The initial state for the transient engine model.
The scope of this chapter is to assess the performance of hybrid power plants and more specifically demonstrate the challenges of partnering the wind turbines with gas turbines. A dynamic engine model of a gas turbine along with a wind turbine model is developed to simulate plethora of scenarios for optimizing their operation in terms of efficiency, fuel consumption and NOx emissions. Moreover, a comparison between the hybrid power plant and a twin gas turbine power plant is carried out to assess the improvement in both NOx emissions and fuel consumption. The results demonstrate and illustrate the significant impact that dynamic performance modeling has in the optimization and controller design of hybrid power plant.
- wind energy
- gas turbine
- wind turbine
- dynamic modeling
- engine control
The expansion of wind power plants has transformed the gas turbines operation. The intermittent nature of wind prompts the gas turbines to operate with increased flexibility, for supporting their renewable plant partners and maintaining the stability of the electricity grid [1, 2]. Fast starts, shut downs and part load operation [3, 4, 5] are governing the operating profile of modern engines. It is vital, for an effective operation and maintenance (O&M) strategy, to employ tools and technologies that will support our understanding for these complex and nonlinear machines. Towards this end, gas turbine manufacturers have developed a suite of programs and systems that can model, monitor and analyse a plants performance .
Performance models of gas turbines, also called digital twins, play a significant role [7, 8] towards optimizing their operation. Apart from a few examples in the literature [9, 10, 11] most studies focus on steady state performance of gas turbines. Recently, their transient behaviour has attracted attention since they are required to act in partnership with renewables which are characterized by their intermittent nature.
Dynamic performance models of gas turbines are capable of facilitating the design of controllers that will enable the engines to fulfil their demanding new role . From a condition based maintenance point of view, dynamic engine models enable health monitoring, diagnostics [13, 14, 15, 16] and prognostics [17, 18] capabilities.
Consequently, the recent shift in the operating envelope of the gas turbine has amplified the interest for developing real-time computationally efficient and accurate engine models that can help gas turbine operators to have an informed judgment about their assets. Furthermore, the monitored behaviour of the engine at transient conditions can facilitate the controller design for plethora of scenarios that involve gas turbines working in partnership with other energy sources.
Among the various methods [19, 20, 21, 22] proposed in the literature for gas turbine performance simulation, the most common is the zero dimensional (0-D) approach [14, 23] which can be also used for real time monitoring, diagnosis and prognosis. From the transient performance analysis of a gas turbine one can identify important trends in performance that could potentially initiate surge of compressor or exceed temperature limits of engine. The simulation of plethora of scenarios provides important insights of the engine’s behaviour and this is evident in cases where carrying out an experiment is either not feasible or may be catastrophic for the engine .
The two fundamental approaches for dynamic engine simulation are the iterative constant mass flow (CMF) method [25, 26, 27] and the inter-component volume (ICV) method . Both of these methods have been extensively used for performance simulation studies of gas turbines [29, 30, 31, 32, 33, 34, 35]. The ICV approach is based on the flow imbalances during transient operation, where the CMF approach relies on the iterative minimization of key thermodynamic parameters that are initially guessed.
In this chapter, a model of a two-shaft gas turbine is developed in MATLAB/Simulink environment and coupled with a wind turbine model in order to assess the behaviour of the hybrid power plant in dynamic operating conditions. The developed engine model combines the above two approaches, since the CMF iterative method [36, 37] used for steady state is subsequently integrated with the ICV method for transient performance simulation.
The dynamic engine model utilizes component characteristic maps and is coupled to the governing thermodynamic equations of the engine cycle. The simulated scenarios of the engine operating under transient conditions provided key findings that would be hazardous for an actual gas turbine. An engine controller has been developed for enabling smooth and safe engine operation. The engine model has been validated towards PROOSIS  gas turbine simulation software. Furthermore, the behaviour of model is examined when the engine is coupled to a wind farm in a hybrid arrangement.
A generic model of a wind turbine has been developed in Simulink and coupled with the gas turbine model. The energy demand and the wind speed are designed to vary with respect to time which forces the gas turbine to work under transient conditions. This scenario provides additional information on the dynamic behaviour of the gas turbine and can also serve as a guide in controller design for hybrid plants. Finally, the hybrid plant’s performance is compared to a twin gas turbine only power plant for estimating the capability of the gas turbines to shut down and their emissions.
The remainder of this chapter is organized as follows. In Section 2, the methodology employed for the transient performance simulation along with the controller design are described. The results of the case studies are presented and discussed in Section 3, followed by the conclusions in Section 4.
2.1 Gas turbine mathematical model
For this study, the industrial gas turbine developed by the author in MATLAB/Simulink , is briefly discussed in this chapter. The main components of the gas turbine are the compressor, combustor, and turbine. The gas turbine’s exhaust gases are driving a free power turbine which is coupled to an electricity generator, as seen from Figure 1.
Station ‘1’ denotes ambient air pressure and temperature. The following notation is used throughout the chapter. Temperatures and pressures are denoted by and , respectively where subscript represents the engine station.
The performance of the compressor is represented by a characteristic map which presents the interrelationships between pressure ratio , isentropic efficiency , corrected mass flow , and corrected shaft rotational speed . Scaled maps from PROOSIS  simulation software have been used in this model.
Once the outputs of the map are determined, the temperature rise across the compressor is computed as follows:
The work required to drive the compressor is given by
where denotes the specific heat of air.
The energy balance equation is governing the performance of the combustor as follows:
where represents the fuel’s low heat value, and is the specific heat of combustion products. The heat input of the system is expressed as follows:
which is further implemented for estimating the cycle’s thermal efficiency .
Regarding emissions, the nitrogen oxides model developed by Rokke et al. , and validated by Pires et al. , is implemented in this gas turbine model. The emissions are estimated from the following equation:
where denotes compressor pressure ratio, denotes air mass flow rate, and denotes fuel to air ratio (i.e. ). The emissions are measured in parts per million by volume (ppmv) at 15% .
Similar to the compressor, turbine performance is represented by a set of characteristic maps that present the interrelationships between turbine pressure ratio , corrected mass flow , efficiency , and corrected rotational speed .
It follows that the temperature drop across the turbine is computed by:
where is the heat capacity ratio of combustion products and for preliminary performance calculations it may be assumed constant, i.e. . The work extracted by the turbine is given by:
where represents the specific heat of combustion gases and is the mechanical efficiency.
2.1.4 Power turbine
Similar to the turbine, the performance of the power turbine is represented by characteristic maps that present the interrelationship between pressure ratio , corrected mass flow , efficiency , and corrected rotational speed .
The temperature drop across the power turbine is given by:
In this chapter, the speed of the free power turbine is assumed constant since it is connected to an electricity generator. The work delivered by the power turbine is the useful work of the cycle and is given by:
The thermal efficiency of the gas turbine system is given by:
and expressed as a percentage.
2.2 Dynamic simulation
The ICV method has been implemented in the development of the engine model in MATLAB/Simulink environment [45, 46]. This method works on the principle that mass flow imbalances occur during transient operation. Two plenum volumes, one before the turbine and one after the turbine, have been added to the model, as seen from Figure 2. The component maps for compressor, turbine and power turbine are the same as the steady state model.
The fuel addition initiates the mass flow imbalances which are used to calculate the rate of pressure variations. The description of the process is provided in the following subsections.
Combustor: Volume 1—The mass flow continuity is used to calculate the pressure in the combustor volume, as follows:
where , , and denote gas constant, combustor volume, and compressor delivery pressure, respectively. The combustor outlet pressure can be calculated as a simple proportionality from:
where is the combustor pressure loss factor and for this study a 5% drop in pressure is assumed.
Duct: Volume 2—The pressure at the exit of the gas turbine is given by:
where and denote duct volume and turbine delivery pressure, respectively. The turbine outlet pressure can be calculated as a simple proportionality from:
where is the turbine pressure loss factor and for this study we assumed that there are no losses between the turbine and the power turbine, i.e. .
Shaft—The difference between compressor and turbine work , is used in the computation of the engine’s acceleration which is given by:
where is the shaft polar moment of inertia measured in kg m2.
System states—Assuming that the system’s state is denoted by , and the set of variables is represented by then the state and control variables are defined as follows:
The pressures and , and shaft rotational speed , at design point conditions are the input parameters of the model. To summarize, the gas turbine dynamics may be expressed as:
2.2.2 Simulation process
The initial state values for the transient engine model are summarized in Table 1.
|Compressor discharge pressure||1472||kPa|
|Turbine exit pressure||406||kPa|
|Gas generator shaft rotational speed||9000||rpm|
It is noted that at steady state conditions the derivatives , and are all zero.
2.3 Controller design
Controller design is crucial for achieving a safe and reliable engine operation. Among a variety of controllers suitable for gas turbine engines, the one implemented in this study is a PI controller. Its objective is to regulate the fuel flow rate by comparing the speed demand with the measured speed of the gas turbine. To achieve this both the fuel flow actuator and the speed sensor are modelled by simple first order transfer functions [23, 32].
The process of the controller’s operation is schematically represented in Figure 3. The actuating signal is driving the controller to generate a demand for fuel flow rate which is then translated to the movement of the actuator in order to admit fuel into the combustor. The engine responds to this command and the measured engine speed is compared to the desired one.
The control function of this PI controller can be expressed as follows:
where , and , denote the coefficients of the proportional and the integral terms, respectively. The transfer functions for the fuel system actuator and the speed sensor are given by:
The reader is prompted to , if a more advanced controller design is pursued. However, for this study which focuses on enabling the engine to respond in a safe manner during transient operation the proposed controller is capable to achieve this objective. The proposed model has been validated towards PROOSIS gas turbine simulation software and a full description of the validation case studies can be found in .
2.4 Wind turbine model
A generic model of a wind turbine, available from MATLAB/Simulink , is used in this study in order to assess the operation of a hybrid power plant when the gas turbine is coupled to a wind farm.
The wind turbine’s performance is governed by pitch angle , wind speed and wind turbine speed . These are commonly represented in a performance map, as seen in Figure 4. The power output of the wind turbine is given by :
where denotes the mean air density over the rotor swept area , denotes mechanical efficiency of bearings, gear box, generator, etc., denotes electrical efficiency of transformer, converter, etc., denotes the mean of the cubic wind speed and denotes the power coefficient. The power coefficient depends on the blade tip ratio and the blade pitch angle . For this study a generic equation is used as follows :
where , , , , , and . The blade tip ratio relationship with pitch angle is given by:
The wind turbine model has three inputs namely , , , and one output .
The hybrid gas/wind power plant consists of a gas turbine and a wind farm with variable power output. The total power output from the hybrid power plant is given by:
The energy gap imposed by the wind turbines is covered by the gas turbine. This difference is expressed as follows:
Any instant that the demand is not met, then the gas turbine has to respond by adjusting its fuel flow regulation. An algebraic constraint is used to constrain the difference to zero (i.e. ) by tuning the value of the demanded speed from the gas turbine. The schematic diagram of the developed models is shown in Figure 5.
It should be highlighted that the wind turbine used here is a generic and simple model that fits the objective of this study. If one seeks a high fidelity performance assessment of wind turbines, the reader is prompted to studies [41, 42, 43, 44] which address the dynamic response of the wind turbine at a greater detail.
3. Results and discussions
3.1 Case study 1: transient step response with PI controller
This case study examines the transient performance of the engine when a PI controller is implemented. The controller enables a smooth and safe engine operation. The schematic diagram of this control arrangement is shown in Figure 6.
The PI controller tunes the fuel flow rate according to the actuating signal arising from the difference of demanded and measured shaft speed. The controller design toolbox in Simulink provides a visual representation of the system’s behaviour and the user can select the desired response characteristics. this translates into a unique set of control coefficients and , that update the engine’s controller. The compressor surge and combustor flame-out limits, described in detail in , are also integrated into the controller subsystems of the model, as seen from Figure 7.
The controller has to regulate the fuel flow into the engine by ensuring that this command lies within the surge and flame-out limits. So depending on the demanded shaft speed and the ambient conditions , , two look up tables are used to calculate the fuel flow rates that correspond to the surge and flame-out limits of the engine. When then fuel flow rate computed by the PI controller violates these limits, then a switch is used to bound the final fuel flow rate demand within them, as seen from Figure 7.
For this case study, the coefficients of the PI controller and the transient response characteristics are summarized in Table 2.
Repeating the simulation of the engine model in Simulink results in a controlled engine behaviour. A comparison between the behaviour of the engine model without and with a PI controller is seen in Figure 8.
It becomes clear from Figure 8 that is no longer exhibiting an oscillating behaviour during this sudden increase in the demanded engine speed, since the fuel flow has been modified through the PI controller.
It is evident from Figure 8 that without a PI controller, where the fuel flow command was not regulated, a large operational regime has occurred that would have violated the firing temperature limits and may have led to compressor surge. The implemented controller has resolved the above issue by regulating a fuel flow rate that results in a smoother engine operating profile.
3.2 Case study 2: hybrid gas/wind power plant
The objective of this case study is to assess the performance of the gas turbine when it is coupled to a wind farm. The design point performance of the wind turbine is summarized in Table 3, and this refers to a generic wind turbine model available in .
The time increment of the simulation is 1 ms and for a 10 s simulation there are 10,000 operating points. The results are correlated to a 10 h operation, which means that for every minute there are 16 operating points. The size of the data support the above decision as the nonlinear behaviour of the gas turbine is well captured. The hybrid power plant, seen in Figure 9, consists of a gas turbine and 14 wind turbines.
The variation of wind speed with respect to time can be seen from Figure 10. This variation is designed by having in mind that the gas turbine will commence its operation close to its design point. At the 2 and 5 h mark the gas turbine will have to respond to this change by decelerating and following the demand according to the intermittent power output of the wind turbines.
The required power from the power plant ranges from 28 MW up to 37 MW. The above is combined with the varying wind speed, and the resultant power output of each system is shown in Figure 11.
The PI controller discussed in case study 1 is utilized here in combination with the algebraic constraint optimizer. The PI controller parameters are the same as case study 1.
The power output varies with respect to time, as seen from Figure 12, where the percentage of power output of each system is illustrated. The wind farm contributes up to 70% of the demanded power, while the maximum power output contribution from the gas turbine is 75%. A closer look at the shaft rotational speed and exhaust gas temperature , from Figures 13 and 14, reveals the dynamic response of the gas turbine.
Figure 13 shows that the speed of the gas turbine’s is dependent on the wind speed which essentially dominates the behaviour of the wind farm. A pattern of similar form is shown in the variation of the gas turbine’s exhaust temperature, seen in Figure 14.
3.3 Case study 3: hybrid power plant comparison with a twin gas turbine plant
The primary aim of this case study is to carry out a comparative study between the hybrid power plant and a plant that consists of two gas turbines only. To make the comparison easier the hybrid power plant is referred to as Plant A and the twin gas turbine plant is referred to as Plant B. Plant B’s gas turbine engines are identical to the one of Plant A. The demanded power from both plants is the same. The simulated scenario of this study corresponds to 10 h operation. The emission and fuel consumption for both plants are assessed. The power demanded from each plant can be seen in Figure 15.
It should be noted that the demanded power signal has been designed in such a way so that there are two occasions during which the power drops significantly and peaks up again. There are two periods for which the engine of Plant A will be required to shut down, in order to assess its shut down capabilities.
Figure 16 shows that the power output from the gas turbine and wind turbines of Plant A. One hour into the operation, the gas turbine slowly decreases its power output until the 2 h mark and will remain shut for half hour. After the 30 min break the engine will fire up again, reach a power output of 25 MW and hover over this power setting for another 3 h. At the 6 h mark, the engine will experience another shut down event and will remain inactive for 1 h before starting up again and remaining at approximately 26 MW for the final 2 h of operation.
1 h of operation, the power required from the engine decreases slowly with respect to time and forces the engine to shut down and remain inactive for 30 min. It then starts up again and in approximately 25 min reaches a power setting close to its design point for the next 3 h. At the 6 h mark, the power output reduces faster as it takes approximately 10 min to shut down the engine.
Traditionally, current industrial gas turbine engines are capable of shutting down in less than 10 min . On the other hand, a hot start up (i.e. less than 8 h standstill) process may take less than 0.1 h (i.e. 6 min) with a ramp rate up to 15% of nominal load per minute . In addition, the fastest the start-up  and shut downs are, the greater the economic benefit and the life cycle reduction are going to be. Therefore start up and shut down processes should be optimized by taking into consideration several operational constraints. The gas turbine of the hybrid plant in this case study is exhibiting fast response behaviour which is beneficial for the wind turbines (Figure 17).
Meanwhile, the wind turbines remain operational during the entire 10 h. Given that the power demanded from the plant has two occasions with significant load fluctuations, both of them have to be accommodated by the flexibility of the gas turbine since the wind farm’s power capacity has a priority in the grid for this hybrid power plant.
For Plant B, both gas turbines have an identical load distribution, as shown in Figure 17, and meet the demanded power. In contrast to the Plant A gas turbine, Plant B engines operate at part load off-design conditions. The power output has a substantial effect in the emissions of gas turbines, as observed from Eq. (5), since the higher the pressure ratio, the higher the TET and therefore the higher the emissions are going to be.
The emissions of both plants are shown in Figure 18. As expected, the emissions from Plant B are significantly higher than those of Plant A. The amount of emissions reduction is illustrated in Figure 19, where the emissions of Plant A are compared to those of Plant B as a percentage.
The emissions of Plant A are initially 43% less than that of Plant B and increase to 100% when the gas turbine of Plant A shuts down. Regarding the fuel consumption, Plant A consumes less fuel compared to Plant B, and this accounts to 48%, as seen in Figure 20. Note that the fuel reduction represented in Figure 20 refers to the accumulated fuel flow. This case study amplifies the significance of transient observations arising from simulating various dynamic operating scenarios of gas turbines. Key findings about their behaviour, performance, environmental impact and flexibility add value to our understanding of this technology especially when it is coupled with renewables. Finally, fast transient gas turbine manoeuvers are essential to the stability of the grid in hybrid power plant arrangements. Additional promising technologies for wind speed forecasting might enable smoother transient gas turbine operation in a hybrid gas/wind power plant.
As far as practical issues are concerned the developed model can be further improved by a number of useful additions such as variable pitch control of the wind turbine [50, 51], wind forecasting models , and adaptive model-tuning. Another important aspect of this developed model is the fact that it enables users to simulate numerous scenarios and can potentially feed its simulated measurements into a multi-objective optimization process for improving the performance of gas turbine. In addition, the model can accommodate degradation case studies  at component and system level for improving the prediction accuracy and the computational efficiency of diagnostic and prognostics algorithms.
In this chapter, a novel gas turbine engine model is presented that aims to capture the nonlinear behaviour of modern gas turbines. The gas turbine model is created in MATLAB/Simulink.
The engine model consolidates the iterative constant mass flow approach in steady state conditions for initializing the state parameters to the dynamic model, which utilizes the inter-component volume technique. The dynamic response of the model has been evaluated for a hybrid gas/wind power plant comprising of 14 wind turbines. The result of this analysis features the quick transient trajectories that the gas turbine encounters as the consequence of variable wind speeds and fluctuating energy demand. In addition, the behaviour of the hybrid power plant underlined the requirement for transient simulation scenarios since several operating challenges must be addressed to maintain stability in the grid. Finally, the comparative study of the hybrid power plant to a twin gas turbine plant for a 10 h operation showed that the emissions decrease from 40% to 100% depending on the power setting of the engine.
The modularity, robustness and computational efficiency are key feature of the developed engine model. The above features facilitate the performance assessment and controller design of gas turbines that operate under transient conditions. Furthermore, the developed engine model can improve our understanding for these complex machines and enables us to optimize the energy dispatch of a hybrid power plant. The proposed model can also serve as a useful tool and guide in optimizing the performance of a gas turbine powered-plant, monitoring its emissions and establishing a reference for subsequent model-based diagnostics and prognostics studies.