EXHIBIT 99.418
OPTIMIZATION MODELS IN CALIFORNIA'S
RESTRUCTURED MARKETS
Paul Gribik
Perot Systems Corporation
[PEROT SYSTEMS LOGO] 1
TOPICS
- -> California Markets
[] Coordination of Forward Energy and
Transmission Markets
[] Ancillary Service Markets
[PEROT SYSTEMS LOGO] 2
CALIFORNIA MARKET STRUCTURE
[] California has a mix of several interrelated markets:
- Markets are defined by the commodities traded
o Energy
o Transmission
o Ancillary Services (Reserves and Regulation)
- Markets are defined by time-frame of the trade
o Day-ahead
o Hour-ahead
o Real-time
o Possibly month-ahead and week-ahead.
[PEROT SYSTEMS LOGO] 3
ENERGY MARKETS
[] Structure allows multiple forward energy markets.
- Bilateral Markets (Scheduling Coordinators -- SCs)
o Marketers develop their own trading and pricing rules.
- California Power Exchange (PX -- a particular SC)
o Day-ahead and hour-ahead auctions with market clearing prices.
- Futures Markets (e.g. PX Block Forward)
o Arrange financial transactions between suppliers and consumers.
[] A single real-time (spot) energy market run by the Independent System
Operator (ISO)
[] Producers and consumers can select the energy markets in which they wish to
trade.
4
[PEROT SYSTEMS LOGO]
TRANSMISSION MARKETS
[] ISO runs day-ahead and hour-ahead transmission markets via Congestion
Management (CM)
- PX and other SCs bid for transmission access. process.
- Real-time congestion management integrated in ISO's real-time energy
market.
[] ISO also auctions Firm Transmission Rights.
- Financial rights to collect congestion revenues with FTRs auctioned
yearly by ISO physical tie-breaker rights.
- FTRs auctioned yearly by ISO
- FTRs can be traded freely in multiple secondary markets.
[PEROT SYSTEMS LOGO] 5
ANCILLARY SERVICE MARKETS
[] ISO specifies A/S requirements by SC.
[] ISO runs day-ahead and hour-ahead markets:
- Suppliers can bid to sell reserves or regulation capacity.
- SCs can purchase their requirements.
[] SCs can also self-provide their A/S requirements.
- PX developing Block Forward A/S market.
[PEROT SYSTEMS LOGO] 6
OPTIMIZATION & MARKET INTERACTIONS
[] The separate markets interact.
- SCs buy transmission.
- Generation capacity can supply energy or several A/S.
[] Several markets based on optimization models.
- ISO transmission markets.
- PX energy markets.
- ISO A/S markets.
[] Coordination of the markets depends upon modeling the interactions between
markets in the optimization processes.
[PEROT SYSTEMS LOGO] 7
TOPICS
[] California Markets
- -> Coordination of Forward Energy and Transmission Markets
[] Ancillary Service Markets
[PEROT SYSTEMS LOGO] 8
PX DAY-AHEAD ENERGY MARKET
[] PX day-ahead energy market uses optimization.
- Minimize cost of supplies minus value of demands scheduled in each
hour.
- Schedule at intersection of supply and demand curves.
[GRAPH]
[PEROT SYSTEMS LOGO] 9
PX DAY-AHEAD ENERGY MARKET
[]PX runs energy auctions in each hour of the day:
- Parties bid to sell energy
PX
[] Seller G : (650 MWh @ $40/MWh)
1
PX
[] Seller G : (700 MWh @ $50/MWh)
2
- Parties bid to buy energy
PX
[] Buyer D : (100 MWh @ $40/MWh)
1
PX
[] Buyer D : (600 MWh @ $70/MWh)
2
[] Auction in one hour is independent of auctions in the other hours of the day.
- Inter-temporal constriants not modeled.
[PEROT SYSTEMS LOGO] 10
PX ENERGY MARKETS
[] Supply & Demand curves intersect at
(700 MWH, $40/MWh):
[GRAPH] - [FORMULA OMITTED] schedules 650 MWh.
- [FORMULA OMITTED] schedules 50 MWh.
- [FORMULA OMITTED] schedules 100 MWh.
- [FORMULA OMITTED] schedules 600 MWh.
[] If there is no congestion, ISO will
accept these schedules.
[] What if there is transmission
congestion?
11
[PEROT SYSTEMS LOGO]
ISO DAY-AHEAD TRANSMISSION MARKET
[] SCs bid for the transmission they need for their energy schedule
in each hour of the day.
[] ISO allocates transmission capacity to SCs so as to maximize the value
of the available transmission.
- ISO allocates does not run a forward energy market.
o ISO does not arrange trades between SCs beyond those that the SCs
arrange themselves.
[] CM process does not model inter-temporal constraints.
- CM process in one hour is independent of CM process in other hours
of the day.
12
[PEROT SYSTEMS LOGO]
COORDINATING ENERGY AND TRANSMISSION
[] SCs develop preferred energy schedules and adjustment bids.
- Supplies indicate how much more they would want to sell if price rises
and how much less they would want to sell is price falls.
- Demands do the same.
[] ISO uses adjustment bids to determine the value of transmission to an SC.
- Cost to an SC of adjusting its schedule to alleviate congestion.
[PEROT SYSTEMS LOGO] 13
TRANSMISSION OPTIMIZATION MODEL
[] Objective
- Minimize total cost over all SCs.
o Cost of supplies scheduled less value of demands scheduled ion the
hour as measured by adjustment bids submitted by SCs.
[] Controls:
- Supplies and demands of all SCs in the hour.
[] Constraints:
- DC power flow model.
- Path flow within limits.
- Each resource scheduled within range bid.
- Each SC's total supply equals its total demand.
[PEROT SYSTEMS LOGO] 13
RESULTS
[] ISO clears its transmission forward market:
- ISO allocates congested transmission to the SCs that place
the highest value on the capacity.
[] ISO does not run a forward energy market.
- The ISO does not arrange energy trades between SCs.
- The SCs arrange their own voluntary trades.
[] Each SC's forward energy market is "cleared."
- SC's scheduled supplies equal its scheduled demands.
- Cost of SC's supplies minus value of SC's demands is
minimized given the transmission capacity ISO allocated to SC.
[PEROT SYSTEMS LOGO] 15
RESULTS
[] SCs able to use locational marginal cost pricing.
- Locational marginal cots depend upon the SC.
- Difference between marginal costs at two locations does NOT
depend upon the SC.
[] ISO uses marginal costs pricing for transmission.
- Congestion charges depend upon the DIFFERENCE between a SC's
locational marginal costs.
- Congestion price for moving energy from one location to
another is independent of the SC.
[PEROT SYSTEMS LOGO] 16
RESULTS
[] Markets that use the resulting marginal costs to set energy prices are
revenue neutral.
- PX payments to suppliers plus PX congestion payments to ISO equal PX charges
to demands.
- ISO congestion charges to SCs equal ISO payments to transmission owners.
[PEROT SYSTEMS LOGO] 17
TRANSMISSION AND ENERGY MARKETS
[GRAPH]
- - PX submits its Initial Preferred Schedule to ISO.
- - SC2 also submits its Initial Preferred Schedule to ISO.
- - The combined schedules violate the transmission constraint between A and B.
18
[PEROT SYSTEMS LOGO]
ADJUSTMENT BIDS
[GRAPH]
- - PX can serve [FORMULA OMITTED] using either [FORMULA OMITTED] or [FORMULA
OMITTED].
Difference in cost is $10/MWh. This is the value of transmission to PX.
- - SC2 can serve [FORMULA OMITTED] using [FORMULA OMITTED] or curtail [FORMULA
OMITTED].
Difference in cost is $15/MWh. This is the value of transmission to SC2.
19
[PEROT SYSTEMS LOGO]
ADJUSTMENT BIDS
[GRAPH]
ISO first allocates transmission to SC2 since it values it the most:
Value to PX is $10/MWh.
Value to SC2 is $10/MWh.
20
[PEROT SYSTEMS LOGO]
INTER-TEMPORAL EFFECTS
[] CM does not model inter-temporal effects.
- Does not model ramping constraints that limit the change in a
resource's schedule from one hour to next.
[] SCs can submit adjustment bids that limit ability of CM to adjust schedules
over several hours or risk final schedules that are not physically
feasible.
- CM does not capture effect on marginal costs of starting the ramp of
resource early in day when its energy is not economical but will be
needed to meet load later in day.
[] Could model inter-temporal effects in CM.
[PEROTSYSTEMS LOGO] 21
TRANSMISSION MODEL INCLUDING TIME
[] Objective:
- Minimize total cost over all SCs and all hours of day.
[] Controls:
- Supplies and demands of all SCs in each hour.
[] Constraints:
- DC power flow model in each hour.
- Path flows within limits in each hour.
- Each resource scheduled within range bid in each hour.
- Each SC's supply equals its demand in each hour.
- Change in each resource's schedule from one hour to next within
ramping limits for the resource.
[PEROT SYSTEMS LOGO] 22
TOPICS
[] California Markets
[] Coordination of Forward Energy and
Transmission Markets
- -> Ancillary Service Markets
[PEROTSYSTEMS LOGO] 23
ISO ANCILLARY SERVICE (A/S) AUCTIONS
[] Five Ancillary Services in California structure:
- Regulation Up.
- Regulation Down.
- Spinning Reserves.
- Nonspinning Reserves.
- Replacement Reserves.
[] ISO sets requirement for each Ancillary Service.
- Determines A/S self-provided by SCs that it can use.
- Runs auctions to acquire remaining A/S capacity.
24
[PEROT SYSTEMS LOGO]
BIDS FOR ANCILLARY SERVICES
[] Bid from a resource to supply Ancillary Services.
- Capacity for Regulation Down
- Capacity for Regulation Up
- Capacity for Regulation Up and Spinning Reserves
- Capacity for Reg Up, Spin, and Nonspinning Reserves
- Capacity for Reg Up, Spin, Nonspin, and Replacement reserves.
[] Two part price bid for each Ancillary Service:
- Capacity Price ($/MW) and Energy Price ($/MWh).
o ISO uses capacity price in selecting resources to provide A/S.
25
[PEROT SYSTEMS LOGO]
BIDS FOR ANCILLARY SERVICES
[] A MW of capacity from a single resource may be bid to provide several
Ancillary Services.
- Restricted by capability of resource.
[] A Given MW can only be selected to provide one Ancillary Service.
- A MW of capacity may bid to provide Spinning Reserves or Replacement
Reserves.
- The same MW cannot be selected to provide both Spinning Reserves and
Replacement Reserves.
[PEROT SYSTEMS LOGO] 26
ANCILLARY SERVICE OPTIMIZATION MODELS
[] Original optimization process treated A/S markets sequentially.
- Weakly modeled interaction of A/S markets.
[] ISO improved modeling of interactions.
- "Rational Buyer."
[] Possible to further improve model of interaction of A/S markets in
optimization process.
- Simultaneous auctions.
- Integrate with Congestion Management.
[PEROT SYSTEMS LOGO] 27
RATIONAL BUYER APPROACH
[] ISO may buy "higher quality" A/S to substitute for lower quality A/S.
- Nonspinning reserves can be used for Replacement.
- Spinning can be used for Nonspinning or Replacement.
- Regulation Up can be used for Spinning, Nonspinning or Replacement
Reserves.
- Substitution allowed if it lowers total payment by ISO.
[] Rational Buyer Price (RBP) for an A/S is the price of the highest priced
bid ISO accepts for that A/S.
[PEROT SYSTEMS LOGO] 28
RATIONAL BUYER AUCTIONS
[] Treat A/S from Reg Up through Replacement.
[FORMULA OMITTED]
[PEROT SYSTEMS LOGO] 29
RATIONAL BUYER APPROACH
o Search over all sets of prices that the RBPs could potentially take [FORMULA
OMITTED].
- [FORMULA OMITTED] for Ancillary Service j must be a price in a bid to
supply Ancillary Service j.
- For a particular set of RBPs, buy capacity from each bid with price < or =
RBP (with adjustments of quantities of RBP).
o ISO must satisfy each requirement by Ancillary Service of the same or
higher quality as the requirement.
o Select RBPs to minimize ISO's total A/S payments.
- Combinatorial search problem.
- Time to solve could grow exponentially with size.
30
EXAMPLE WITH 2 ANCILLARY SERVICES
<Table>
<Caption>
ISO ISO
UNIT A UNIT B UNIT C UNIT D BUY REQ.
------- --------- -------- ------- ----- -----
SPINNING RESERVE BIDS 70 MW @ 40 MW @ No Offer 80 MW @ 75 MW
$1.0/MW $1.1/MW $90/MW
REPLACE. 70 MW No Offer 100 MW 80 MW @ 125 MW
RESERVE BIDS $1.0/MW $2.5/MW $90/MW
TOTAL CAPACITY 70 MW 40 MW 100 MW 80 MW
</Table>
[PEROTSYSEMS LOGO] 31
EXAMPLE WITH 2 ANCILLARY SERVICES
[] Least cost procurement achieved with RBPs are set at:
[] RBPSpin = $1.10/MW and RBPRepl = $2.50/MW
<Table>
<Caption>
ISO ISO
Unit A Unit B Unit C Unit D Buy Req.
------ ------ -------- ------ ------ ------
SPINNING 70 MW 40 MW No Offer 0 MW 110 MW 75 MW
RESERVES @ @ @
SELECTED $1.0/MW $1.1/MW $90/MW
REPLACE. 0 MW No Offer 90 MW 0 MW 90 MW 125 MW
RESERVES @ @ @
SELECTED $1.0/MW $2.5/MW $90/MW
</Table>
[] ISO pays a total of $346 for both A/S:
- ISO pays $121 for 110 MW of Spin.
- ISO pays $225 for 90 MW of Replacement.
[PEROT SYSTEMS LOGO] 32
NOT REVENUE NEUTRAL
[] Payments to suppliers may be greater or less than charges to buyers.
- In example:
o ISO pays suppliers a total of $346 for both A/S:
- ISO pays $121 for 110 MW of Spin.
- ISO pays $225 for 90 MW of Replacement.
o ISO charges demand a total of $405 for both A/S:
- ISO charges $82.50 for 75 MW of Spin requirement.
- ISO charges $312.50 for 125 MW of Replacement requirement.
[] ISO may need uplift or downlift.
- In example, ISO has downlift of $59 that it refunds to SCs.
- Demand and supply see different pricing signals.
[PEROT SYSTEMS LOGO] 33
RBP MAY NOT BE MARGINAL COST
[] Increase ISO requirement for Spin by 1 MW.
[] ISO can substitute 1 MW less of Spin for Replacement.
<Table>
<Caption>
ISO ISO
Unit A Unit B Unit C Unit D Buy Req.
------ ------ -------- ------ ------ ------
SPINNING 70 MW 40 MW No Offer 0 MW @ 110 MW 76 MW
RESERVES @ @ $90/MW
SELECTED $1.0/MW $1.1/MW
REPLACE. 0 MW @ No Offer 91 MW 0 MW @ 91 MW 125 MW
RESERVES $1.0/MW @ $90/MW
SELECTED $2.5/MW
</Table>
- Payments by ISO to providers of Ancillary Services increases $2.50.
- Costs (as measured by bids) of providing A/S increases by $2.50.
[] Marginal CostSpin = $2.50/MW is not equal to RBPSpin.
[PEROT SYSTEMS LOGO] 34
SIGNALS FROM RATIONAL BUYER
[] Rational Buyer may send garbled price signals.
- [FORMULA OMITTED] set by Rational Buyer may not be marginal cost of
providing Ancillary Service j.
[] Participants will respond to pricing signals.
- Could change prices in bids for different A/S.
- Could change quantities in bids for different A/S.
[] How they respond may induce instability.
- RBPs may become unstable.
- Auction results may become unstable.
35
[PEROT SYSTEMS LOGO]
SIMULTANEOUS AUCTIONS APPROACH
[] Possible to improve coordination in the optimization process.
[] Minimize total cost of A/S (as measured by bids).
- Linear Programming problem.
- Not combinatorial.
[] ISO may buy "higher quality" Ancillary Services to substitute for lower
quality Ancillary Services.
[] Market Clearing Price for Ancillary Service j ([FORMULA OMITTED]) set to
marginal cost of meeting the requirement for Ancillary Service j.
36
[PEROT SYSTEMS LOGO]
SIMULTANEOUS AUCTIONS APPROACH
[] Treat A/S from Reg Up through Replacement.
[FORMULA OMITTED]
subject to
[FORMULA OMITTED]
[] MCPj = d(Total Cost)/d(Requirement)j
37
[PEROT SYSTEMS LOGO]
EXAMPLE WITH 2 ANCILLARY SERVICES
<Table>
<Caption>
UNIT A UNIT B UNIT C UNIT D ISO ISO
BUY REQ.
------- -------- -------- ------ --- ------
SPINNING 70 MW 40 MW NO OFFER 80 MW 75 MW
RESERVE @ @ @
BIDS $1.0/MW $1.1/MW $90/MW
REPLACE 70 MW NO OFFER 100 MW 80 MW 125 MW
RESERVE @ @ @
BIDS $1.0/MW $2.5/MW $90/MW
TOTAL 70 MW 40 MW 100 MW 80 MW
CAPACITY
</Table>
38
[PEROT SYSTEMS LOGO]
EXAMPLE WITH 2 ANCILLARY SERVICES
[] Least cost procurement:
<Table>
<Caption>
UNIT A UNIT B UNIT C UNIT D ISO ISO
BUY REQ.
------- -------- -------- ------ ------ ------
SPINNING 70 MW 40 MW NO OFFER 0 MW 110 MW 75 MW
RESERVES @ @ @
SELECTED $1.0/MW $1.1/MW $90/MW
REPLACE 0 MW NO OFFER 90 MW 0 MW 90 MW 125 MW
RESERVES @ @ @
SELECTED $1.0/MW $2.5/MW $90/MW
</Table>
[] MCP(Spin) = $2.50/MW and MCP(Repl) = $2.50/MW
[] ISO pays a total of $500 for both A/S.
39
[PEROT SYSTEMS LOGO]
REVENUE NEUTRALITY
[] Payments to suppliers equal charges to demand.
- In example:
o ISO pays suppliers a total of $500 for both A/S:
o ISO charges demands a total of $500 for both A/S:
- $187.50 for 75 MW of Spin.
- $312.50 for 125 MW of Replacement.
[] ISO does not need uplift of downlift.
- Demand and supply see the same pricing signals.
40
[PEROT SYSTEMS LOGO]
SIGNALS FROM SIMULTANEOUS AUCTIONS
[] Simultaneous Auctions send clear price signals.
- MCPj for A/S j is the marginal cost (as measured by the bids) of meeting
the requirement for A/S j.
[] Absent market power, a participant cannot unilaterally adjust its bids to
increase its profit.
- Suppose a participant bids its opportunity cost of providing A/S
capacity.
- At the MCPs, each participant's schedule maximizes its profits --
Participant's Schedule x (MCP - Opp. Cost).
[] Stable results.
41
[PEROT SYSTEMS LOGO]
COORDINATION OF A/S AND TRANSMISSION
[] At present, A/S cannot compete with energy to schedule transmission.
- CM process allocates transmission to energy only.
- If a path is congested after CM, ISO breaks A/S market into regional
markets.
[] Allowing A/S to compete with energy for transmission capacity would improve
efficiency.
- SCs must be able to bid for transmission capacity in ISO's congestion
market for A/S.
- SCs must be able to schedule A/S on their FTRs.
[PEROT SYSTEMS LOGO] 42
COMBINED EXAMPLE
[GRAPH]
[] Minimize cost of energy and A/S simultaneously.
- Keep transmission within limits.
- Use bid costs in minimization.
[PEROT SYSTEMS LOGO] 43
COMBINED SOLUTION
[FORMULA CHART]
[] Set price for energy and A/S at each location at marginal cost.
[] Compatible with Simultaneous Auctions for Ancillary Services.
- Rational Buyer pricing problematical
[PEROT SYSTMES LOGO] 44
EXTENDING RATIONAL BUYER TO COMBINED A/S TRANSMISSION MARKET
[] In single region:
- Based on A/S bids, assume 10 possible RBPs per A/S.
- 10(5) possible price combinations to evaluate.
o Assume 10(-6) sec. to evaluation one combination.
o Running Rational Buyer would take << 1 second.
[] In two regions connected by a congested path:
- Based on A/S bids, 10 possible RBPs per A/S per region.
- Based on adj. bids, assume 10 possible usage charges.
- 10(5) x 10(5) x 10 = 10(11) possible price combinations.
o Running Rational Buyer would take > 1 day.
- With three regions, evaluation time > 3,000 years.
45
[PEROT SYSTEMS LOGO]
CONCLUSION
[] ISO congestion management optimization process provides for coordination of
separate energy markets with the transmission market.
[] A/S optimization process provides for imperfect coordination among the
A/S markets.
[] Optimization processes could be modified to improve coordination of separate
energy, A/S and transmission markets.
[] Optimization processes could be modified to improve inter-temporal
coordination.
46
[PEROT SYSTEMS LOGO]