Introduction Model Results Further research References Backup

Coordinating storage and grid: efficient regulationin 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

Overview1 Introduction

Motivation and reserach question2 Model

General model descriptionScenarios DescriptionSolution strategies

3 ResultsDSO investmentSystem costsDSO objectiveIllustrationComparing

4 Further researchFurther research

References5 Backup

Introduction Model Results Further research References Backup

Introduction

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

“Transmission and distribution system must also be sized to handle peakpower transfer requirements, even if only a fraction of that power transfercapacity 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) withdifferent network levels?

How can incentives be designed to induce efficient storageoperation and balance conflicting objectives in a second bestworld?

Introduction Model Results Further research References Backup

Gerneral model setup

D

M

Im

G

PV

PRS_D

STORkWh

2 7 1 8 2 8

CAP_DSO

Players

System Operator (Market + Generation)DSO, Prosumage, Demand, Import

Prosumage Optimizes profit;consists of PV generation, storageand demand

ISO balances supply and demand(M), dispatches conventionalgeneration (G)

DSO provides distributioncapacities and invests in grid ifnecessary

Import and Demand exogenous

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Scenario overview

Different scenarios of integration between prosumage and DSO

No coordination case

DSO has to provide sufficient capacities, cannot influence prosumage; similar tocurrent policies

Incentive / policy cases (α, β)

DSO can somewhat influence prosumage behavior (setting constraints onfeed-in or self-consumption)

Minimum costs

Total costs minimization (first best benchmark)

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Maximum feed-in policy case (α)

D

M

Im

G

PRS_D

STORkWh

2 7 1 8 2 8

PVCAP_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 prosumagereaction and accompanied necessary grid investment

2 Prosumage realizes profit optimizing storage dispatch given DSO decision

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Minimum self-consumption policy case (β)

D

M

Im

G

PV

PRS_D

STOR

CAP_DSOkWh

2 7 1 8 2 8

t

P [

MW

]

PV_GEN

β⋅PV_GEN

INCβ

Min. PV self-consumptionMax. PV feed-in

DSO imposes minimum self-consumption (and curtailment) share ofinstantaneous PV-generation

PRS compensated to obey the constraint

Two-level problem as in α case

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No coordination and minimum costs cases

No coordination case

Prosumage acts solely market price oriented and does notconsider associated DSO costs

DSO has no possibility to interfere and has to providesufficient grid capacities

Can be achieved by fixing α = 1 or β = 0 in policy cases

Minimum costs case

Welfare perspective considering all occurring costs andtrade-offs between them

Simple one-level minimization

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Solution strategy: mixed integer linear program

Problem resembles MPEC: mixed complementarity problemwith equilibrium constraints

First order KKT-conditions for lower level are computed andimplemented as constraints to the upper level

Disjunctive constraints are used to replace complementarityconditions

Linearization of bi-linear DSO-objective using additionalbinary and auxiliary variables

β is discretized in 1 % steps

Global solution

Implemented and solved in GAMS

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Results: DSO investment

0

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)

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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 tono-coordination

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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 thesystem costs

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Results: Comparing α and β cases

5.35.8

DD

M

Im

G

PV

DPRS

STOR

CAP_DSO00

00

1.530

00

21.2

00.8

00

34.7

42

p=

p=

3.47

4.2

0

2 3

0

M

Im

G

PV

DPRS

STOR

CAP_DSO1.74

5.33

02.8

00

00

00

33

47

42

p=

p=

4.7

4.2

10

3 5

-5

t1 t2

00

00

charge discharge

00

1.530.8

charge discharge

1.74

02.8

In α case pt2 ≥ pt1In β case pt2 = pt1Compensation is equal to pt2 − ηpt1

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Three-level analysis

TSO line

DSO line

Conv. gen.

Demand

Prosumage

TSO

DSO1

max𝑖𝑛𝑣𝑇𝑆𝑂

𝑊

DSO2

GEN

PRS1

GEN

PRS2

𝑖𝑛𝑣2𝐷𝑆𝑂 𝑖𝑛𝑐2

𝐷𝑆𝑂

I

II

III

DD

𝑖𝑛𝑣𝑇𝑆𝑂

ISO1

balan

ce

ISO

2b

alan

ce

𝑖𝑛𝑣1𝐷𝑆𝑂

𝑖𝑛𝑐1𝐷𝑆𝑂

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 byproviding the right amount of network capacity

DSOs only take own costs and region into consideration

Computational: equilibrium problem with equilibrium constraints (EPEC)

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Calibration for Germany

TSO line

DSO grid

Conv. gen.

Demand

Prosumage

State-wise aggregation ofdemand, prosumage andgeneration

Inter-state transmissioncapacities

Approximated capacities ofschematic DSO grids

Introduction Model Results Further research References Backup

Thank you for feedback andcomments!Contact: roman.mendelevitch@hu-berlin.de

We thank the Mathematical Optimization for Decisions Lab at Johns HopkinsUniversity 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 derstromverteilnetze in deutschland bis 2030. Technical report, DeutschEnergie-Agentur.

Denholm, P. and R. Sioshansi (2009). The value of compressed air energystorage 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 forthe grid: a battery of choices. Science 334(6058), 928–935.

Ecofys and Fraunhofer IWES (2017). Smart-market-design in deutschenverteilnetzen. Technical report, Agora Energiewende.

Elsland, R., T. Bossmann, A.-L. Klingler, A. Herbst, M. Klobasa, andM. Wietschel (2016). Netzentwickulungsplan strom - entwicklung derregionalen stromnachfrage und lastprofile. Technical report, Fraunhofer ISI.

Seidl, H., S. Mischinger, M. Wolke, and E.-L. Limbacher (2017).dena-netzflexstudie: Optimierter einsatz von speichern fur netz- undmarktanwendungen in der stromversorgung. Technical report, dena.

Virasjoki, V., P. Rocha, A. S. Siddiqui, and A. Salo (2016). Market impacts ofenergy storage in a transmission-constrained power system. IEEETransactions 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

minall variables

obj SP =∑

obj =∑nd ,nt(DSO MC · inv DSOnd ,nt) +

∑nt,t(G MCnt ·

gnt,t ·gnt,t2 )

s.t.

ISO constraints

DSO constraints

PRS constraints

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Lower level solution for ISO

ISO constraints:0 ≥ gnt,t − G CAPnt ∀nt, t0 =

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

IMPORTnt,t − gnt,t ∀nt, t

ISO FOCs0 ≥ 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

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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 variablesbi 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 DSOobjective and contains two auxiliary variables cost DSO B, dummy DSO

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Linearizing bilinear DSO objective (upper level)

Auxiliary constraint for DSO objective0 ≥ obj DSO + BETAbe · PV GENnd,t · lambda PRS beta− obj DSO Bbe −dummy DSObe ∀be

New upper-level optimization

mininv DSO, bi betabe

∑be obj DSO Bbe

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

whereobj DSO B ≈ obj DSO + compensation, if BETAbe ≈ β∗

dummy DSO allows satisfying the constraints for other BETAbe

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Linearization: disjunctive formulation

Disjunctive properties:

obj DSO Bbe

{= 0 if bi betabe = 0

free otherwise

dummy DSObe

{= 0 if bi betabe = 1

≥ 0 otherwise

Respective disjunctive equations:

obj DSO Bbe ≤ bi betabe · M costs DSO

obj DSO Bbe ≥ −bi betabe · M costs DSO

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

dummy DSObe ≥ 0

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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

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Minimum self-consumption policy case (β)

D

M

Im

G

PV

PRS_D

STOR

CAP_DSOkWh

2 7 1 8 2 8

DSO imposes minimum self-consumption (and curtailment)share of instantaneous PV-generation

DSO objective

mininv DSO, beta

obj DSOnd+β · PV GENnd,t · lambda PRS beta

PRS objective

minf A2B, curt, lol

obj 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

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Maximum feed-in policy case (α)

D

M

Im

G

PRS_D

STORkWh

2 7 1 8 2 8

PVCAP_DSO

DSO imposes maximum gridfeed-in share of the maximumPV-generation

DSO objective

mininv DSO, beta

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

PRS objective

minf A2B, curt, lol

obj 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

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Next steps: integration of third level

TSO

DSO1

max𝑖𝑛𝑣𝑇𝑆𝑂

𝑊

DSO2

GEN

PRS1

GEN

PRS2

𝑖𝑛𝑣2𝐷𝑆𝑂 𝑖𝑛𝑐2

𝐷𝑆𝑂

I

II

III

DD

𝑖𝑛𝑣𝑇𝑆𝑂

ISO1balan

ce

ISO2balance

Background

TSO invests in transmission capacityto maximize welfare

Transmission flows follow from price

differential of TSO nodes and

capacity constraints

p1,t − p2,t = λTSOcap

t∑t λ

TSOcap

t = TSO MC

No player decides explicitly on flow

No information flow between differentDSO networks except resultingimports / exports

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Next steps: integration of third level

TSO

DSO1

max𝑖𝑛𝑣𝑇𝑆𝑂

𝑊

DSO2

GEN

PRS1

GEN

PRS2

𝑖𝑛𝑣2𝐷𝑆𝑂 𝑖𝑛𝑐2

𝐷𝑆𝑂

I

II

III

DD

𝑖𝑛𝑣𝑇𝑆𝑂

ISO1balan

ce

ISO2balance

Possible approach

1 Derive prices at TSO node forunconnected DSO grids

2 Compute TSO flows such that pricedifferentials are converged

3 Derive new prices with exogenouslygiven flows

4 Repeat to find equilibrium flow

Caveats

Practicability for multiple nodes,transmission lines and time periods?

Computationally intensive

Maybe no / multiple equilibria?