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
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)