The Mathematics
Basic needs
- Original proof of performance test data
- Overall diagram of the power station
Why do you need this?
- To provide a baseline to check the model
- to allow the station to be broken into separate blocks for analysis
- to confirm sufficient data is collected to allow standard thermodynamic and energy balance equations to be defined and solved.
Note that resolving fuel calorific value and boiler performance is difficult. Exergy systems use flue gas composition to do this which has been shown to be of satisfactory accuracy.
This level of analysis is standard first law power station engineering. The next stage is to calculate the second law characteristics of each thermodynamic block (i.e. entropy gain).
Why we need to do this?
- It gives an insight into the work available in each stage
- because entropy is additive stage to stage it allows combinations of parts of the thermodynamic system as well as an overall picture of the complete system to be used in analysis.
This is still standard thermodynamics.
The next steps make the model station specific:
- The data collection points for stages may not correspond to the thermodynamic boundaries so calculation from the point of measurement to the boundary of the thermodynamic block is often required.
- Because the program depends on these calculations and the accuracy of the data provided by the instruments calibration and possibly some additional instrumentation may be required.
At this point you will have a standard thermodynamic system model in terms of mass and energy balance but which now includes the entropy gain of each block in the model and therefore the entropy gain of the whole system.
Up to this point the system has been analysed using standard techniques and equations.
Once this component has been completed the entropy/exergy software takes over as the analysis described has generated all the necessary input and produced an entropy based analysis system for the whole plant. This is the Entropy Monitoring System.
What does the system do with the output from this thermodynamic model?
- It takes commissioning data and benchmarks the thermodynamic performance of the station as a whole
- by looking at actual performance (because the model takes the instrument data and runs the equations in real time) it can identify when the station is not operating to deliver/absorb the work that is benchmarked by the commissioning data
- because the entropy gain of the whole station equals the sum of the entropy gain of each element it enables drill down to assess the performance of individual blocks.
The entropy suite reports this non-conformance in usable and understandable terms. Although this does not optimise performance it provides data and advice to operators to make adjustments to settings that will return the station to its original design performance and provides information on where maintenance effort should be concentrated or identifies plant items that are deteriorating or not performing as expected.
The same data set that is the basis for the Entropy Monitoring System provides the input for the Exergy Optimiser. This requires no more inputs than the Entropy Monitoring System.
Based on a full mathematical approach developed by Dr Yasni which was the basis of his PhD the optimiser allows the performance of the power station as reported by the real-time measurements of the station’s control variables to be optimised using rigorous mathematical techniques. The system transfers the operating parameters from the normal irreversible cycle of the power station to a theoretical construct that models the station as a reversible system as there is proof that the parameters of both systems are the same at their boundaries.
Using geometric space and standard min max optimisation to minimise losses in the reversible system and reversible mapping to transfer the optimised parameters back to the actual system those control variables (common to both systems) can be used to bring the real station to optimum performance. This can be done either by operator intervention or automatically by a closed loop control system.
The Entropy Monitoring System has been used successfully for many years at stations around the world including Eshkol, Kwinana, Bayswater, Mount Piper, Hagit, Macau (diesel), Eraring, and Huntly.
The Exergy Optimiser is still a prototype which has been field tested at Huntly and Kwinana but Dr Yasni’s untimely death stopped development at this stage however he had just reported good results from the Kwinana, a combined cycle station. Preliminary tests at Huntly had already shown up to a 4% improvement in heat rate.