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

RODERICK GO 1 , ANYA CASTILLO 2 , SONJA WOGRIN 3 , AND DENNICE GAYME 1 OPTIMAL PORTFOLIO INVESTMENT OF AN ENERGY STORAGE MERCHANT IN THE ENERGY IMBALANCE MARKET FERC WORKSHOP/TRANS-ATLANTIC INFRADAY, OCTOBER 30, 2015 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

PRESENTATION OUTLINE 1. Motivation 2. Model Formulations 3. Numerical Case Study and 
 Initial Results 4. Discussion and Future Work Nature (2010) 2

PROJECT MOTIVATION …But • Growing interest in energy storage to Energy Storage Management Energy Storage System Energy Storage System Power Electronics Vendors provide ancillary services to support System Vendors Vendors Developers renewables: Residential Segment • California: 1,300 MW storage mandate Non- • FERC Orders 755 and 784 for fast and Residential Segment accurate energy/power services • We focus on storage providing energy and power services in the energy imbalance Utility-Scale Segment market GTM Research (2010) 3

PROJECT MOTIVATION (CONT.) • Previous studies have demonstrated storage can suppress LMP differences on a network PEAK SHAVING and increase system welfare ENERGY ARBITRAGE • Profit-maximizing operators could withhold storage services to increase arbitrage value INVESTMENT DEFERRAL • Different storage technologies at different locations/scales can serve different purposes • Locational marginal prices (LMPs) provide RENEWABLE SMOOTHING price signals for investors 4

RESEARCH QUESTIONS • 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 one when siting, sizing, and allocating storage? • Does a profit-maximizing strategy negatively impact system welfare? 5

SINGLE LEVEL (CENTRAL SYSTEM OPERATOR) MODEL 2 # h 2 i 4X n p g n p g X X X X C s,inv C g, 1 n,t + C g, 2 n p w − C s j r d C w C ens p ens min ∆ t + j,n,t + n,t + + k j,n n n,t n,t j Ω g,t n,t n,t j,n,t j,n subject to 2 3 ⇣ ⌘ X X − p g • Modified power balance: 4 P d r c j,n,t − r d n,t − p w n,t − p ens 5 ≤ 0 0 : λ n,t ∆ t n,t + B k ( δ n,t − δ i,t ) + : j,n,t n,t k ( i,n ) j • Economic dispatch + DCOPF: • Storage constraints: ≤ ≤ 0 ≤ r c j,n,t ≤ R c j,n,t , β + − δ max ≤ δ n,t − δ i,t ≤ δ max ( n,i ) ,t , φ + : β − : φ − j j,n,t ( n,i ) ,t 0 ≤ r d j,n,t ≤ R d j,n,t , γ + : γ − k ( n,i ) ,t , ρ + − F max ≤ B k ( δ n,t − δ i,t ) ≤ F max : ρ − j j,n,t k k k ( n,i ) ,t ⇣ ⌘ η c j r c j,n,t − r d j,n,t / η d ≤ p g n,t , σ + P min n,t ≤ P max s j,n,t − 1 − s j,n,t + ∆ t = 0 : θ j,n,t : σ − j n n n,t n ≤ p g n,t − p g n,t , ϕ + j,n,t , µ + RR d n,t − 1 ≤ RR u 0 ≤ s j,n,t ≤ k j,n : µ − : ϕ − n n,t j,n,t n,t ≤ P w,max n,t , ζ + 0 ≤ p w s j,n,t =1 − s j,n,t = T = 0 : ζ − : υ j,n,t n,t n,t n,t = P w,max p w − − p w s j,n,T = 0 : κ n,t n,t n,t n,t , α + 0 ≤ p ens n,t ≤ ω ens P d : α − n n,t n,t 6

SINGLE LEVEL (CENTRAL SYSTEM OPERATOR) MODEL 2 # h 2 i 4X n p g n p g X X X X C s,inv C g, 1 n,t + C g, 2 n p w − C s j r d C w C ens p ens min ∆ t + j,n,t + n,t + + k j,n n n,t n,t j Ω g,t n,t n,t j,n,t j,n subject to 2 3 ⇣ ⌘ X X − p g • Modified power balance: 4 P d r c j,n,t − r d n,t − p w n,t − p ens 5 ≤ 0 0 : λ n,t ∆ t n,t + B k ( δ n,t − δ i,t ) + : j,n,t n,t k ( i,n ) j • Economic dispatch + DCOPF: • Storage constraints: ≤ ≤ 0 ≤ r c j,n,t ≤ R c j,n,t , β + − δ max ≤ δ n,t − δ i,t ≤ δ max ( n,i ) ,t , φ + : β − : φ − j j,n,t ( n,i ) ,t 0 ≤ r d j,n,t ≤ R d j,n,t , γ + : γ − k ( n,i ) ,t , ρ + − F max ≤ B k ( δ n,t − δ i,t ) ≤ F max : ρ − j j,n,t k k k ( n,i ) ,t ⇣ ⌘ η c j r c j,n,t − r d j,n,t / η d ≤ p g n,t , σ + P min n,t ≤ P max s j,n,t − 1 − s j,n,t + ∆ t = 0 : θ j,n,t : σ − j n n n,t n ≤ p g n,t − p g n,t , ϕ + j,n,t , µ + RR d n,t − 1 ≤ RR u 0 ≤ s j,n,t ≤ k j,n : µ − : ϕ − n n,t j,n,t n,t ≤ P w,max n,t , ζ + 0 ≤ p w s j,n,t =1 − s j,n,t = T = 0 : ζ − : υ j,n,t n,t n,t n,t = P w,max p w − − p w s j,n,T = 0 : κ n,t n,t n,t n,t , α + 0 ≤ p ens n,t ≤ ω ens P d : α − n n,t n,t 6

BILEVEL (STRATEGIC INVESTMENT) MODEL • Model investment and operations as Upper Level: sequential decisions Maximize profit from energy arbitrage 
 (minus variable O&M and capital costs) • Leader (upper level) can strategically h ⇣ ⌘ i X X r d j,n,t − r c − C s j r d C inv Ω U ∆ t k j,n λ n,t max site and size installations from portfolio j,n,t j,n,t − j j,n,t j,n of 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 7

BILEVEL (STRATEGIC INVESTMENT) MODEL • Model investment and operations as Upper Level: sequential decisions Maximize profit from energy arbitrage 
 (minus variable O&M and capital costs) • Leader (upper level) can strategically h ⇣ ⌘ i X X r d j,n,t − r c − C s j r d C inv Ω U ∆ t k j,n λ n,t max site and size installations from portfolio j,n,t j,n,t − j j,n,t j,n of ESS technologies s,inv k j,n • Follower (lower level) reacts in a Lower Level: 
 predictable manner, providing price Minimize system operational costs subject to 
 signals for investment decisions Modified power balance 
 Economic dispatch + DCOPF 
 • Storage units are price takers once Storage constraints installed on the network 7

BILEVEL (STRATEGIC INVESTMENT) MODEL • Model investment and operations as Upper Level: sequential decisions Maximize profit from energy arbitrage 
 (minus variable O&M and capital costs) • Leader (upper level) can strategically h ⇣ ⌘ i X X r d j,n,t − r c − C s j r d C inv Ω U ∆ t k j,n λ n,t max site and size installations from portfolio j,n,t j,n,t − j j,n,t j,n of ESS technologies ⇣ ⌘ s,inv k j,n r d − r c λ n,t j,n,t j,n,t ,t • Follower (lower level) reacts in a Lower Level: 
 predictable manner, providing price Minimize system operational costs subject to 
 signals for investment decisions Modified power balance 
 Economic dispatch + DCOPF 
 • Storage units are price takers once Storage constraints installed on the network 7

BILEVEL (STRATEGIC INVESTMENT) MODEL • Model investment and operations as Upper Level: sequential decisions Maximize profit from energy arbitrage 
 (minus variable O&M and capital costs) • Leader (upper level) can strategically h ⇣ ⌘ i X X r d j,n,t − r c − C s j r d C inv Ω U ∆ t k j,n λ n,t max site and size installations from portfolio j,n,t j,n,t − j j,n,t j,n of ESS technologies ⇣ ⌘ s,inv k j,n r d − r c λ n,t j,n,t j,n,t ,t • Follower (lower level) reacts in a Lower Level: 
 predictable manner, providing price Minimize system operational costs subject to 
 signals for investment decisions Modified power balance 
 Economic dispatch + DCOPF 
 • Storage units are price takers once Storage constraints installed on the network 7

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS 8

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS 1. Formulate bilevel model as MPEC using first- order, KKT conditions (NLP) 8

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS 1. Formulate bilevel model as MPEC using first- order, KKT conditions (NLP) Primal = Dual 2. Use strong duality condition , rather than h i X R c j,n,t + R d j β + j γ + j,n,t + k j,n µ + LHS = RHS ∗ − disjunctive ( bigM-type ) complementarity to j,n,t j,n,t reduce # of binaries when converting to MIP 8

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS 1. Formulate bilevel model as MPEC using first- order, KKT conditions (NLP) Primal = Dual 2. Use strong duality condition , rather than h i X R c j,n,t + R d j β + j γ + j,n,t + k j,n µ + LHS = RHS ∗ − disjunctive ( bigM-type ) complementarity to j,n,t j,n,t reduce # of binaries when converting to MIP n h i X k j,n = ∆ k 2 i b k j j,n,i a. Efficiently linearize bilinear term (k ! + ) in i =0 n strong duality condition using binary h i X k j,n µ + j,n,t = ∆ k 2 i z k j j,n,t,i expansion i =0 j,n,t,i ≤ M (1 − b k 0 ≤ µ + j,n,t − z + j,n,i ) 0 ≤ z + j,n,t,i ≤ Mb k j,n,i 8

OVERVIEW OF BILEVEL MODEL TRANSFORMATIONS 1. Formulate bilevel model as MPEC using first- order, KKT conditions (NLP) Primal = Dual 2. Use strong duality condition , rather than h i X R c j,n,t + R d j β + j γ + j,n,t + k j,n µ + LHS = RHS ∗ − disjunctive ( bigM-type ) complementarity to j,n,t j,n,t reduce # of binaries when converting to MIP n h i X k j,n = ∆ k 2 i b k j j,n,i a. Efficiently linearize bilinear term (k ! + ) in i =0 n strong duality condition using binary h i X k j,n µ + j,n,t = ∆ k 2 i z k j j,n,t,i expansion i =0 j,n,t,i ≤ M (1 − b k 0 ≤ µ + j,n,t − z + j,n,i ) 0 ≤ z + j,n,t,i ≤ Mb k 3. Assuming daily cycling , use strong duality j,n,i and complementarity to substitute bilinear h ⇣ ⌘i X r d j,n,t − r c = LHS − RHS ∗ ∆ t λ n,t terms ( " r c , " r d ) in bilevel objective j,n,t j,n,t 8