Combine Heat Balance with Data Analytics to Monitor and Detect Changes in Performance


Multi-Variable Correlations

Overview

Correlations work well when one variable (such as gas turbine power) is a function of several independent variables. This is usually the case for the output of equipment whose operation depends upon control settings and the properties of the inlet flow streams. Examples are condenser pressure, HRSG steam flow, steam turbine power, gas turbine power and heat rate, boiler efficiency and compressor efficiency. 


Regression analysis fits a correlation to historic (training) data. The correlation is a formula that specifies the value on one variable (Y) as a function of up to five independent variables [X(i)]. Once the correlation is established, it can be used to predict the expected value of the Y variable as operating conditions change. 


Gas turbine vendors typically provide correction curves that predict the change in baseload power of the gas turbine as ambient conditions and inlet-outlet pressure losses change. If the curves do not match your engine's performance or if you want to predict part-load performance, you can create a correlation and train it with historic data from your engine. 


Part-load is implemented by the control system by closing the inlet guide vanes and lowering the firing temperature.  The correlation uses the measured inlet guide vane angle and the  turbine inlet temperature calculated by the heat balance as X variable.


The figure above shows the measured and predicted powers over ten days of operation at part-load where the guide vanes were partially closed and the turbine inlet temperature (TIT) was less than the baseload TIT (1250 C). The correlation predicted the measured power with an average error of less than 0.5%.


Correlations are particularly useful when correction curves are not available or do not cover the typical range of operation of the equipment. The HP steam flow of an HRSG (heat recovery steam generator) is a function of the inlet gas flow, temperature and composition. Vendors do not supply correction curves for these variables, but it is easy to generate a correlation that will accurately predict the expected steam flow. The gas flow to the HRSG is calculated by the MapEx heat balance and the gas turbine exhaust gas temperature is measured. If the water content of the gas is expected to vary, the water fraction of the exhaust gas can be added as an additional X variable in the correlation.

Applications

Correlations can be used to predict expected values for:

   Aux power

   Boiler efficiency

   Condenser pressure

   Fan power

   Feedwater heater TTD and DCA 

   Gas turbine heat rate

   HRSG steam generation

   HRSG efficiency

   Plant heat rate

   Plant power

   Steam turbine efficiency

   Steam turbine discharge enthalpy

   Steam turbine power