How does the approach temperature of cooling water affect the power cycle efficiency of CSP plant?

Hello. I've been try to understand how the approach temperature of cooling water affects the power cycle conversion efficiency of a hypothetical wet-cooled parabolic-trough CSP plant located in Mojave, Californa. The attached figure shows the yearly average efficiency as a function of the approach temperature. My question is why T_approach = 10C has the highest efficiency instead of T_approach = 5C. Thank you.

Dear Ablimit,

First, note that the design point rated cycle conversion efficiency, ambient temperature at design, and design cooling requirements are all inputs that you specify on the Power Cycle page. For evaporative cooling as described in see Wagner 2011 "Technical Manual for the SAM Physical Trough Model" available at sam.nrel.gov/concentrating-solar-power/csp-publications.html :

cycle condenser temperature = ambient temperature at design + reference condenser water dT + approach temperature + 3

If you increase the value of an any variable on the right hand side of that equation without changing the design cycle efficiency, the calculated design point cycle condenser temperature increases, but the design point cycle efficiency stays the same. During the simulation, the operating cycle efficiency should be less than the design cycle efficiency when the operating cycle condenser temperature is hotter than design, and greater than the design cycle efficiency when the calculated cycle condenser temperature is colder than the design efficiency.

Second, the power cycle model calculates the operating efficiency and other performance parameters by interpolating data in a lookup table as a function of cycle condenser temperature (among other variables). The available condenser temperatures in the data table range from 24.1 °C (condenser min pressure constraints) to 66.7 °C (practical cycle max operating value), and the model does not allow condenser temperatures outside of this range. So if you choose a design values that results in a condenser temperature of 80 °C, the model still returns the efficiency at the maximum 66.7 °C. Similarly, if the condenser temperature is 10 °C, the model returns the efficiency at the minimum 24.1 °C. These limits are critical to how the model behaves as design point temperatures change.

Consider the following design scenarios, all with the same design point efficiency:

Scenario 1: Ambient temperature = 42°C; cycle condenser temperature = 52°C

During the annual simulation, the efficiency typically will increase between ambient temperatures from 42°C and 14.1°C, and decrease between ambient temperatures from 42°C to 56.7°C. Temperatures colder than 14.1°C will have the same efficiency as the 14.1°C point and temperatures warmer than 56.7°C will have same efficiency as the 56.7 °C point.

Scenario 2: Ambient temperature = 42°C; cycle condenser temperature = 66°C

During the annual simulation, the efficiency typically will increase between ambient temperatures from 42 to 0 °C, and decrease between ambient temperatures from 42°C to 42.7°C. Temperatures colder than 0°C will have the same efficiency as the 0 °C point and temperatures warmer than the 42.7C point will have the same efficiency as the 42.7°C point.

Scenario 3: Ambient temperature = 42°C; cycle condenser temperature = 80°C.

During the simulation, the efficiency typically will remain constant until the ambient temperature drops below 28°C, then decrease from 28°C to -13.8°C.

So in Scenario 1 the cycle efficiency stops increasing at temperatures colder than 14.1°C, while in Scenario 3 the cycle efficiency does not begin increasing until the temperature drops below 28°C. However, in Scenario 2 the cycle efficiency increases between ambient temperatures from 42°C to 0°C.

In reality, maintaining a constant design point cycle efficiency while increasing the design point condenser temperature is a thermodynamically challenging task that, if even possible, requires significant additional cycle component cost. We encourage users to adjust the cycle efficiency input if they are also adjusting either the design ambient temperature, reference condenser water dT, or approach temperature.

Best regards,
Paul.

Hi Paul. Thank you very much for the detailed answer.