Exhibit 99.204
MARKET SEPARATION AND INTERZONAL TRANSMISSION
CONGESTION MANAGEMENT IN FORWARD MARKETS
Paul R. Gribik George Angelidis Ross Kovacs
Perot Systems Corporation Pacific Gas and Electric Southern California Edison
Los Angeles, CA San Francisco, CA Rosemead, CA
ABSTRACT: The congestion management protocols for the restructured electric
power industry in California, give the Power Exchange and Bilateral Contract
parties comparable access to the transmission grid. In adjusting schedules to
manage interzonal congestion, the Independent System Operator keeps the
portfolio of generation and load for the Power Exchange and the portfolio for
each Schedule Coordinator individually in balance. We call this concept "market
separation." Employing market separation, the Independent System Operator is
able to allocate the available transmission capacity to the parties that value
it the most and charge all users of a congested transmission path the same
transparent marginal price. The ISO clears its market for transmission without
forcing the parties to engage in energy trades. All trades are voluntary and are
the responsibility of the individuals involved.
KEYWORDS:
I. INTRODUCTION
The California Public Utilities Commission (CPUC) considered two different
approaches to restructuring California's electric utility industry -- Power Pool
and Bilateral Contracts. Each approach had proponents among the utilities, power
producers and consumers. In its December 20, 1995 restructuring decision [1],
the CPUC combined aspects of the bilateral contracts and the power pool
approaches. In this compromise, the transmission grid is to be managed by the
Western Independent System Operator (ISO). The ISO is to be separate from the
power pool (the Western Power Exchange or PX) and the other market participants.
The compromise outlines several goals that the ISO is to achieve in managing the
transmission system:
- - Provide comparable transmission service (prices and access) to the PX and
bilateral contract parties.
- - Use marginal cost pricing for major transmission paths to send correct
economic signals with respect to limited transmission resources.
- - Limit changes to the preferred schedules of the PX and bilateral contract
parties to those that relieve transmission congestion (the ISO is not to
completely reschedule the resources of the PX and the bilateral contract
parties to minimize total system cost).
On the surface, these appear to be conflicting goals. To develop marginal costs
that reflect the economic value of transmission capacity, the ISO must find
schedules for the PX and bilateral contract parties that minimize resource costs
subject the constraints (e.g. network constraints, operating constraints, etc.).
That is, the ISO must clear the markets. To clear the combined market
(consisting of all bilateral contract parties and the PX), the ISO would
reschedule the "pooled" resources of all of the market participants. In essence,
the ISO would impose all trades between market participants that serve to lower
costs -- trades between different bilateral contract parties as well as trades
between the PX and bilateral contract parties. In the process, the ISO is likely
to schedule trades that do not reduce transmission congestion but which only
reduce the costs of the resources scheduled. However, giving the ISO the ability
to impose such schedule changes would violate the compromise reached among the
market participants.
We were able to design congestion management protocols that achieve the goals by
clearly delineating the markets with which we are dealing:
- - the energy market of the PX
- - the energy markets of the bilateral contract parties
- - the Ancillary Services markets
- - the transmission market.
The congestion management protocols keep the different energy and ancillary
service markets separate. These markets only interact through the transmission
market.
II. INTERZONAL AND INTRAZONAL TRANSMISSION CONGESTION
The ISO deals with two types of transmission constraints. 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 of greater cost to relieve. In addition,
the transmission constraints between zones differ from the constraints within a
zone:
- - Interzonal constraints take the form of limits on real power flows across
zonal interfaces.
- - Intrazonal constraints are more varied, e.g.:
a. MW flow limits
b. MVA flow limits
c. Amperage limits
d. Voltage limits.
The ISO allocates the interzonal transmission capacity to the participants to
maximize the economic value of the interzonal transmission capacity to the
users. A user of interzonal transmission capacity will pay a congestion fee
based on the differences in locational marginal costs.
In relieving intrazonal transmission constraint violations, the schedules of the
bilateral contract parties and the PX are to be disturbed as little as possible.
The cost of relieving intrazonal constraint violations is to be charged to all
users as an uplift.
We only discuss the interzonal congestion management protocol in this paper.
III. FORWARD MARKETS FOR ENERGY AND TRANSMISSION
In addition to operating in real time, the participants in the proposed
California industry structure must plan their operations in forward time frames.
Scheduling and congestion management is done in two forward time frames:
- - Day-ahead (scheduling resources in each hour of the following day)
- - Hour-ahead (scheduling resources for an hour -- scheduling begins after
the day-ahead market closes).
We only consider congestion management and scheduling of generation, load and
losses in the forward markets. We will not address the ancillary services
markets; however, the results can be extended to cover the scheduling ancillary
services such as reserves.
Several entities will be involved in the proposed forward energy and
transmission markets:
i. Schedule Coordinators (SCs)
a. Manage their own energy markets
b. Set the rules for their own energy forward markets
c. Communicate preferred schedules and prices to adjust those schedules
to the Western Independent System Operator
ii. Western Power Exchange (PX) -- a specific schedule coordinator with
defined duties
a. Runs a market in which parties can buy and sell energy
b. Develops preferred schedules for the forward markets
c. Develops locational marginal costs for energy purchases and sales
d. Communicate its preferred schedules and prices to adjust those
schedules to the Western Independent System Operator
iii. Western Independent System Operator (ISO)
a. Manages the transmission system in the forward market
b. Develops marginal cost of using congested transmission paths
The PX and the SCs submit their preferred schedules to the ISO. The SCs and PX
specify their desired generation and loads in each hour of the relevant forward
market (day-ahead or hour-ahead). They will also submit price curves that the
ISO will use in congestion management:
i. Adjustment price curves for generation (along with minimum and maximum
generation levels)
ii. Adjustment price curves for load reduction (along with limits)
The ISO combines the preferred schedules of the PX and SCs and check for
congestion in each hour. If there is congestion, the ISO adjusts the schedules
to relieve the congestion.
Fig. 1 shows the steps that will be taken in relieving congestion in the
day-ahead market. The PX and SCs may be given an opportunity to modify their
preferred schedules after the ISO eliminates interzonal congestion. The
hour-ahead market is similar except that the ISO does not produce advisory
schedules or give the SCs and PX an opportunity to revise their schedules. We
focus on interzonal congestion management and pricing in a single hour in this
paper.
[FLOW CHART]
Fig. 1: Day-Ahead Congestion Management
IV. SEPARATION OF MARKETS
Pacific Gas and Electric, Southern California Edison, and San Diego Gas and
Electric outlined the operation of the PX and ISO in their initial filing to the
Federal Energy Regulatory Commission [2]. However, this filing did not
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specify how the ISO would relieve interzonal congestion while providing
nondiscriminatory access to transmission. Instead, some rather broad principles
were outlined. These include:
- - The ISO is to reschedule the PX and other SCs to maximize the economic
value achieved by their use of interzonal transmission.
- - The ISO is to charge the users of congested interzonal transmission the
marginal cost for the congested interface -- the marginal costs calculated
must send correct economic signals regarding the use of congested
transmission.
In theory, these goals can be achieved if all SCs including the PX are required
to buy and sell energy through a common pool when congestion exists. In this
case, the ISO would adjust the schedules to minimize total costs as measured by
the bid adjustment prices subject to the power flow constraints and interzonal
transmission limits. The optimization clears the combined energy forward market
consisting of the PX and the other SCs. It also provides the marginal cost of
serving load at each bus as well as the marginal value of transmission capacity
on each interzonal path.
There is, however, an undesirable discontinuity in this congestion management
process. As long as interzonal transmission constraints are not violated, the
ISO would not impose any trades between SCs, even if the trades would serve to
lower costs. Once any constraint is violated, the ISO would impose any and all
trades that serve to lower costs, regardless of whether they serve to reduce the
constraint violation.
It is possible that an SC could make an arbitrarily small change to its
preferred schedule and cause a violation of an interzonal constraint. This small
change could flip the ISO from accepting all of the preferred schedules to
completely rescheduling the resources of the PX and the other SCs. Consequently,
this congestion management protocol is unstable. Ideally, a small violation of
an interzonal constraint should be relieved by making small changes to the
preferred schedules, not by their total revision.
Additional guidelines were included in [2] (page C-10)to prevent the ISO from
making schedule changes that have little effect on reducing interzonal
congestion:
- - "the ISO may only adjust the scheduled output of generation, based on the
price bids, and then only as required to relieve congestion."]
- - "The ISO will only make scheduling adjustments which act to relieve
congestion, and will cease making adjustments when congestion is relieved.
There are several ways in which the protocols could be modified to meet these
new goals. The protocols could be modified so that the ISO stops the
rescheduling process before it minimizes total costs subject to the constraints.
However, the ISO would not maximize the economic use of the transmission system
nor could it produce valid marginal costs. The protocols must be designed so
that the ISO reschedules to minimize total costs subject to appropriate
constraints. The key is to define the constraints.
We incorporate constraints in the interzonal congestion management procedures
that draw sharp lines between the energy forward markets managed by the various
SCs (including the PX). An SC must balance its generation and its load (plus its
allocated share of losses) in its preferred schedule. When the ISO adjusts the
schedules of the SCs to eliminate interzonal transmission violations, the
additional constraints require that the ISO keep each SC's schedule in balance.
That is, an SC's adjusted generation must equal its adjusted loads and allocated
share of the losses. In essence, the constraints prevent the ISO from imposing
trades between different SCs.
As a result, the interzonal congestion management protocol allows the PX and the
other SCs to manage their own energy forward markets individually without the
ISO interfering by arranging trades. Any trades between SCs are arranged by the
SCs under terms that they set. The ISO only manages the transmission forward
markets. It does not participate in the energy forward markets by arranging
trades between SCs.
V. TRANSMISSION LOSSES AND NETWORK MODEL
In the ISO protocols, losses are modeled via meter multipliers. The generation
at a location is multiplied by the meter multiplier for the location to provide
power to account for 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 cost effect of multiplying
effective generation by the meter multipliers, we scale the adjustment price
curves and the ranges over which effective 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 equation
by assuming negligible line resistances and small voltage angle differences.
[FORMULA OMITTED]
where:
|V[i]| is the voltage magnitude at bus i
(delta)[i] is the voltage angle at bus i
P[i] is the net real power injection at bus i
and G[ik] + JB[ik] is an element of the Y[BUS] matrix
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Assuming that G[ik] << B[ik], sin((delta)[k] - (delta)[i])almost equal to
((delta)[k] - (delta)[i]), 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 interzonal real power flow constraints are linearized in a similar fashion.
VI. INTERZONAL CONGESTION MANAGEMENT OPTIMIZATION PROBLEM
[FORMULA OMITTED]
For schedule coordinator k (SCk), let
(P[k]) be the vector of effective real power generation
(D[k]) be the vector of real power demands
(C(g)[k,i])(P[k,i]) be the convex adjustment price function bid
for effective generation at node i
(C(D)[k,i])((D[k,i])) be the convex adjustment price function bid
for reducing load at nodei .
In addition, let
(delta) be the vector of voltage angles at buses i=1, ..., N-1.
(We treat bus N as the reference bus so (delta[n])= 0.)
The ISO solves a linearly constrained optimization problem to allocate and price
interzonal transmission capacity:
[FORMULA OMITTED](3)
(k): SC index; i: node index
(B): linearized active power flow Jacobian
(F): interface power flow constraint coefficient matrix
(P[Fmax]: interface power flow limit vector
In solving (3), the ISO achieves several goals:
- - The ISO allocates interzonal transmission capacity to maximize its value
to the SCs in the forward market.
- - The ISO clears its forward market for interzonal transmission.
- - Each SC's forward energy market is individually cleared.
Suppose that a schedule coordinator submits a preferred schedule and adjustment
price bids such that its preferred schedule is optimal when only that SC is
considered. That is, the SC's preferred schedule is least-cost with respect to
the SC's adjustment price bids, and the SC's schedule satisfies the linear power
flow constraints (or a subset of them). In this case, the adjustments that the
ISO makes to the SC's schedule will be those that serve to eliminate constraint
violations. The ISO will not simply adjust the SC's schedule to lower the SC's
costs without reducing a constraint violation.
An SC could conceivably submit a preferred schedule and adjustment prices such
that its preferred schedule is not optimal given the prices bid. That is, the SC
could adjust its schedule to lower its costs. The interzonal congestion
management protocol permits an SC to bid in this fashion if it so desires. The
protocol contains provisions for adding constraints that prevent the ISO from
making adjustments to an SC's preferred schedule to reduce the SC's costs
without reliving violated interzonal constraints. These constraints restrict the
ISO's actions to optimize an SC's portfolio within a single zone. These
constraints do not affect the results that we derive, so we will not discuss
them further in this paper.
VII. PRICING INTERZONAL CONGESTION
The Lagrangian for the interzonal congestion management optimization problem (3)
provides the marginal prices that the ISO charges for the use of congested
interzonal transmission paths:
[FORMULA OMITTED](4)
Schedule coordinator k's marginal cost of serving an additional unit of load at
bus i in its energy forward market is given by the Lagrange multipliers:
[FORMULA OMITTED](5)
[FORMULA OMITTED](6)
PROPOSITION 1: The congestion price for using a unit of capacity on an
interzonal transmission path in an hour of a forward market is the same for all
schedule coordinators.
PROOF: The congestion prices that the ISO charges schedule coordinator k for
using interzonal transmission are based on the differences in SC k's locational
marginal costs in the SC k's forward energy market. SC k would be charged
[FORMULA OMITTED](7)
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to inject one unit of energy at bus j and withdraw it at bus i. The right-hand
side of (7) shows that the transmission congestion prices do not depend upon the
schedule coordinator. / /
PROPOSITION 2: The following ways of calculating the transmission congestion
charge to a schedule coordinator for use of interzonal transmission in an hour
of a forward market are equivalent:
- - Sum over all buses: the SC's net withdrawal at a bus times the SC's
locational marginal cost at that bus.
- - Sum over all interzonal paths: the SC's scheduled flow on a path times
marginal value of capacity on that path.
PROOF: Under the first of these methods, the interzonal transmission charges to
schedule coordinator k are given by:
[FORMULA OMITTED](8)
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](9)
The vector of flows on the interzonal paths due to schedule coordinator k is
given by
[FORMULA OMITTED](10)
Among the Kuhn Tucker conditions is the equation
[FORMULA OMITTED](11)
Partition (11) to separate the reference bus, and rearrange terms:
[FORMULA OMITTED](12)
Using (10) and (12), we can write (8) as:
[FORMULA OMITTED](13)
(13) 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.
/ /
VIII. EXAMPLE
Consider an example problem (Fig. 2) to illustrate the congestion management
procedure. The example problem has two schedule coordinators (SC1 and SC2) and
three buses. It treats a single hour. The preferred schedules, adjustment price
bids, and flow limits between zones are given in Fig. 2. While the scheduled
generation in the hour is constant, each generator may be rescheduled over the
range 0 MW to 200 MW. All demands are fixed and constant for the hour.
[FLOW CHART]
Fig. 2: Preferred Schedules and Adjustment Bids
The preferred schedules violate the flow limit 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]
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[FLOW CHART]
Fig. 3: Solution and Marginal Costs
To better understand the marginal costs, look at the marginal cost for Schedule
Coordinator 1 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. Why is this the case? To answer this
question, let us look at SC1's response to an increase in its load at bus 1.
SC1 could choose to increase its generation by 1 MW at bus 1. The cost to SC1
would be $5. This is not its optimal response.
SC1's optimal response is to increase its generation at bus 2 to serve the
increased load at bus 1:
(P2[SC1]) changed from 30 to 31 MWh at a cost to SC2 of $10.
Because SC1 increased its generation at bus 2, it frees transmission capacity
that SC2 can use to reduce its generation costs:
(P1[SC2]) changed from 100 to 101 MWh at a cost to SC2 of $11.
(P2[SC2]) changed from 20 to 19 MWh with a savings to SC2 of $17.
The total cost to all SCs increases by $4 = ($10+$11-$17). This gives the
marginal cost to SC1 at bus 1.
SC1 is not being altruistic. To see this, let's calculate SC1's costs before
incrementing the load at bus 1:
Generation Costs:
[FORMULA OMITTED]
Congestion Costs:
[FORMULA OMITTED]
Total cost to SC1 is $1600.
Now, lets calculate SC1's costs after incrementing the load at bus 1:
Generation Costs:
[FORMULA OMITTED]
Congestion Costs:
[FORMULA OMITTED]
Total cost to SC1 is $1604:
SC1's total costs increase by $4. This is SC1's marginal cost at bus 1.
The above example shows that a schedule coordinator can reduce its costs by
reducing its use of congested lines. A schedule coordinator can actually
increase its revenues by scheduling reverse flows on congested transmission
lines. Such reverse flows serve to increase the flows that other schedule
coordinators may schedule on a congested path. In essence, reverse flows serve
to increase the capacity of the path. A schedule coordinator will be paid the
marginal value of capacity on the path for such reverse flows.
IX. 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:
- - Adjustment price curves for its generators
- - Adjustment price curves for its loads.
The value of interzonal transmission capacity to the SC is implicit in these
price curves. 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 prices 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
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the value of the package of transmission capacity to the schedule coordinator.
Table 1: Transmission Capacity Needed to Send 1 MW and the value of the Capacity
to a Schedule Coordinator
- --------------------------------------------------------------
SC From MW on MW on MW on Imputed
Sending 1 Bus Path Path Path Value
MW /To Bus 1->3 1->2 2->3 $/MW 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
- --------------------------------------------------------------
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 capacity allocation and the marginal values are identical to those
determined by the interzonal congestion management optimization problem.
Table 2: Transmission Allocation that Maximizes Value
- -------------------------------------------------------------
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 3: Marginal Value of Transmission Capacity
- --------------- -------------- ---------------- ----------------
Marginal Value Path 1->3 Path 1->2 Path 2->3
=============== ============== ================ ================
$19/MW $0/MW $4/MW
- --------------- -------------- ---------------- ----------------
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 at which an SC may inject power and the number of points at
which an SC may withdraw power from the grid. The formulation based on
minimizing total bid price with separation of markets does not exhibit this
combinatorial growth.
X. BIDDING STRATEGIES WHEN GENERATION AND LOAD ARE IN DIFFERENT ZONES
An SC may not have generation resources in the same zone as its loads.
Consequently, an SC may have to rely on a congested interface to schedule load
in a forward market. Because of the separation of the markets, the ISO will not
arrange an energy sale to this SC from another SC. An SC in this situation has
several options:
i. The SC can submit adjustment bids that specify that the ISO cannot reduce
the loads in the SC's preferred schedule for the forward market. In this
case, the SC is stating its willingness to pay whatever marginal
transmission price the ISO determines so that the ISO will allocate it the
necessary transmission capacity.
ii. The SC can submit bids for reducing the loads in its preferred schedule
for the forward market. The SC can determine the adjustment prices for
these loads in several ways:
a. The SC can estimate the cost of relying on later forward markets or
the real-time market to serve any loads not scheduled in the forward
market.
b. The SC can estimate the cost of shedding load or demand-side
management.
The ISO does not bear any responsibility or risk for arranging energy trades
between SCs in the energy forward markets. An SC bears the sole responsibility
and risk for balancing its generation and load in a forward market. The
congestion management protocols place the responsibility and risk on the parties
that will reap the rewards and face the penalties.
XI. CONCLUSION
Transmission capacity can be efficiently allocated in forward markets when the
energy forward markets of the various schedule coordinators are kept separate by
the ISO. Each schedule 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 leads to efficient transmission
allocation 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.
The separation of markets lets the parties develop competing markets for energy
and ancillary services. Consumers can choose from among the competing providers
based on the prices and services offered by each. The PX and bilateral
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contract parties will be under competitive pressure to evolve so that they can
best meet their customers' needs at a good price. The interzonal congestion
management protocol supports this evolution by letting the parties compete on a
level playing field for the transmission services that they will need to deliver
energy and ancillary services.
XII. 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, Carl Imparato and Bill Englebrecht.
XIII. 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.
XIV. BIOGRAPHIES
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