The initial state for the transient engine model.

## Abstract

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.

### Keywords

- wind energy
- gas turbine
- wind turbine
- dynamic modeling
- MATLAB/Simulink
- engine control

## 1. Introduction

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 [6].

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 [12]. 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 [24].

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 [28]. 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 [14] 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

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. Methodology

### 2.1 Gas turbine mathematical model

For this study, the industrial gas turbine developed by the author in MATLAB/Simulink [14], 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

#### 2.1.1 Compressor

The performance of the compressor is represented by a characteristic map which presents the interrelationships between pressure ratio

Once the outputs of the map are determined, the temperature rise

The work required to drive the compressor is given by

where

#### 2.1.2 Combustor

The energy balance equation is governing the performance of the combustor as follows:

where

which is further implemented for estimating the cycle’s thermal efficiency

Regarding emissions, the nitrogen oxides model developed by Rokke et al. [38], and validated by Pires et al. [39], is implemented in this gas turbine model. The

where

#### 2.1.3 Turbine

Similar to the compressor, turbine performance is represented by a set of characteristic maps that present the interrelationships between turbine pressure ratio

It follows that the temperature drop

where

where

#### 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

The temperature drop

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

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.

#### 2.2.1 Dynamics

Combustor: Volume 1—The mass flow continuity is used to calculate the pressure in the combustor volume, as follows:

where

where

Duct: Volume 2—The pressure at the exit of the gas turbine is given by:

where

where

Shaft—The difference between compressor

where ^{2}.

System states—Assuming that the system’s state is denoted by

The pressures

#### 2.2.2 Simulation process

The initial state values for the transient engine model are summarized in Table 1.

Symbol | Parameter | Value | Units |
---|---|---|---|

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

### 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

The process of the controller’s operation is schematically represented in Figure 3. The actuating signal

The control function of this PI controller can be expressed as follows:

where

The reader is prompted to [32], 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 [14].

### 2.4 Wind turbine model

A generic model of a wind turbine, available from MATLAB/Simulink [40], 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

where

where

The wind turbine model has three inputs namely

The hybrid gas/wind power plant consists of a gas turbine and a wind farm with variable power output. The total power output

The energy gap

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.

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

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

For this case study, the coefficients of the PI controller and the transient response characteristics are summarized in Table 2.

Parameter | Value | Units |
---|---|---|

8.562E−05 | — | |

0.794E−03 | — | |

Rise time | 0.896 | Seconds |

Settling time | 1.676 | Seconds |

Overshoot | 0 | % |

Peak | 1 | — |

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

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 [40].

Symbol | Parameter | Value | Units |
---|---|---|---|

Wind speed | 12 | m/s | |

Generator speed | 1800 | rpm | |

Power output | 1500 | kW |

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

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

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 [47]. 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 [48]. In addition, the fastest the start-up [49] 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

The

The

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 [51], 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 [17] at component and system level for improving the prediction accuracy and the computational efficiency of diagnostic and prognostics algorithms.

## 4. Conclusions

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

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.

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