Yi-Hsu Chen The Johns Hopkins University, Baltimore, MD Fieke A.M. - - PowerPoint PPT Presentation

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Yi-Hsu Chen The Johns Hopkins University, Baltimore, MD Fieke A.M. - - PowerPoint PPT Presentation

Mar 01, 2023 142 likes •371 views

Applications of Complementarity Complementarity- -Based Models Based Models Applications of of Transmission- -Constrained Power Markets: Constrained Power Markets: of Transmission B- -NL Market Integration & NL Market Integration

slide-1
SLIDE 1

Yi-Hsu Chen

The Johns Hopkins University, Baltimore, MD

Fieke A.M. Rijkers

Dienst Uitvoering en Toezicht Energie (Dte), Den Haag, NL

Benjamin F. Hobbs

The Johns Hopkins University, Baltimore, MD California ISO Market Surveillance Committee, Folsom, CA “Hartilijk danke” to NSF, ECN, & FERC for support; Todd Munson, Sven Leyffer, & Adrian Wals for their collaboration

Applications of Applications of Complementarity Complementarity-

  • Based Models

Based Models

  • f Transmission
  • f Transmission-
  • Constrained Power Markets:

Constrained Power Markets: B B-

  • NL Market Integration &

NL Market Integration & Power Power-

  • NOx

NOx Market Interactions in PJM Market Interactions in PJM

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SLIDE 2

Specific Questions: Specific Questions:

  • What are the benefits of Belgian-Dutch power

market integration?

– Methodology: COMPETES (a LCP Cournot model of transmission-constrained markets) – Effect of inefficient transmission & arbitrage

  • What strategies might generators use to

exploit the interaction of electric power and NOx markets?

– Methodology: MPEC Stackelberg model of NOx and power markets (transmission constrained) – Demonstrates ability to solve large scale (~20,000 variable) MPECs

slide-3
SLIDE 3

Computational Approach: Computational Approach: Direct Solution of Equilibrium Conditions Direct Solution of Equilibrium Conditions

  • 1. Derive first-order conditions for each player
  • 2. Impose market clearing conditions
  • 3. Solve resulting system of conditions (complementarity problem)

using PATH PATH Choose Choose gen gen & & sales to sales to maximize profit maximize profit s.t. capacity s.t. capacity ⇒ ⇒ 1 1st

st order

  • rder

conditions conditions Producer A Producer A Market Clearing Conditions Market Clearing Conditions

ISO: Choose Transmission Flows to Max Value of Network ISO: Choose Transmission Flows to Max Value of Network

s.t. transmission constraints s.t. transmission constraints⇒ ⇒ 1 1st

st order conditions

  • rder conditions

Choose Choose gen gen & & sales to sales to maximize profit maximize profit s.t. capacity s.t. capacity ⇒ ⇒ 1 1st

st order

  • rder

conditions conditions Producer B Producer B Consumers: Max Value Consumers: Max Value -

  • Expenditures (Demand Curve)

Expenditures (Demand Curve)

slide-4
SLIDE 4

B B-

  • NL Analysis

NL Analysis COMPETES COMPETES Market Structure

Market Structure

  • Cournot generators compete in

bilateral market

  • Competitive arbitragers in some

markets

  • Two transmission pricing systems:

–Physical network

  • Linearized DC load flow
  • Several nodes per country

–Path-based representation

  • One node per country
  • ne market price per country
  • Interfaces defined between countries
  • Crediting for counterflows (netting vs. no-netting)

NL D F B

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SLIDE 5

COMPETES COMPETES

Inputs Inputs

  • Demand

– 12 periods → 3 seasons, 4 load periods – Allocated to the nodes

  • Generation

– 15 large power generating companies

  • 4 NL, 1 B, 2 F, 8 G

– Plus competitive fringe – 5272 generating units – MC based on heat rate and fuel type

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SLIDE 6

Congestion management B Congestion management B ↔ ↔ NL NL

Current Auction System Current Auction System

  • Yearly, monthly, daily
  • Available capacity for auction [www.tso-

auction.nl]

– B - NL: 1150 MW – Germany - NL: 2200 MW

  • Total import capacity to NL ≤ 400 MW

per party

  • Price set by lowest accepted bid
  • Daily auction takes place before APX

settles

slide-7
SLIDE 7

Congestion management B Congestion management B ↔ ↔ NL NL

Proposal for market integration Proposal for market integration

  • Single market

– One market price – TSO responsible for re-dispatch – Payments for constrained-off or -on

  • Market Coupling (Splitting)

– Similar to the NordPool – If Congestion: two separate market prices

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SLIDE 8

Effects of Market Coupling Effects of Market Coupling

Differences relative to current situation Differences relative to current situation

1) Increased market access into Belgium

– For (foreign) Generators and – For Traders → Introduce arbitrage

2) Netting of transmission capacity 3) Efficient co-ordination of ‘Auction’ and APX

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SLIDE 9

Effects of Market Coupling Effects of Market Coupling

Definition of scenarios Definition of scenarios

Import cap on firms Import cap on arbitrageurs Netting B NL NL B NL B

Electrabel

B NL NL B G ↔ NL Competitive No limit No limit No limit No limit No limit No limit Yes Current situation 400 950 200 No limit No C O U R N O T Market splitting None* None* None* No limit No limit No limit B ↔ NL

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SLIDE 10

18.9 18.9 14.3 14.3 28.0 28.0 29.1 29.1 9.1 1.1 10.2 4.6

Model results Model results

Competitive scenario Competitive scenario €/ €/MWh MWh

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SLIDE 11

Model results Model results

Current Situation vs. Competitive €/ Current Situation vs. Competitive €/MWh MWh

  • No netting

No netting

  • Arbitrage NL

Arbitrage NL↔ ↔G G

  • Belgium

Belgium ‘ ‘closed closed’ ’

  • Imports NL 400 MW

Imports NL 400 MW per party per party

22.5 22.5 (+3.6) (+3.6) 14.0 14.0 ( (-

  • .3)

.3) 33.5 33.5 (+5.5) (+5.5) 45.9 45.9 (+16.9) (+16.9) 10.9 22.3 7.9

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SLIDE 12

Model results Model results

Market Splitting vs. Current Situation €/ Market Splitting vs. Current Situation €/MWh MWh

  • Netting NL

Netting NL↔ ↔B B

  • Arbitrage NL

Arbitrage NL↔ ↔G G

  • Belgium open:

Belgium open: Arbitrage NL Arbitrage NL↔ ↔ B B 22.2 22.2 ( (-

  • .4)

.4) 14.1 14.1 (+.1) (+.1) 37.9 37.9 (+4.4) (+4.4) 37.4 37.4 ( (-

  • 8.5)

8.5) 1.0 16.1 0.4 14.7 7.5

slide-13
SLIDE 13

Welfare Compared to Perfect Competition Welfare Compared to Perfect Competition

  • 3500
  • 2500
  • 1500
  • 500

500 1500 2500 Current Situation Market Splitting Difference with competitive Million €/yr Consumer Surplus Generators profit Transmission revenue Welfare

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SLIDE 14

Effects of Market Coupling Effects of Market Coupling

  • Market Coupling affects prices, increases

welfare (+ 182 M€/yr more than current)

– Induced by lower prices in Belgium – Increased welfare is mainly in Belgium

  • What is “in it” for the Netherlands?

– Profits Dutch generators increase – But consumer surplus decreases more

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SLIDE 15

PJM Power Market PJM Power Market & USEPA & USEPA NO NOx

x Program Analysis

Program Analysis

Can the NOx market be profitably manipulated by a large generator who is long on allowances? PJM Market

– Peak Load 50,000 MW – Average Load-weighted Price - 30.7 $/MWh

USEPA NOx Program

– Cap-and-Trade – 9 states participated in 2000 – Total Allowances: 195,401 tons

PJM Transmission Zones

Source: www.pjm.com

PS PS PN PN PL PL BC BC PEP PEP DPL DPL AE AE JC JC PE PE ME ME

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SLIDE 16

Model Assumptions Model Assumptions

  • Market structure

– Generators compete to sign bilateral contracts – ISO provides transmission services between nodes

  • Network

– 500 kV network: 14 nodes, 18 arcs, no transmission losses – Linearized “DC” load flow approximation: Power Transfer Distribution Factors (PTDFs)

  • Producers

– 791 generation units – 6 largest producers (capacity share: 4% to 18%)

  • Largest is Stackelberg leader
  • Others:

– Cournot strategy in electricity market – Price taking in NOx market

– Remaining producers are price takers (3 producers)

  • Consumers

– Linear demand at each node – 5 demand periods in ozone season

  • ISO allocates transmission capacity to highest value
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SLIDE 17

1 2

A B

d1 P1 d2

NOx Market

Power Market

P2

Stackelberg Leader L L’s decisions XL: {Allowance bought qNOx,L Energy decisions gi,A,si,L} pNOx(XL) pi(XL) Wi(XL)

Stackelberg Stackelberg Analysis Analysis

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SLIDE 18
  • The firm with a longest position in NOx market and greatest

power sales is designated as the leader:

= Stackelberg’s NOx withholding variable [tons] = Firm’s available NOx allowances [tons]

Stackelberg Stackelberg Leader’s Problem Leader’s Problem

w

q

≠

− − + − − − −

∑ ∑

, ,

{[ ( [ ( ) ] [ ( )] ) ] }

W if i x x x f

if if i if i if ig i if s g q i g f NO NO w NO f f

p C g MAX p s s W E q W s g q

  • Other Producer Complementarity Equilibrium Conditions
  • Market Clearing Conditions

x

NO f

q

s.t.:

≤ ∀ = ≥ ∀ ≤ ≤

∑ ∑

,

, 0,

x

if if if if i i if if NO W f

g CAP i s g s g i q q ( )

x x x

NO NO NO w f f f

p E q q ≤ ⊥ − + ≤

∑

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SLIDE 19
  • ISO’s decision variables:

= transmission service from hub to i = generation purchases from node i (to make up losses) = positive flow from i to j

  • ISO’s maximizes the “value of services” :

– Solution allocates transmission capacity to most valuable transactions

  • Define the model’s KKTs (complementarity conditions), one per

variable xISO

ISO Optimization Problem ISO Optimization Problem Quadratic Loss Functions Quadratic Loss Functions

π

∈ ∈

= − − + − − ≤ ∀ − = ∀ ∈ = ≤ ≤ ∀ ≥ ∀

∑ ∑ ∑ ∑

( ) ( , ) ( )

( , , ) ( ) . .: ( (1 ) ) 0, ( ) 0, ,( , ) ( ) , , 0,

Losses Losses ISO ij i i i i i i i Losses i i ij ji ji ji j J i ij ij ji i j v k i i ij ij Losses i

MAX t y q W y p q s t y q t L t t i R t t k i j v k y t T i j q i Tij = capacity of line (i,j) Kirchhoff’s Current Law Kirchhoff’s Voltage Law

i

y

Losses i

q

ij

t Services Balance

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SLIDE 20

Model Statistics Model Statistics

  • 18,618 variables; 9739 constraints

– Order of magnitude larger than test problems in

  • R. Fletcher and S. Leyffer, “Numerical

Experience with Solving MPECs as NLPs,” Univ.

  • f Dundee, 2002
  • Solved by PATH and SQP (SNOPT, FILTER)

(Thanks to Todd Munson & Sven Leyffer!)

  • 9,536 seconds (1.8 MHz Pentium 4)

– Other MPECs took much less time

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SLIDE 21

Stackelberg Stackelberg Results Results

Compared to the Cournot Case:

  • Stackelberg leader:

– withholds 5,536 5,536 tons of allowances (7.2 7.2% of total) – … increasing NOx price from 0 to 1,173 [$/ton]

  • Output:

– other producers shrink their power sales sales (87.4 87.4→ →83.5 83.5 x106 MWh) due to increased NOx price – … while the leader expands its output (24.6 24.6→ →28.7 28.7 x106 MWh)

  • Profit:

– Stackelberg leader earns more profit (893 893 → → 970 970 M$) – … at the expense of other producers (2394 2394 → → 2273 2273 M$)

  • Consumers:

– are only marginally better off with a gain of 14 14 [M$] in consumer surplus, as power prices almost unchanged

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SLIDE 22

Conclusions Conclusions

  • Detailed market representations make possible:

– a variety of welfare and efficiency analyses, – insights on player strategies, – detailed distributions of impacts of policy

  • B-NL analysis shows how models can quantify

benefits of improving market efficiency

  • Large scale Stackelberg models can be solved

– Nonlinear (lossy) DC load flow – Leader maximizes subject to Cournot/fringe market equilibrium – Manipulating allowances market is profitable