Coordinating storage and grid: efficient regulation in a multilevel - - PowerPoint PPT Presentation

Introduction Model Results Further research References Backup

Coordinating storage and grid: efficient regulation in a multilevel system with strategic actors

Roman Mendelevitch, Paul Neetzow

Humboldt-Universitaet zu Berlin roman.mendelevitch@hu-berlin.de

September 6, 2017

Introduction Model Results Further research References Backup

Overview

1

Introduction Motivation and reserach question

2

Model General model description Scenarios Description Solution strategies

3

Results DSO investment System costs DSO objective Illustration Comparing

4

Further research Further research References

5

Backup

Introduction Model Results Further research References Backup

Introduction

Figure: Projected feed-in and load driven distribution network stress from self-optimizing prosumage in Germany 2030 (case study, Seidl et al. (2017)).

“Transmission and distribution system must also be sized to handle peak power transfer requirements, even if only a fraction of that power transfer capacity is used during most of the year” (Dunn et al., 2011) Projected decentral storage capacity in Germany projected up to 9 GW, 18 GWh (Elsland et al., 2016) Storage may relief (Virasjoki et al., 2016; Denholm and Sioshansi, 2009; dena, 2012) or intensify (dena, 2012; Ecofys and Fraunhofer IWES, 2017) network stress

Introduction Model Results Further research References Backup

Research questions

What are the interactions of storage (prosumage) with different network levels? How can incentives be designed to induce efficient storage

• peration and balance conflicting objectives in a second best

world?

Introduction Model Results Further research References Backup

Gerneral model setup

D M Im G PV PRS_D

STOR

kWh

2 7 1 8 2 8

CAP_DSO

Players System Operator (Market + Generation) DSO, Prosumage, Demand, Import Prosumage Optimizes profit; consists of PV generation, storage and demand ISO balances supply and demand (M), dispatches conventional generation (G) DSO provides distribution capacities and invests in grid if necessary Import and Demand exogenous

Introduction Model Results Further research References Backup

Scenario overview

Different scenarios of integration between prosumage and DSO

No coordination case DSO has to provide sufficient capacities, cannot influence prosumage; similar to current policies Incentive / policy cases (α, β) DSO can somewhat influence prosumage behavior (setting constraints on feed-in or self-consumption) Minimum costs Total costs minimization (first best benchmark)

Introduction Model Results Further research References Backup

Maximum feed-in policy case (α)

D M Im G PRS_D

STOR

kWh

2 7 1 8 2 8

PV CAP_DSO t PV_GEN α⋅PV_GEN_PEAK

INCα

• Max. PV and STOR feed-in

P [MW]

DSO imposes maximum grid feed-in share of the maximum PV-generation PRS compensated to obey the constraint Two-level problem:

1

DSO decides on incentive payment under consideration of prosumage reaction and accompanied necessary grid investment

2

Prosumage realizes profit optimizing storage dispatch given DSO decision

Introduction Model Results Further research References Backup

Minimum self-consumption policy case (β)

D M Im G PV PRS_D

STOR

CAP_DSO

kWh

2 7 1 8 2 8

t P [MW] PV_GEN β⋅PV_GEN

INCβ

• Min. PV self-consumption
• Max. PV feed-in

DSO imposes minimum self-consumption (and curtailment) share of instantaneous PV-generation PRS compensated to obey the constraint Two-level problem as in α case

Introduction Model Results Further research References Backup

No coordination and minimum costs cases

No coordination case Prosumage acts solely market price oriented and does not consider associated DSO costs DSO has no possibility to interfere and has to provide sufficient grid capacities Can be achieved by fixing α = 1 or β = 0 in policy cases Minimum costs case Welfare perspective considering all occurring costs and trade-offs between them Simple one-level minimization

Introduction Model Results Further research References Backup

Solution strategy: mixed integer linear program

Problem resembles MPEC: mixed complementarity problem with equilibrium constraints First order KKT-conditions for lower level are computed and implemented as constraints to the upper level Disjunctive constraints are used to replace complementarity conditions Linearization of bi-linear DSO-objective using additional binary and auxiliary variables

β is discretized in 1 % steps

Global solution Implemented and solved in GAMS

Introduction Model Results Further research References Backup

Results: DSO investment

0,5 1 1,5 2 2,5 3 3,5

DSO_MC= 85 DSO_MC= 90 DSO_MC= 95 DSO_MC= 100 DSO_MC= 105 DSO_MC= 110 inv_DSO

NC beta alpha min_cost

Optimal investment achieved with α-policy (max. feed-in)

Introduction Model Results Further research References Backup

Results: System costs

0% 20% 40% 60% 80% 100%

DSO_MC= 85 DSO_MC= 90 DSO_MC= 95 DSO_MC= 100 DSO_MC= 105 DSO_MC= 110 System costs

NC beta alpha min_cost

At high DSO-costs α-policy reaches optimum, β-policy close to no-coordination

Introduction Model Results Further research References Backup

Results: DSO objective

0% 20% 40% 60% 80% 100%

DSO_MC= 85 DSO_MC= 90 DSO_MC= 95 DSO_MC= 100 DSO_MC= 105 DSO_MC= 110 Obj_DSO

NC beta alpha min_cost

Cost reductions for the DSO are small but significant for the system costs

Introduction Model Results Further research References Backup

Results: Comparing α and β cases

5.3 5.8

D D M Im G PV DPRS

STOR

CAP_DSO 1.53 2 1.2 0.8 34.7 42

p= p=

3.47 4.2 2 3

M Im G PV DPRS

STOR

CAP_DSO 1.7 4 5.3 3 2.8 3 3 47 42

p= p=

4.7 4.2 10 3 5

• 5

t1 t2

charge discharge 1.53 0.8 charge discharge 1.7 4 2.8

In α case pt2 ≥ pt1 In β case pt2 = pt1 Compensation is equal to pt2 − ηpt1

Introduction Model Results Further research References Backup

Three-level analysis

TSO line DSO line

• Conv. gen.

Demand Prosumage TSO DSO1 max

𝑗𝑜𝑤𝑈𝑇𝑃 𝑋

DSO2

GEN PRS1 GEN PRS2

𝑗𝑜𝑤2

𝐸𝑇𝑃

𝑗𝑜𝑑2

𝐸𝑇𝑃

I II III

D D

𝑗𝑜𝑤𝑈𝑇𝑃 ISO1 balance ISO2 balance 𝑗𝑜𝑤1

𝐸𝑇𝑃

𝑗𝑜𝑑1

𝐸𝑇𝑃

Integration of multiple DSO grids connected via transmission network Prosumage, demand and generation within each DSO grid Transmission system operator (TSO) aims on optimizing welfare by providing the right amount of network capacity DSOs only take own costs and region into consideration Computational: equilibrium problem with equilibrium constraints (EPEC)

Introduction Model Results Further research References Backup

Calibration for Germany

TSO line DSO grid

• Conv. gen.

Demand Prosumage

State-wise aggregation of demand, prosumage and generation Inter-state transmission capacities Approximated capacities of schematic DSO grids

Introduction Model Results Further research References Backup

Thank you for feedback and comments!

Contact: roman.mendelevitch@hu-berlin.de

We thank the Mathematical Optimization for Decisions Lab at Johns Hopkins University for valuable support as well as the DAAD for providing funding

Introduction Model Results Further research References Backup

References

dena (2012). dena-verteilnetzstudie ausbau-und innovationsbedarf der stromverteilnetze in deutschland bis 2030. Technical report, Deutsch Energie-Agentur. Denholm, P. and R. Sioshansi (2009). The value of compressed air energy storage with wind in transmission-constrained electric power systems. Energy Policy 37, 3149–3158. Dunn, B., H. Kamath, and J.-M. Tarascon (2011). Electrical energy storage for the grid: a battery of choices. Science 334(6058), 928–935. Ecofys and Fraunhofer IWES (2017). Smart-market-design in deutschen

• verteilnetzen. Technical report, Agora Energiewende.

Elsland, R., T. Bossmann, A.-L. Klingler, A. Herbst, M. Klobasa, and

• M. Wietschel (2016). Netzentwickulungsplan strom - entwicklung der

regionalen stromnachfrage und lastprofile. Technical report, Fraunhofer ISI. Seidl, H., S. Mischinger, M. Wolke, and E.-L. Limbacher (2017). dena-netzflexstudie: Optimierter einsatz von speichern f¨ ur netz- und marktanwendungen in der stromversorgung. Technical report, dena. Virasjoki, V., P. Rocha, A. S. Siddiqui, and A. Salo (2016). Market impacts of energy storage in a transmission-constrained power system. IEEE Transactions on Power Systems 31(5), 4108–4117.

Introduction Model Results Further research References Backup

Base case (cost minimizing)

Minimize overall costs while serving inelastic demand Social planner objective min

all variables obj SP = obj =

• nd,nt(DSO MC · inv DSOnd,nt) +

nt,t(G MCnt · gnt,t·gnt,t 2

)

s.t. ISO constraints DSO constraints PRS constraints

Introduction Model Results Further research References Backup

Lower level solution for ISO

ISO constraints: 0 ≥ gnt,t − G CAPnt ∀nt, t 0 =

nd(Dnd,t + f M2DPRSnd,t + f M2Snd,t − f PV2Mnd,t − f S2Mnd,t) −

IMPORTnt,t − gnt,t ∀nt, t ISO FOCs 0 ≥ pnt,t − gnt,t · G MC − lambda Gnt,t ∀nt, t ISO Disjs (for each inequality constraint or FOC) 0 ≥ −M1 G capacitynt,t · bi G capacitynt,t − (gnt,t − G CAPnt) 0 ≥ lambda Gnt,t − (1 − bi G capacitynt,t) · M2 G capacitynt,t 0 ≥ −M1 FOC ISO gnt,t ·bi FOC ISO gnt,t −(pnt,t −gnt,t ·G MC−lambda Gnt,t) 0 ≥ gnt,t − (1 − bi FOC ISO gnt,t) · M2 FOC ISO gnt,t

Equivalently done for prosumage

Introduction Model Results Further research References Backup

Linearizing bilinear DSO objective (upper level)

Creation of set be to ”loop” different β Discretizing β → BETAbe = {0, 0.1, ..., 1} Selection of BETAbe by help of set be and biniary variables bi betabe ∈ {0, 1} ∀be,

be bi betabe = 1

Chose bi betabe such that

be BETAbe · bi betabe ≈ β∗.

Former DSO objective must be evaluated for each BETAbe Therefore, we introduce a new constraint that resembles former DSO

• bjective and contains two auxiliary variables cost DSO B, dummy DSO

Introduction Model Results Further research References Backup

Linearizing bilinear DSO objective (upper level)

Auxiliary constraint for DSO objective 0 ≥ obj DSO + BETAbe · PV GENnd,t · lambda PRS beta − obj DSO Bbe − dummy DSObe ∀be New upper-level optimization min

inv DSO, bi betabe

• be obj DSO Bbe

s.t. {DSO constraints}, aux. constr., disj. constr. where

• bj DSO B ≈ obj DSO + compensation, if BETAbe ≈ β∗

dummy DSO allows satisfying the constraints for other BETAbe

Introduction Model Results Further research References Backup

Linearization: disjunctive formulation

Disjunctive properties:

• bj DSO Bbe
• = 0 if bi betabe = 0

free otherwise dummy DSObe

• = 0 if bi betabe = 1

≥ 0 otherwise Respective disjunctive equations:

• bj DSO Bbe ≤ bi betabe · M costs DSO
• bj DSO Bbe ≥ −bi betabe · M costs DSO

dummy DSObe ≤ (1 − bi betabe) · M costs DSO dummy DSObe ≥ 0

Introduction Model Results Further research References Backup

Two policy cases with shared DSO-PRS constraint

t P [MW] PV_GEN β⋅PV_GEN t PV_GEN α⋅PV_GEN_PEAK

INCβ INCα

• Min. PV self-consumption
• Max. PV feed-in
• Max. PV and STOR feed-in

DSO sets constraint towards PRS PRS compensated to obey the constraint Incentivend,t: PRS-DSO incentive constraint (dual: lambda PRS inc)

0 ≥ β · PV GENnd,t − f PV2Snd,t − f PV2DPRSnd,t − curtnd,t ∀nd, t 0 ≥ (1 − α) · PV GEN PEAKnd,t − (PV GEN PEAKnd,t − f S2Mnd,t − f PV2Mnd,t) ∀nd, t

Introduction Model Results Further research References Backup

Minimum self-consumption policy case (β)

D M Im G PV PRS_D

STOR

CAP_DSO

kWh

2 7 1 8 2 8

DSO imposes minimum self- consumption (and curtailment) share

• f

instantaneous PV- generation DSO objective

min

inv DSO, betaobj DSOnd+β · PV GENnd,t · lambda PRS beta

PRS objective

min

f A2B, curt, lolobj PRSnd−(f PV2Snd,t + f PV2DPRSnd,t + curtnd,t)·lambda PRS beta

Incentivend,t: PRS-DSO incentive constraint (dual: lambda PRS beta)

0 ≥ β · PV GENnd,t − f PV2Snd,t − f PV2DPRSnd,t − curtnd,t ∀nd, t

Introduction Model Results Further research References Backup

Maximum feed-in policy case (α)

D M Im G PRS_D

STOR

kWh

2 7 1 8 2 8

PV CAP_DSO

DSO imposes maximum grid feed-in share of the maximum PV-generation DSO objective

min

inv DSO, betaobj DSOnd+(1 − α) · PV GEN PEAKnd,t · lambda PRS alpha

PRS objective

min

f A2B, curt, lolobj PRSnd−(PV GEN PEAKnd,t − f S2Mnd,t − f PV2Mnd,t) · lambda PRS alpha

Incentivend,t: PRS-DSO incentive constraint (dual: lambda PRS alpha)

0 ≥ (1 − α) · PV GEN PEAKnd,t − (PV GEN PEAKnd,t − f S2Mnd,t − f PV2Mnd,t) ∀nd, t

Introduction Model Results Further research References Backup

Next steps: integration of third level

TSO DSO1 max

𝑗𝑜𝑤𝑈𝑇𝑃 𝑋

DSO2

GEN PRS1 GEN PRS2

𝑗𝑜𝑤2

𝐸𝑇𝑃

𝑗𝑜𝑑2

𝐸𝑇𝑃

I II III

D D

𝑗𝑜𝑤𝑈𝑇𝑃 ISO1 balance ISO2 balance

Background

TSO invests in transmission capacity to maximize welfare Transmission flows follow from price differential of TSO nodes and capacity constraints

p1,t − p2,t = λTSOcap

t

• t λTSOcap

t

= TSO MC

No player decides explicitly on flow No information flow between different DSO networks except resulting imports / exports

Introduction Model Results Further research References Backup

Next steps: integration of third level

TSO DSO1 max

𝑗𝑜𝑤𝑈𝑇𝑃 𝑋

DSO2

GEN PRS1 GEN PRS2

𝑗𝑜𝑤2

𝐸𝑇𝑃

𝑗𝑜𝑑2

𝐸𝑇𝑃

I II III

D D

𝑗𝑜𝑤𝑈𝑇𝑃 ISO1 balance ISO2 balance

Possible approach

1

Derive prices at TSO node for unconnected DSO grids

2

Compute TSO flows such that price differentials are converged

3

Derive new prices with exogenously given flows

4

Repeat to find equilibrium flow Caveats Practicability for multiple nodes, transmission lines and time periods? Computationally intensive Maybe no / multiple equilibria?