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Multiple Electricity Markets Design Undergoing Asymmetric Policies on Renewables Expansion: Capacity Adequacy and Revenue Sufficiency


This paper investigates the impact of decentralized and heterogeneous renewable energy sources (RES) expansion policies on providing adequate resources within multiple electricity markets (MEMs). Also, the sharing of the economic interest between different wholesale electricity markets participating in MEMs is analyzed. For this purpose, a new formulation of the stochastic multi-objective mixed-integer non-linear programming problems is used in the agent-based simulation framework to model the impact of different MEMs designs on capacity adequacy (CA) and revenue sufficiency (RS) undergoing asymmetric RES expansion policies. By this modelling, the vulnerability of the different market designs in terms of CA and RS within MEMs is investigated. Also, the power plants’ behavior in declaring capacity between wholesale electricity markets is to be analyzed. The results show, regardless of the market mechanism and new invested capacity in each wholesale electricity market, the CA index in all markets participating in the MEMs will be balanced. However, the use of different market designs creates more challenges in providing adequate resources in the capacity mechanism in comparison with the energy-only electricity markets. That means more investment in the conventional power plants in a market does not necessarily increase the capacity adequacy (CA) indices on that market within MEMs. According to the simulation result, high RES development policies do not necessarily lead to reduce the investment of new conventional power plants. Also, different auction mechanisms reduce the power plants' net present value (NPV) in the high-penetrated RES electricity market.

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\(t \in {T}\) :

Set of time

\(se \in S\) :

Set of renewable generation scenarios

\(b \in buses\) :

Set of buses


Set of buses in markets 1,2,3

\(bml,Bnl,brl\) :

Starting/ending bus of line l

i :

Index of existing power plants

j :

Index of new power plants

l :

Index of transmission lines

L1 /L2/L3:

Set of lines in markets 1,2,3


Set of common tie–lines between markets


Index of iteration


EM,ER, Set of existing power plants in markets 1,2,3

EN2/EN3/EM1 /EM3/ER1/ER2:

Set of existing power plants in markets 1,2 and 3 that participate in the other markets


Set of new power plants in markets 1,2,3

NN2/NN3/NM1 /NM3/NR1/NR2:

Set Of New Power Plants In Market 1 /2/3 That Participate In The Other Markets

\(\varphi _{{{\text{bi}}}}\) :

Set of generators which are connected to bus b

\(\varphi _{{{\text{bl}}}}\) :

Set of lines which are connected to bus b

\(s_{\text{t,se,i}}^{ + } ,s_{\text{t,se,i}}^{ - }\) :

Positive variable for balancing power

\({\text{Z}}_{{{\text{t}},{\text{se}},{\text{i}}}} \in \left\{ {0,1\} } \right.\) :

Expansion variable

\(P_{{{\text{t}},{\text{se}},{\text{i}}}}\) :

Power output of existing power plant i (MW)

\(P_{{{\text{t}},{\text{se}},{\text{i}}}}^{{\text{c}}}\) :

Power output of new power plant i (MW)

\(\varvec{P}11_{{{\mathbf{t}},{\mathbf{i}}}} /{\text{P}}11N_{{{\text{t}},{\text{i}}}}\) :

Capacity of existing/ new power plant i in market 1 which is declared in market 1 (MW)

\(\varvec{P}12_{{{\mathbf{t}},{\mathbf{i}}}} ,\varvec{P}13_{{{\mathbf{t}},{\mathbf{i}}}} /\varvec{P}12\varvec{N}_{{{\mathbf{t}},{\mathbf{i}}}} ,\varvec{P}13\varvec{N}_{{{\mathbf{t}},{\mathbf{i}}}}\) :

Capacity of existing/ new power plant i in market 1 which is declared in the other markets (MW

\(\varvec{Cvar}_{{{\text{t}},{\text{i}}}}\) :

Variable cost of power plant i ($/MWh)

\(\varvec{C}_{{\varvec{inves},\varvec{i}}}\) :

Investment cost of power plant i (M$/GW)

\(\varvec{CF}_{{\varvec{t},\varvec{se},\varvec{i}}}\) :

Cash flow for power plant i ($)


Discount rate

\(\varvec{RD}_{{\varvec{t},\varvec{se},\varvec{b}}}\) :

Residual demand (MW).

\(\varvec{f}_{{\mathbf{l}}}^{{{\mathbf{max}}}}\) :

Maximum capacity of line l (MW)

\(\varvec{LMP}11,22,33_{\varvec{t}}\) :

Locational marginal price in markets 1,2,3

\(\varvec{\pi }_{{{\mathbf{t}},{\mathbf{se}},{\mathbf{i}}}}\) :

Power plant's price ($/MWh).

\(\varvec{\pi }_{{{\mathbf{CM}}}}\) :

Capacity price ($/MWh)

\(\varvec{LS}_{{{\mathbf{t}},{\mathbf{se}},{\mathbf{b}}}}\) :

Load shedding (MWh)

\(\varvec{f}_{{{\mathbf{t}},{\mathbf{se}},{\mathbf{l}}}}\) :

Line flow

\(\varvec{f}_{\varvec{l}}^{{\varvec{max}}}\) :

Maximum capacity of line l (MW)

\(\varvec{Prb}_{{{\mathbf{t}},{\mathbf{se}}}}\) :

Probability of scenario se

\(\varvec{Pc}_{{\mathbf{i}}}^{{\mathbf{max}}}\) :

Maximum capacity of new power plant i (MW)

\(\varvec{P}_{{\max \varvec{trca~i}}}\) :

Maximum declared capacity in the other markets by each GenCo (MW)


Load shedding cost ($/MWh)

\(\varvec{xP}_{{{\mathbf{t}},{\mathbf{se}},{\mathbf{i}}}} \varvec{~}\) :

Power output balancing parameter for power plants in the markets (MW)


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Correspondence to Asghar Akbari Foroud.

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Appendix 1

Appendix 1

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Table 6 Probability of occurrence of the load scenarios and installation of each power plant type in each market


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Mozdawar, S.A., Akbari Foroud, A. & Amirahmadi, M. Multiple Electricity Markets Design Undergoing Asymmetric Policies on Renewables Expansion: Capacity Adequacy and Revenue Sufficiency. Arab J Sci Eng 47, 2781–2796 (2022).

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