Geographic Integration, Transmission Constraints, and Electricity Restructuring

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Geographic Integration, Transmission
Constraints, and Electricity Restructuring
March, 2005 Not for Quotation without Authors
Permission
Andrew N. KleitJames D. Reitzes

• Pennsylvania State University and The Brattle
  Group, respectively.
• The authors can be contacted at ank1_at_psu.edu and
  james.reitzes_at_brattle.com.

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Topics for Discussion

• How to Estimate Arbitrage Costs
• How to Modify the Arbitrage Cost Model for
  Electricity Markets in Order to
• Estimate the Impact of ISO formation on
  Electricity Trading Costs
• Assess the Prevalence of Binding Transmission
  Constraints under Different Transmission
  Organizational Regimes
• ? How to Estimate the Shadow Value of Adding
  Further Transmission Capacity
• All with easily available data!

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Arbitrage Cost Estimation

• Basic Methodology

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Arbitrage Cost Estimation Basic Methodology

• The basic arbitrage cost model was developed by
  Spiller and Wood (1988), who examined integration
  of regional gasoline markets.
• Other papers using a similar model include
  Sexton et al. (1991) for celery Kleit and
  Palsson (1996, 1999) for Canadian cement and
  Kleit (1998) in natural gas.

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Arbitrage Cost Estimation Basic Methodology
(cont.)

• Use maximum likelihood techniques to distinguish
  two regimes
• (a) Arbitrage (Unconstrained Trade) -
  inter-regional price differences represent
  marginal trading costs.
• (b) Autarky - inter-regional price differences
  most likely reflect differing regional supply and
  demand conditions.
• Under autarky,
• (i) no trade occurs, or
• (ii) trade occurs on a long-term contract basis
  but does not respond to short-term
  arbitrage opportunities.

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Arbitrage Cost Methodology

• Assume a (stochastic) cost of arbitrage the
  cost of shippinga good from Region 1 to Region 2
  (or vice versa).
• The price difference between the two regions
  cannot exceed arbitrage costs.

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Basic Arbitrage Cost Model

• Let P1 price of the good in Region 1,
• Let P2 price of the good in Region 2,
• Let Y P1-P2.
• Without the threat of arbitrage, the price
  difference between the two regions is determined
  by the autarky relationship
•   ?PN ? ?, (1)
• ? constant ? N(0, ?2).

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Basic Arbitrage Cost Model (cont.)

• If price in Region 1 becomes much higher than
  price in Region 2, buyers in 1 will arbitrage the
  difference by buying the good in 2 and shipping
  to 1.
• Now define the arbitrage (i.e., trading) cost of
  sending the good from Region 2 to Region 1
• T1 T 1 ? 1, (2)
• ? 1 N(0, ? 12), truncated from below at
  -T1  
• The reason for the truncation from below is that
  arbitrage costs must be nonnegative, (i.e., T1
  gt0).

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Basic Arbitrage Cost Model (cont.)

• Now, an observed price difference, Y P1-P2gt0,
  could result from two possible states
• (1) autarky (i.e., the absence of arbitrage),
  implying that
• arbitrage costs exceed the observed price
  difference
• ?PN Y and T1gtY.
• (2) arbitrage, implying that the price
  difference would be larger under autarky
• T1Y and ?PN gt Y.

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Basic Arbitrage Cost Model (cont.)

• The likelihood of observing a particular value of
  Y is therefore as follows
• L(Yi) Likelihood (?PNYi and T1gtYi)
• Likelihood (T1Yi and ?PNgtYi), (3)
• L(Yi) f(?PNYi)(1-F(T1Yi))
• f(T1Yi)(1-F (?PNYi)), (4)
• where f pdf, Fcdf.
• This is a variant of Tobit with stochastic limits.

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An Extension to the Basic Arbitrage Cost Model

• Autarky price differences should be related to
  structural factors (i.e., cost and demand
  conditions) in each regional market.

(7)
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Electricity Restructuring and Market Integration
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Electricity Restructuring and Market Integration

• ISOs were designed to facilitate wholesale
  electricity trading by lowering trading costs and
  mitigating incentives to manipulate the
  transmission system.
• --- Has this occurred?
• Hardly any analysis has been performed on this
  question.
• Thus, we examine the impact of forming the PJM
  ISO on electricity trading costs between PJM and
  New York and between PJM and the ECAR Reliability
  Region.

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Modified Arbitrage Cost Model

• Adding Quantity-Constrained Trade

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Adjusting the Arbitrage Cost Estimator for
Electricity Markets

• Since transmission capacity limits and
  institutional impediments may constrain the
  quantity of electricity that can be traded
  between regions, we modify the traditional
  arbitrage cost model to consider three possible
  equilibrium states
• (1) autarky
• (2) arbitrage (i.e., unconstrained trade), and
• (3) quantity-constrained trade.

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Quantity-Constrained Trade

• Quantity-constrained trade represents a state
  where trade takes place up to some capacity
  limit, and no more.
• Capacity limit can be a physical or institutional
  trading barrier.
• .

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Quantity-Constrained Trade

• We express the price differential between regions
  1 and 2 under quantity-constrained trade as
• Ci Ai - FLOWi ?
• Zi'? - FLOWi ? (9)
• Thus, the quantity constrained price difference
  equals the autarky price difference, less FLOW1,
  where FLOW1 represents the change in the price
  difference induced by the flow of electricity
  from one region to another up to the available
  quantity limit.

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Likelihood Function with Quantity-Constrained
Trade
L(Yi) Likelihood (?PiNYi and T1i Yi)
Likelihood (T1iYi and ?PiN gtYi C1i)
Likelihood (C1iYi and ?PiN gt Yi gtT1i).
(10)
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Modified Trading Cost Equation

• We add indicator variables to estimate the impact
  on trading costs of
• (a) the formation of the PJM ISO (April 1,
  1998)
• (b) PJMs switch from cost-based to
  market-based
• bidding (April 1, 1999)
• Revised trading cost specification is
• T1 T 1 ß98I98 ß99I99 ? 1,
  (2')
• where I98 1 after April 1, 1998 else 0
• I99 1 after April 1, 1999 else 0
• ? 1 N(0, ? 12), truncated from below at -(T1
  ß98I98 ß98I99)

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Calculating Regime Probabilities Using
Bayesian Updating

• From (10), we obtain

Recall Pr(AB) Pr (AnB)/Pr(B). Writing
in likelihood space, Pr(AutarkyYi)
L(AutarkynYi)/L(Yi) We calculate probabilities
similarly for the unconstrained and constrained
trading states.

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Institutional Detail and Data
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Institutional Detail

• Our analysis focuses on arbitrage costs
  involving
• PJM - New York
• PJM ECAR
• On April 1, 1998, the PJM exchange market began
  with only cost-based bidding permitted.
• However, no explicit mechanism existed for
  monitoring compliance with costs.
• PJM members were allowed to supply electricity at
  market-based rates outside of PJMs service
  territory (and through bilateral transactions
  within PJMs territory).

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Institutional Detail (cont.)

• After April 1, 1999, market-based bids were
  allowed within PJMs service territory.
• We use indicator variables to distinguish 3
  periods
• (i) before April 1998
• (ii) between April 1998 and March 1999
• (iii) April 1999 and after.

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Data

• Time period
• January 1997-July 2002
• --- 1350 observations
• Dependent variable
• daily electricity prices (PJM, NY, ECAR)
• --- volume-weighted averages of the contract
  prices
• for pre-scheduled, day-ahead 1x16
  electricity blocks
• (Power Markets Week)

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Data (cont.)

• Demand shifter
• temperatures (PJM, NY, ECAR)
• --- summer and winter degree days calculated
  from NOAA temperature data
• Cost shifter
• fuel costs
• --- Henry Hub gas prices

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The Results

• PJM New York

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Autarky Parameters PJM/NYISO(t-stats in
parentheses)
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Transaction Costs PJM/NYISO(t-stats in
parenthesis)
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Mean Transaction Costs PJM/NYISO(/MWh)
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Expected State Probabilities PJM/NYISO
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Conclusions PJM-NYISO

• Transaction costs fell to PJM from NY, subsequent
  to formation of PJM ISO.
• Transaction costs to NY from PJM rose by more
  than 2/MWh after PJM switched from cost-based to
  market-based bidding.
• Explanation (1) more inward focus by PJM
  suppliers after market-based bidding (2)
  differing ISO protocols, perhaps.
• Prevalence of quantity-constrained trade similar
  in each direction for PJM-NY, but results will be
  different for PJM-ECAR!

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The Results

• PJM ECAR

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Autarky Parameters PJM/ECAR(t-stats in
parentheses)
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Transaction Costs PJM/ECAR(t-stats in
parenthesis)
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Mean Transaction Costs PJM/ECAR(/MWh)
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Expected State Probabilities PJM/ECAR
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Conclusions PJM-ECAR

• Transaction costs to PJM from ECAR fell by nearly
  1/MWh after formation of PJM exchange market.
• Improved price discovery, perhaps.
• Transaction costs to PJM from ECAR rose by more
  than 2/MWh after PJM switched from cost-based to
  market-based bidding.

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Conclusions PJM-ECAR (cont.)

• High prevalence of quantity-constrained trade
  when ECAR has higher prices than PJM is striking,
  given apparent lack of binding physical
  transmission constraints moving from PJM into
  ECAR.
• Results suggest that significant efficiencies in
  transmission usage may arise from PJMs westward
  expansion and the formation of an effective MISO.

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The Value of Expanding Transmission Capability
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Estimating the Shadow Cost of Quantitative Trade
Constraints

• Little research has attempted how to estimate the
  efficiency losses imposed by existing quantity
  constraints on electricity flows.
• Estimating the shadow cost of quantity
  constraints in terms of their marginal
  contribution to inter-regional price differences
  represents a means of assessing the value that
  additional transfer capability (e.g.,
  transmission capacity) could provide.

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Estimating the Shadow Cost of Quantitative Trade
Constraints

• A two-stage process is used to estimate the
  shadow cost arising from quantity constraints
  on electricity flows.
• (1) We take the observed price difference on each
  day and subtract our estimated mean transaction
  cost, assuming constrained trading.
• Assuming quantity-constrained trade, an
  incremental increase in electricity flows from a
  lower-priced to a higher-priced region will
  reduce energy costs by the observed price
  difference, less the transaction cost.
• (2) The amount in (1) is multiplied by the
  estimated probability that the observed
  inter-regional price difference on that day
  is associated with quantity-constrained trade.

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Estimated Annual Shadow Cost of Quantity Trade
Constraints (/MW)

• Annual Shadow Cost (Total Shadow Cost)/5.33
  years.
• Total Shadow Cost S (Actual Daily Observed
  Price Difference - Estimated Mean Transaction
  Cost) (Probability That Observed State Is
  Quantity-Constrained Trade).

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Conclusions Value ofIncreased Transmission
Capability

• Additional transmission capability has
  substantial peak load value.
• Most of shadow value is derived from lessening
  price spikes in summer months.
• Highest shadow value of increased transmission
  capability is to ECAR from PJM (nearly 19,000
  per MW year), which may not be a physical
  transmission constraint but rather an
  institutional constraint.