Carbon price in an electricity market provides incentives for carbon emission abatement and renewable generation technologies. Policies constraining or penalizing carbon emissions can significantly impact the capacity planning decisions of both fossil-fueled and renewable generators. Uncertainties due to intermittency of various renewable generators can also affect the carbon emission policies. This paper proposes a Cournotbased long-term capacity expansion model taking into account carbon cap constraint for a partly concentrated electricity market dealing with stochastic renewables using a Bayesian game. The stochastic game is formulated as a centralized convex optimization problem and solved to obtain a Bayes-Nash Equilibrium (Bayes-NE) point. The stochastic nature of a generic electricity market is illustrated with a set of scenarios for wind availability, in which three generation firms (coal, gas, and wind) decide on their generation and long-term capacity investment strategies. Carbon price is derived as the dual variable of the carbon cap constraint. Embedding the carbon cap constraint in the game indicates more investment on renewable generators and less on fossil-fueled power plants. However, the higher level of intermittency from renewable generation leads to a higher carbon price to meet the cap constraint. This paves the way towards storage technologies and diversification of distributed generation as means to encounter intermittency in renewable generation. 1

Abstract-Recent studies show that the fast growing expansion of wind power generation may lead to extremely high levels of price volatility in wholesale electricity markets. Storage technologies, regardless of their specific forms e.g. pump-storage hydro, large-scale or distributed batteries, are capable of alleviating the extreme price volatility levels due to their energy usage time shifting, fast-ramping and price arbitrage capabilities. In this paper, we propose a stochastic bi-level optimization model to find the optimal nodal storage capacities required to achieve a certain price volatility level in a highly volatile electricity market. The decision on storage capacities is made in the upper level problem and the operation of strategic/regulated generation, storage and transmission players is modeled at the lower level problem using an extended Cournot-based stochastic game. The South Australia (SA) electricity market, which has recently experienced high levels of price volatility, is considered as the case study for the proposed storage allocation framework. Our numerical results indicate that 80% price volatility reduction in SA electricity market can be achieved by installing either 340 MWh regulated storage or 420 MWh strategic storage. In other words, regulated storage firms are more efficient in reducing the price volatility than strategic storage firms.

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