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 Introduction 1 Motivation and reserach question Model 2 General model description Scenarios Description Solution strategies Results 3 DSO investment System costs DSO objective Illustration Comparing Further research 4 Further research References Backup 5
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 operation and balance conflicting objectives in a second best world?
Introduction Model Results Further research References Backup Gerneral model setup Players System Operator (Market + Generation) Im DSO, Prosumage, Demand, Import G Prosumage Optimizes profit; M consists of PV generation, storage and demand PV CAP_DSO ISO balances supply and demand kWh (M), dispatches conventional STOR 2 7 1 8 2 8 generation (G) D PRS_D 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 ) Im P [MW] G Max. PV and STOR feed-in M PV_GEN PV CAP_DSO α ⋅ PV_GEN_PEAK kWh STOR 2 7 1 8 2 8 D t PRS_D INC α DSO imposes maximum grid feed-in share of the maximum PV-generation PRS compensated to obey the constraint Two-level problem: DSO decides on incentive payment under consideration of prosumage 1 reaction and accompanied necessary grid investment Prosumage realizes profit optimizing storage dispatch given DSO decision 2
Introduction Model Results Further research References Backup Minimum self-consumption policy case ( β ) Im Min. PV self-consumption P [MW] G Max. PV feed-in M PV_GEN PV CAP_DSO kWh STOR β ⋅ PV_GEN 2 7 1 8 2 8 D t PRS_D INC β 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 3,5 3 2,5 2 1,5 1 0,5 0 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 100% 80% 60% 40% 20% 0% 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 100% 80% 60% 40% 20% 0% 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 0 -5 Im Im t 1 t 2 3.47 4.7 G G p= p= 34.7 47 4.2 4.2 0 M 0 M 0 0 0 p= 42 p= 42 5.3 0 3 0 10 PV PV 0 1.7 0 5.3 4 CAP_DSO CAP_DSO 1.53 0 5.8 0 3 2.8 0 3 STOR STOR 0 0 0 0 0 2 0 3 0 D D 0.8 3 0 5 D PRS D PRS 2 0 1.2 0 charge discharge charge discharge 0 1.53 1.7 0 0 0.8 4 2.8 In α case p t 2 ≥ p t 1 In β case p t 2 = p t 1 Compensation is equal to p t 2 − η p t 1
Introduction Model Results Further research References Backup Three-level analysis 𝑗𝑜𝑤 𝑈𝑇𝑃 𝑋 max TSO I 𝑗𝑜𝑤 𝑈𝑇𝑃 TSO line DSO 1 DSO 2 DSO line II 𝐸𝑇𝑃 𝐸𝑇𝑃 𝐸𝑇𝑃 𝐸𝑇𝑃 𝑗𝑜𝑤 1 𝑗𝑜𝑤 2 𝑗𝑜𝑑 2 𝑗𝑜𝑑 1 Conv. gen. ISO 1 balance ISO 2 balance PRS 1 D PRS 2 D Demand III Prosumage GEN GEN 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 State-wise aggregation of demand, prosumage and generation Inter-state transmission capacities TSO line DSO grid Approximated capacities of Conv. gen. schematic DSO grids Demand Prosumage
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 all variables obj SP = � obj = min g nt , t · g nt , t � nd , nt (DSO MC · inv DSO nd , nt ) + � nt , t (G MC nt · ) 2 s.t. ISO constraints DSO constraints PRS constraints
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