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

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## Abstract

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.

## Keywords

Energy storage system Offer curve Day-ahead market Virtual power plant## List of Symbols

## Indices and Index Sets

*t*Index of time

*k*Index of scenario

*T*Set of time index

*K*Set of scenario index

## Parameters

- \(\eta\)
Efficiency of an energy storage system (ESS)

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

- \(SOC_{min}\)
Minimum SOC(\(\text {kW}\))

*PR*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*(\(\text {KRW/kWh}\))- \(L_{t}\)
Load at time

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

*t*(\(\text {kW}\))

## Decision Variables

- \(PL_{t}\)
Power flow from PV to load at time

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

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

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

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

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

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

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

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

*t*(\(\text {kW}\))- \(EG_{t}^{NOT}\)
Power flow from ESS to grid not applying REC at time

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

*t*charged from PV (\(\text {kW}\))- \(SOC_{t}\)
SOC of ESS at time

*t*(\(\text {kW}\))- \(\varDelta E_{t}\)
Sum of charging and discharging amount at time

*t*(kW)- \(QC_{t}^{da}\)
Charging amount of ESS at time

*t*(\(\text {kW}\))- \(QD_{t}^{da}\)
Discharging amount of ESS at time

*t*(\(\text {kW}\))- \(u_{t}^{c}\)
Binary variables for charging at time

*t*- \(u_{t}^{d}\)
Binary variables for discharging at time

*t*

## Notes

### Acknowledgements

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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