# Transaction Mechanism Based on Two-Dimensional Energy and Reliability Pricing for Energy Prosumers
## 1 Introduction  
Along with the development of the smart grid, more and more distributed generation has been deployed in power systems. This often includes renewable energy sources due to their availability, applicability, and environmentally friendly nature [1]. With distributed renewable generation, traditional passive consumers, such as households and small businesses, are now participating as producers in the electricity market [2]. These newly introduced users are called prosumers, as they both share surplus energy generated domestically as well as consume energy from the energy utility [3]. The presence of prosumers is expected to bring some benefits. These include: (1) a modular and tailored energy service to specific end uses, which can vary in quality; (2) grid diversification, by encouraging the large amount of distributed generation deployed to complement decentralized storage options; and (3) efficient wholesale market operations, with minimal transmission congestion and constraints [4]. However, an increase in renewable sources and decentralization can cause reliabilityproblems, introducing multiple unknowns and risks that must be addressed and managed in grid operation [5]. In order to address the reliability problem, a direct approach based on control, or a soft or indirect approach based on pricing, can be used. The direct approach is hardware-centric. To solve the grid operation issues, additional equipment, such as smart inverters [6], static synchronous compensators (STACOM) [7], and/or electric energy storage (EES) [8; 9], can be deployed. The grid operation structures are improved to enable cooperation with the distributed resources via the introduction of advanced distribution network operating systems [10]. Applying this direct approach is effective in terms of operations. However, there are additional investment and regulatory problems. Alternatively, the soft/indirect approach pursues a similar operation effect statistically by providing additional signals to participants. This approach requires more sophisticated technologies, and it lessens the direct investment of utilities necessary to operate the grid. A pricing-based approach is a typical mechanism for indirect control [11]. It is a demand-side management mechanism that improves grid reliability by indirectly controlling the prosumer's energy usage to the price factor, such as demand charges and energy charges [12]. However, conventional pricing that consists of demand charges and energy charges usually has limitations in considering load or generation uncertainties [13]. Under conventional pricing systems, distributed renewable generators have limited responsibility and limited rewards for their uncertainties, as the pricing is determined regardless of generation uncertainty [14]. Dynamic pricing, such as real-time pricing (RTP) [15] or time-of-use (TOU) pricing [16], can lead generators to produce electricity at higher-price times. However, this method cannot help to decrease generation uncertainty. From the viewpoint of utilities that operate grids, generation uncertainty is important in operational planning. Here, uncertainty can be represented as generation predictability. As such, a more advanced pricing method has been introduced to improve generation predictability by assigning the responsibility of prediction to generators and by instituting a penalty and reward system for their commitments. Even in this advanced pricing system, utilities have limited information for generation prediction, because even though prosumers commit their generation amount, they do not have information about the uncertainty of their generation amount. Prosumers with renewable generation capabilities may try to keep their commitments to avoid or reduce penalties [17]. The utilities, however, are unaware of the situation and intend to honor prosumers' generation commitments, and thus can only estimate the amount of the generation based on historical statistical information. The exact same issue occurs in load estimation.