從古至今，為了要縮短交通時間，人類持續不斷的改善交通方式。傳統上，車輛使用石化燃料當作動力來運作。然而，石化燃料造成嚴重的空氣汙染，而且因為世界上的需求日漸增加，石化燃料的儲存量已經快速地減少。電動車被視為是一個有希望的方法來解決環境保育和能源短缺的問題，因為可以利用再生能源來產生它的電力。所以，許多以再生能源為電力的充電設施的相關研究在近年來被相繼提出。此外，一些相關的議題也被廣泛的研究，例如電力價格和放電。隨著電動車越來越普及，電網的穩定性也變成一項重要的議題。其中，車輛放電的許多優點也被廣泛討論，例如車輛放電到家庭(V2H)和車輛放電到電網(V2G)。一方面，電力提供者能夠藉由調整電力價格來降低電網的負載和獲取收益。另一方面，電動車用戶能夠藉由放電來賺取收益同時達到保護電網的功能。在我們的研究中，我們研究充放電站的各種效能指標，其中充放電站具有批次到達、再生能源、價格敏感型電動車的特性。我們假設有兩種類型的電動車，一種是充電另一種是放電。電動車是以批次到達，其中每一批次的電動車數量是隨機變數。此外，價格敏感型電動車是指他們會根據接受機率來決定是否進入充放電站。而接受機率不僅受到充放電站的電動車數量所影響，還有輸入再生能源的多寡也會改變接受機率。在本篇論文中，我們首先推導相關系統的解析模型，接著利用疊代演算法來找到穩態機率分布。第二，我們提出一項近似方法來計算相關的效能指標。第三，我們研究不同的系統參數所產生的影響，這些參數包含各種電動車的抵達速率和服務速率。最後，我們利用C程式語言寫出一個電腦模擬模型來探討解析模型的準確性。

From ancient times to the present, the human being keep improving transportation in order to save time. Traditionally, automobiles operate on fossil fuel for its power. However, fossil fuel causes air pollution and its storage rapidly decreases due to the increasing consumption in the world. Electric Vehicles (EVs) are considered as a promising solution about environmental conservation and energy shortage since electricity can be generated from renewable energy. Consequently, various works on EVs charging infrastructure with electricity power generated from renewable energy are proposed in recent years. Furthermore, some related issues are widely studied, e.g., electricity price and discharging. As EVs are more and more popular, the stability of power grid is becoming a more important issue. Furthermore, many benefits can be obtained from the discharging of vehicles, e.g., vehicle-to-home (V2H) and vehicle-to-grid (V2G). On one hand, the electricity providers can adjust the electricity price to reduce the load of the power grid and increase the profit. On the other hand, EVs’ users can discharge the power to make profit and protect the power grid at the same time. In our work, we study the performance evaluation of a charging and discharging public station (CDPS) with batch arrivals, renewable energy, and price-sensitive EVs. There are two classes of EVs, charging EVs and discharging EVs. The EVs arrive in batches, where the number of EVs in each batch is a random variable. Additionally, EVs are price-sensitive, i.e., they decide whether to enter the CDPS based on an acceptance probability. The acceptance probability is based on not only the number of EVs in the CDPS but also the imported renewable energy. First, we derive the analytical model for the considered system. Then, the steady-state probability distribution is found by an iterative algorithm. Second, an approximation method is presented to evaluate the performance measures of interest. Third, we study the influence of different system parameters, such as the arrival rate and service rate of EVs of either class, on various performance measures. Finally, we use the C language to write a simulation program to explore the accuracy of the analytical model.

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