Abstract
Due to the small number of participants in realistic cases, the Nash equilibrium generated by an oligopolistic market is more appropriate for depicting the actual energy market than the competitive equilibrium generated by a competitive market. However, the market efficiency decreases when the Nash equilibrium is used rather than the competitive equilibrium because of the strategic behaviors of the participants. In this paper, we propose two new mechanisms (subsidization and punishment) for each generator, both of which drive the Nash equilibrium to the competitive equilibrium in heterogeneous oligopolistic energy markets with a uniform pricing mechanism. Under the two proposed mechanisms, the equivalence of the Nash equilibrium and the competitive equilibrium is strictly proven. Furthermore, we apply a distributed algorithm to numerically confirm that both mechanisms perfectly eliminate the market efficiency loss. Finally, these two mechanisms are applied to the energy market under three different stages of development. Simulation results illustrate that the additional costs caused by the mechanisms converge to a low value and that the subsidization mechanism slightly outperforms the punishment mechanism.
Highlights
Centralized cost minimization optimization models have long been used since the energy market was organized as regulated monopolies in the early 1950s, which apply the same principle of maximizing social welfare as the current securityconstrained unit commitment [1] and security-constrained economic dispatch [2]
FIGURE DEPICTION We have shown the competitive equilibrium equivalence achieved by the two proposed mechanisms
A distributed supply function bidding algorithm based on the dual gradient algorithm [23] and the alternative direction multiplier method [24] was proposed in [10] to obtain the competitive equilibrium and Nash equilibrium in a demand response market
Summary
Centralized cost minimization optimization models have long been used since the energy market was organized as regulated monopolies in the early 1950s, which apply the same principle of maximizing social welfare as the current securityconstrained unit commitment [1] and security-constrained economic dispatch [2]. References [10] and [15] applied a reverse-engineering technique from the Nash equilibrium for heterogeneous and uniform clearing price markets to a global optimization problem, which better characterizes the efficiency of the Nash equilibrium. In contrast to previous works, our paper proposes two mechanisms (subsidization and punishment) that drive the Nash equilibrium to a competitive equilibrium in heterogeneous oligopolistic energy markets with a uniform pricing mechanism, which perfectly eliminates the market efficiency loss. Mathematical programs with equilibrium constraints [19] and equilibrium programs with equilibrium constraints [20] are widely used to address bi-level optimization market problems with single and multiple strategic generators Novel approaches such as contact theory, which improves the profit of both the energy market and the participants [21], have been developed.
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