EXHIBIT 99.448


                           January 1998

    EQUILIBRIUM AMONG POWER MARKETS COMPETING FOR TRANSMISSION

             JAMES G. KRITIKSON AND ROBERT B. WILSON


ABSTRACT. We demonstrate that in a power system in which several markets or
"power exchanges" for energy compete for customers and for transmission
services, as in California, there are multiple equilibria. In one of these each
market accepts the transmission usage charges imposed by the system operator,
whereas in the other each market uses an internal system of usage charges to
curtail its transmission demand so that the system operator sees no congestion.
Because the latter equilibrium enables each market to avoid payments of usage
charges, we expect that this equilibrium will prevail.


INTRODUCTION

The restructured power industry in California allows several power exchanges to
compete for customers and for transmission services. The enabling legislation
created the Independent System Operator (ISO) to manage transmission, and the
Power Exchange (PX) to provide daily and hourly markets for energy. The PX is
not a monopoly, however. The thee investor-owned utilities are required to trade
though the PX for the first few years, but other producers and consumers can
trade though any other qualified "scheduling coordinator" (SC). Besides the PX,
the entities that can operate as SCs include private energy markets that compete
with the PX for customers and for transmission services. The basic requirement
imposed on a SC is that its schedules submitted to the ISO are balanced; i.e.,
injections must equal extractions from the transmission system. The ISO treats
all SCs equally; e.g., each SC, including the PX, is responsible for its own
losses and ancillary services, and each pays the same usage charge ($/MWh) for
transmission between zones. Each SC can participate in all of the markets run by
the ISO. These markets include day-ahead and hour-ahead markets for transmission
and a real-time market for supplemental energy to meet the ISO's requirements
for system balancing on a short time frame; in addition, the ISO runs central
markets for ancillary services from which each SC can purchase whatever
resources it does not provide itself To simplify exposition, however, we
concentrate here on the day-ahead market for delivery in a single hour.

The PX's day-ahead market is a pool in which all transactions are settled at an
hourly clearing price for energy, plus a transmission usage charge specific to
each hour and zone (which need not be exactly the same as the ISO's usage
charges). In contrast, other SCs can base their transactions on other market
designs, such as bilateral contracting. Thus, the restructured California market
is unique in its provision for various power exchanges, each operating as a SC,
to compete for customers based on different market designs and





the extent and quality of auxiliary services. In principle, all SCs are on an
equal footing, except for the PX's initial monopoly on trading by the utilities.
Presumably their competition for customers will reveal the relative efficiency
of their alternative market designs, each of which has inherent strengths and
weaknesses. For instance, as a pure-exchange market-clearing mechanism the PX is
limited in its ability to take a net position long or short in the market, or to
conduct arbitrage, but it has the advantage that its market structure meshes
exactly with the ISO's markets. Similarly, a private bilateral market must be
carefully managed to ensure efficient utilization of transmission, and to
reconcile long-term contracts with the near-term forward markets for
transmission, but it has the advantage of more flexibility (e.g., a SC can trade
in the PX or with other SCs, but the PX cannot easily trade directly in another
SC).

In this article we examine a basic theoretical issue at the core of the vigorous
debate that surrounds the California restructuring. This issue concerns the
outcome of the SCs' competition for transmission services. Will the outcome be
efficient? How can the PX or any other SC conduct an energy market in advance of
the ISO's transmission market? We begin with a description of how the ISO
actually conducts its transmission market, and then we address this issue with a
theoretical prediction about the nature of an equilibrium among the strategies
used by the various SCs. This prediction will be tested empirically in the next
few years by the actual operations of the California market.

THE ISO'S TRANSMISSION MARKET

The IS 0's day-ahead market for inter-zonal transmission operates as follows. At
a prescribed time each morning, each SC submits a balanced schedule, called its
preferred schedule, together with "adjustment bids" whose role will be described
below. For the PX, the preferred schedule is the result of financially binding
transactions in its energy market, but for other SCs there is no requirement
that the preferred schedule is based on completed transactions. The adjustment
bids are options offered to facilitate congestion management by the ISO; they
may be, but need not be, bids that were rejected in the energy market. Using
these preferred schedules and adjustment bids, the ISO uses an optimal power
flow (OPF) program to calculate a modification to each preferred schedule,
called the advisory re-dispatch, and the associated inter-zonal transmission
charges obtained from this optimization. As the name indicates, the advisory
re-dispatch schedules and the associated usage charges are not binding on the
SCs; they are merely indicative of what the ISO's final schedules and usage
charges will be if none of the preferred schedules are modified (and no
alteration in transmission limitations occurs in the interim). After receiving
its advisory re-dispatch and the associated usage charges, each SC has an hour
to decide whether it chooses to (a) adhere to its preferred schedule, (b) accept
the advisory re-dispatch, or (c) submit a revised schedule. Adjustment bids
cannot be changed but they can be withdrawn for use in a revised schedule, and
they can be traded among SCs. Finally, at noon the ISO repeats the OPF
calculations to determine the final set of adjustment bids used to achieve
inter-zonal balancing, and the day-ahead inter-zonal usage charges that are now
binding on each SC. Subsequent deviations from these final schedules are
reconciled in the hour-ahead and real-time markets at newly calculated prices
(except that the cost of intra-zonal balancing during real-time operations is
absorbed by the ISO).





The OPE works as follows. Its objective is to minimize the cost of achieving
inter-zonal transmission feasibility. This cost is nil if the aggregate of the
SCs' preferred schedules (plus anticipated loop flow, etc.) implies inter-zonal
flows within specified limits, but if some of these limits are exceeded then the
program selects adjustment bids to reduce the flows until they are within the
limits imposed by line capacities and security considerations. Each adjustment
bid applies to a particular supply unit or demand node and the zone in which it
is located, and it is classified as either an increment (me) or a decrement
(dee). An inc from a supply unit specifies a supply curve indicating the
schedule of energy prices ($/MWh) at which that unit's output rate can be
increased at the option of the ISO. Similarly, a supply dec specifies a demand
curve indicating the schedule of energy prices at which that unit's output rate
can be decreased, interpreted as a buy-back of supplied energy previously
committed in the preferred schedule. Thus a supply inc entials a payment to the
supplier and a supply dec entails a payment from the supplier.

Demand incs and decs are analogous, but we will mostly ignore their role here.
Transmission feasibility can be achieved by some combination of two basic
operations, simplified here by ignoring loop flow so that one can suppose that
one zone is an import zone and another is an export zone. The flow across the
lines between an import zone and an export zone can be reduced by either: (a)
invoking supply ines in the import zone and the same quantity of supply decs in
the export zone, or (b) invoking demand decs in the import zone and the same
quantity of demand ines in the export zone. As mentioned, the OPF selects the
least cost combination of ines and decs that achieve transmission feasibility,
but this is subject to an important constraint that is the novel feature of the
California design.

The novel constraint is that each SC's advisory re-dispatch can use only incs
and decs submitted with its preferred schedule. This constraint is enforced in
the OPF by appending the constraint, one for each SC, that its advisory
re-dispatch must also be balanced, with injections equaling extractions, just
like its preferred schedule. This constraint ensures that the advisory
re-dispatches do not implicitly trade energy among the SCs by incrementing one
SC's schedule and matching it with a decrement from another SC's schedule. On
the other hand, this constraint allows trades "in kind," in the sense that
invoking adjustment bids from one SC enables another SC to avoid adjustments.
The "in kind" feature of these implicit trades is evident in the following
consequence. Suppose that the PX's adjustment bids are relative to an energy
price of $20 /MWh so that supply ines are offered at higher prices and decs are
offered at lower prices, whereas another SC's adjustment bids are relative to an
energy price of $30 /MWh. The key fact is that this $10 /MWh difference is
irrelevant in the OPF calculations: the same result would obtain if all the SC's
adjustment bids were decreased by $10 /MWh so that they are relative to the same
energy price of $20 /MWh. One way to see this is to realize that from the
perspective of the OPF (after appending the novel constraint) all that matters
is the difference, say in basic operation (a) above, between the offered price
of the supply inc in the import zone and the matching dec in the export zone.
For instance, if the SC's pair of adjustment bids invoked are a supply inc at
$32 /MWh in the import zone and a dec at $28 /MWh in the export zone, then the
cost of these adjustments perceived by the OPE is only the net cost of
$32-$28=$4 /MWh for the pair. Exactly the same net





cost would result if the SC's adjustment bids were standardized around the PC's
energy price of $20 /MWh, so that the calculatiOn of the net cost would be
($32-$l0)-($28-$10)= $4 /MWh.

The advisory re-dispatch received by a SC consists of its preferred schedule as
modified by its offered adjustment bids that are invoked in the OPF
calculations. The ISO's associated inter-zonal usage charge is the most
expensive of the adjustment options invoked among all the SCs. For example, it
might be that the most expensive of the PX's adjustment pairs invoked in the OPE
calculation costs $2 /MWh, obtained from a supply inc offered at $21 IMWh and a
dec at $19 /MWh, whereas among all the SCs the most expensive pair costs $4
1MM/h, obtained from a supply inc offered at $32 /MWh and a dec offered at $28
/MWh. In this case the ISO reports an inter-zonal usage charge (for flows in the
direction from the export zone to the import zone) of $4 IMWh. Thus, the PX is
subject to the system-wide usage charge of $4 1MM/h even though internally no
pair was invoked that is so expensive. The usual reason for this disparity is
that the ines and decs are offered as discontinuous step-functions, so when the
PX's cheapest pair after the $2 1MM/h pair is exhausted costs $5 /MWh for the
next step, the OPF selects the cheaper pair offered by another SC at anet cost
of $4 1MM/h.

In the hour between receipt of the advisory re-dispatches and the final
submissions due at noon, the SCs can trade adjustment bids among themselves.
This provision gives the SCs a last chance to arbitrage differences between
their basic energy prices. Usually the PX cannot trade profitably in this
informal market for adjustment bids, however, since it cannot trade adjustment
bids for money (which would require it to take a net position), and all the
potential gains from trade "in kind" were exhausted in the advisory
redispatches.

The OPF calculation run after the final submissions is analogous, except that
each SC's preferred schedule might be replaced by its advisory re-dispatch
schedule or by a revised schedule. The analog of the advisory re-dispatch is now
the final schedule for each SC, and the newly computed inter-zonal usage charges
are now binding financial obligations payable to the ISO, which conveys them to
the owners of the transmission assets. Notice that if all SCs adhere to their
preferred schedules then the final schedules will be the same as the advisory
re-dispatch schedules, since the OPE will again find the same set of adjustment
pairs to be the cost minimizing ones. Similarly, if every SC accepts its
advisory re-dispatch then no further adjustments are necessary.

SELF-MANAGEMENT OF TRANSMISSION CONGESTION

This brings us to our main subject, which is the role of self management of
transmission congestion by the SCs. To understand congestion self-management
(CSM) it is easiest to consider first the case that the PX is the only SC. In
this case, traders in the PX might strongly prefer that usage charges be imposed
by the PX rather than the ISO. For instance, suppose that if the PX adheres to
its preferred schedule then the ISO's usage charge will be $4 /MWh, paid to the
owners of transmission assets (which include the utilities that trade in the PX
as well as those municipal utilities that choose to join the ISO). The PX
traders and management know in advance the amount of this usage charge




because it is reported to them along with the advisory re-dispatch.
Consequently, they can also foresee that if the PX itself imposes a $4 /MWh
usage charge then this will sufficiently curtail transmission demand to prevent
the ISO from imposing any usage charges at all. Thus, by imposing its own usage
charge of $4 /MWh and submitting at noon a revised schedule (e.g., its advisory
re-dispatch) that in effect invokes its own adjustment bids, the PX can earn a
surplus ($4 /MWh minus the average cost of the adjustment pairs invoked) that
would otherwise have been paid to transmission owners. This surplus must
ultimately be refunded to the traders in the PX, but if this is done in a way
that preserves the inter-zonal price differences then this refund will not
disturb the traders' incentives.

[[It should be noted that this scenario depends on the current plan in
California for the ISO to convey usage charges to the owners of transmission
assets. An alternative scheme weakens the incentives for CSM. In this scheme the
PX traders operate essentially as a cooperative. Transmission congestion
contracts (TCCs, in the form of contracts for differences compared to a strike
price) are auctioned to the traders and the proceeds conveyed to the
transmission owners; thereafter, usage charges are payable to the owners of
TCCs, which in effect are the traders themselves, so the incentives for CSM are
muted]]

The question we address here is whether the incentives for CSM persist when
several SCs compete for transmission access. The matter is more complicated in
this case because of a fundamental free-rider problem. For example, the PX
prefers that other SCs curtail their demand for transmission to reduce or
eliminate the ISO's usage charges, thereby enabling the PX to obtain its
preferred schedule without invoking any adjustments. When the PX and all other
SCs take this position, the net result is that no reduction in usage charges
occurs, and each winds up with its advisory re-dispatch as its final schedule,
and each pays usage charges to the ISO.


EQUILIBRIUM IN THE TRANSMISSION MARKET

There are several candidates for an equilibrium among the SCs' strategies. The
three pure symmetric candidates correspond to the three options available in
responding to the advisory re-dispatch. We label these:

         (A) All SCs adhere to their preferred schedules.
         (B) All SCs accept their advisory re-dispatch schedules.
         (C) All SCs submit revised schedules.

Asymmetric mixtures among these are also possible, but here we consider only
these three candidates. Although (C) is not specified exactly, what we have in
mind is CSM, in the sense that (as in the PX example above) each SC submits a
revised schedule that reduces congestion by invoking sufficient adjustment pairs
to reduce its transmission demand to the amount in its advisory re-dispatch. For
the PX, which operates as a pool, there is essentially only one way to do this,
which is to impose its own internal usage charges. This follows from the fact
that any pricing rule that yields an efficient allocation of trades subject to
transmission limitations is equivalent to a uniform clearing price for energy,
plus a system of usage charges for inter-zonal transmission. This is in fact the
rule used by the PX, which bases all settlements on zonal prices that are
equivalent to a






uniform state-wide energy price plus usage charges represented by the
differences between zonal prices (if one zone is designated as a reference
zone, then its zonal price is the same as the. state-wide energy price).

Our main proposition is that each one of these three candidates is in fact an
equilibrium. That is, given that one SC, say the PX, expects the others to
follow the strategy indicated in (A), then the PX cannot benefit from following
a different strategy -- and similarly for (B) and (C). But there is an important
corollary. The equilibrium (A) entails payment of usage charges to the ISO,
whereas the others do not. Consequently, we expect that over time the most
likely equilibrium is (B) or (C), and due to its simplicity, we expect (B) to
prevail. The following subsections consider each candidate in turn.

EQUILIBRIUM (A)

Suppose that all but one SC adheres to its preferred schedule. For convenience,
suppose the exception is the PX. We now ask whether it could be better for the
PX to choose one of the other two options. To see that neither of these options
is better than adhering to its preferred schedule, observe that in both
alternatives the traders in the PX forego gains from Wade in order to reduce
congestion, and a portion of the benefits accrue to traders in the other SCs who
do not contribute to reducing congestion, since these other SCs adhere to their
preferred schedules. Moreover, and this is the key, every adjustment pair that
the PX accepts (as in B) or invokes voluntarily (as in C) merely eliminates the
ISO's need to invoke an adjustment pair in the PX or some other SC. Thus, each
self-management effort made by the PX is nullified by the open door for further
transmission it provides to other SCs.

To see this argument in operation, consider an example in which there is only
one SC besides the PX and for each of these two SCs its preferred schedule
implies transmission of 150 MWh from the export zone to the import zone, whereas
its advisory re-dispatch implies transmission of 100 MM/h, for which the
associated usage charge is $4 [MM/h. Suppose further that the energy supply and
demand curves in each are linear, so that for each the potential gain from trade
lost because of limited transmission capacity is (150-100 MWh)x($4 /MWh)/2 $100,
which is in addition to the $400 that each must pay in usage charges for the 100
MM/h it transmits, so the actual total is $500 for each. Now assume that the
other SC adheres to its preferred schedule that implies 150 MM/h of
transmission, and consider the decision problem of the PX. Since supply and
demand curves are linear, it suffices to consider just one case, which we take
to be the one in which the PX curtails its transmission demand from 150 MWh to
100 MWh as indicated in the advisory re-dispatch. This reduces the aggregate
demand for transmission from 300 MWh to 250 MWh, but there remains an excess
demand of 50 MM/h, so the ISO still needs to invoke adjustment pairs to achieve
feasible schedules. Presumably the PX has used up its least expensive adjustment
pairs in curtailing its transmission demand by 50 MM/h, so those pairs remaining
all cost more than $4 1MM/h. Therefore, for its final schedules the ISO invokes
adjustment pairs only from the other SC, and in doing so it uses those 50 MWh of
adjustments with costs increasing up to $4 /MM/h. Thus, the net result is that
the usage charge remains $4 1MM/h and the final schedules allow 100 MM/h of
transmission by each SC. Each SC pays $400 in usage charges and foregoes $100 in





potential gain from trade. Thus, if the other SC adheres to its preferred
schedule, then the PX cannot gain by accepting the advisory re-dispatch, nor by
submitting a revised schedule.

These arguments are subject to several qualifications. For instance, they assume
that more than one SC contributes to congestion. And they assume that each SC's
marginal cost of transmission reduction (the cost of its marginal adjustment
pair) is the same; e.g., in the above example, if the PX's marginal cost is $4
1MM/h but the other SC's marginal cost is $3 /MM/h then voluntary reduction by
the PX might indeed reduce the usage charge from $4 /MM/h to $3 /MWh.

In general, our argument is that

o    If each SC is a perfect substitute for the other in terms of the cost of
     its marginal adjustment pair, then each cannot do better than to adhere to
     its preferred schedule when it expects the others to do so.

This equilibrium indicates that vigorous pursuit of gains from CSM might be
fruitless in the California context. This reflects a presumption that the SCs
competing for transmission access will have, at the margin, marginal costs of
adjustment pairs that are closely comparable. There may be occasional situations
in which one's marginal cost is significantly higher than others (e.g., because
the others are all at capacity limits), so its CSM efforts could reduce usage
charges to the level of the highest among the other SCs. As we shall see,
however, there is a more basic reason why CSM might actually succeed, which is
that there is another equilibrium such as (B) or (C) in which all SCs are better
off than in equilibrium (A).

EQUILIBRIA (B) AND (C)

Next we demonstrate that (B) and (C) are equilibria. We lump these together
because they are similar when (C) is interpreted as each SC's submission of a
revised schedule that approximates its advisory re-dispatch. So, we focus on
(B), in which each SC accepts its o advisory re-dispatch.

If the SCs were to collude, acting like a single entity, then the situation
would be comparable to the special case examined above in which the PX is the
only SC, for which we previously established that an internal system of usage
charges could prevent the payment of usage charges to the ISO and the
transmission owners. Our argument here, however, is that even when there are
multiple SCs, a common strategy of accepting advisory re-dispatches is a stable
arrangement. Thus, we need to show that no one SC, such as the PX, can gain by
reverting to an alternative strategy.

Suppose then that the PX expects all other SCs to accept their advisory
re-dispatches, and consider the decision problem of the PX about whether to do
the same. We claim that in this case the PX cannot gain from adhering to its
preferred schedule, nor from submitting a revised schedule. An example conveys
the main idea. As in the example illustrating equilibrium (A), suppose that each
SC's preferred schedule implies transmission of 150





MM/h from the export zone to the import zone, whereas its advisory re-dispatch
implies transmission of 100 MM/h, for which the associated usage charge is $4
1MM/h. Also, the energy supply and demand curves in each SC are linear, so the
potential gain from trade lost because of limited transmission capacity is $100.
If the PX accepts its advisory redispatch, as do all the others, then there is
no residual congestion and the ISO's final schedule imposes no usage charges.
Consequently, the only cost to the PX is the foregone gain from trade of $100.
Alternatively, suppose it adheres to its preferred schedule. Because the other
SCs have accepted their advisory re-dispatches, the only excess demand for
transmission is the 50 MM/h from the PX's preferred schedule. To eliminate this
excess demand, the ISO will not invoke any adjustment pairs of the other SCs,
since all those whose cost is less than $4 1MM/h were used up in constructing
their advisory re-dispatch schedules, so the OPE will select only the 50 MM/h of
adjustment pairs from the PX whose costs are no more than $4 /MM/h. Thus, the
net result is that the PX's re-submitted preferred schedule is modified by the
ISO to obtain a final schedule that is the same as its advisory re-dispatch.
Moreover, the final usage charge imposed by the ISO is $4 1MM/h, since that is
the cost of the marginal pair invoked from the set offered by the PX. The total
cost to the PX is the $100 of foregone gain from trade plus $400 in usage
charges, which is distinctly worse than the outcome if the PX had accepted its
advisory re-dispatch. One can also imagine howls of protest from the other SCs,
since now they too must each pay $400 in usage charges as a consequence of the
PX's deviant action.

The PX's other alternative is to submit a revised schedule. As the foregoing
example illustrates, however, no revised schedule can do better than its
advisory re-dispatch, since that succeeds totally in eliminating usage charges
payable to the ISO, and any further reduction in transmission demand would
unnecessarily sacrifice gains from trade that are obtainable within the
available transmission capacity.

Thus, our second conclusion is that:

o    If each SC is a perfect substitute for the other in terms of the cost of
     its marginal adjustment pair, then each cannot do better than to accept its
     advisory-redispatch when it expects the others to do so.

This second equilibrium indicates that CSM might indeed succeed in California.
Although both (A) and (B) are possible equilibria, (B) has the advantage for the
SCs that they retain the usage charges that would otherwise be passed through
the ISO to the transmission owners.

However, (B) is a more fragile equilibrium than the analogous version of (C) in
which the SCs curtail their transmission demands further to reduce the chance
that the ISO might stilt impose usage charges. For instance, suppose that at
noon it is revealed that new estimates of loop flow indicate that transmission
capacity is less than previously estimated. In equilibrium (B) this results in
usage charges of $4 /MM/h or more, because all of the less expensive adjustment
pairs are exhausted by the SCs' advisory redispatches, so the OPE selects
additional adjustment pairs that cost more. In contrast, in equilibrium (C) each
SC can voluntarily restrain its transmission demand more than





required by the advisory re-dispatch to reduce the risk that revisions in the
estimates of transmission capacity will require further adjustments.

CONCLUSION

The thrust of our exposition is that the California design admits two basic
equilibria, one (A) in which each scheduling coordinator adheres to its
preferred schedule, and another (B) in which each accepts its advisory
re-dispatch or (C) submits a revised schedule that approximates its advisory
re-dispatch. These differ substantially, however, because in (A) they pay usage
charges to the ISO, whereas in (B) and (C) they avoid these charges.
Implementing (A) is straightforward, since each SC can pay the invoice from the
ISO simply by passing on these charges to its traders. Implementing (B) or (C)
is more complicated because it requires that each SC imposes internally a system
of usage charges, and then refunds to its traders the difference between the
revenue collected and the cost of the adjustment pairs invoked in some way that
does not weaken their incentives to curtail transmission demand. The simplest
policy is to refund the surplus pro rata based on each trader's volume of
transactions: since this refund does not differ by zones, it preserves the zonal
price differences in settlements and thereby maintains the right incentives to
curtail demand for transmission.