**CONGESTION INDICES AND SHADOW PRICES**

**Alternatives and Considerations**

**26 January 2006**

SUMMARY

The SSG-WI modeling group put together a summary report on its work and
attempted to rank the paths in the West that were studied. There are
several possible indices, all based on shadow prices that are output
from the studies, that could be used to rank paths as candidates for
potential upgrades to relieve congestion. This paper briefly describes
them and their pros and cons.

SHADOW PRICES - BACKGROUND

Shadow prices convey very useful information and are central to many of
the approaches, so it is important to understand what they are and are
not. A shadow price in a linear program (LP) solution is the change in
the value of the objective function with respect to a one unit change in
the value of a constraint.

The objective function in the SSGWI studies is minimization of total
system production costs. Constraints are applied to path capabilities,
generator capabilities, and loads that must be met. So the shadow price
on a transmission path is the change in total system production cost for
a one unit (one megawatt) change in the limit on the transfer capability
of that path.

Because the shadow price measures a marginal value, applying it to large
changes in the constraint is problematic, because one cannot tell by
inspection what the valid extension of the range of application is.

TOTAL FLOW METHOD

This is the method initially suggested by the modeling group. The index
value was calculated by multiplying the shadow price of the path
constraint by the total flow on the path. This was done to add some
sense of the total value of relieving a constraint to a number defined
as the effect of a one megawatt change in a constraint. The advantages
of this method, or what would be equivalent, multiplying by the transfer
limit on the path, are that the information is readily available and it
distinguishes roughly between a major path and a small line as
candidates for upgrade.

The problem with this method is that it doesn't actually measure what
needs to be measured - the amount of additional power that would flow
over the path if its transfer limit were raised, which could be either a
large or a small amount. A large amount could justify additional
investment; a small amount would likely not.

CAISO METHOD

This characterization is derived from the Transmission Economic Analysis
Method (TEAM) report on methodology (June 2004), and is the methodology
I believe was suggested as an alternative during the December FUSS
meeting.

The TEAM method appears to be based on a calculation of what total
congestion revenues would be in a nodal pricing framework (which is what
the CAISO uses). Generally, it measures benefits in a total welfare
(consumer surplus/producer surplus) framework, where consumer and
producer surpluses are calculated from nodal price (i.e., load and
generator shadow price) information. These two pieces will not balance
in a system with congestion; the difference (assuming no losses and a DC
power flow) is the congestion rent or congestion revenue, and is
equivalent to the shadow price on the line multiplied by the total line
capacity. This leads to roughly the same result as the Total Flow Method
described above.

Note also that the CAISO chose the welfare approach in order to be able
to distinguish parties who gained and lost among the upstream and
downstream loads and generators, and transmission rights holders, when
considering an expansion. This is not a consideration for the SSG-WI
report.

This result described above is fairly straightforward in a simply system
with two buses and one line. However, as the report notes, the shadow
price on a path is not simply derivable from the bus shadow prices at
both ends of the path in a meshed network. The report proposes an
approach for addressing this.

However, and more to the point of our use of the shadow price
information, the nodal pricing framework in which this makes sense, is
not the framework in which most of the West operates, and the key
problem, as in the previous method, is calculating a value using the
total capacity of the line rather than the additional flow on the live
were the constraint to be relaxed.

Moreover, the report notes that the total welfare difference collapses
into the production cost difference with and without the line in the
presence of perfectly inelastic demand (and for relatively inelastic
demand, may not be significantly different). With this consideration as
well, we are brought back to the original problem of what gets
multiplied by what.

ADDED FLOW METHOD

One way of getting closer to the answer is to multiply the shadow price
on the path by the difference between the flow on the path in an
unconstrained case and the reference case.

This has problems of its own, however, given the current modeling. The
unconstrained case has both no path limits and no losses (losses were
added to the loads to be met rather than being a function of the
physical characteristics of the lines and the distance between
generation and loads in all the modeling). The result of not having
losses as a function of transmission is to cause over-reliance on
generation that is cheap to run but extremely far from the loads, thus
artificially increasing the amount of unconstrained flow that would be
on intermediate paths. (There were apparently other causes of this
phenomenon in the unconstrained case as well. The relative sizes of the
impacts are unclear.)

One way to deal roughly with this would be to impose loss factors on the
various paths of interest. While this would end up over-generating by
the amount of the double-counted losses (2-3 percent?), it would give a
more realistic value to the unconstrained generation and since both the
constrained and the unconstrained cases would have the double counted
losses, the delta might be even less unrealistic.

This would not, however, deal with the problem of extrapolating a shadow
price's application outside of its range, which would cause errors of
unknown magnitude.

SHADOW PRICE PLUS JUDGMENT METHOD

This approach simply uses the shadow prices alone as the index of
relative importance, with judgment being applied to put aside relatively
small, and presumably less important paths. In general, however, the
listing of shadow prices themselves (assuming no surprises in their
averaging across study hours) itself could well be a reasonable
indicator of importance for paths that are in roughly similar capacity
classes (e.g., capacity between 400 and 900 MW, or some similar
category).

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c:\\documents and settings\\gibson\\desktop\\congestion indices
26jan06.doc (Wally Gibson)