یک مدل کارآمد برنامه ریزی خطی و الگوریتم بهینه سازی برای تولید سه گانه

Trigeneration is a booming technology for efficient and clean provision of energy. It has potential for reducing pollution emissions dramatically. Similar to combined heat and power (CHP) production, cost-efficient operation of a trigeneration system can be planned using an optimization model based on hourly load forecasts. A long-term planning model decomposes into thousands of hourly models, which can be solved separately. In this paper, we model the hourly trigeneration problem as a linear programming (LP) model with a joint characteristic for three energy components to minimize simultaneously the production and purchase costs of three energy components, as well as CO2 emissions costs. Then we explore the structure of the problem and propose the specialized Tri-Commodity Simplex (TCS) algorithm that employs this structure efficiently. The speed of TCS is based on extremely fast basis inverse operations and reuse of old basic solutions from previously solved hourly models. We compare the performance of TCS with realistic models against an efficient sparse Simplex code using the product form of inverse. In test runs, TCS is from 36 to 58 times faster when starting from the initial basis and from 43 to 179 times faster when reusing the old basis.

Trigeneration is the conversion of a single fuel source into three useful energy products. Three energy products can take different forms based on the specific applications. For example, one kind of a trigeneration system that produces electricity, gas and steam is called integrated gas and steam generator (IGSG). In the plastic and rubber industry, electric power, steam or thermal oil, and chilled water can be produced at the same time [1]. A district heating-and-cooling system produces electricity, steam or hot water, and chilled water simultaneously. Sometimes steam itself is produced at several pressure levels, e.g., high, medium and low pressure. Moreover, trigeneration has also been referred to as combined heating, cooling and power generation (CHCP). So trigeneration and the related three energy products can be used in a broader sense. Trigeneration provides greater efficiency than is possible by producing the three products separately or by combined heat-and-power (CHP) production (simultaneous production of useful heat and power). CHP production and trigeneration are universally accepted as the most energy-efficient means of producing electricity. In 2002, 9% of national electricity in the USA and 12% of total electricity in EU was produced in CHP plants. The Department of Energy has called for the doubling of electrical power generated from CHP power plants – from the existing 46 GW to 92 GW by the year 2010. When this goal is reached, CHP production will represent about 14% of the total US generating capacity of electricity. The American Council for Energy-Efficient Economy (ACEEE) estimates that an additional 95 GW of CHP capacity could be added between 2010 and 2020, resulting in 29% of total US electric-power generation being generated through CHP technology. Europe is also dramatically increasing the number of CHP plants over the next decade. The European Commission states that CHP is one of the very few technologies which can offer a significant short- or medium-term contribution to the energy efficiency issue in the European Union (EU) and can make a positive contribution to the environmental policies of the EU. The Commission wishes to raise the share of electricity produced in CHP from 9% to 18% by 2010 [2]. It is expected to reduce CO2 emissions by 150 million tons per year or approximately 4% of the total CO2 emissions of the EU in 2010. The historical success of CHP production has been the foundational basis for extending the efficiency of CHP to trigeneration or even quadgeneration – with each new recovered energy form resulting in higher efficiency, lower fuel consumption, and less emissions. Development of trigeneration technology started in the last decade and the number of operating plants worldwide is still not large. Some research has focused on the economic analysis of trigeneration systems and highlighted the higher efficiency of fuel use for trigeneration as compared with the production of separate energy products [3], [4] and [5]. Goodell [6] further demonstrated the superior efficiency of trigeneration over that of CHP using a simple factory prototype, where the cooling is generated by an electric-driven compression chiller in CHP production and by an absorption or adsorption chiller in trigeneration, respectively. In this example, trigeneration saves about 24.5% of primary energy. In practice, the trigeneration in food industry [7] can produce refrigeration of high economic value by using low value heat to drive ammonia absorption refrigeration plants, thus increasing the overall efficiency of the plant. In general, a trigeneration system may consist of multiple trigeneration plants, CHP plants and plants for producing the different energy products separately. The cost-efficient operation of trigeneration systems (integrated energy systems) can be planned using an optimization model. The possible number of decision variables for the problem of the mixed energy production is large, especially when multi-period operational planning is involved. Efficient search for the optimal solution in a multi-dimensional space requires a powerful algorithm. Sakawa et al. [8] presented a mixed 0–1 linear programming (LP) model for operational planning of district heating and cooling plants (trigeneration) in consideration of the starting and stopping of the instruments and developed genetic algorithms for it. Curti et al. [9] formulated the design, installation, and operation of integrated energy systems as non-linear mixed integer programming models. Their model aimed at simultaneous minimization of the operating costs and emissions. This model was then solved using genetic algorithms [10]. Burer et al. [11] developed an evolutionary multiple-objective algorithm to deal with the trigeneration problem, minimizing simultaneously the annual total cost of power, heat and cooling generation as well as annual CO2 emissions. Tracing back to the successful experience of the operational planning of the CHP systems [12], [13] and [14], we can see that efficient algorithms for the integrated energy system can be developed by formulating the problem more efficiently and exploiting the special structure of the problem. Medium- and long-term planning of integrated systems is based on hourly demand forecasts for the associated energy products. Using various decomposition techniques, the multi-period planning problems can be decomposed into a large number of hourly models, which need to be solved once or multiple times to obtain a solution for the overall problem. Furthermore, more advanced analyses, such as risk analysis through stochastic simulation require solving a large number of multi-period models rapidly [15]. Therefore, efficient solution of the hourly models is extremely important. In this paper, we propose modeling convex trigeneration systems as a LP model with a special structure to minimize simultaneously the production and purchase costs of the three energy components, as well as CO2 emissions costs. Then we develop the Tri-Commodity Simplex (TCS) algorithm that uses this structure efficiently. The model and algorithm can manage any three commodities in joint production. In principle, this model and algorithm is an extension of the CHP model and the specialized Power Simplex algorithm [13]. However, the problem structure is more complicated. Furthermore, we consider CO2 emissions costs in the cost structure. Observe that non-convex problems can be decomposed into multiple convex sub-problems and TCS can be used to solve the convex sub-problems efficiently. Combined with other techniques, such as Branch and Bound and dynamic programming, TCS can find its way in dealing with non-convex trigeneration problems. Makkonen and Lahdelma [16] have adopted the non-convex decomposition techniques in dealing with CHP problems. This paper is organized as follows. In Section 2, we describe the hourly trigeneration model. Then in Section 3, we review the Revised Simplex algorithm for solving LP problems. In Section 4, we present the TCS algorithm for solving the trigeneration models efficiently. In Section 5, we present results of numerical experiments.

Changes of the energy market, increasing environmental awareness and novel energy production technologies create a need for new kinds of decision support tools for energy companies. Trigeneration is a booming technology in the energy world. Efficient solution of hourly trigeneration models is important because long-term planning models can be decomposed into solving thousands of hourly models and more advanced analyses, such as risk analysis requires the solution of a large number of long-term models. In this paper, we have developed the Tri-Commodity Simplex (TCS) algorithm that exploits the special structure of the trigeneration models efficiently. The speed of TCS is based on extremely fast basis inverse operations and reuse of old basic solutions. In test runs with realistic models, TCS is 36–58 (average 45.6) times faster than the sparse LP2 Simplex code when starting from the initial basis. When reusing old basic solutions, TCS is from 43–179 times (average 87.3) faster. In addition, the improvement of TCS over LP2 for the trigeneration problem is much greater than that of the Power Simplex over LP2 for the CHP problem. Power Simplex has been implemented as part of the EHTO NEXUS energy optimization system [20], which is in commercial use at several energy companies. Thus it is expected that TCS also can find its way in practice if the trigeneration technology is adopted widely.