Energy storage (ES), with its flexible characteristics, has been gaining attention in recent years. The ES planning problem is highly significant to establishing better utilization of ES in power systems, but different market regulations impact the ES planning strategy. Thus, this paper proposes a novel ES capacity planning model under the joint capacity and energy markets, which aims to minimize the total cost for power consumers. The great challenge is that the ES planning model has a large number of time periods, which significantly increases the problem dimensionality. In order to alleviate the computational burden, a fully parallel algorithm is proposed to temporally decompose the original problem into a series of small sub-problems, which can be solved in parallel. Moreover, we find that the corresponding analytical solutions to the sub-problems remarkably accelerate the calculation speed while ensuring accurate results. Finally, numerical results verify the effectiveness of the proposed model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Energy storage (ES) has become more and more essential to guaranteeing power balance in power and energy systems by shifting peak loads to valley loads. However, investors may face challenges to ES capacity planning due to the lack of business models. To address this challenge, price tariffs should be carefully investigated. In the practical power system, the market price should consider both the energy price and capacity price for industries and big companies. In the energy market, investors can gain a profit by selling energy at the peak load (high price) and buying energy in the valley (low price). It should be noted that the energy market cannot recover the ES investment cost, but investors can, in fact, reduce their capacity cost since ES can reduce the peak load. Consequently, we have designed a new business model for ES planning under joint capacity and energy markets to analyze the profits via the two market regulations. The computational burden is another challenge for the proposed multi-period convex optimization model. The model must consider a long-term simulation, potentially containing thousands of time periods, which can be difficult to solve. In order to alleviate the computational burden resulting from the long-term market simulation, we further propose a fully parallel algorithm to solve the proposed business model for ES quickly. To sum up, the proposed model and method have been tested on a practical company with a practical price tariff in China to show their effectiveness.
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