1、 外文文献 : The Optimal Operation Criteria for a Gas Turbine Cogeneration System Abstract: The study demonstrated the optimal operation criteria of a gas turbine cogeneration system based on the analytical solution of a linear programming model. The optimal operation criteria gave the combination of equ
2、ipment to supply electricity and steam with the minimum energy cost using the energy prices and the performance of equipment. By the comparison with a detailed optimization result of an existing cogeneration plant, it was shown that the optimal operation criteria successfully provided a direction fo
3、r the system operation under the condition where the electric power output of the gas turbine was less than the capacity. Keywords: Gas turbine; Cogeneration; Optimization; Inlet air cooling. 1. Introduction Cogeneration, or combined heat and power production, is suitable for industrial users who re
4、quire large electricity as well as heat, to reduce energy and environmental impact. To maximize cogeneration, the system has to be operated with consideration electricity and heat demands and the performance of equipment. The optimal operation of cogeneration systems is intricate in many cases, howe
5、ver, due to the following reasons. Firstly, a cogeneration system is a complex of multiple devices which are connected each other by multiple energy paths such as electricity, steam, hot water and chilled water. Secondly, the performance characteristics of equipment will be changed by external facto
6、rs such as weather conditions.For example, the output and the efficiency of gas turbines depend on the inlet air temperature. Lastly,the optimal solution of operation of cogeneration systems will vary with the ratio of heat demand to electricity demand and prices of gas, oil and electricity. Because
7、 of these complexities of cogeneration systems, a number of researchers have optimal solutions of cogeneration systems using mathematical programming or other optimization techniques. Optimization work focusing on gas turbine cogeneration systems are as follows. Yokoyama et al. 1 presented optimal s
8、izing and operational planning of a gas turbine cogeneration system using a combination of non-linear programming and mixed-integer linear programming methods. They showed the minimum annual total cost based on the optimization strategies. A similar technique was used by Beihong andWeiding 2 for opt
9、imizing the size of cogeneration plant. A numerical example of a gas turbine cogeneration system in a hospital was given and the minimization of annual total cost was illustrated. Kong et al. 3 analyzed a combined cooling, heating and power plant that consisted of a gas turbine, an absorption chille
10、r and a heat recovery boiler. The energy cost of the system was minimized by a linear programming model and it was revealed that the optimal operational strategies depended on the load conditions as well as on the cost ratio of electricity to gas. Manolas et al. 4 applied a genetic algorithm (GA) fo
11、r the optimization of an industrial cogeneration system, and examined the parameter setting of the GA on the optimization results. They concluded that the GA was successful and robust in finding the optimal operation of a cogeneration system. As well as the system optimization, the performance impro
12、vement of equipment brings energy cost reduction benefits. It is known that the electric power output and the efficiency of gas turbines decrease at high ambient temperatures. Some technical reports 5, 6 show that the electric power output of a gas turbine linearly decreases with the rise of the amb
13、ient temperature, and it varies about 5 % to 10 % with a temperature change of 10 C. Therefore, cooling of the turbine inlet air enhances electric output and efficiency. Some studies have examined the performance of the gas turbine with inlet air cooling as well as the effect of various cooling meth
14、ods 7, 8, 9. The cooling can be provided without additional fuel consumption by evaporative coolers or by waste heat driven absorption chillers. The optimal operation of the system will be more complex, however, especially in the case of waste heat driven absorption chillers because the usage of the
15、 waste heat from the gas turbine has to be optimized by taking into consideration the performance of not only the gas turbine and the absorption chiller but also steam turbines, boilers and so on. The heat and electricity demands as well as the prices of electricity and fuels also influence the opti
16、mal operation. The purpose of our study is to provide criteria for optimal operation of gas turbine cogeneration systems including turbine inlet air cooling. The criteria give the minimum energy cost of the cogeneration system. The method is based on linear programming and the Kuhn-Tucker conditions
17、 to examine the optimal solution, which can be applied to a wide range of cogeneration systems. 2. The Criteria for the Optimal Operation of Gas Turbine Cogeneration Systems The criteria for the optimal operation of gas turbine cogeneration systems were examined from the Kuhn-Tucker conditions of a
18、linear programming model 10. A simplified gas turbine cogeneration system was modeled and the region where the optimal solution existed was illustrated on a plane of the Lagrange multipliers. 2.1. The Gas Turbine Cogeneration System Model The gas turbine cogeneration system was expressed as a mathem
19、atical programming model. The system consisted of a gas turbine including an inlet air cooler and a heat recovery steam generator (HRSG), a steam turbine, an absorption chiller, a boiler and the electricity grid. Figure 1 shows the energy flow of the system. Electricity, process steam, and cooling f
20、or process or for air-conditioning are typical demands in industry, and they can be provided by multiple suppliers. In the analysis, cooling demands other than for inlet air cooling were not taken into account, and therefore, the absorption chiller would work only to provide inlet air cooling of the
21、 gas turbine. The electricity was treated as the electric power in kilowatts, and the steam and the chilled water were treated as the heat flow rates in kilowatts so that the energy balance can be expressed in the same units. Figure 1. The energy flow of the simplified gas turbine cogeneration syste
22、m with the turbineinlet air cooling. The supplied electric power and heat flow rate of the steam should be greater than or equal to the demands, which can be expressed by Eqs. (1-2). (1) (2) where, xe and xs represent the electric power demand and the heat flow rate of the steam demand. The electric
23、 power supply from the grid, the gas turbine and the steam turbine are denoted by xG, xGT and xST, respectively. xB denotes the heat flow rate of steam from the boiler, and xAC denotes the heat flow rate of chilled water from the absorption chiller. The ratio of the heat flow rate of steam from the
24、HRSG to the electric power from the gas turbine is denominated the steam to electricity ratio, and denoted by GT. Then, GTxGT represents the heat flow rate of steam from the gas turbine cogeneration. The steam consumption ratios of the steam turbine and the absorption chiller are given as ST and AC,
25、 respectively. The former is equivalent to the inverse of the efficiency based on the steam input, and the latter is equivalent to the inverse of the coefficient of performance. The inlet air cooling of the gas turbine enhances the maximum output from the gas turbine. By introducing the capacity of
26、the gas turbine, XGT, the effect of the inlet air cooling was expressed by Eq. (3). (3). It was assumed that the increment of the gas turbine capacity was proportional to the heat flow rate of chilled water supplied to the gas turbine. The proportional constant is denoted by GT. In addition to the e
27、nhancement of the gas turbine capacity, the inlet air cooling improves the electric efficiency of the gas turbine. Provided that the improvement is proportional to the heat flow rate of chilled water to the gas turbine, the fuel consumption of the gas turbine can be expressed as GTxGTGTxAC, where GT
28、 is the fuel consumption ratio without the inlet air cooling and GT is the improvement factor of the fuel consumption by the inlet air cooling. As the objective of the optimization is the minimization of the energy cost during a certain time period, t, the energy cost should be expressed as a functi
29、on of xG, xGT, xST, xB and xAC. By defining the unit energy prices of the electricity, gas and oil as Pe, Pg and Po, respectively, the energy cost, C, can be given as: (4) where, B is the fuel consumption ratio of the boiler, which is equivalent to the inverse of the thermal efficiency. All the para
30、meters that represent the characteristics of equipment, such as GT, ST, AC, B, GT, GT and GT, were assumed to be constant so that the system could be modeled by the linear programming. Therefore, the part load characteristics of equipment were linearly approximated. 2.2. The Mathematical Formulation
31、 and the Optimal Solution From Eqs. (14), the optimization problem is formed as follows: (5) (6) (7) (8) where, x = (xG, xGT, xST, xB, xAC). Using the Lagrange multipliers, = (1, 2, 3), the objective function can be expressed by the Lagrangian, L(x,). (9) According to the Kuhn-Tucker conditions, x a
32、nd satisfy the following conditions at the optimal solution. (10) (11) (12) (13) The following inequalities are derived from Eq. (10). (14) (15) (16) (17) (18) Equation (11) means that xi 0 if the derived expression concerning the supplier i satisfies the equality, otherwise, xi = 0. For example, xG
33、 has a positive value if 1 equals Pet. If 1 is less than Pet, then xG equals zero. With regard to the constraint g3(x), it is possible to classify the gas turbine operation into two conditions.The first one is the case where the electric power from the gas turbine is less than the capacity,which mea
34、ns xG 0 on the operational condition II. 2.3. The Optimal Solution where the Electric Power from the Gas Turbine is less than the Capacity On the operational condition I where xG 0, when the solution exists on the line which represents the supplier i. Figure 2 illustrates eight cases of the feasible
35、 solution region appeared on the 1-2 plane. The possible optimal solutions are marked as the operation modes “a” to “g”. The mode a appears in the case A, where the grid electricity and the boiler are chosen at the optimal operation. In the mode b,the boiler and the steam turbine satisfy the electri
36、c power demand and the heat flow rate of the steam demand. After the case C, the electric power from the gas turbine is positive at the optimal operation.In the case C, the optimal operation is the gas turbine only (mode c), the combination of the gas turbine and the boiler (mode d) or the combinati
37、on of the gas turbine and the grid electricity (mode e). In this case, the optimal operation will be chosen by the ratio of the heat flow rate of the steam demand to the electric power demand, which will be discussed later. When the line which represents the boiler does not cross the gas turbine lin
38、e in the first quadrant, which is the case C, only the modes c and e appear as the possible optimal solutions. The modes f and g appear in the cases D and E, respectively. The suppliers The cases A through E will occur depending on the performance parameters of the suppliers and the unit energy pric
39、es. The conditions of each case can be obtained from the graphical analysis. For example, the case A occurs if 1 at the intersection of G and B is smaller than that at the intersection of GT and B, and is smaller than that at the intersection of ST and B. In addition, the line B has to be located ab
40、ove the line AC so that the feasible solution region exists. Then, the following conditions can be derived. (19) (20) (21) Equation (19) means that the gas cost to produce a certain quantity of electricity and steam with the gas turbine is higher than the total of the electricity and oil costs to pu
41、rchase the same quantity of electricity from the grid and to produce the same quantity of steam with the boiler. Equation (20) means that the electricity cost to purchase a certain quantity of electricity is cheaper than the oil cost to produce the same quantity of electricity using the boiler and t
42、he steam turbine. Equation (21) indicates that the reduction of the gas cost by a certain quantity of the inlet air cooling should be smaller than the oil cost to provide the same quantity of cooling using the boiler and the absorption chiller. Otherwise, the optimal solution does not exist because
43、the reduction of the gas cost is unlimited by the inlet air cooling using the absorption chiller driven by the boiler. Figure 2. The possible cases of the optimal solution on the operational condition I Similarly, the following conditions can be derived for the other cases. The condition given as Eq
44、. (21) has to be applied to all the cases below. Case B: (22) (23) Equation (22) compares the production cost of the electricity and the steam between the gas and the oil. The gas cost to produce a certain quantity of electricity and steam by the gas turbine is higher than the oil cost to produce th
45、e same quantity of electricity and steam by the combination of the boiler and the steam turbine. Equation (23) is the opposite of Eq. (20), which means that the oil cost to produce a certain quantity of electricity by the boiler and the steam turbine is cheaper than the purchase price of electricity
46、. Case C: (24) (25) (26) (27) Equation (24) is the opposite case of Eq. (19). Equation (25) compares the boiler and the gas turbine regarding the steam production, which is related to the mode d. In the case C, the oil cost for the boiler is cheaper than the gas cost for the gas turbine to produce a
47、 certain quantity of steam. If the gas cost is cheaper, mode d is not a candidate for the optimal solution, as illustrated in the case C. Equations (26) and (27) evaluate the effectiveness of the steam turbine and the inlet air cooling by the absorption chiller,respectively. The grid electricity is superior to the steam turbine and to the inlet air cooling in this case. Case D: In addition to Eq. (25), (28) (29) (30) Similarly to the ca
