The dynamic model of the combined cycle plant illustrated in this research study is the multi-shaft arrangement. The gas turbine modeled in this study is a linear, non-dynamic device with a specified operating range. In this dynamic model, two main types of controllers, namely the speed controller and the temperature controller, control the CCP of study.
(I) Speed Controller
The speed controller consists of the speed governor, acceleration control, fuel limits and fuel system control.
A speed governor is the main means of control on the operation of the gas turbine, which is used to control the speed of the gas turbine based on whether the CCP is operating in parallel or isolated from the grid.
When the CCP is operating in parallel, the gas turbine is fitted with a droop governor having a droop setting of 10% to 2%. This controller is used or regulate the gas turbine power output that operates on the speed error formed between the reference speed (taken as 1.0 per unit) and the actual speed. The speed control dynamics is described by a differential equation:
On the other hand, when the CCP is operating in isolation with the grid, the gas turbine is fitted with an isochroous governor that integrates the speed error until the speed deviation from the reference is zero, that is, the speed error is zero.
The acceleration control in this model acts as a limiter on the fuel request signal, fr as its output is being fed into the Low Value Select, which will then output whichever requires the least amount of fuel. The primary function of this control is to limit the rate of rotor acceleration during the gas turbine startup. During normal operation, this control helps to reduce the fuel flow to prevent over-speeding in the event that the turbine generator separates from the grid.
In this control, the actual measured speed signal is fed to a differentiator to form an acceleration signal, which is then compared with the maximum acceleration. The acceleration error is then computed based on the difference between the maximum acceleration and the acceleration signal that is then sensed by the acceleration limiter.
The fuel request signal, fr output from the Low Value Select will pass through a fuel limit that comprises of the upper and lower fuel limits (set at 0.7 to 1.5) used to limit the flow of the fuel into the system. A 0.23 offset that takes into account the minimum fuel limit at no-load and self-sustaining conditions is essential to maintain the compressor in operation.
In the fuel system, a time lag, denoted by Tcd, which is associated with the combustion reaction time, is a first order time constant associated with the axial flow compressor discharge volume. Both the torque and the exhaust temperature characteristics of the gas turbine are essentially linear with respect to the fuel flow, Wf and the turbine speed, ω.
Block F1 corresponds to the calculation of gas turbine torque, where the gas turbine torque, Tm varies with the changes of the fuel flow, Wf and the rotor speed, ω:
Tm = 1.3*(Wf – 0.23) + 0.5*(1 - ω)
Block F2 corresponds to the calculation of the exhaust temperature, which can be calculated by processing Wf through F2 when the turbine is working with the IGV fully open. In addition, it can also be calculated by dividing the output of block F2 by the output of block F3 when the IGVs are modulated at partial loads. The equation involved is:
Tex = Tref – 453*(ω2 – 4.21ω + 4.42)*0.82*(1 – Wf) + 722*(1 – ω) + 1.94*(1 – Ligv)
(II) Temperature Controller
The temperature controller consists of the temperature control and inlet guide vane (IGV) control.
In the temperature control, the measured exhaust temperature, Texm, is compared with the reference exhaust temperature, Tref, which is usually taken as 1.0 per unit. The error computed based on the difference between these two values, will then act on the temperature controller. The measured exhaust temperature, Texm is developed from the actual exhaust temperature, Tex via the radiation shield time lag, Trs and the thermocouple time lag, Ttc.
If the error computed is positive, Tref is greater than Texm; the temperature limiter will be at its maximum limit. Hence, the temperature limit will integrate up until its output, Ft, is at its maximum limit. Conversely, if the error computed in negative, Tref is lesser than Texm; the temperature limiter will now come off the maximum limit and integrate down to the point where the output, Ft, takes control over the fuel request signal, fr, by reducing the fuel flow through the Low Value Select.
Therefore, with this temperature control loop in the model, it helps to limit the maximum exhaust temperature, Texm, by limiting the fuel flow. The temperature control dynamics is described by three differential equations:
The next part of the temperature controller is the inlet guide vane (IGV) control where its position is controlled to ensure the firing temperature is kept at an adequate level at all times. This control modulates the angular position of the compressor IGVs in order to control the airflow. This is usually carried out to ensure the efficiency of the turbine to be at its highest possible level under all possible operating conditions.
In this dynamics, the operation of the IGV begins with the measured exhaust temperature, Texm, to be compared with the reference exhaust temperature, Tref. Thus, the error computed will then act on the IGV regulator through an inverting block, -1. For a positive error, Texm less than Tref and the output actuates the IGVs to close by reducing the airflow until the exhaust temperature rises to reference level. However, when the error is negative, Texm greater than Tref, the output will then actuate the IGVs to open by increasing the airflow until the measured exhaust temperature, Texm falls back to the reference level.
The general operation of this IGV control can be reflected using two components, namely, the IGV Regulator and the IGV dynamic. The IGV regulator is a Proportional-Integral (PI) controller that controls the exhaust temperature so that the exhaust temperature error is zero when in operation. However, the IGV dynamic is represented by a first-order time lag, Tv associated with the response time of the IGV position.
This inlet guide vane (IGV) control dynamics is described by the differential equations:
