning in Saudi Arabia, and the Electric Power

Research Institute.

Dr.

Baughman is a member of the Intemational Association

of Economists and registered ProfessionalEngineer in the state of

Texas.

N. Siddiai was bom in

Chittagong, Bangladesh on

September

1,1964.

He received a

B.Sc. (Engineering) from Bangladesh

University of Engineering and

Technology in 1988. He received a

Masterdegree n Electrical

Engineeringfrom he University

of

Texas at Austin in

1989.

He has been

a Graduate Research Assistant with

the Center for Energy Studies at the

University of Texas at Austin since September,1988, where he is

pursuing a PhD in the Departmentof Electrical and Computer

Engineering.

economics, electricity pricing, and optimal power dispatch.

His esearch interests are in the areas of power systems