Journal of Electrical Engineering & Technology

, Volume 14, Issue 6, pp 2277–2287 | Cite as

Offer Curve Generation for the Energy Storage System as a Member of the Virtual Power Plant in the Day-Ahead Market

  • Sooyeon Kim
  • Wook-Hyun Kwon
  • Hyeon-Jin Kim
  • Kyemyung Jung
  • Gi Soo Kim
  • Taehyoung Shim
  • Duehee LeeEmail author
Original Article


We build an offer curve for an energy storage system (ESS), which is a member of the virtual power plant (VPP) with photovoltaic (PV) modules and load. The offer curve should be built based on the optimal VPP operations while having many pairs of bidding prices and amounts in order to respond to unknown prices. Therefore, we propose the VPP operation strategy and predict the scenarios of DA electricity prices, PV outputs, and load separately by using three autoregressive models. Then, we build the offer curve for the ESS at each hour for 24 h by considering optimal VPP operations and three predicted scenarios. Finally, we verify the optimality of the VPP operation strategy by comparing it to a fixed-time strategy. We also compare the profit of our ESS offer curve to that resulting from a single offer.


Energy storage system Offer curve Day-ahead market Virtual power plant 

List of Symbols

Indices and Index Sets


Index of time


Index of scenario


Set of time index


Set of scenario index



Efficiency of an energy storage system (ESS)


Maximum state of charge (SOC) (\(\text {kW}\))


Minimum SOC(\(\text {kW}\))


Power rating of ESS (\(\text {kW}\))

\(\pi _{t}\)

Day-ahead (DA) price at time t (\(\text {KRW/kWh}\))

\(\pi _{t}^{REC}\)

DA price applying REC at time t (\(\text {KRW/kWh}\))


Load at time t (\(\text {kW}\))


Photovoltaic (PV) output at time t (\(\text {kW}\))

Decision Variables


Power flow from PV to load at time t (\(\text {kW}\))


Power flow from PV to grid at time t (\(\text {kW}\))


Power flow from PV to ESS at time t (\(\text {kW}\))


Power flow from PV to ESS can be applied REC at time t (\(\text {kW}\))


Power flow from PV to ESS can not be applied REC at time t (\(\text {kW}\))


Power flow from Grid to load at time t (\(\text {kW}\))


Power flow from Grid to ESS at time t (\(\text {kW}\))


Power flow from ESS to load at time t (\(\text {kW}\))


Power flow from ESS to grid at time t (\(\text {kW}\))


Power flow from ESS to grid not applying REC at time t charged from PV (\(\text {kW}\))


Power flow from ESS to grid applying REC at time t charged from PV (\(\text {kW}\))


SOC of ESS at time t (\(\text {kW}\))

\(\varDelta E_{t}\)

Sum of charging and discharging amount at time t (kW)


Charging amount of ESS at time t (\(\text {kW}\))


Discharging amount of ESS at time t (\(\text {kW}\))


Binary variables for charging at time t


Binary variables for discharging at time t



This work was supported by the National Research Foundation of Korea (NRF) (No. NRF-2017M1A2A2092209). This research was supported by Korea Electric Power Corporation (No. R18xa06-24).


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Copyright information

© The Korean Institute of Electrical Engineers 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringKonkuk UniversitySeoulKorea
  2. 2.Jubix Co., Ltd.SuwonKorea
  3. 3.Seondo Electric Co., Ltd.AnsanKorea
  4. 4.Electronics and Telecommunications Research Institute (ETRI)DaejeonKorea

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