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Chief Economic Advisor Federal Energy Regulation Commission NAS Resource Allocation: Economics and Equity The Aspen Institute Queenstown, MD March 20, 2002

This does not necessarily reflect the view of the Commission.

Richard P. O’Neill Federal Energy Regulatory Commission Benjamin F. Hobbs The Johns Hopkins University and Energieonderzoek Centrum Nederland Paul M. Sotkiewicz University of Florida William Stewart College of William and Mary Michael Rothkopf Rutgers University Udi Helman Federal Energy Regulatory Commission and The Johns Hopkins University

menu gin scotch hot dog burger $4 $6 $3 $5

value gin scotch hot dog burger $5 $9 $3 $5 You must order from the menu  $5

Adam Smith on network regulation

“The tolls for the maintenance of a high road, cannot with any safety be made the property of private persons. ... It is proper, therefore, that the tolls for the maintenance of such work should be put under the management of commissioners or trustees.”

[Wealth of Nations ,

Book V, Chap 1, p. 684

]

 If Adam Smith is not enough, why intervene?

 To provide for reliability  To ensure revenue adequacy (no subsidies)  To facilitate entry generation, transmission, consumption  To mitigate market power  To provide competitive price signals  To protect property rights 

How to intervene?

 nondiscriminatory  lower transactions costs  more not less options  control market power  highly efficient  “just” prices  will prices be too low?

 Are low prices bad?

 are market prices unconstitutional?

All power corrupts, but we need the electricity .

Electric markets are incomplete and complex

 incomplete if not pricing all desired products  asymmetric markets: vertical demand curve  bidding nonconvexities  Supply: start-up and no-load  demand: for y continuous hours at < $x  intertemporal dependencies  reactive (imaginary/orthogonal) power  socialize transient stability/ voltage  socialize generation and load characteristics  can decentralized markets handle this?

Basics of market design

 Contracts (not compacts)  Marginal/incremental cost bidding  Start-up and min run  Trading rules  Financially sound  Market clearing prices  Incentives  For doing “good” things  For not doing “bad” things(socal gas, no withholding)  With collars for political reasons  Information

Auction Design Principles

"Everything should be made as simple as

  Don'ts  Create gaming opportunities in the name of simplicity Do's 

possible ... but not simpler." Einstein

 =22/7  Foreclose marginal (incremental) cost bids  Assume away non-convexities  increase risk  Allow bids that are not firm offers  favor large players  = 4[1 -1/3 + 1/5 – 1/7 + …] Allow marginal cost bidding  market clearing price (with scarcity rents)  make the process internally consistent  Create property rights and simple alternatives  Allow self scheduling

differences in auction vs. COS based regulation

Issue estimating short run marginal costs estimating capacity hold-up problem estimating return on equity estimating depreciation estimating units of service cost allocation estimating proper discounts measuring withholding free-rider problem Auction yes yes yes no no no no no yes yes COS yes yes yes yes yes yes yes yes yes no

market design objectives max bid efficiency within constraints

 All RTO (centralized) markets are optional  self-scheduling and voluntary market bids  low transactions costs; no new risks  allow marginal costs bidding(multipart bids)  minimize incentives for market power abuse  don’t favor large participants/portfolio  max arbitrage/min averaging  simultaneous market clearing  lots of information



Coexistence of RTO and off-RTO markets

 eliminate bias between off-RTO and RTO markets  RTO markets should not be severely constrained to promote off-RTO markets  Allow clearing of mutually beneficial trades?  Why are there mutually beneficial trades?

 Should off-RTO markets be subsidized? No  Should the RTO be in the insurance biz? No  bilateral physical markets: who pays for the cleanup after the party?

Self supply options

 Self designed zonal configurations  balanced scheduling  self supply of ancillary services  self designed transmission rights  optional bidding in RTO/ISO markets  no bill from RTO/ISO  pay or get paid for imbalances

 Pre-day-ahead markets  for transmission rights: CRT/TCC/TRCs/FGRs  for generation capacity/resevres (ICAP)  market power mitigation via options contracts  day-ahead market for reliability(valium substitute)  simultaneous nodal market-clearing auctions for energy, ancillary services and congestion  allow multi-part bidding  higher of market or bid cost recovery  allow self scheduling  allow price limit bids on ancillary and congestion  Real-time balancing myopic market  markets are nodal-based LMP with fish protection

Pre-day-ahead markets

 Annual, seasonal, monthly, weekly  Simultaneous clearing of all products  Demand side bidding or capacity options (physical?)  Capacity markets (two year ahead for entry)  Transmission contracts  energy forward contracts: FCCs, FTCs  energy options contracts: CRTs  flow gate options: FGRs  FTR options for reserves  Unbalanced contracts!

 market power mitigation contracts  bid marginal costs including start up and no load  pay higher of market clearing price or costs

Day-ahead reliability management

 Optimize system topology over large areas  reserves, real and reactive power balanced  clear most congestion  reserves in place including tx capacity  set imports  clear mutually beneficial trades  interperiod interdependencies: start-up, ramp rate and minimum load

Design principles for day-ahead RTO market

 Objective: max efficiency within reliability 

allow

marginal cost bids(start-up/min load)  self-scheduling with optional bidding  simultaneous clearing of all services at LMP  pay higher of bid costs or market clearing price  financially binding/physically if needed  low risk and transactions costs

Can the real-time market handle reliability by itself?

 Is a real-time market enough? In theory yes  can too much real-time scheduling threaten system stability?

 Neighborhood reliability of the AC load flow What if it was a DC load flow? Simple  should there be an incentive not to be more than x% out of balance?

 first, eliminate all bias to be in the RTM

Design principles for real-time RTO market

 No other markets need be in real-time balance  max efficiency within system balance  deviations from day-ahead priced at market  those operating as scheduled in day-ahead pay nothing  physically binding  pay market clearing price  low risk and transactions costs  fast market info: prices and quantities

non-simultaneous auctions without LMP and marginal cost bidding

 Socialize not privatize cost  higher cost passthroughs: uplift  create incentives for market power to lower the risks of the market design  higher transactions cost of bid preparation  market power mitigation is more difficult  constant redesign to correct flaws  problems in England, Columbia, California  Australia moving from zonal to nodal

 Zonal markets (Cal, PJM, NE, UK)  Sequential markets for energy and anc services  One settlement systems  Infeasible markets (Cal PX and UK)  Ignore nonconvexities (start-up and no-load)  Ignore market power  As-bid pricing 

all ended in administrative intervention



No property rights to market power or poor market design

monopoly and scarcity rents

< withheld capacity >

demand

0.8

0.6

0.4

0.2

monopoly price

monopoly rents

lost surplus

scarcity rents

0 0

variable costs

5 10 20

competitive price

25 30

good market design allows proper mitigation

 Pre-day-ahead markets  Tx rights  Pre commitment of generators  Feasibility of capacity markets  Day-ahead market  Demand bidding  Marginal costs bid includes startup, noload and running costs  Real-time balancing market  Bid running costs if you did not bid in DAM  Reliability by adjusting generators via bids  No fault market power mitigation

C 150 MW A 100 MW 2/3 150 MW 1/3 100 MW 1/3 100 MW B

Max bt

βt

+

B

(

y

)

(

) <=

(

) Sequence of auctions; forward and real-time 40,000+ nodes 400, 000+ contingency constraints Could be highly redundant constraints K(y) can be non-convex (electromagnetic eqns) Bids are non-convex mixed integer Solvable? Bixby says not to worry: 6 orders of magnitude in 10 years

A Four Node Network with Nomogram Flowgate

NW NE SW

Nomogram Flowgate

Bidder

B1 B2 B3 B4 B5 B6 S1 Bid Type Bid ($/MW) Quantity awarded Reduced cost

PTDFs:

10 100 10 0.0

FB option,

. Buy up to 100 MW FB option,

. Buy up to 100 MW PtP forward,

. Buy up to 100 MW PtP option,

. Buy up to 100 MW PtP forward,

. Buy up to 100 MW.

PAR capacity. Buy up to 100 MW.

Forward generation at

. Sell up to 200 MW.

30 20 25 25 25 -10 100 5 1.0

0 -5 0.8

100 0 0.8

40 0 0.6

20 25 0.0

200 20 0.0

Shadow Price:

NW NE

SE SE

PAR SF nomogram 1.0

0.0

-0.2

0.2

0.0

0.2

0.0

0.6

0.4

0.0

1.0

0.0

-1.0

0 0 25 5 30

Application: Electric Power Generator Unit Commitment

Maximize:    (

C g i it



S i fixed z it



su S z i it su



sd S z i it sd

)

i t

subject to:  

g it

 

d t

 t,

i g it



z G it i

min  0  i, t,

g it z it



z G it i

max  1 

z it su

  0 0  i, t,  i, t, 

z it z it su , z it sd

 

 1 

z sd it

 0  i, t,

{0,1}; all other variables



0; z it < 1

Problem 1: Single Period, 3 Plants

Plant 1 2 3

MIN Q MAX Q 50 150 MC/unit Fixed$/hr 4 125 StartUp$ 25 ShutDown$ 0 0  Load  400 100 200 2 50 150 0 20 50 6 0 0 0

7 6 5 2 1 4 3 0 0

Commodity Price

100 200

Quantity

300 400

8 7 6 5 2 1 4 3 0 0

Average Cost vs. Price

Average Cost Price 100 200

Quantity

300 400

Startup Payments

200 150 100 50 0 0 Start P1 Start P2 Start P3 100 200

Quantity

300 400

Unit Commitment Extensions

1. Multi-Period Considerations: e.g., ramp rate limits -

Problem 2 (2 hours):

Assume RR limit = 105 MW/hr, demands = 180 MW and 395 MW - Both plants start up in period 1 because of ramp rate - Plant 1 gets paid $150 to start up in period 1 (commodity price alone supports operation only in period 2); profit = $175 - Degeneracy/multiple duals a problem 2. Ancillary Services 3. Transmission Congestion Payments 4. Demand Bidding

Smokestack versus High Tech (from Scarf, 1994

) Production Characteristics

Capacity Construction Cost Marginal Cost Average Cost at Capacity Total Cost at Capacity

Smokestack (Type 1 Unit)

16 53 3 6.3125

101

High Tech (Type 2 Unit)

7 30 2 6.2857

Let:

Formulate and Solve MIP (Simulates Bid Evaluation by Auctioneer)

z 1 , z 2 = construction decisions of types 1 & 2, respectively q 1 , q 2 = output for types 1 & 2

MIP:

Max  i  i (53z (q 1i 1i + q 2i + 3q 1i ) = Q ) Σ i (30z 2i + 2q 2i ) -16z 1i + q 1i  0; z 1i  {0, 1}, q 1i  0, i =1,2,… -7z 2i + q 2i  0; z 2i  {0, 1}, q 2i  0, i =1,2,…

Efficient Outcome

• To optimally satisfy a demand of, say, 61 units: #Type 1 # Type 2 Type 1 Type 2 Total Demand Units Units Output Output Cost 61 3 2 47 14 388 Note that one Type 1 does not operate at capacity • The output price according to the LP solution is $3 – But both types make

negative

 not an equilibrium outcome profits

6.43

6.42

6.41

6.4

6.39

6.38

6.37

6.36

6.35

6.34

6.33

6.32

6.31

6.3

6.29

6.28

55 56

Average cost as a function of demand for Scarf's problem

57 58 59 60 61 62 63

demand

64 65 66 67 68 69 70

optimal value as a function of demand for Scarf's problem

450 440 430 420 410 400 390 380 370 360 350 340 55 56 57 58 59 60 61 62 63

demand

64 65 66 67 68 69 70

450 440 430

optimal value as a function of demand for Scarf's problem

420 410 400 390 380 370 360 350 340 55 56 57 58 59 60 61 62 63

de mand

64 65 66 67 68 69 70

LP That Solves the MIP

Max  i  i (q 1i (53z 1i + q 2i + 3q ) = Q 1i ) Σ i -16z 1i + q 1i  (30z 0 , i =1,2,.. 2i + 2q 2i ) -7z z 1i q 1i = z 1i *  0 2i + q 2i  0 , i =1,2,..

z 2i q 2i = z 2i *  0,

Duals

(y 0 **) (y 1i ) (w 1i **) (y 2i ) (w 2i **) ** Used in payment scheme

Prices at an Output of 61

Unit type 1 (Smokestack)

(y) (w 1i ) (y 1i ) Demand Commodity Price Start-up Capacity 61 3

-53

Unit type 2 (High Tech)

(w 2i ) (y 2i ) Start-up Capacity -23

Prices paid by unit to auctioneer Thus, each unit is paid a start-up cost, ensuring nonnegative profit (here, 0)

Dual Prices for Scarf's Problem Unit 1 (Smokestack) Unit 2 (High Tech) Dual Price Set

Set I Set II Set III

Commodity Price

3 6.3125

6.2857

Start-up Price

53 0 .429

Capacity Price

0 -3.3125

-3.2857

Start-up Price

23 -.1875

Capacity Price

-1 -4.3125

-4.2857

Non-Convexities in Markets

• While market models often assume away non-convexities (e.g., integral decisions and economies of scale), … they exist!

• Electric utility industry: – Still economies of scale in generation and especially transmission – Unit commitment: start-up, shut-down costs; minimum run levels • Why disregard non-convexities in market models? … with convex profit maximization problems (concave objective, convex feasible region), we can usually: – define linear (“one-part”) market clearing prices – establish existence, uniqueness properties for market equilibria – create tests for entering activities

The Problem with Non-Convexities

• Linear prices can no longer clear the market … an equilibrium cannot be guaranteed to exist • E.g., electric power operations: – At P < P*, inadequate supply – At P > P*, a lump of additional supply enters that breaks even (covers fixed costs), but supply exceeds demand. If force any generator to back off, its profit < 0 – “Administrative” solution to reach the optimum: • Adjust outputs to restore feasibility • Side payments to ensure no one loses money • As Scarf (1990, 1994) then points out, there is no price test for Pareto improving entry of new production processes

Why Address Non-Convexities in Auctions Now?

1) New markets for electric power have non-convexities 2) A debate surrounding these power markets: the use of prices to induce efficient, decentralized decisions

a la

Walrasian auctions 3) Auction mechanisms in the NYISO and PJM attempt to account for integer decisions 4) California said no to such an auction because of complaints: these prices are not “equilibrium supporting” and - administrative adjustments appear arbitrary (e.g., Johnson, Oren, Svoboda 1998) 5) Our result: If integral decisions can be priced, a market equilibrium can be supported

Some Related Literature

• Scarf (1990, 1994) – Emphasized the divergence of math programming and economics – Searched (unsuccessfully) for a way to find prices in the presence of integral choices, and for pricing tests for improvements • Gomory and Baumol (1960) – The use of cutting plans that are combinations of existing constraints to arrive at an integer solution – Interpreted duals of those planes; stopped short of pricing individual integer activities • Wolsey (1981) – Pure IP with integer constraint coefficients & RHSs – Approaches to constructing price functions yielding dual problems that satisfy weak and strong duality. Functions generally nonlinear • Williams (1996) – Examines possible duality for integer programs, but concludes no “satisfactory” duals (Lagrange multipliers) exist

Pricing Integral Activities

• One can think of the traditional pricing approach as a misspecification of the commodity space – The commodity space could include integer decisions as an “intermediate good” • The pricing system derived here is similar to multi-part pricing for utilities – For example, an demand charge (fixed costs) and an energy charge • Buyers’ clubs with multipart contract

Our Approach to Addressing Non-Convexities

1. Formulate the non-convex problem as a maximization MIP. Bids include all costs and internal constraints.

2. Solve MIP – Take advantage of modern MIP technology 3. Take integer solutions z* and define equality constraints z=z* in a LP - “convexifying” the problem.

4. Solve LP 5. Duals on z=z* are prices on the integer variables – If market/auction participant pays those prices, together with the duals on commodity and other coupling constraints… ….

then

those prices support an equilibrium – For (0,1) variables, can use only negative prices for z*=1 and positive prices for z* = 0

General Formulation: MIP

Let:

k = index for auction participants x k , z k = activities c k , d k = marginal benefits of activities (cost, if <0). (c k x k + d k z k is the total benefit to participant k) A k1 , A k2 , B k1 , B k2 = constraint coefficients b 0 0 = commodities to be auctioned. In double auction, b 0 = b k = RHS of internal constraints of participant k

MIP:

max  k subject to: (c k x k + d k z k )  k (A k1 x k B k1 x k + A k2 z k )  + B k2 z k  b k } b 0 x k  0, z k  {0,1} all k

An LP That Solves The MIP

LP(z*):

Max  k (c k x k + d k z k ) s.t. B k1 x k  k + B (A k1 x k k2 z k  z k x k  = z k * 0 + A k2 z k )  b k } all k b 0 where z* indicates an optimal value of z in MIP

Definition of Equilibrium

Definition 1.

A “market clearing” set of contracts has the following characteristics: 1. Each bidder is in equilibrium in the following sense. Given • prices {y 0 *, w k *} and payment function P k (x k ,z k ) defined by the contract • no restrictions on x k (B k1 x k + B k2 z k  b k ) and z k other than k’s internal constraints then no bidder k can find feasible x k ’, z k ’ for which: (c k x k ’ + d k z k ’ P k (x k ’ ,z k ’ ) )

(c k x k * + d k z k * P k (x k * ,z k * ) ) Thus, the prices support the equilibrium {x k *,z k *}.

2. Supply meets demand for the commodities. I.e.,  k (A k1 x k * + A k2 z k *)

b 0

A Candidate Set of Market Clearing Prices and Quantities

Definition 2.

Consider the contract T k with the following terms: 1. Bidder k sells z k =z k *, x k0 =x k0 * (where x k0 with nonzero A k1 ) is the subset of x k 2. Bidder k pays auctioneer: P k (x k ,z k ) = y 0 * (A k1 x k +A k2 z k ) + w k * z k .

where * indicates an optimal solution to MIP / LP(z*)

Variant

. Define: w k *

’

= Max(0, w k *) if z k * = 0 = Min(0, w k *) if z k * = 1 P k (x k ,z k ) = y 0 * (A k1 x k +A k2 z k ) + w k *

’

z k

Existence of Market Clearing Contracts for MIP Auction

Theorem.

T  { T k } is a market clearing set of contracts.

• Proof exploits complementary slackness conditions from auction LP to show that at the candidate equilibrium prices, {z k *,x k0 *} is optimal for each bidder’s own MIP: Max [c k x k s.t. B k1 x k + d k z k ] - [y 0 * (A k1 x k +A k2 z k ) + w k * z k ] + B k2 z k  b k x k  0, z k  {0,1} • There may be alternative optima for the bidder • Profits nonnegative • If w k * < 0 and z k * =1, interpretable as NYISO/PJM mechanism for preventing winning bidders from losing money • In this framework, there are payments directly for individual capacity

A Welfare Result

Corollary.

If each participant k bids truthfully (submits a bid reflecting its true valuations (c k x k (B k1 x k + B k2 z k  b k ; x k  0; z k  + d k z {0,1}), k ) and true constraints ... Then an auction defined as follows will: (a) maximize net social benefits (  k [c k x k + d k z k ]) and (b) clear the market The auction includes the following steps: 1.

The auctioneer solves MIP, yielding primal {x k0 *,z k *}; The auctioneer solves LP(z*), obtaining prices {y 0 *, w k *} The auctioneer imposes contract T upon the bidders

Extensions

• Tests for Pareto improving entry of new activities • How useful is this really likely to be? – For small systems, where lumpiness looms large, market power is important – For large systems, the duality gap shrinks .. into irrelevancy?

• Strategic bidding over these integral activities.

– Comparisons to iterative single part bid auctions.

– Do more bidding degrees of freedom facilitate strategic behavior? What are the impacts? • Consequences for distribution of rents in the market between consumers and producers, and among groups of producers • Tests on larger systems

Wholestic Market Design AGORAPHOBIA

You don’t always get it right the first time.

Now you have experience Try LMP Are you a Copernican or a Ptolemain?

We had to destroy the market to save it