Exhibit 99.302
BID COST VS. PAYMENT MINIMIZATION IN THE PRODUCT SPECIFIC
SIMULTANEOUS (PSS) METHOD FOR AS PROCUREMENT
In this report I further elaborate on the formulation of minimizing bid cost
solutions vs. payment minimizing solutions. The development is performed in the
context of the Product Specific Simultaneous (PSS) approach for procuring
ancillary services (AS). I will refer to this approach simply as the "LP"
approach as it uses a Linear Program (LP) to simultaneously minimize the total
cost of procuring ancillary services in all five auctions (Regulation UP,
Regulation DOWN, Spin, Non-Spin and Replacement Reserves). I have developed and
presented the formulation of the PSS method in a separate document that is
included in the AS Redesign items that have been circulated to the Market
Participants (MPs). We have implemented the PSS method using an LP solver. This
method is compared with the Sequential method the ISO is currently using for
procuring AS. I'll illustrate the comparison of the two methods with a simple
example. For convenience I'll use the same example we have used before that
involves two services (Regulation and Spin) and four generating units.
EXAMPLE:
ISO Requirements:
ISO Regulation Requirement = 2000 MW,
ISO Spin Requirement = 800 MW
Unit Bids:
Unit 1: 1800 MW Reg. @ $10/MW
Unit 2: 1000 MW Reg. @ $30/MW
Unit 3: 200 MW Reg or Spin @ $20/MW
Unit 4: 800 MW Spin @ $40/MW
The results of the two methods (Sequential auctions and the LP optimization) are
shown below:
Sequential method LP solver (PSS method)
-------------------- ----------------------
$/MW UNIT REG MW SPIN MW REG MW SPIN MW
- ---- ---- ------ ------- ------ -------
10 1 1800 0 1800 0
30 2 0 0 200 0
20 3 200 0 0 200
40 4 0 800 0 600
COSTS Reg $ Spin $ Total Unit $ Reg $ Spin $ Total Unit $
1 18000 0 18000 18000 0 18000
2 0 0 0 6000 0 6000
3 4000 0 4000 0 4000 4000
4 0 32000 32000 0 24000 24000
ISO Total 54000 52000
PAYMENTS Reg $ Spin $ Total Unit $ Reg $ Spin $ Total Unit $
1 36000 36000 54000 54000
2 0 0 6000 6000
3 4000 4000 8000 8000
4 32000 32000 24000 24000
ISO Total 72000 92000
The results show that the Sequential auction results in a higher total cost (as
reflected by bid offers) but lower total payments by the ISO to the providers of
the AS services. IN FACT, THE SEQUENTIAL AUCTION RESULTS COINCIDE WITH THE
PAYMENT MINIMIZING SOLUTION FOR THIS EXAMPLE. Since one of the goals of the AS
redesign effort has been to figure out approaches that would reduce or minimize
the ISO's payments to the AS providers the use of the LP solver that implements
the PSS method seems to come into question.
In the following I'll attempt to provide some insights in the workings on the
two formulations. Furthermore, I'll provide some arguments related to the AS
bidders' incentives to convince you that despite this problem the current cost
bid optimization formulation of the PSS method is the preferred approach. Let's
examine this specific example in more detail. The only unit that bids in both
regulation and spin markets is generating unit 3. We can see that by picking the
payment minimizing solution (which in this example coincides with the Sequential
method) over the cost minimizing solution (which is represented here by the PSS
method), we reduce the payments to unit 3 by half (from $8000 to $4000). This is
a DIRECT CONSEQUENCE of unit 3's choice of offering its capacity to both
markets. If unit 3 were a rational bidder that makes decisions according to its
best interests it would react to this situation by not submitting a bid in the
regulation market (which has a lower price) and only bid in the higher priced
spin market. In fact, it can be shown that even if unit 3 were to merely remove
1 MW of capacity from the regulation market and offer it exclusively into the
spin market, the ISO's total payments would rise from $72000 to $92000 (the same
as those in the cost minimizing solution).
This argument gives credence to the claim that attempts to move away from the
cost minimizing solution (i.e., the current PSS formulation) to a payment
minimizing solution will result at reduced revenues for flexible bidders. I.e.,
transition to a payment minimizing approach is done at the cost of the flexible
bidders. Such a bidder would choose to react strategically by bidding in the
higher priced market TAKING AWAY ANY BENEFITS OF THE PAYMENT MINIMIZING
SOLUTION. It is important to evaluate these methods in the context of strategic
bidding by taking into account the dynamic and repetitive nature of the auctions
in the California markets. In this case, it is very easy to see that it will
take only few days for the AS bidders to adjust their behavior and remove all
the perceived benefits of any payment minimization formulation. By neglecting
the market dynamics and performing a static analysis almost surely we'll come to
the wrong conclusion.
What would happen in a pure sequential auction? First, as observed earlier, in
this specific example, the payment minimizing solution coincides with the
results of the sequential auction. If unit 3 (the only bidder that offers to
have its bids carried over from the reg. auction to the spin auction) observes
consistently higher prices in the spin market than in the reg market, it would
bid only in the spin market.
IT IS PRECISELY THIS BEHAVIOR OF ARBITRAGING BETWEEN THE DIFFERENT AS MARKETS
THAT KEEPS THE PRICES IN THE AS MARKET FROM FLUCTUATING IN THE COUNTER-INTUITIVE
MANNER. I.E., HAVING CONSISTENTLY PRICES FROM LOWER QUALITY SERVICES (SPIN)
HIGHER THAN PRICES FROM HIGHER QUALITY SERVICES (REG). I CLAIM THAT
TRANSITIONING TO A PAYMENT MINIMIZING FORMULATION WILL FORCE BIDDERS MAKE
SUB-OPTIMAL DECISIONS TO THE DETRIMENT OF THE AS MARKET AND POSSIBLY THEIR OWN
REVENUES. THE LP BASED COST MINIMIZING SOLUTION OF THE PSS METHOD MAY OFFER A
BETTER ALTERNATIVE TO THIS PROBLEM.
Additionally, the example above appears biased to over-emphasize the payment
increase caused by the LP solution. Note that if we allow the option of rolling
over unused bids from a superior ancillary service to an inferior ancillary
service within the sequential auction structure(1) the results will change. Thus
in this example Units 1 and 2 which had bid to sell regulation are eligible to
sell spin as well. The results of the modified example are shown below.
- -----------------
(1) Some market participants feel that such rolling over of bids should be a
natural choice for all rational bidders who want to maximize the capacity
selected from their bids. Since there have been at least some instances where
such rational behavior has been found to be missing in the bids submitted to the
ISO, an alternative (called the rational buyer approach) was proposed where
unused bids from one auction are rolled over the next auction.
MODIFIED EXAMPLE
Reg.Requirement = 2000 MW, Spin Requirement = 800 MW
Unit 1: 1800 MW Reg or Spin @ $10/MW
Unit 1: 1000 MW Reg or Spin @ $30/MW
Unit 3: 200 MW Reg or Spin @ $20/MW
Unit 4: 800 MW Spin @ $40/MW
SEQUENTIAL LP
$/MW UNIT REG MW SPIN MW REG MW SPIN MW
- ---- ---- ------ ------- ------ -------
10 1 1800 0 1800 0
30 2 0 800 0 800
20 3 200 0 200 0
40 4 0 0 0 0
COSTS Unit Total $ Unit Total $
1 18000 0 18000 18000 0 18000
2 0 24000 24000 0 24000 24000
3 4000 0 4000 4000 0 4000
4 0 0 0 0 0 0
ISO Total 46000 46000
PAYMENTS 1 36000 36000 36000 36000
2 0 24000 24000 0 24000 24000
3 4000 4000 4000 4000
4 0 0 0 0
ISO Total 64000 64000
However, we observe that in this particular example the LP has more than one
solution. An alternative solution with exactly the same total cost of $46,000
involves shifting 800 MW of regulation from unit 1 to unit 2 and 800 MW of spin
from unit 2 to unit 1. This raises the total payments to $68,000, which happens
to be higher than $64,000.
GENERAL OBSERVATIONS ON THE COST VS. PAYMENT MINIMIZATION DEBATE:
1.) MONOTONICITY:
Any modification of cost minimization approaches to reduce payments runs the
danger of giving non-monotonic solutions, i.e. solutions that involve increasing
the selected quantities from higher priced bids by passing over lower priced
bids. This results in instabilities in pricing. I observed this behavior on a
consistent basis in the context of developing the PX energy auction during the
WEPEX process by using a centralized optimization method that minimizes the
payments paid by the consumers. Results from minimizing payments in an energy
auction
are included in an IEEE paper we published in 1997. I sent you this paper last
month. For convenience, I am also attaching it in this email. While this is
certainly undesirable for dispatching in the energy market, its consequences may
not be as severe in the ancillary services market. Further investigation is
required to study this problem in more detail.
2.) CONVEXITY:
It is my impression that for some convex problems under some mild assumptions,
the cost minimizing solution is also a payment minimizing solution. Is this
really true in the general case? Certainly not. However, I am not sure what
source of non-convexity cause the biggest problem. Further investigation is
required to study this problem in more detail.
3.) COMPLEXITY
The payment minimization formulation requires the solution of a non-linear
problem. I have provided the basic formulation of such a solution in a separate
email I sent you last month. An alternative formulation for solving this very
difficult non-linear problem is also attached in this email. Implementation
details need to be worked out, but obviously a major implementation effort is
needed to implement such a method. On the contrary, the LP solver that
implements the current version of the PSS method is straightforward and easy to
understand.