EXHIBIT 99.491

TRANSMISSION ACCESS AND PRICING WITH MULTIPLE SEPARATE ENERGY FORWARD MARKETS

<Table>

Paul R. Gribik George A. Angelidis Ross R. Kovacs
Member Senior Member
Perot Systems Corporation Pacific Gas and Electric Company Southern California Edison
Los Angeles, CA San Francisco, CA Rosemead, CA
</Table>

ABSTRACT: California's congestion management protocols provide comparable access
and prices to all users of the transmission system (power exchange and bilateral
contract parties). The parties submit implicit bids for interzonal transmission
capacity, and an Independent System Operator (ISO) allocates the available
transmission capacity to maximize its value as measured by the bids. The ISO
accomplishes this by keeping each party's portfolio of generation and load
individually in balance when adjusting schedules to relieve interzonal
congestion. Everyone scheduling flow on a congested path is charged the same
price, namely the marginal value of capacity on the path. By keeping the
portfolios of the different parties separate, the ISO clears its transmission
market without arranging energy trades between parites. The parties involved in
an energy trade are responsible for arranging the trade. The ISO does not become
involved in the energy markets.

KEYWORDS: Transmission Congestion, Transmission Access, Transmission Pricing,
Independent System Operator, Optimal Power Flow, Utility Industry Restructuring

I. INTRODUCTION

California's utilities, power producers, consumers and the California Public
Utilities Commission (CPUC) considered two different approaches to restructuring
California's electric power industry: one based on a power pool and one based on
bilateral contracts. Several parties reached a compromise that combined the two
approaches. In addition, the CPUC's restructuring decision [1] also put forth an
industry structure that combined the two approaches. Pacific Gas and Electric,
Southern California Edison, and San Diego Gas and Electric further developed the
industry structure and rules in their Phase I filing [2] and Phase II filings
[3], [4] to the Federal Energy Regulatory Commission.

In the proposed structure, a Power Exchange (PX) establishes a market in which
generators and consumers can bid to sell and buy energy. In addition, bilateral
contract parties can schedule their own energy transactions outside the PX's
market. An Independent System Operator (ISO), which is separate from the other
market participants, operates the grid. According to the rules outlined in the
Phase I filing, the ISO is to manage the transmission system following certain
principles, including:

i. Provide comparable transmission service (prices and access) to the PX and
bilateral contract parties.

ii. Use marginal-cost pricing for major transmission paths to send correct
economic signals with respect to limited transmission resources.

iii. Limit changes to the preferred schedules of the PX and bilateral contract
parties to those that relieve transmission congestion. The ISO is not
allowed to completely reschedule the pooled resources of the PX and the
bilateral contract parties.

These are conflicting goals. To develop marginal costs that reflect the economic
value of transmission capacity, the ISO must minimize generation and load
reduction costs (as provided in bids) subject to appropriate constraints. The
ISO could place the resources of the bilateral contract parties and the PX in a
common pool in this minimization problem. This type of approach is described in
detail by Hogan [5]. The ISO would arrange all trades between market
participants that serve to lower costs. This includes trades between different
bilateral contract parties as well as trades between the PX and bilateral
contract parties. The ISO is likely to schedule trades that reduce costs but
that do not reduce congestion. This violates (iii).

The PX and the bilateral contract parties voluntarily provide the ISO with the
prices of adjusting their generation and loads. For example, these prices may
reflect the costs that an energy marketer would incur as it shifts generation
from one location to another; they may or may not reflect the prices at which
the marketer is willing to sell energy to a competing energy trader.
Consequently, giving the ISO the ability to make all schedule changes needed to
reach a least-cost schedule for the combined pool would allow the ISO to force
parties to engage in energy trades without their expressed consent. This would
violate the compromise that led to [2].

There may be other reasons not to place the resources of the PX and the
different bilateral contract parties in a common pool for purposes of congestion
management. The different energy markets (the PX and those of the bilateral
contract

parties) will operate under their own, possibly disparate, rules. At present, we
do not know how the non-PX energy markets will structure their rules or how
their rules will change over time. Differences in rules among the several
markets could give rise to different bidding strategies for participants in
different markets. In particular, they may affect the energy adjustment bids
that the market participants will submit to the ISO for congestion management.

For example, the different markets may treat fixed costs differently. In one
market, a generator's fixed costs may be covered by a payment that is separate
from its energy payments. In another market, a generator may only receive
payments for energy, in which case its fixed costs must be recovered through the
energy payments it receives. In the first case, a generator may find it
advantageous to bid energy prices equal to its incremental energy costs. In the
second, a generator may find it advantageous to bid energy prices equal to its
incremental energy costs plus an estimate of the $/MWh it will need to cover its
fixed costs. If the different markets pass these bids to the ISO for purposes of
congestion management, the price curves from different markets could be
vertically shifted relative to each other.

To develop workable protocols in the spirit of the comprimise that lead to the
Phase I filing, we defined the types of schedule adjustments that the ISO may
and may not make. The first step in developing these rules is to clearly
delineate the markets treated:

o the energy market of the PX

o the energy markets of the bilateral contract parties

o the ancillary services markets

o the transmission market.

Under the proposed congestion management procedures, the ISO keeps the different
energy and ancillary service markets separate as it relieves interzonal
congestion. These markets interact through the ISO's transmission market.

The ISO uses the price information voluntarily provided by the PX and bilateral
contract parties to determine the value that each places on using transmission.
The ISO adjusts schedules to maximize the value that the users can derive from
the available transmission capacity. It then prices transmission capacity at its
marginal value to the users.

In this paper, we only treat the energy and transmission markets. The results
can be extended to cover ancillary services.

II. PARTICIPANTS IN ENERGY AND TRANSMISSION
FORWARD MARKETS

Several entities are involved in the proposed industry structure:

1. Scheduling Coordinators (SCs)
- Manage their own energy forward markets
- Set the rules for their own energy forward markets
- Submit preferred schedules and adjustment bids to the ISO and work
with the ISO to adjust their schedules

2. Western Power Exchange (PX) -- a specific scheduling coordinator
- Runs a forward market in which parties can bid to buy and sell energy
- Develops a preferred schedule for its forward market
- Develops marginal costs for its energy purchases and sales
- Submits its preferred schedule and adjustment bids to the ISO and
works with the ISO to adjust its schedule

3. California Independent System Operator (ISO)
- Schedules the use of the transmission system in the forward market
- Develops marginal costs for use of congested transmission paths
- Controls real-time operation after the forward markets.

These parties schedule their resources in forward time frames as well as operate
in real time. Scheduling and congestion management are done in two forward time
frames:

o Day-ahead (scheduling resources in each hour of the following day)

o Hour-ahead (scheduling resources for an hour -- scheduling begins after the
day-ahead market closes).

The PX and the other SCs specify their preferred schedules of generation and
loads in each hour of the relevant forward market (day-ahead or hour-ahead).
Each SC including the PX must balance its generation and its load (plus its
allocated share of losses) in its preferred schedule.

The PX and the other SCs voluntarily provide adjustment bids that the ISO uses
for congestion management:

o Adjustment bids for generation consisting of price curves for generation
with generation limits

o Adjustment bids for load reduction consisting of price curves for reducing
load along with limits on reduction.

We only treat the forward markets in this paper.

III. INTERZONAL AND INTRAZONAL TRANSMISSION
CONGESTION MANAGEMENT

The ISO deals with two types of transmission constraints. Following the
framework of [2], the transmission system is divided into zones using experience
and engineering studies. Within a zone, it is assumed that transmission
congestion will be relatively infrequent and of low cost to relieve. Between
zones, it is assumed that transmission congestion will be more frequent and cost
more to relieve.

The ISO combines the preferred schedules of the PX and SCs and checks for
congestion in each hour. If there is congestion, the ISO adjusts the schedules
to relieve the congestion. Fig. 1 shows the congestion management process in the
day-ahead

DO NOT CITE DRAFT 16 (4/29/97) 2

market. The hour-ahead market is similar except that the ISO does not produce
advisory schedules nor does it give the PX and the other SCs an opportunity to
revise their schedules.

[GRAPHIC OMITTED]

Fig. 1: Day-Ahead Congestion Management

When adjusting schedules to relieve interzonal congestion, the ISO maximizes the
value of the available interzonal transmission capacity to those using it. The
PX and other SCs using interzonal transmission capacity pay congestion fees
based on differences in locational marginal costs.

We incorporate constraints in the interzonal congestion management procedures
that keep the energy forward markets of the PX and the other SCs separate. When
the ISO adjusts their schedules to eliminate interzonal transmission violations,
it keeps each party's total schedule in balance. That is, the adjusted aggregate
generation of the PX or another SC must equal the adjusted aggregate loads and
allocated share of the losses for that PX or SC. These constraints prevent the
ISO from imposing trades between different SCs. For interzonal transmission, the
ISO only manages the transmission forward market. It does not participate in the
energy forward markets by arranging trades between SCs.

When adjusting schedules to relieve intrazonal transmission constraint
violations, the ISO disturbs the schedules of the PX and the other SCs as little
as possible. The cost of relieving intrazonal constraint violations is charged
to all consumers in a zone as an uplift. Marginal cost pricing is not used for
intrazonal congestion management.

In this paper, we focus on interzonal congestion management and pricing in a
single hour.

IV. TRANSMISSION MODEL

In the ISO protocols, losses are modeled by using meter multipliers. The
scheduled generation at a location is multiplied by the meter multiplier for the
location to provide power to cover losses. Since losses are treated by meter
multipliers, the interzonal congestion management process uses a lossless
network model to avoid double counting losses. Consequently, the interzonal
congestion management model treats effective generation. To account for the
effect of multiplying generation by the meter multipliers, we scale the
adjustment price curves and the ranges over which generation may be adjusted by
the appropriate meter multiplier for the location.

A linear DC power flow formulation is used in the interzonal congestion
management protocol. This model is used for simplicity and for reliable, robust
marginal cost calculation. It can be derived from the real power flow equations
(1) by assuming negligible line resistances and small voltage angle differences.

[FORMULA OMITTED]
(1)

where:

[FORMULA OMITTED] is the voltage magnitude at bus i
[FORMULA OMITTED] is the voltage angle at bus i
[FORMULA OMITTED] is the real power injection at bus i
[FORMULA OMITTED] is the real power load at bus i
and [FORMULA OMITTED] is an element of the Y BUS matrix.

Assuming that [FORMULA OMITTED], and that the voltage magnitudes are in a narrow
range about 1 p.u., we can write the real power balance equations as the DC
power flow equations:

[FORMULA OMITTED]
(2)

The constraints on real power flows on interzonal paths are linearized in a
similar fashion.

V. INTERZONAL CONGESTION MANAGEMENT AND
PRICING

For scheduling coordinator k (SC k):

P k is the vector of effective real power generation at buses i = 1, 2,..., N.

D k is the vector of real power loads at buses i = 1, 2,..., N.

[FORMULA OMITTED] is the convex adjustment price function for effective
generation at bus i

[FORMULA OMITTED] is the convex adjustment price for reducing load at bus i.

The vector of voltage angles at buses i = 1, 2,..., N-1 is denoted by [FORMULA
OMITTED]. The reference bus is bus N so [FORMULA OMITTED].

The ISO solves a linearly-constrained optimal power flow problem to allocate and
price interzonal transmission:

[FORMULA OMITTED]
(3a)

subject to

DO NOT CITE DRAFT 16 (4/29/97) 3

[FORMULA OMITTED]
(3b)
[FORMULA OMITTED]
(3c)
[FORMULA OMITTED]
(3d)
[FORMULA OMITTED]
(3e)
[FORMULA OMITTED]
(3f)

where

k is an SC index and i is a bus index
B is the DC power flow matrix
H is the linearized interface flow matrix
F MAX is the vector of interface flow limits.

Constraints (3b) are the DC power flow equations, (3c) are the flow limits on
the interzonal paths, and (3f) are the market separation constraints.

In solving (3), the ISO achieves several goals:

o The ISO schedules the use of interzonal transmission capacity to maximize
its value to the PX and other SCs.

o The ISO clears its forward market for interzonal transmission.

o The energy forward markets of the PX and other SCs are cleared
individually.

The Kuhn-Tucker conditions for the interzonal congestion management optimization
problem (3) provide the marginal prices that the ISO charges for the use of
congested interzonal transmission paths. The Lagrangian for (3) is

[FORMULA OMITTED]
(4)

Let [FORMULA OMITTED] and [FORMULA OMITTED] be optimal for (3).

Furthermore, let [FORMULA OMITTED] satisfy the Kuhn Tucker conditions at the
optimum point.

The marginal cost of scheduling injection at bus j and equal withdrawal at bus i
does not depend upon the SC and is equal to [FORMULA OMITTED]. The congestion
charges to SC k are:

[FORMULA OMITTED]
(5)

The marginal value of capacity on the various interzonal paths are the elements
of [FORMULA OMITTED]. The congestion charges to SC k can also be calculated by
summing the flow that SC k schedules on each path times the marginal value of
capacity on the path:

[FORMULA OMITTED]
(6)

The superscript (CARET) indicates that the reference bus is removed.

The congestion charges as calculated by (5) and (6) are equal. Details of the
derivations are in the appendix.

VI. EXAMPLE

Consider an example problem (Fig. 2) to illustrate the interzonal congestion
management procedure. The example problem has two scheduling coordinators (SC1
and SC2), one of which may be the PX. We have three zones consisting of one bus
each, and we treat a single hour. The preferred schedules, adjustment price
bids, and flow limits between zones are given in Fig. 2. For each generator, the
adjustment range bid is 0 MW to 200 MW. All demands are fixed and constant for
the hour. No load reduction adjustment bids are submitted by the SCs.

[CHART]

Fig. 2: Preferred Schedules and Adjustment Bids

The preferred schedules violate the flow limit on the line between buses 1 and
3. Solving the interzonal congestion management optimization problem (3), the
ISO determines the schedules and locational marginal costs given in Fig. 3.

Based on the solution in Fig. 3, the ISO determines the following congestion
charges to the SCs:

Transmission congestion charge to SC1

[FORMULA OMITTED]

Transmission congestion charge to SC2

[FORMULA OMITTED]

DO NOT CITE DRAFT 16 (4/29/97) 4

[CHART]

Fig. 3: Solution and Marginal Costs

To better understand the marginal costs, look at the marginal cost for
Scheduling Coordinator 1 to serve load at bus 1. The cost of SC1's generator at
bus 1 is $5/MWh while the marginal cost for SC1 at bus 1 is $4/MWh. To
understand the source of this difference, look at SC1's response to a 1 MWh
increase in its load at bus 1.

SC1's optimal response is to increase PSC1,2 by 1 MWh at a generation cost of
$10. Because SC1 increased PSC1,2, it frees transmission that SC2 can use to
reduce its generation costs: SC2 increases PSC2,1 by 1 MWh at a generation cost
of $6 and reduces PSC2,2 by 1 MWh with a savings of $12. The total cost to all
SCs increases by ($10+$6-$12) = $4. This is the marginal cost to SC1 at bus 1.

SC1 is not being altruistic. To see this, calculate SC1's costs before the load
at bus 1 is increased by 1 MWh: Generation Costs = $1300, Congestion Costs =
$300, Total = $1600. Now, calculate SC1's costs after the changes: Generation
Costs = $1310, Congestion Costs = $294, Total = $1604. SC1's total costs
(generation plus congestion) increase by $4. This is SC1's marginal cost at bus
1.

This example shows that the PX or other SC may increase its use of more
expensive generation if it can reduce its congestion charges by doing so. A
scheduling coordinator can even receive congestion payments by scheduling
reverse flows on congested transmission lines. Such reverse flows serve to
increase the flows that other scheduling coordinators may schedule on a
congested path. In essence, a reverse flow serves to increase the capacity of
the path. A scheduling coordinator will be paid the marginal value of capacity
on the path for its reverse flow. All SC's are shown the same marginal value for
transmission capacity on a given path.

VII. BIDDING FOR INTERZONAL TRANSMISSION

In the congestion management protocols, an SC provides the following price
information that the ISO uses to allocate capacity on interzonal paths:

o Adjustment bids for its generators

o Adjustment bids for its loads.

The value of interzonal transmission capacity to the SC is implicit in these
bids. If an SC has generation at two locations, the difference in the generation
prices between the two generators gives the value to the SC of transmission
capacity connecting the two locations. If an SC has generation at one location
and load at another, the difference in price between adjusting the generation
and reducing the load gives the value to the SC of transmission capacity
connecting the two locations.

In solving the interzonal congestion management optimization problem (3), the
ISO allocates the interzonal transmission capacity to the SCs so that it
maximizes the implicit value of the available capacity to the SCs.

Return to the example of the previous section and calculate the amount of
capacity that SC1 would use on each path to send 1 MW of power from bus 1 to bus
3: 0.8 MW on path 1->3, 0.2 MW on path 1->2, 0.2 MW on path 2->3. Based on the
difference between SC1's generation prices at buses 1 and 3, SC1 implicitly
values this "package" of transmission at $20/MW - 5/MW = $15/MW. Table 1 gives
the transmission capacity on each path that an SC would need to send 1 MW of
power from one bus to another. It also gives the value of the package of
transmission capacity to the SC.

Table 1: Transmission Capacity Needed to Send 1 MW and
its Value to a Scheduling Coordinator

<Table>
<Caption>
From MW MW MW Imputed
SC Bus on on on Value
Sending 1 /To Path Path Path $/MW
MW Bus 1->3 1->2 2->3 Sent
=========== ====== ====== ====== ====== =========

SC1 1/3 0.8 0.2 0.2 15

SC1 2/3 0.4 -0.4 0.6 10

SC1 3/3 0 0 0 0

SC2 1/3 0.8 0.2 0.2 24

SC2 2/3 0.4 -0.4 0.6 18

SC2 3/3 0 0 0 0
</Table>

SC1 needs sufficient transmission capacity to deliver 80 MW to bus 3, and SC2
needs sufficient transmission capacity to deliver 120 MW of power to bus 3.

Table 2 gives the allocation of transmission capacity that maximizes the value
of the available capacity. Table 3 gives the marginal value of transmission
capacity on each path. The

DO NOT CITE DRAFT 16 (4/29/97) 5

capacity allocation and the marginal values are identical to those determined by
the interzonal congestion management optimization problem (3).

Table 2: Transmission Allocation that Maximizes Value

<Table>
<Caption>
Capacity MW on Path MW on Path MW on Path
Allocation 1->3 1->2 2->3
================ ============== ============== ==============

SC1 12 MW -12 MW 18 MW

SC2 88 MW 12 MW 32 MW
</Table>

Table 3: Marginal Value of Transmission Capacity

<Table>
<Caption>
Marginal Value Path 1->3 Path 1->2 Path 2->3
================ ============== ============== ==============

$19/MW $0/MW $4/MW
</Table>

The ISO's interzonal congestion management protocols could be structured so that
the SCs bid directly for transmission capacity. Each SCs would be required to
bid the price that it is willing to pay for transmission capacity from one point
on the network to another. Each SC would also be required to bid the total
amount of transmission capacity that it wishes to acquire.

The computational burden of the two approaches is different. The size of the
formulation based on transmission paths is a combinatorial function of the
number of points on the grid at which an SC may inject and withdraw power. The
formulation based on minimizing total bid price with separation of markets does
not exhibit this combinatorial growth.

VIII. CONCLUSION

Transmission capacity can be efficiently allocated in forward markets when the
energy forward markets of the various scheduling coordinators are kept separate
by the ISO. Each scheduling coordinator can devise strategies and take voluntary
actions to control its costs and gain profits while all participants face the
same transparent marginal price for using a congested transmission path. This
transparent marginal price for transmission supports efficient allocation of
transmission to the highest valued users. It also leads to a stream of hourly
short-run marginal price signals that can indicate the need for investment in
transmission facilities to avoid the stream of hourly congestion costs.

IX. ACKNOWLEDGMENTS

The authors would like to thank the many people who participated in the WEPEX
Congestion Management Subteam. Their open and frank discussion of the issues and
review of the methodologies and models were instrumental in the development of
this approach to interzonal congestion management. In particular, we would like
to acknowledge the work of Ashish Bhaumik, Bill Englebrecht, Shangyou Hao,
Dianne Hawk, Carl Imparato, and Alex Papalexopolous. We would also like to thank
Dariush Shirmohammadi for his comments and insight.

X. REFERENCES

[1] California Public Utilities Commission Decision 95-12-063 (December 20,
1995), as modified by Decision 96-10-009 (January 10, 1996)

[2] Joint Application of Pacific Gas and Electric Company, San Diego Gas &
Electric Company, and Southern California Edison for Authorization to
Convey Operational Control of Designated Jurisdictional Facilities to an
Independent System Operator, Federal Energy Regulatory Commission Docket
No. EC96-19000, April 29, 1996.

[3] The Phase II Filing of the California Power Exchange Corporation, Federal
Energy Regulatory Commission Docket Nos. EC96-19-001 and ER96-1663-001,
March 31, 1997.

[4] The Phase II Filing of the California Independent System Operator
Corporation, Federal Energy Regulatory Commission Docket Nos. EC96-19-001
and ER96-1663-001, March 31, 1997.

[5] W.W. Hogan, "Contract Networks for Electric Power Transmission: Technical
Refernece," John F. Kennedy School of Government, Harvard University,
December 1991.

[6] M.C. Caramanis, R.E. Bohn, and F.C. Schweppe, "Optimal Spot Pricing:
Practice and Theory," IEEE Transactions on Power Systems, Volume PAS-101,
No. 9, September 1982.

[7] A.V. Fiacco, Introduction to Sensitiviy and Stability Analysis in Nonlinear
Programming, Academic Press, New York, 1983.

[8] E.G. Read, "Short-Run Transmission Pricing Issues in New Zealand," Report
to Trans Power, University of Canterbury, October 1988.

XI. APPENDIX: PRICING INTERZONAL CONGESTION

Calculating the locational marginal cost of serving load is well understood
(e.g. Caraminis et.al. [6]). Our problem involves a slightly more complicated
sensitivity analysis due to the market separation constraints, but the
mathematics is still well defined (e.g. Fiacco [7]). Our approach to
transmission pricing bears some similarity to that of New Zeland [8] but with
the added complexity of market separation constraints.

To determine an SC's marginal cost of serving load, we perturb the interzonal
congestion management problem (3):

[FORMULA OMITTED]
(7)

subject to

[FORMULA OMITTED]

where the ith element of the vector [FORMULA OMITTED] is the perturbation of
load at bus i for SC k.

The marginal cost of serving load at bus i for SC k is

[FORMULA OMITTED]
(8)

If Value [FORMULA OMITTED] is differentiable at (0,...,0), then scheduling
coordinator k's marginal cost of serving load at bus i in its energy forward
market is given by the Lagrange multipliers:

[FORMULA OMITTED]
(9)

If Value [FORMULA OMITTED] is not differentiable at (0,...,0), then the marginal
costs for SC k depend upon the directions in which SC k's loads are moved. In
this case there are multiple sets of Lagrange multipliers that satisfy the Kuhn
- -Tucker conditions, and (9) gives directional derivatives for SC k.

PROPOSITION 1: The congestion price for scheduling the use of a unit of capacity
on an interzonal transmission path in a forward market is the same for all
scheduling coordinators.

PROOF: The congestion prices that the ISO charges scheduling coordinator k for
using interzonal transmission are based on the differences in SC k's locational
marginal costs in SC k's energy forward market. The ISO would charge SC k

[FORMULA OMITTED]
(10)

to inject one unit of energy at bus j and withdraw it at bus i. The right-hand
side of (10) is independent of the scheduling coordinator selected. QED

PROPOSITION 2: The following ways of calculating an SC's transmission congestion
charge are equivalent:

o Sum over all buses: {the SC's scheduled withdrawal minus injection at the
bus times the SC's locational marginal cost at that bus}.

o Sum over all interzonal paths: {the SC's scheduled flow on a path times
marginal value of capacity on that path}.

PROOF: Using Proposition 1, the interzonal transmission charges to scheduling
coordinator k under the first approach are given by:

[FORMULA OMITTED]
(11)

Partitioning the matrix B and the vectors P* and D* by separating out the
reference bus N, we write the DC power flow equations (2) as:

[FORMULA OMITTED]
(12)

The vector of flows on the interzonal paths due to SC k is given by

[FORMULA OMITTED]
(13)

The Kuhn Tucker conditions include

[FORMULA OMITTED]
(14)

Partition (14) to separate the reference bus, and rearrange terms:

[FORMULA OMITTED]
(15)

where [FORMULA OMITTED]

Using (3f), (13) and (15), we can write (11) as:

[FORMULA OMITTED]
(16)

The final term in (16) is simply the sum over all interzonal paths of the
product of the flow on an interzonal path due to SC k and the marginal value of
capacity on that path. QED

The congestion charges collected from the PX and other SCs will be distributed
to others, e.g. the transmission owners or the owners of financial rights. The
owners of a path or the owners of rights on a path would receive the congestion
charges paid by the users of that path. The total due could be defined as the
marginal value of capacity on the path times

the available capacity on the path. If we define the payments in this way, we
have:

PROPOSITION 3: The congestion charges collected from the PX and other SCs equals
the payments due to the rights owners.

PROOF: The sum of interzonal congestion charges to the PX and other SCs is:

[FORMULA OMITTED]
(17)

The vector of flows on the interzonal paths is given by

[FORMULA OMITTED]
(18)

Using (15) and (18), we can write (17) as:

[FORMULA OMITTED]

[FORMULA OMITTED] by complimentary slackness. QED

XII. BIOGRAPHIES

PAUL GRIBIK is an Associate with Perot Systems Corporation where he assists
utilities in developing methodologies and systems to improve their operations in
the face of changing regulations and increasing competition. He has provided
consulting services to the electric and gas industries for nine years through
Arthur D. Little, Mykytyn Consulting Group, and Perot Systems. He also worked
for the Pacific Gas and Electric Company for ten years. He received a B.S. in
Electrical Engineering in 1971, an M.S. in Industrial Administration in 1973 and
a Ph.D. in Industrial Administration and Operations Research in 1976 from
Carnegie-Mellon University.

GEORGE A. ANGELIDIS was born in Athens, Greece, in 1962. He received his
Ptychion degree from the Aristotle University of Thessaloniki in 1984, and his
M.A.Sc. and Ph.D. degrees from the University of Toronto in 1988 and 1992,
respectively, all in Electrical Engineering. He is currently with the Pacific
Gas and Electric Company where he works on issues related to the California
electricity industry restructuring. His research interests and expertise are in
advanced computer applications in large-scale electric power systems, with
emphasis on steady-state and dynamic analysis and optimization. Dr. Angelidis is
a member of IEEE and the Technical Chamber of Greece.

ROSS R. KOVACS (SM '87) received a BEE from Georgia Institute of Technology and
an MBA in Finance from Georgia State University. From 1977 to 1993, he worked
for the Southern Company in various areas including system planning,
transmission planning, financial analysis and electrical engineering. Since
1993, he has worked for Southern California Edison in the Grid Planning and
Strategy division where his major responsibilities have been power industry
restructuring, leading development of open access tariffs, and developing new
methods for a restructured power industry. Ross is a registered Professional
Engineer in the state of Georgia.