A model of two-settlement electricity markets is introduced, which accounts for flow congestion, demand uncertainty, system contingencies, and market power. We formulate the subgame perfect Nash equilibrium for this model as an equilibrium problem with equilibrium constraints (EPEC), in which each firm solves a mathematical program with equilibrium constraints (MPEC). The model assumes linear demand functions, quadratic generation cost functions, and a lossless DC network, resulting in equilibrium constraints as a parametric linear complementarity problem (LCP). We introduce an iterative procedure for solving this EPEC through repeated application of an MPEC algorithm. This MPEC algorithm is based on solving quadratic programming subproblems and on parametric LCP pivoting. Numerical examples demonstrate the effectiveness of the MPEC and EPEC algorithms and the tractability of the model for realistic-size power systems.Subject classifications: noncooperative games: Cournot equilibrium; electricity market, two settlements; programming: mathematical program with equilibrium constraints, equilibrium problem with equilibrium constraints, linear complementarity problem.

Taking advantage of technology of spatio-temporal reconstruction and dispersive Fourier transform (DFT), we experimentally observed the buildup dynamics of dissipative soliton in an ultrafast fiber laser in the net-normal dispersion regime. The soliton buildup dynamics were analyzed in both the spectral and temporal domains. We firstly revealed that the appearing of the spectral sharp peaks with oscillation structures during the mode-locking transition is caused by the formation of structural dissipative soliton. The experimental results were explained by the numerical simulations. These findings would give some new insights into the dissipative soliton buildup dynamics in ultrafast fiber lasers.

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a performance-based regulatory intervention. In this paper we explore the implications of these two alternative mechanisms in a two-settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and horizontal market power. As an illustrative test case, we use the 53-bus Belgian electricity network with representative generator costs but hypothetical demand and ownership structure. Compared to a price-uncapped two-settlement system, a forward cap increases firms' incentives for forward contracting, whereas a spot cap reduces such incentives. Moreover, in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified.

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