Parallel Coordinates and Application to Analysis and Control

Thermodynamic Surface Representations

The high pressure turbine icon as well as the five feedwater heater icons on the power plant cycle diagram below provide information regarding the thermodynamic status of the input and output stages of each component. For example, by clicking on the icon labeled FWH1, an image appears with 4 horizontal colored lines and 4 vertical parallel lines (parallel coordinates) labled TIME, PRESSURE, ENTHALPY, and TEMPERATURE. Each horizontal line represents the pressure, enthalpy, and temperature of either a real or ideal, inlet or outlet process. (See the KEY below the diagram)

In any component case, (FWH1 for example) a real process is defined by data obtained from a steam power plant performance program (PSLAM). On the other hand, the ideal process for the feedwater heaters is defined by a steady-flow, adiabatic, constant pressure process. By choosing the inlet to the first feedwater heater as a datum, the ideal inlet and outlet state data can be calculated for all five of the feedwater heaters using the first law of thermodynamics. The ideal processes, (P1,h1,T1) and (P2,h2,T2), represent an upper and lower boundary surface for a component. The areas between the real and ideal input or output lines contains quantitative information on the performance of the feedwater heater. For instance, to achieve a greater efficiency, the real process lines (P1,h1,T1) and (P2,h2,T2) should lie within area of the upper and lower boundary surface. For the diagram below with five feedwater heaters, a greater temperature is reached ideally at the outlet state of FWH5 in comparsion to the real process. Since less heat would have to be added to the working fluid in the boiler (the next component after FWH5) the net thermal efficiency of the cycle would increase. Thus, as the real output polygonal line approaches the ideal output line, a greater net thermal efficiency will be achieved.

A similar procedure was used to represent the thermodynamic surface of the high pressure turbine. First a group of state parameters (P1,T1,V1) was chosen for the inlet of HP turbine. There are two paths to the outlet state of the turbine: one is the ideal process and the other is the real process. It is assumed that the pressure at the outlet (P2) is the same in these two cases, but the tempurature (T2) and specific volume (V2) are different. For a turbine, the ideal process is an adiabatic process. The ideal (T2) and (V2) data is caluclated by hand using the first law of thermodynamics while the real process data is obtained from the PSLAM program. In parallel coordinates, the real process (P1,T1,V1) will form an upper boundary surface and (P2,T2,V2) of the ideal process will form a lower boundary. The polygonal line representing the real process lies within this surface. As the red line approached the green line in this case, a greater thermal efficiency can be achieved.

Power Plant Cycle Diagram

Power Plant Diagram

Click on HP Turbine or FWH 1-5 to access Thermodynamic Data

Key to Feedwater Heater Images:
Blue Line: P1,h1,T1 REAL Process (Inlet)
Red Line: P1,h1,T1
IDEAL Process (Inlet)
Green Line: P2,h2,T2
REAL Process (Outlet)
Pink Line: P2,h2,T2
IDEAL Process (Outlet)

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