condenser
R142b HP unit
Si evapr/condnsr dump nden!
steam power bottoming unit
cooling water feed pump
Figure 7.11 Flowsheet of second configuration: mechanicallydriven cooling and heating.
configuration two recovery ideas are introduced: a gas turbine regenerator and a vaporcompression cooling unit. The configuration has in total 33 devices, 60 states and 106 decision variables. The decision variables consist of 53 efficiency parameters (local decisions), 5 global. The rest are boundary and groundrules decisions.
The second configuration (Figure 7.11) consists of a gas turbine operating as a combined cycle producing only power. Cooling is supplied by a mechanical vaporcompression system and heating is provided by a heat pump. Refrigerant R142b is the working fluid in both mechanical systems. The heat pump is fed by part of the combined cycle condenser heat. The configuration has 28 process devices, 48 active states and 90 decision variables. The decision variables are 51 efficiency decisions and 7 global. The rest are boundary and groundrules decisions.
403530252015105
power cooling
;ooling power heatine cooling power pooling power
.heating hot wtr heating heating
Demand Profiles Main Features Of Demand Profiles
Max and Min Power MW 30 & 8 Load Factor 0.6778
Max and Min Cooling MW 36& 20 Load Factor 0.7940
Max and Min Heating MW 15& 3 Load Factor 0.4389
Max and Min Hot wtr MW 10& 2 Load Factor 0.6000
Average delivery MW of MW Exergy
61.49 22.96
403530252015
Power 2
Coolirfg 1
Heating 1
12 16
20 24
Production Profiles Of The Reference Cases Of Configurations 1 And 2
Figure 7.12 Demand and available profiles: reference cases of configurations 1 and 2.
The local and the global decisions can be handled by automated optimization. All the decisions can be changed manually. However, the boundary and the fixed decisions are kept constant throughout the investigation.
Figure 7.12 shows the demand profiles of power, cooling, heating and hot water assumed as given and the values that characterize their variability. The figure also shows the available powermatching cooling, heating and hot water profiles for the reference case of the first configuration and the power profile for that of the second configuration.
The period r of repeatable pattern is taken 24 h. The minimum duration of a load is taken as 1 h. Neither the period nor the duration put any limitation to the method as described in the section of timedependent production. In evaluating the ideal offdesign operation, it is helpful to think of the load factors of the demand profiles as being also time duration ratios of onoff operation at design conditions. The powertofuel efficiency obeys a relation described by Equation 6.4. The extrapolated zeroload efficiency a is set at 0.2 that of the design efficiency and the design efficiency is set at the peak power load.
Each configuration is first treated as baseload production system at four efficiency levels. The highest efficiency assumed high firing temperature using cooledblade turbine. At each level the system is run through the repeatable pattern of the load profiles to compute the offdesign fuel penalty for the assumed system efficiencytoload relation. The objective function J is the production cost and is computed on two steps according to the Equation 6.3.
For the first configuration, mismatches are simply handled by dumping and refiring. Hot gases are vented at the exit of the gas turbine when heat available is more than demanded and refiring more fuel at the exit of the gas turbine when heat available is less than demanded. When heating and cooling demands are satisfied and excess heat goes to the domestic hot water, hot water is dumped.
A regenerator is proposed to recover heat from the vented gas by heating the air before entering the gas turbine combustion chamber.
A vaporcompression refrigeration cycle for cooling (R12) is proposed to reduce refiring when the absorption refrigeration cooling is less than demanded.
No measures are taken to recover heat from the dumped domestic hot water.
For the second configuration, the fuel input is controlled to meet the sum of the electrical power, the power for the mechanical vapor compressor and the power for the heat pump. No dumping or refiring is needed for this configuration. Another advantage is that the sum of the three loads tends to have less variability than the individual demands.
The efficiency levels of the second configuration are higher than the first and so is the cost.
7.2.2.2 Results using the simplified offdesign systemefficiency: Several runs were made to investigate the influence of a number of factors on offdesign performance. These factors include: changing the design points of each configuration, changing the design points of the added offdesign recovery devices and changing the quoted overall system performance equation as function of the power loading ratio. The results are summarized in the costefficiency diagram of Figure 7.13. The results are also tabulated in Table 7.5. The following observations may be noted:
• The handling of the timedependent problem as a baseload problem and an offdesign penalty problem appears encouraging. In this application the two problems can be assumed decomposed.
• Variable operation reduces efficiency and increases cost per unit product or unit reference product in more than one product system.
• Higher baseload design efficiency allows higher operation efficiency.
• Added recovery devices to reduce the fuel penalty of dumping and refiring of the first configuration depend on the system design efficiency. This complexity emphasizes the importance of a screening method.
 For example, for the reference design efficiency of about 30%, the regenerator and the vapor compression solutions were costineffective. Dumping and refiring seem to be the answer.
 For the lower efficiency of about 20%, the VC solution was not needed because of the absence of refiring, and the use of the regenerator became costeffective
Efficiency = Sum of Energies Delivered / Fuel Exergy
Figure 7.13 The costefficiency diagram: variableload cost penalty vs. baseload cost.
Efficiency = Sum of Energies Delivered / Fuel Exergy
Figure 7.13 The costefficiency diagram: variableload cost penalty vs. baseload cost.
Table 7.5 Penalties of timedependent production systems.
Parameter Configuration 1 (Venting/Refiring) Configuration 2
Reference Optimum Low Eff HiFire Optm Reference: Optimum Low Eff HiFire Optm
Reference Optimum Low Eff HiFire Optm Reference: Optimum Low Eff HiFire Optm
Design 
1551 
1279 
2597 
1085 
1515 
1434 
2036 
1194 
Ideal operation 
1182 
997 
1958 
819 
1237 
1176 
1636 
975 
Expected operation 
1309 
1221 
2109 
1040 
1299 
1233 
1723 
1023 
2. Fuel rate (MW) 








Design 
114.4 
87.5 
198.2 
82.5 
101.5 
92.0 
147.8 
78.4 
Ideal operation 
77.6 
59.3 
134.3 
55.9 
73.7 
66.0 
107.8 
56.5 
Expected operation 
90.3 
81.7 
149.4 
78.0 
79.9 
71.9 
116.4 
61.2 
3. Devices ($/h) 








(design, operation) 
407 
404 
615 
260 
500 
514 
558 
410 
4. Products exergy cost ($/kWh) 








Design 
0.0453 
0.0364 
0.0759 
0.0309 
0.0449 
0.0425 
0.0603 
0.0354 
Ideal operation 
0.0515 
0.0425 
0.0853 
0.0349 
0.0546 
0.0519 
0.0722 
0.0430 
Expected operation 
0.0570 
0.0520 
0.0918 
0.0443 
0.0573 
0.0544 
0.0760 
0.0451 
5. Second law efficiency 








Design 
0.3179 
0.4072 
0.2046 
0.4320 
0.3507 
0.3874 
0.2412 
0.4550 
Expected operation 
0.2763 
0.3120 
0.1670 
0.3271 
0.3079 
0.3426 
0.2115 
0.4024 
6. Timedependence penalty 








Fuel penalty (MW) 
7.540 
17.40 
43.80 
17.40 
6.124 
5.667 
8.714 
4.825 
Cost penalty (%) 
25.8 
42.9 
21.0 
43.5 
4.043 
3.952 
4.280 
(icontinued)
Table 7.5 (Continued)
Configuration 1 with energy recovery
Expected operation with a regenerator
Regenerator cost (S/h) 
14.40 
 
103.7 
 
Fuel saving ($/h) 
6.864 
 
136.4 
 
Net saving ($/h) 
7.551 
 
32.8 
 
Products exergy cost ($/kWh) 
0.0573 
 
0.0904 
 
Second law efficiency 
0.2784 
 
0.1838 
 
Expected operation with a VC chiller 




VC cost (S/h) 
41.40 
68.0 
 
69.0 
Fuel saving ($/h) 
13.90 
80.9 
 
84.0 
Net saving (S/h) 
27.54 
12.9 
 
15.0 
Products exergy cost ($/kWh) 
0.0582 
0.0515 
 
0.0437 
Second law efficiency 
0.2806 
0.3426 
 
0.3666 
Design exergy delivered = 34 MW, exergy to be delivered = 23 MW, revenues = 1964 S/h. Main ground rules
Fuel price 0.01 $/kWh (higher heating value).
Products market values $/kWh: power 0.045, chilled water 0.03, Heating water 0.02, Hot water 0.01. Common capital costing equations (common design models). Common load profiles, no power exchange with the grid.
Common offdesign to design efficiency profile (quadratic efficiency vs. power load ratio equation). Common temperatures for chilled water, heating water, hot water and ambient.
350"
Performance eqn: Qj= 
ai+b,*XLi2 
b; Mwpwr 
eff % 
1 90.0 96.0 83 
44.5 
2 60.7 21.3 27 
33.0 
3 186.7 53.3 120 
50.0 
4 224.0 171.0 150 

 Figure 7.14 Performance equations of a mix of plants.
after allowing for storing the energy of the vented gas. Designing on mean load, the costeffectiveness of the regenerator improved.
 For the higher efficiency of about 40%, the regenerator solution was not needed because of the absence of gas dumping and the VC solution became more cost effective than refiring. Designing the VC on mean load and allowing for an icemaking storage unit improved further the cost effectiveness.
• The sensitivity of the quoted overall system performance equation from similar existing plants does not seem to have relevant effect on the reliability of the screening method.
 The extrapolated zero load efficiency of Equation 6.4 set at 0.2 was changed from 1 (ideal control) to —0.2. The deviation factors (Equations 11 and 12) from ideally controlled performance were less than 1.5. The cost increase from the ideally controlled performance case was only 6%.
• Runs assuming constant power production by allowing buying and selling transactions with the grid at prevailing power market price showed in general higher efficiency and lower cost than those in the standalone case. The value of the produced power influences both cost and efficiency.
7.2.3 The optimal operation of a mix of power plants
The application considers a group of single purpose power plants available for operation. The overall performance equation of each plant can be satisfactorily
Table 7.6 Load assignment for optimal operation of a facility of plants 380 MW.
Run 
Load P, 
Qf 
Xu 
Xl2 
*L3 
XL4 

MW 
MW 
_ 

_ 
_ 
1 
380 
903.0 
1.000 
1.000 
1.000 
1.000 
2 
360 
859.4 
0.915 
0.978 
1.000 
0.917 
3 
340 
819.8 
0.830 
0.940 
1.000 
0.836 
4 
320 
783.7 
0.752 
0.891 
1.000 
0.757 
5 
300 
751.5 
0.673 
0.832 
1.000 
0.678 
6 
280 
722.6 
0.594 
0.767 
1.000 
0.600 
7 
260 
697.3 
0.517 
0.696 
1.000 
0.522 
8 
240 
675.3 
0.440 
0.620 
1.000 
0.445 
Optimal and arbitrary assignment
280 
722.6 
0.594 
0.767 
1.000 
0.600 
280 
726.7 
0.494 
0.561 
1.000 
0.691 
280 
726.3 
0.644 
0.717 
0.950 
0.621 
280 
750.6 
0.794 
0.867 
0.700 
0.711 
280 
780.3 
0.894 
0.967 
0.500 
0.798 
expressed by a quadratic equation between load ratio 1 and a minimum allowable load ratio around 0.3. A facility of four available power plants is considered. The quadratic form assumed is Q = a + bX2, where Q = fuel consumption rate in kW and X = the load fraction. The performance equations are shown in Figure 7.14 and the results of arbitrary and optimal operation are given in Table 7.6. The loading of the plants is such that total fuel consumption is minimized. The minimization procedure is that of the Lagrange multiplier using only one multiplier. The fuel consumption equation is augmented by a constraint that expresses the sum of partial loads to be equal to the demand, for a time period of constant demand, along with an undetermined multiplier to the constraint to treat the load fractions as decision variables. This ties the constant b of a load to the Lagrange multiplier. The procedure is detailed in Section 6.4.
It may be noted that the overall performance equation can be fuel consumption per unit product or product per unit fuel (efficiency). The first form is to be minimized. The second is to be maximized. The analysis is also applicable to two product plants if the demand for one of the products is constant.

Was this article helpful?
Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. Get My Free Ebook
 
Post a comment