以數學規劃法作混合電力系統之極限目標值分析

Abstract

近年來由於全球暖化與能源短缺等問題日益嚴重，致使與再生能源相關的研究與發展議題更加受到重視。為了降低再生能源的不連續性與不可預測性等特性造成的影響，可將再生能源與公共輸配電網整合，進而發展出混合型電力系統(hybrid power system, HPS)。 本文將數學規劃法應用在HPS之設計，可求得最佳化目標值以及電力配置。其中最佳化的目標值，包含公用系統最小補給電量及儲能設備的最小儲能容量。我們將化工傳統熱交換器網路模型設計的概念做一些應用與發展，並且提出兩種解題模式，分別為緻密型轉運模型(Condensed Transshipment Model, CTM)及延展型轉運模型(Expanded Transshipment Model, ETM)。考慮到單一和多種種類的儲能設備之ETM模式，分別以ETM1模式和ETM2模式來論述。主要考慮的混合電力系統有兩種，分別為理想無電力損耗的電力系統，以及考慮到有電力損耗情形的電力系統。 最近，諸多學者解HPS最適化問題的方法為狹點分析法，其方法需要使用大量的物理判斷步驟來計算儲能串級表中的各個物理量。在這樣的計算過程中，不僅計算過程繁瑣，而且耗費時間。為了改善狹點分析法的缺失，本文將所有HPS的補給用電設備電力之策略考慮在CTM與ETM兩種模式中，利用數學規劃法建立其數學模式。將已知參數輸入以General Algebraic Modeling System (GAMS)所建立之上述數學模式中，便可在極短時間內求得HPS最適化結果。其中ETM模式下的結果甚至比狹點分析方法更佳，顯示數學規劃法無可取代之處。此外，調整ETM2模式的參數，可計算出不同類型的儲能設備(例如:電池、水庫等)搭配不同類型的公用電網之HPS的分配電力。透過不同組合的HPS之電力分配表，可以評估HPS設備與能源的成本，進行不同的HPS設計。 本文考慮到的各種設計參數，包括充放電後電力恢復率、儲能設備的自放電耗損率、再生能源發電頻率，均假設為常數。因此，未來若要做HPS更進階的設計時，可以引進非線性參數，以便更精確計算出HPS的公用電網需求和儲能設備之容量需求，做出更進階之HPS電力分配設計。

In recent years, renewable energy (RE) has been proposed to address global warming and energy shortage problems. However, to solve the discontinuity and unpredictability of RE, researchers and industries problems have integrated RE with public grid electricity to develop a hybrid power system (HPS). This study applies mathematical programming (MP) to the design of HPS to find the optimal targets and power distribution, which includes the minimum electricity outsourced from the grid and the minimum capacity for electricity storage. Two mathematical models—condensed transshipment model (CTM) and expanded transshipment model (ETM)—are developed to solve HPS optimization problems by making use of the design concept of traditional chemical heat exchanger networks (HEN's). ETM is divided into two categories: those with single storage equipment (ETM1) and those with multiple equipment (ETM2). Two types of HPS are considered in this study: those involving no electricity loss (the ideal type) and that involving three types of loss (charging/discharging electricity loss, and self-discharging loss). Recently, many researchers use power pinch analysis (PPA) method to solve HPS optimization problems. This method uses a tremendous amount of procedures to calculate physical quantities, which renders this method complicated and time-consuming. To deal with the disadvantages of PPA, this article considers all the supply electricity routes in CTM and ETM, and establishes mathematical models using mathematical programming (MP). With the construction of CTM and ETM models in General Algebraic Modeling System (GAMS), the optimized results of HPS can be obtained nearly instantly, indicating the indispensability of MP. Adjusting the parameters of ETM2, we can consider different types of energy storage devices (e.g.: battery, reservoirs, etc.) and different types of public grids in HPS, in which the costs of energy and equipment can be analyzed for later design. Most parameters in this article—including charging and discharging recovery ratios, and self-discharging recovery ratios—are assumed to be constant. In the future research, these parameters can be thought to be variables to establish a more complete HPS.