OPTIMAL PORTFOLIO INVESTMENT OF AN ENERGY STORAGE MERCHANT IN THE - - PowerPoint PPT Presentation

SLIDE 1

OPTIMAL PORTFOLIO INVESTMENT OF AN ENERGY STORAGE MERCHANT IN THE ENERGY IMBALANCE MARKET

RODERICK GO1, ANYA CASTILLO 2, SONJA WOGRIN3, AND DENNICE GAYME 1

1 Johns Hopkins University, Baltimore, MD, USA 2 Johns Hopkins University, Baltimore, MD, USA, and Federal Energy Regulatory Commission, Washington, DC, USA 3 Universidad Pontificia Comillas, Madrid, Spain

FERC WORKSHOP/TRANS-ATLANTIC INFRADAY, OCTOBER 30, 2015

SLIDE 2

PRESENTATION OUTLINE

2

• 1. Motivation
• 2. Model Formulations
• 3. Numerical Case Study and 


Initial Results

• 4. Discussion and Future Work

Nature (2010)

SLIDE 3

…But

Power Electronics Vendors Energy Storage System Vendors Energy Storage System Developers

Residential Segment Non- Residential Segment Utility-Scale Segment

Energy Storage Management System Vendors

GTM Research (2010)

PROJECT MOTIVATION

3

• Growing interest in energy storage to

provide ancillary services to support renewables:

• California: 1,300 MW storage mandate
• FERC Orders 755 and 784 for fast and

accurate energy/power services

• We focus on storage providing energy and

power services in the energy imbalance market

SLIDE 4

RENEWABLE SMOOTHING PEAK SHAVING ENERGY ARBITRAGE

PROJECT MOTIVATION (CONT.)

4

• Previous studies have demonstrated storage

can suppress LMP differences on a network and increase system welfare

• Profit-maximizing operators could

withhold storage services to increase arbitrage value

• Different storage technologies at different

locations/scales can serve different purposes

• Locational marginal prices (LMPs) provide

price signals for investors

INVESTMENT DEFERRAL

SLIDE 5

RESEARCH QUESTIONS

5

• Can a merchant energy storage investor act

strategically to recover costs and increase profit through energy arbitrage?

• Does a strategic, merchant investor make

different investments than a cost-minimizing

• ne when siting, sizing, and allocating

storage?

• Does a profit-maximizing strategy negatively

impact system welfare?

?

SLIDE 6

• Modified power balance:
• Economic dispatch + DCOPF:
• Storage constraints:

SINGLE LEVEL (CENTRAL SYSTEM OPERATOR) MODEL

6

min

Ω

∆t 2 4X

g,t

h Cg,1

n pg n,t + Cg,2 n pg n,t 2i

+ X

j,n,t

Cs

j rd j,n,t +

X

n,t

Cw

n pw− n,t +

X

n,t

Cens

n

pens

n,t

# + X

j,n

Cs,inv

j

kj,n subject to

: φ−

(n,i),t, φ+ (n,i),t

: ρ−

k(n,i),t, ρ+ k(n,i),t

: σ−

n,t, σ+ n,t

: ϕ−

n,t, ϕ+ n,t

: ζ−

n,t, ζ+ n,t

: κn,t : α−

n,t, α+ n,t

− δmax ≤ δn,t − δi,t ≤ δmax − F max

k

≤ Bk (δn,t − δi,t) ≤ F max

k

P min

n

≤ pg

n,t ≤ P max n

RRd

n ≤ pg n,t − pg n,t−1 ≤ RRu n

0 ≤ pw

n,t ≤ P w,max n,t

pw−

n,t = P w,max n,t

− pw

n,t

0 ≤ pens

n,t ≤ ωens n

P d

n,t

: β−

j,n,t, β+ j,n,t

: γ−

j,n,t, γ+ j,n,t

: θj,n,t : µ−

j,n,t, µ+ j,n,t

: υj,n,t ≤ ≤ 0 ≤ rc

j,n,t ≤ Rc j

0 ≤ rd

j,n,t ≤ Rd j

sj,n,t−1 − sj,n,t + ∆t ⇣ ηc

jrc j,n,t − rd j,n,t/ηd j

⌘ = 0

0 ≤ sj,n,t ≤ kj,n sj,n,t=1 − sj,n,t=T = 0 sj,n,T = 0 : λn,t

∆t 2 4P d

n,t +

X

k(i,n)

Bk (δn,t − δi,t) + X

j

⇣ rc

j,n,t − rd j,n,t

⌘ − pg

n,t − pw n,t − pens n,t

3 5 ≤ 0 :

SLIDE 7

• Modified power balance:
• Economic dispatch + DCOPF:
• Storage constraints:

SINGLE LEVEL (CENTRAL SYSTEM OPERATOR) MODEL

6

min

Ω

∆t 2 4X

g,t

h Cg,1

n pg n,t + Cg,2 n pg n,t 2i

+ X

j,n,t

Cs

j rd j,n,t +

X

n,t

Cw

n pw− n,t +

X

n,t

Cens

n

pens

n,t

# + X

j,n

Cs,inv

j

kj,n subject to

: φ−

(n,i),t, φ+ (n,i),t

: ρ−

k(n,i),t, ρ+ k(n,i),t

: σ−

n,t, σ+ n,t

: ϕ−

n,t, ϕ+ n,t

: ζ−

n,t, ζ+ n,t

: κn,t : α−

n,t, α+ n,t

− δmax ≤ δn,t − δi,t ≤ δmax − F max

k

≤ Bk (δn,t − δi,t) ≤ F max

k

P min

n

≤ pg

n,t ≤ P max n

RRd

n ≤ pg n,t − pg n,t−1 ≤ RRu n

0 ≤ pw

n,t ≤ P w,max n,t

pw−

n,t = P w,max n,t

− pw

n,t

0 ≤ pens

n,t ≤ ωens n

P d

n,t

: β−

j,n,t, β+ j,n,t

: γ−

j,n,t, γ+ j,n,t

: θj,n,t : µ−

j,n,t, µ+ j,n,t

: υj,n,t ≤ ≤ 0 ≤ rc

j,n,t ≤ Rc j

0 ≤ rd

j,n,t ≤ Rd j

sj,n,t−1 − sj,n,t + ∆t ⇣ ηc

jrc j,n,t − rd j,n,t/ηd j

⌘ = 0

0 ≤ sj,n,t ≤ kj,n sj,n,t=1 − sj,n,t=T = 0 sj,n,T = 0 : λn,t

∆t 2 4P d

n,t +

X

k(i,n)

Bk (δn,t − δi,t) + X

j

⇣ rc

j,n,t − rd j,n,t

⌘ − pg

n,t − pw n,t − pens n,t

3 5 ≤ 0 :

SLIDE 8

Upper Level: Maximize profit from energy arbitrage
 (minus variable O&M and capital costs)

BILEVEL (STRATEGIC INVESTMENT) MODEL

7

• Model investment and operations as

sequential decisions

• Leader (upper level) can strategically

site and size installations from portfolio

• f ESS technologies
• Follower (lower level) reacts in a

predictable manner, providing price signals for investment decisions

• Storage units are price takers once

installed on the network

max

ΩU ∆t

X

j,n,t

h λn,t ⇣ rd

j,n,t − rc j,n,t

⌘ − Cs

j rd j,n,t

i − X

j,n

Cinv

j

kj,n

SLIDE 9

Upper Level: Maximize profit from energy arbitrage
 (minus variable O&M and capital costs)

BILEVEL (STRATEGIC INVESTMENT) MODEL

7

• Model investment and operations as

sequential decisions

• Leader (upper level) can strategically

site and size installations from portfolio

• f ESS technologies
• Follower (lower level) reacts in a

predictable manner, providing price signals for investment decisions

• Storage units are price takers once

installed on the network

Lower Level:
 Minimize system operational costs subject to
 Modified power balance
 Economic dispatch + DCOPF
 Storage constraints

s,invkj,n

max

ΩU ∆t

X

j,n,t

h λn,t ⇣ rd

j,n,t − rc j,n,t

⌘ − Cs

j rd j,n,t

i − X

j,n

Cinv

j

kj,n

SLIDE 10

Upper Level: Maximize profit from energy arbitrage
 (minus variable O&M and capital costs)

BILEVEL (STRATEGIC INVESTMENT) MODEL

7

• Model investment and operations as

sequential decisions

• Leader (upper level) can strategically

site and size installations from portfolio

• f ESS technologies
• Follower (lower level) reacts in a

predictable manner, providing price signals for investment decisions

• Storage units are price takers once

installed on the network

Lower Level:
 Minimize system operational costs subject to
 Modified power balance
 Economic dispatch + DCOPF
 Storage constraints

s,invkj,n

max

ΩU ∆t

X

j,n,t

h λn,t ⇣ rd

j,n,t − rc j,n,t

⌘ − Cs

j rd j,n,t

i − X

j,n

Cinv

j

kj,n

,t

λn,t ⇣ rd

j,n,t

− rc

j,n,t

⌘

SLIDE 11

Upper Level: Maximize profit from energy arbitrage
 (minus variable O&M and capital costs)

BILEVEL (STRATEGIC INVESTMENT) MODEL

7

• Model investment and operations as

sequential decisions

• Leader (upper level) can strategically

site and size installations from portfolio

• f ESS technologies
• Follower (lower level) reacts in a

predictable manner, providing price signals for investment decisions

• Storage units are price takers once

installed on the network

Lower Level:
 Minimize system operational costs subject to
 Modified power balance
 Economic dispatch + DCOPF
 Storage constraints

s,invkj,n

max

ΩU ∆t

X

j,n,t

h λn,t ⇣ rd

j,n,t − rc j,n,t

⌘ − Cs

j rd j,n,t

i − X

j,n

Cinv

j

kj,n

,t

λn,t ⇣ rd

j,n,t

− rc

j,n,t

⌘

SLIDE 12

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS

8

SLIDE 13

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS

8

• 1. Formulate bilevel model as MPEC using first-
• rder, KKT conditions (NLP)

SLIDE 14

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS

8

• 1. Formulate bilevel model as MPEC using first-
• rder, KKT conditions (NLP)
• 2. Use strong duality condition, rather than

disjunctive (bigM-type) complementarity to reduce # of binaries when converting to MIP

Primal = Dual LHS = RHS∗ − X

j,n,t

h Rc

jβ+ j,n,t + Rd jγ+ j,n,t + kj,nµ+ j,n,t

i

SLIDE 15

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS

8

• 1. Formulate bilevel model as MPEC using first-
• rder, KKT conditions (NLP)
• 2. Use strong duality condition, rather than

disjunctive (bigM-type) complementarity to reduce # of binaries when converting to MIP

• a. Efficiently linearize bilinear term (k!+) in

strong duality condition using binary expansion

kj,n = ∆k

j n

X

i=0

h 2ibk

j,n,i

i kj,nµ+

j,n,t = ∆k j n

X

i=0

h 2izk

j,n,t,i

i 0 ≤ µ+

j,n,t − z+ j,n,t,i ≤ M(1 − bk j,n,i)

0 ≤ z+

j,n,t,i ≤ Mbk j,n,i

Primal = Dual LHS = RHS∗ − X

j,n,t

h Rc

jβ+ j,n,t + Rd jγ+ j,n,t + kj,nµ+ j,n,t

i

SLIDE 16

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS

8

• 1. Formulate bilevel model as MPEC using first-
• rder, KKT conditions (NLP)
• 2. Use strong duality condition, rather than

disjunctive (bigM-type) complementarity to reduce # of binaries when converting to MIP

• a. Efficiently linearize bilinear term (k!+) in

strong duality condition using binary expansion

• 3. Assuming daily cycling, use strong duality

and complementarity to substitute bilinear terms ("rc, "rd) in bilevel objective

kj,n = ∆k

j n

X

i=0

h 2ibk

j,n,i

i kj,nµ+

j,n,t = ∆k j n

X

i=0

h 2izk

j,n,t,i

i 0 ≤ µ+

j,n,t − z+ j,n,t,i ≤ M(1 − bk j,n,i)

0 ≤ z+

j,n,t,i ≤ Mbk j,n,i

Primal = Dual LHS = RHS∗ − X

j,n,t

h Rc

jβ+ j,n,t + Rd jγ+ j,n,t + kj,nµ+ j,n,t

i ∆t X

j,n,t

h λn,t ⇣ rd

j,n,t − rc j,n,t

⌘i = LHS − RHS∗

SLIDE 17

IEEE 14-BUS TEST CASE

9

• 5-minute demand/generation data for 1 day
• f operations
• Wind available at 5 buses (blue), co-located

with thermal generators

• Simulate congestion by tightening thermal

line limits near nodes of largest thermal generator (n1) and highest demand (n3)

SLIDE 18

DEMAND AND WIND PROFILES

10

5 10 15 20 25 Time [hr] 50 100 150 200 250 300 Demand [MW]

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14

6 12 18 24 Time [hr] 20 40 60 80 100 Wind Production [MW]

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14

SLIDE 19

6 12 18 24 Time [hr] 100 200 300 400 Wind Production [MW]

6 12 18 24 Time [hr] 200 400 600 800 Demand [MW]

DEMAND AND WIND PROFILES

10

SLIDE 20

ENERGY STORAGE TECHNOLOGY PARAMETERS

11

Efficiency 
 [%] Energy Capacity 
 [MWh/unit] Power Rating 
 [MW/unit] Capital Cost 
 [$/unit-day] Discharge Cost
 [$/MWh] PSH 80% 224 28 $2890 $4 CAES 70% 25 5 $395 $3 VRB 77% 5 1 $292 $1 LIION 90% 1 1 $164 $7 FES 90% 0.5 2 $149 $1

SLIDE 21

BASE CASE RESULTS (SYSTEM COSTS AND STORAGE PROFIT)

12

Investment Cost [thousand $/day] Operational Cost [thousand $/day] Storage Profit [thousand $/day] Competitive $3.3 $364.0 $104.6 Strategic $2.2 $402.6 $441.5 Δ%

• 32.1%

8.5% 322%

SLIDE 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Nodes 50 100 150 200 250 Storage Capacity [MWh]

PSH CAES LIION FES VRB

NUMERICAL CASE RESULTS (INVESTMENTS)

13

COMPETITIVE MODEL BILEVEL MODEL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Nodes 50 100 150 200 250

PSH CAES LIION FES VRB

SLIDE 23

6 12 18 24 Time [hr] 500 1000 1500 LMPs [$/MWh]

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14

NUMERICAL CASE RESULTS (LMPs)

14

COMPETITIVE MODEL BILEVEL MODEL

6 12 18 24 Time [hr] 500 1000 1500 $

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14

SLIDE 24

ILLUSTRATION OF ENERGY v. POWER SERVICES

15

6 12 18 24 Time [hr] −5 5 Net Charging Rate [MW]

ENERGY SERVICES POWER SERVICES

6 12 18 24 Time [hr] −5 5

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14

6 12 18 24 Time [hr] −5 5

CAES VRB LIION

SLIDE 25

SECONDARY CASE (COMPETITIVE PRICE SUPPRESSION)

16

COMPETITIVE MODEL BILEVEL MODEL

SLIDE 26

TERTIARY CASE (BILEVEL ARBITRAGE VALUE)

6 12 18 24 Time [hr] 500 1000 1500 LMPs [$/MWh] 6 12 18 24 Time [hr] −20 20 Net Charging Rate [MW]

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14

SLIDE 27

DISCUSSION

18

Economic

• In most cases, merchant investor invests in a

smaller, more profitable portfolio than central operator.

• While merchant does not have ability to

directly withhold storage services during

• perations, strategic siting can favorably

influence LMPs, increasing the value of energy arbitrage.

• Installed storage units provide both energy

and power services to network. Algorithmic

• Demonstrated behavior of profit-maximizing

storage merchant using a bilevel program.

• Linearization of the k!+ bilinear term leads to

a weak relaxation of the MIP .

• Storage constraints, especially roundtrip

inefficiency ratings, impose significant computational burden.

SLIDE 28

FUTURE WORK

19

• Develop efficient solution algorithms, such as

implementing Bender’s decomposition

• Test on larger test network to better

understand effect of scale in storage allocation decisions.

• Test with more granular timescale (1-min)

to capture power services of high power/ energy ratio techs (e.g. LIION, FES)

• Incorporate coordinated scheduling (strategic

storage operations).

Nature (2010)

SLIDE 29

REFERENCES

20

• A. Castillo and D. F. Gayme, “Grid-scale energy storage applications in renewable energy

integration: A survey,” Energy Conversion and Management, vol. 87, pp. 885 – 894, 2014.

• R. Sioshansi, P

. Denholm, T. Jenkin, and J. Weiss, “Estimating the value of electricity storage in PJM: Arbitrage and some welfare effects,” Energy, vol. 31, pp. 269–277, 2009.

• S.Wogrin and D.F. Gayme. “Optimizing storage siting, sizing, and technology portfolios in

transmission-constrained networks,” IEEE Trans. on Power Syst., vol. PP , no. 99, pp. 1–10, 2014.

• V. Viswanathan, M. Kintner-Meyer, P

. Balducci, C. Jin, National Assessment of Energy Storage for Grid Balancing and Arbitrage, Phase II, Volume 2: Cost and Performance Characterization, Tech. Rep. PNNL-21388, Pacific Northwest National Laboratory (September 2013).

SLIDE 30

QUESTIONS?

21

THANK YOU FOR YOUR ATTENTION