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A Risk-Based Gaming Framework for VPP Bidding Strategy in a Joint Energy and Regulation Market

  • Morteza Shafiekhani
  • Ali BadriEmail author
Research Paper
  • 6 Downloads

Abstract

This paper presents a risk-based game theoretic model for virtual power plant (VPP) bidding strategy in both energy and balancing markets, in the presence of conventional generation companies (GenCos) as rivals. The objective is to provide a method for finding strategic bidding of VPP comprising traditional units, wind turbine, interruptible and shiftable loads along with other strategic rivals. In this regard, a novel shifting load scheme is introduced into the VPP portfolio in which VPP is penalized based on shifting load amount and shifting load time as well. A bi-level mathematical program with equilibrium constraint (MPEC) is represented for modeling behavior of each producer in which the upper level deals with profit maximization of each strategic unit and the lower level encompasses social welfare maximization considering transmission constraints. Power transfer distribution factors are employed to model transmission constraints. The proposed bi-level problem is converted to a traceable mixed-integer linear programming problem using duality theory and Karush–Kuhn–Tucker optimization conditions. Simultaneous solution of all MPECs forms an equilibrium problem with equilibrium constraint that results in market Nash equilibrium point. Finally, information gap decision theory is employed for modeling load price uncertainty and evaluating risk of VPP decision making. The proposed model is tested on a standard IEEE-24 bus system, and the accuracy of the results is indicated.

Keywords

Virtual power plant Game theory Optimal bidding Risk Energy Regulation 

List of Symbols

Indices

\(t\)

Index for time period

\(b\)

Index for demand/generation block

\(g\)

Index for generation units of VPP

\(w\)

Index for wind scenario

\(\tau\)

Index for rival scenarios

\(m\) and \(n\)

Index for buses

\(il\)

Index for interruptible load

\(r\)

Index for rival

\(k\)

Index for line

\(d\)

Index for demand

\(o\)

Index for slack bus

\(q,q^{\prime}\)

Index for players

Constants

\(\lambda_{{\left( {g,b,t} \right)}}^{\text{VPP}}\)

Marginal cost of bth block of gth unit of VPP in period \(t\)

\(\tau_{t,n}^{\text{Bal}}\)

Balancing market price in bus \(n\) in period \(t\)

\(R_{{{\text{VPP}}\left( g \right)}}^{\text{up}}\)

Ramp-up rate for gth unit of VPP

\(R_{{{\text{VPP}}\left( g \right)}}^{\text{down}}\)

Ramp-down rate for gth unit of VPP

\(\lambda_{{\left( {r,b,t} \right)}}^{C}\)

Marginal cost of bth block of strategic conventional unit \(r\) in period \(t\)

\(\lambda_{{\left( {d,b,t} \right)}}^{D}\)

Marginal cost of bth block of dth demand in period \(t\)

\(\lambda_{{\left( {r,b,t} \right)}}^{R}\)

Marginal cost of bth block of rth rival in period \(t\)

\(\lambda_{{\left( {il,t} \right)}}^{\text{IL}}\)

Price of ilth interruptible load in period \(t\)

\(P_{{\left( {t,w} \right)}}^{\text{wind}}\)

Wind power generation in scenario \(w\) of period \(t\)

\(\pi_{{\left( {t,w} \right)}}\)

Probability of scenario w in period \(t\)

\(\theta_{{\left( {\tau ,t} \right)}}\)

Probability of scenario \(\tau\) in period \(t\)

\(v_{\text{aw}}\)

Average wind speed in scenario \(w\)

\(P_{\text{Rated}}\)

Rated power of wind unit

\(v_{\text{ci}}\)

Cut-in wind speed

\(v_{\text{r}}\)

Rated wind speed

\(v_{\text{co}}\)

Cut-out wind speed

\(Ny\)

Maximum iteration number

\(n_{y}\)

Number of iterations

\({\text{upreg}}\)

Up-regulation market price

\({\text{dnreg}}\)

Down-regulation market price

\({\text{MUP}}_{\left( g \right)}^{\text{VPP}}\)

Minimum uptime of gth unit in VPP

\({\text{MDN}}_{\left( g \right)}^{\text{VPP}}\)

Minimum downtime of gth unit in VPP

\({\text{SUC}}_{\left( g \right)}^{\text{VPP}}\)

Start-up cost of gth unit of VPP

\({\text{Pl}}_{\left( t \right)}\)

VPP initial internal load in period t

Variables

\(P_{\left( t \right)}^{\text{VPPDA}}\)

Power cleared for VPP in day-ahead market in period \(t\)

\(P_{{\left( {g,b,t} \right)}}^{\text{VPP}}\)

Power produced by bth block of gth unit of VPP in period \(t\)

\(\lambda_{{\left( {n,t} \right)}}\)

Market-clearing price of bus \(n\) in period \(t\)

\(P_{\left( t \right)}^{\text{up}}\)

Power purchased in up-regulation market in period \(t\)

\(P_{\left( t \right)}^{\text{dn}}\)

Power sold in down-regulation market in period \(t\)

\(P_{{\left( {il,t} \right)}}^{\text{IL}}\)

Interruptible load amount in period \(t\)

\(\sigma_{\left( t \right)}^{\text{VPP}}\)

Offered price of VPP in period \(t\)

\(P_{{\left( {r,b,t} \right)}}^{C}\)

Power produced by bth block of strategic conventional unit \(r\) in period \(t\)

\(P_{{\left( {d,b,t} \right)}}^{D}\)

Power consumed by bth block of dth demand in period \(t\)

\(P_{{\left( {r,b,t,\tau } \right)}}^{R}\)

Power produced by bth block of rth rival in scenario \(\tau\) of period \(t\)

\(\varPsi_{q}^{y}\)

The value of the variables in upper-level problem

\(P_{\left( t \right)}^{ - s}\)

Amount of internal load decrease in period t

\(P_{\left( t \right)}^{ + s}\)

Amount of internal load increase in period t

\(pl_{(t)}\)

VPP internal load in period t

\(\alpha_{{\left( {g,t} \right)}}^{\text{VPP}}\)

Binary variable, 1 if unit is on, 0 otherwise

\(\beta_{{\left( {g,t} \right)}}^{\text{VPP}}\)

Binary variable, 1 if unit starts up

\(\gamma_{{\left( {g,t} \right)}}^{\text{VPP}}\)

Binary variable, 1 if unit shuts down

\(u_{\left( t \right)}^{ - s}\)

Binary variable, 1 if internal load decreases, 0 otherwise

\(u_{\left( t \right)}^{ + s}\)

Binary variable, 1 if internal load increases, 0 otherwise

\(\mu_{t}^{{{\text{VPP}}^{\text{min} } }}\)

Dual variable related to minimum production of VPP in period \(t\)

\(\mu_{t}^{{{\text{VPP}}^{\text{max} } }}\)

Dual variable related to maximum production of VPP in period \(t\)

\(\mu_{r,b,t}^{{R^{\text{min} } }}\)

Dual variable related to minimum production of bth block of rth rival in period \(t\)

\(\mu_{r,b,t}^{{R^{\text{max} } }}\)

Dual variable related to maximum production of bth block of rth rival in period \(t\)

\(\mu_{d,b,t}^{{D^{\text{min} } }}\)

Dual variable related to minimum production of bth block of dth demand in period \(t\)

\(\mu_{d,b,t}^{{D^{\text{max} } }}\)

Dual variable related to maximum production of bth block of dth demand in period \(t\)

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Faculty of Electrical EngineeringShahid Rajaee Teacher Training UniversityTehranIran

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