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Risk-Based Electrical-Thermal Scheduling of a Large-Scale Virtual Power Plant Using Downside Risk Constraints for Participating in Energy and Reserve Markets

  • Research Article-Electrical Engineering
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Abstract

In this paper, risk-based energy management for a virtual power plant (VPP) participation in reserve and energy markets is presented. The proposed VPP consists of various power generation sources, including wind turbines, photovoltaics (PV),combined heat and power (CHP) units, microturbines, and boilers; power storage sources, including battery storage systems (BSS) and thermal buffer tank (BT); and also energy consumers, including electric vehicles (EV) and end consumers. Furthermore, the demand response program (DRP) is considered for better management on the consumer side. Scenarios are generated using the probability distribution function (PDF) based on existing uncertainties in renewable energy generation, energy price, and consumers' demand and are reduced by employing a scenario reduction method. Two-stage stochastic programming is also applied for the management of the proposed VPP. Through four separate case studies, this paper explores the risk impact on the total profit of the VPP and power exchanges using downside risk constraints. Also, a novel modified robust optimization model that has the same performance as the downside risk constraints is presented and implemented on the developed model.

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Abbreviations

t: :

Time index

s: :

Scenario index

i: :

Index of CHP units

m: :

Index of microturbine units

k: :

Index of boiler units

v: :

Index of EVs

N s: :

Number of scenarios

\( L_{t}^{E} ,L_{t}^{{TH}} ,L_{{t,s}}^{E} ,L_{{t,s}}^{{TH}} \): :

Expected and real-time electrical/thermal demands at hour t (kW)

\( P_{t}^{{PV}} ,P_{t}^{W} ,P_{{t,s}}^{{PV}} ,P_{{t,s}}^{W} \): :

Expected and real-time output of PVs and wind turbines at hour t (kW)

\( p_{s} \): :

Normalized probability of scenarios

\( \lambda _{{NG}} \): :

Natural gas price ($/kWh)

\( \lambda R_{t}^{{RET}} \): :

Hourly price of scheduled reserve provided by the grid at hour t ($/kWh)

\( \lambda R_{{t,s}}^{{RET}} \): :

Real-time price of reserve provided by the grid at hour t and scenarios ($/kWh)

\( \lambda _{t}^{{RET}} \): :

Retail electricity price at hour t ($/kWh)

\( \lambda _{t}^{{TH}} \): :

Hourly price for supplying thermal demands ($/kWh)

\( L_{t}^{{Shift,\, min}} ,L_{t}^{{Shift,\, max}} \): :

Minimum/maximum percentage of load shifting at hour t

\( \eta _{m}^{{MT}} ,\eta _{i}^{{CHP}} ,\eta _{k}^{B} \): :

Efficiency of MT, CHP and boiler units (%)

\( P_{m}^{{MT,min}} ,~P_{m}^{{MT,max}} ,~T_{k}^{{B,min}} ,T_{k}^{{B,max}} \): :

Minimum/maximum output of MT and boiler units (kW)

\( C_{i}^{{CHP,U}} ,C_{i}^{{CHP,D}} ,C_{m}^{{MT,U}} ,C_{m}^{{MT,D}} ,C_{k}^{{B,U}} ,C_{k}^{{B,D}} \): :

Startup/shutdown cost of MT, CHP and boiler units ($)

\( \lambda _{{sell,t}}^{{EV}} ,\lambda _{{buy,t}}^{{EV}} \): :

Price of selling/buying electrical power to/from the PHEVs (charging/discharging) in hour t ($/kWh)

\( P_{{v,\,ch}}^{{EV,\,max}} ,P_{{v,\,dch}}^{{EV,\,max}} \): :

Maximum charge/discharge rate of PHEV batteries (kW)

\( E_{v}^{{EV,\,min}} ,E_{v}^{{EV,\,max}} \): :

Minimum/maximum storage capacity of PHEV batteries (kWh)

\( E_{v}^{0} \): :

Initial stored energy level in PHEV batteries (kWh)

\( \eta _{v}^{{EV,ch}}, \eta _{v}^{{EV,dch}} \): :

Charge and discharge efficiency of PHEV batteries(%)

\( D_{{t,v}}^{{EV}} \): :

Predicted travel distance of PHEVs at hour t (mile)

\( P_{{t,\,v}}^{{EV,\,trv}} \): :

Electricity consumption of PHEVs (mile)

\( \Omega _{v} \): :

Electricity consumption of PHEVs (kWh/mile)

\( \eta _{{BSS}} ,\eta _{{BT}} \): :

Charge and discharge efficiency of BSS and BT (%)

\( \lambda _{{BT}} \): :

Thermal BT cost ($/kWh)

\( Cap^{{BSS,\,min}} ,Cap^{{BSS,\,max}} ,Cap^{{BT,\,min}}, Cap^{{BT,\,max}} \): :

Minimum/maximum capacity of BSS and BT (kWh)

\( P_{{{\text{ch}}}}^{{{\text{BSS}},\,\max }} ,P_{{{\text{dch}}}}^{{{\text{BSS}},\,\max }} ,T_{{{\text{in}}}}^{{{\text{BT}},\,\max }} ,T_{{{\text{out}}}}^{{{\text{BT}},\,\max }} \): :

Maximum charge/discharge rate of BSS and BT (kW)

\( {\text{Loss}}^{{{\text{BT}}}} \): :

The loss rate of BT at hour t (%)

\( P_{{\max }}^{{{\text{line}}}} \): :

Maximum power limit of the line between VPP and the grid (kW)

\(\delta \): :

Optimality robustness coefficient

\( R_{t}^{{{\text{RET}}}} ,{\text{RS}}_{{t,s}}^{{{\text{RET}}}} \): :

Hourly and scenario-based revenue of selling power to the consumers ($)

\( C_{t}^{G} ,\,{\text{CS}}_{{t,s}}^{G} \): :

Hourly cost/revenue related to the scheduled and scenario-based energy exchange between the main grid ($)

\( C_{t}^{{{\text{MT}}}} ,CR_{{t,s}}^{{{\text{MT}}}} \): :

Hourly and scenario-based cost of the microturbines ($)

\( C_{t}^{{{\text{CHP}}}} ,{\text{CR}}_{{t,s}}^{{{\text{CHP}}}} \): :

Hourly and scenario-based cost of the CHPs ($)

\( C_{t}^{B} ,\,{\text{CR}}_{{t,s}}^{B} \): :

Hourly and scenario-based cost of the boilers ($)

\( {\text{PRF}}_{t}^{{{\text{EV}}}} \): :

Hourly revenue from the electrical energy supply of electric vehicles ($)

\( C_{t}^{{{\text{BSS}}}} \): :

Degradation cost of BSS ($)

\( C_{t}^{{{\text{BT}}}} \): :

Degradation cost of BT ($)

\( P_{t}^{G} ,P_{{t,s}}^{G} \): :

Scheduled and real-time exchanged power with the grid at hour t (kW)

\( R_{t}^{{G,\,{\text{buy}}}} \): :

Reserve provided by the grid at hour t (kW)

\( R_{{t,s}}^{{G,\;{\text{sell}}}} \): :

Reserve sold to the grid at hour t and scenario s (kW)

\( L_{{t,s}}^{{E,\;{\text{Shifted}}}} \): :

Electrical demand after being shifted at hour t and scenarios (kW)

\( \delta L_{t}^{E} ,L_{t}^{{E,\;{\text{shift}}}} \): :

Amount and percentage of shifted load at hour t and scenarios

\( P_{{m,t}}^{{{\text{MT}}}} ,P_{{m,t,s}}^{{{\text{MT}}}} \): :

Scheduled and real-time generated power of MTs at hour t (kW)

\( R_{{m,t}}^{{{\text{MT}}}} \): :

Reserve provided by MTs at hour t (kW)

\( P_{{i,t}}^{{{\text{CHP}}}} ,\;T_{{i,t}}^{{{\text{CHP}}}} ,\;P_{{i,t,s}}^{{{\text{CHP}}}} ,\;T_{{i,t,s}}^{{{\text{CHP}}}} \): :

Scheduled and real-time electrical/thermal output of CHPs at hour t (kW)

\( {\text{PR}}_{{i,t}}^{{{\text{CHP}}}} ,\;{\text{TR}}_{{i,t}}^{{{\text{CHP}}}} \): :

Electrical and thermal reserve provided by CHPs at hour t (kW)

\( T_{{k,t}}^{B} ,T_{{k,t,s}}^{B} \): :

Scheduled and real-time generated thermal power of boilers at hour t (kW)

\( R_{{k,t}}^{B} \): :

Thermal reserve provided by boilers at hour t(kW)

\(SU_{{{\text{dg}},t}}^{{{\text{DG}}}} ,\;{\text{SU}}_{{{\text{dg}},t}}^{{{\text{DG}}}} ,\;{\text{SD}}_{{{\text{dg}},t}}^{{{\text{DG}}}} \): :

Startup and shutdown state of MT, CHP and boiler units at hour t

\( E_{{t,v}}^{{{\text{EV}},\;E}} \): :

SOC of PHEV batteries at the end of hour t (kWh)

\( P_{{{\text{ch}},v,t}}^{{{\text{EV}}}} ,\;P_{{{\text{dch}},v,t}}^{{{\text{EV}}}} \): :

Charge/discharge power of PHEV batteries at hour t (kW)

\( U_{{t,{\text{ch}}}}^{{{\text{EV}}}} ,\;U_{{t,{\text{dch}}}}^{{{\text{EV}}}} \): :

Binary variables of charge and discharge of EVs

\( P_{{{\text{ch}},\;t}}^{{{\text{BSS}}}} ,\;P_{{{\text{dch}},\;t}}^{{{\text{BSS}}}} \): :

Charge/discharge power of BSS at hour t (kW)

\( E_{t}^{{{\text{BSS}},\;E}} \): :

SOC of BSS at the end of hour t (kWh)

\( T_{{{\text{in}}}}^{{{\text{BT}}}} ,\;T_{{{\text{out}}}}^{{{\text{BT}}}} \): :

Input/output thermal power of BT at hour t (kWh)

\( E_{t}^{{{\text{BT}},\;{\text{Th}}}} \): :

Stored energy level in BT at the end of hour t (kWh)

\( Z_{s} \): :

Profit of each scenario ($)

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Authors and Affiliations

  1. Department of Electrical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

    Amirali Shahkoomahalli & Amangaldi Koochaki

  2. Center of Excellence for Power Systems Automation and Operation, School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran

    Heidarali Shayanfar

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  1. Amirali Shahkoomahalli
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  2. Amangaldi Koochaki
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  3. Heidarali Shayanfar
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Correspondence to Amangaldi Koochaki.

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Shahkoomahalli, A., Koochaki, A. & Shayanfar, H. Risk-Based Electrical-Thermal Scheduling of a Large-Scale Virtual Power Plant Using Downside Risk Constraints for Participating in Energy and Reserve Markets. Arab J Sci Eng 47, 2663–2683 (2022). https://doi.org/10.1007/s13369-021-05722-4

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