Comparison of Gas Turbine and Combined Cycle Models for System Stability Studies

J. C. Mantzaris M. E. Karystianos C. D. Vournas jmantzaris@gmail.com karyst@power.ece.ntua.gr vournas@power.ece.ntua.gr

School of Electrical and Computer EngineeringNational Technical University of Athens

ABSTRACT: The subject of this paper is the comparison of different dynamic models response for Gas Turbine plants and Combined Cycle plants in electric load and frequency transients. In particular one model of open cycle gas turbine and another of combined cycle plant are developed in Matlab/Simulink environment. These models are compared with corresponding models taken from the simulation program PSS/E, which is widely used for dynamic simulation. This study is part of a research project between the Electric Energy Systems Lab of NTUA and the Public Power Corporation of Greece (PPC SA) on the development of Dynamic Models for simulation of

Autonomous Island Systems.

Keywords: Gas Turbine, Open Cycle Plant, Combined Cycle plant, Power System Simulator

I. INTRODUCTION

During the last decades there has been continuous development of combined cycle power generation plants due to their increased efficiency and low emissions. This fact raises the issue of accurate modelling of such plants in power system dynamic simulation studies.

Comparisons made in this paper involve two basic aspects. The first refers to the structure of models and whether certain procedures and subsystems are modelled in detail. In addition it is investigated whether certain simplifications in critical subsystems of the model result in major differences in its response. The second basic aspect is the comparison between different models and refers to their dynamic response in severe disturbance such as load and frequency variations.

The paper is structured as follows: In Section II open cycle gas turbine models are presented and analysed. Section II is divided into four subsections. In the first, a general description of the structure of plants is done. In subsection B and C, two different models are presented and in the fourth, comparison in models dynamic response is made. Section III refers to combined cycle plants and has the same structure. In the last section, conclusions of the comparison of different models are summarized .

II. OPEN CYCLE GAS TURBINE MODELS

A. Description

The basic structure of open cycle gas turbines is presented in Fig. 1. The compressor leads pressured air to the combustion chamber where it is mixed with the fuel, producing the gases that are eventually exhausted in the turbine producing mechanical power. The major parts of gas turbine plants are the speed governor, the fuel system, the combustion chamber, the temperature control and the turbine. Different models of gas turbines mostly refer to certain simplifications of some of the above subsystems.

Figure 1: Gas Turbine

Gas turbines models are mainly based on two control loops. The first is the speed governor which varies according to the type of the plant. The second one is the temperature emergency control loop which measures and calculates exhaust and inlet gas temperatures and produces a second control signal. Both signals are guided to a low value select block. Essentially the second control loop reduces fuel flow whenever temperature exceeds acceptable levels.

B. Detailed model in Matlab/Simulink

The model that is shown in Fig. 2 is based on [1],[2],[3]. The two loops described above are easily identified in Fig. 2 leading to the low value select valve (LVS). The fuel demand signal is guided to the fuel system, which is powered by the shaft, so that fuel flow is proportional to rotational speed. The output of the LVS is driving the fuel system, which defines fuel flow to the combustion chamber, where thermal power is produced.

The parameters that define the thermal power are fuel and air flow, the ambient temperature and pressure. In addition the compressor and fuel system in such plants is also powered by the shaft rotation so frequency of the plant also defines thermal power.

Temperatures and thermal power flow are calculated in the gas turbine block with algebraic equations of energy conversion:

( ) γγ 1

0

−= WPx r

(1)

)1

1(c

idx

ttη−+= (2)

W

Wtttt

fdfdf )( 00 −+= (3)

])1

1(1[ tfe xtt η−−= (4)

WttttKE idefg )]()[(0 −−−= (5)

NgW ⋅= (6)

Note that symbols that are not defined in this paper can be found in nomeclature of [3].

Figure 2: Gas Turbine detailed model

C. Model GAST2A of PSS/E

The structure of GAST2A model [4], taken from PSS/E library, shown in Fig. 3, is similar to the one of the detailed model. Fuel system is almost identical. Temperature control and turbine dynamics are also similar. The major difference between the two models lies on the equations used to calculate the thermal power flow and the exhaust temperature. In the detailed model equations (1)-(6) are used in order to calculate the parameters in the inlet and outlet of the combustion chamber.

In the model of PSS/E only two simplified equations are used in order to calculate the state variables:

2 2 2( ( 1))f f f fEg a b W c N N= + − − (7)

1 1(1 ) ( 1)e r f f fT T a W b N= − − − − (8)

Parameters of the detailed model are defined in [2], [3] adjusted properly to the case of open cycle operation.

Most parameters of GAST2A are defined in [5],[6] while a few ones are adjusted accordingly to the parameters of [2]. In Table 1 parameters of the two models are presented. Rows of Table 1 include corresponding variables of open cycle gas turbine models. In Tables 2,3 the parameters for algebraic equations of energy transform are presented.

Table 1: Parameters for open cycle gas turbine models

Table 2: Parameters for open cycle gas turbine model (energy conversion) GAST2A

af1 bf1 af2 bf2 cf2 Tr

700 550 -0.299 1.3 1.5 950

Parameter Value Value

Matlab GAST2A

Spe

ed

Gov

erno

r

1/R Speed governor regulation 25 W 25Tg Governor time constant (s) 0.05 Y 0.05

X 0

Z 1

Fue

l sys

tem

Fd

maxFuel control upper limit 1.5 Vcemax 1.5

Fd

minFuel control lower limit 0 Vcemin -0.1

K3 Ratio of fuel adjustment 0.77 K3 0.77

K6 Fuel valve lower limit 0.23 K6 0.23

a 1

TvValve positioner time constant

(s)0.05 b 0.05

c 1

TF Fuel system time constant (s) 0.4 tf 0.4

T 0

Kf 0

Tem

pera

ture

con

trol

K4Gain of radiation shield

(instantaneous)0.8

K5 Gain of radiation shield 0.2

T3Time constant of radiation

shield (s)15

T4Time constant of thermocouple

(s)2.5

T5Time constant of temperature

control (overheat) (s)3.3

TtTemperature control (overheat)

integration rate (s)0.4699

Tc

max

Temperature control upper limit

1.1

Tc

min

Temperature control lower limit

0

T6 Time constant of Τf control (s) 60

Tur

bine Tcd Gas turbine time constant (s) 0.2 TCD 0.1

ECR 0.01ETD 0

Table 3: Parameters for detailed open cycle gas turbine model (energy conversion)

Parameter ValuesP

aram

eter

(de

tail

ed m

odel

)

ti0 Ambient temperature (K) 303

td0Nominal compressors discharge

temperature (C)390

tf0 Nominal gas turbine inlet temperature (C) 1085

te0 Nominal exhaust temperature (C) 532

Pr0 Nominal compressor pressure ratio 11.5

γ Ratio of specific heat (Cp/Cv) 1.4

ηc Compressor efficiency 0.85ηt Turbine efficiency 0.85

K0Gas turbine output coefficient

(1/Κ)0.00303

Figure 3: Gas Turbine model GAST2A(PSS/E)

D. Comparing open cycle gas turbine models

The comparison between gas turbine algebraic equation of the two models is presented in Figs. 4-5. Solid line presents power generation and exhaust temperature when frequency is 1.05pu, while dashed line is used when frequency is 0.95pu.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

wf (pu)

Eg

(pu)

detailed model

GAST2A

Figure 4: Comparison of energy conversion equations

As we can easily observe in Fig. 4, power generation equations give similar results. A significant difference is shown in Fig. 5 that is related to the exhaust temperature. This difference does not affect the power response of the model, because temperature is usually lower than nominal

levels, and overheat control is not activated except for serious disturbances.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1400

500

600

700

800

900

1000

wf (pu)

Te

(K)

detailed model

GAST2A

Figure 5: Comparison of energy conversion equations

The dynamic response of the two models is investigated in two cases. In the first case, a step increase of load 10% at 85% of nominal power is applied. In the second case, a step decrease 3% on system frequency is applied at 85% of nominal power. The results are shown in Fig. 6-8 and fig. 9-11 respectively, where GAST2A dynamic response is presented as dashed blue line and detailed model’s response is presented in solid green line.

0 5 10 150.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

time (s)

Pm

(pu

)

detailed model

GAST2A

Figure 6: Power generation (step increase of load)

0 5 10 150.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

time (s)

Tc

Fd

(pu)

Tc

Fd

detailed model

GAST2A

Figure 7: Control variables (step increase of load)

0 5 10 150.993

0.994

0.995

0.996

0.997

0.998

0.999

1

1.001

time (s)

spee

d (p

u)detailed model

GAST2A

Figure 8: Rotor speed (step increase of load)

0 5 10 150.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

1.015

time (s)

spee

d (p

u)

detailed model

GAST2A

Figure 9: Rotor speed (step frequency decrease)

0 5 10 150.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

time (s)

Pm

(pu

)

detailed modelGAST2A

Figure 10: Power generation (step frequency decrease)

0 5 10 150.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

time (s)

Tc

Fd

(pu)

detailed model

GAST2A

Figure 11: Control variables (step frequency decrease)In Fig. 6-11 we can easily observe that the detailed

model has lower damping ratio of power and speed

oscillations. This is due to the difference between gas turbine time constant. Nevertheless, response of two models is similar.

III. COMBINED CYCLE PLANT MODELS

A. Gas and Steam Turbines

Modeling combined cycle plants is based on gas turbine modeling. Dynamic response mainly depends on the contribution of gas turbines, as a possible change in power production of gas turbines takes a few seconds to result in change of steam production and eventually on power generation by the steam turbine.

Modeling combined cycle plants includes certain additional features in comparison to open cycle gas turbines. First of all, a significant change is the fact that power generation is produced by more than one turbines. Steam turbines, respond slower than gas turbines. Additionally, in order to maintain desired exhaust temperature and maximize the efficiency of steam generator, these units regulate the inlet and outlet temperature of the turbine [7]. Inlet guide vans (IGV’s) regulate the airflow at the entrance of the combustion chamber, and through this they control the exhaust temperature.

B. Detailed model in Simulink /Matlab

The detailed model is based on [1], [2], [3] and is shown in Figure 12. Combined cycle model is quite similar to the open cycle gas turbine. Two branches have been added. The first one is the “heat recovery/steam turbine” branch that simulates the steam generator and the steam turbine. In the system of algebraic equations (1)-(6), one additional equation is introduced in order to calculate the thermal power flow to gas turbine and heat recovery:

WtKE es 1= (9)

The second branch that has been added is the air flow control. As mentioned above, this control loop regulates exhaust temperature to nominal levels (or slightly below).

The parameters of the model are presented in Tables 1,3 supplemented with the ones of Table 4.

Table 4: Combined cycle detailed model parametersParameter Value

K0Gas turbine output coefficient

(1/Κ)0,00303

K1Steam turbine output coefficient

(1/Κ)0,000428

Tm Steam turbine time constant (s) 5Tb Heat recovery boiler time constant (s) 20

gmax Air valve upper limit 1,001gmin Air valve lower limit 0,73

C. GGOV1 (PSS/E)

The structure of the model GGOV1 taken from PSS/E library is shown in Fig. 13 and its parameters are

presented in Table 5. This model is also based on a low value select block. Speed governor is a PID controller, which can be driven by multiple signals. The temperature control is much the same as the previous model. The third input signal of the low value select is acceleration control which reduces fuel flow if the acceleration of the shaft exceeds acceptable levels. This branch typically becomes active during plant start up.

Figure 12: Combined cycle detailed model

In model GGOV1, certain features of the main structure are included, but in the same time certain subsystems are neglected as noncritical for dynamic response. Specifically in this model two basic simplifications are made.

The first one refers to the temperature control signal. In GGOV1 it is assumed that exhaust temperature is proportional to fuel flow. This fact does not take into account the IGV’s and accepts that temperature will reach nominal level only when power generation is also at its nominal levels. Furthermore the dependence of airflow on frequency is neglected.

However, as can easily be observed, this model takes into account the fact that fuel system is powered by shaft rotation and that is why fuel flow is multiplied by rotor speed. Fuel system is quite the same apart from the fact that a rate limiter is introduced on the variations of fuel flow. In the previous model there is no such rate limiter. The emergency rate of power generation change is defined through airflow. As it was mentioned above, exhaust temperature is regulated through IGV’s to nominal levels. Any increase on fuel flow demands a proportional increase on airflow in order to maintain temperature to nominal levels according to (3). So the power generation rate of change in the detailed model is not defined from fuel flow rate of change, as it is in GGOV1 but is defined by the airflow change rate limiter.

Table 5 Combined cycle GGOV1 parametersParameter Value

dm 0r Droop 0.04Rselect Selector signal for speed governor 1Tpelect Electrical power transducer time 1

constant (s)maxerr Maximum acceptable speed deviation 0.05Kpgov Speed governor gain 10Kigov Integral gain of speed governor 2Kdgov Derivative gain of speed governor 0Tdgov Governor derivative controller time

constant (s)1

Vmax Maximum valve position limit 1Vmin Minimum valve position limit 0.15Tact Actuator time constant 0.5Kturb Turbine gain 1.5Wfnl No load fuel flow (pu) 0.2Tb Turbine Lead time (s) 0.5Tc Turbine Lag time (s) 0flag Selector for fuel system 1Teng Transport lag time constant for diesel

engine (s)0

Tfload Load limiter time constant (s) 3Kpload Load limiter proportional gain for PI

controller2

Kiload Load limiter integral gain for PI controller

0.67

Ldref Load limiter reference value 1Ropen Max valve opening rate (pu/s) 0.1Rclose Min valve opening rate (pu/s) -0.1Kimw Power controller (reset) gain 0.002aset Maximum acceptable shaft’s

acceleration 0.01

Ka Acceleration limiter gain 10Ta Acceleration limiter time constant (s) 0.1db Speed governor dead band 0Tsa Temperature detection lead time

constant (s)4

Tsb Temperature detection lag time constant (s)

5

Figure 13: Combined cycle mode GGOV1 (PSS/E)The second simplification is related to the power

generation. The fact that IGV’s are neglected results in an assumption that the only parameter that defines power generation is fuel flow. In addition, power generation of the combined cycle is investigated as a whole and not separately for gas and steam turbine. Finally it is assumed that time constant of turbines do not differ much and an average time constant (Tb) is used.

D. Comparison between models of combined cycle plants

The dynamic response of the two models is investigated in two cases. In the first case, a step increase of load 10% at 85% of nominal power is applied with the results shown in Figs. 14-17. In the second case, a 3% step decrease of system frequency is applied at 85% of nominal power, shown in Figs. 18-21. GGOV1 dynamic response is presented as dashed blue line and detailed model’s response is presented in solid green line.

These two models present major differences in dynamic response. In the first case the detailed model overheat control is activated and reduces fuel flow (Fig. 15). On the contrary in the GGOV1 model, overheat control is not activated (Fig. 16).

0 5 10 15 20 25 30 350.988

0.99

0.992

0.994

0.996

0.998

1

1.002

time (s)

spee

d (p

u)

detailed modelGGOV1

Figure 14: Rotor speed (step increase of load)

0 5 10 15 20 25 30 350.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

time (s)

Tc,

Fd(

pu)

Tc

Fd

Figure 15: Control variables of detailed model (step increase of load)

The detailed model tends to increase quickly fuel flow so as to cover the mismatch between power generation and production. For some seconds mechanical power production is increased quickly. This fact causes overheating problems, which are resolved by air control which increases airflow and limits temperature. The rate that IGV's open determines the rate of increase of mechanical power as shown in Fig. 17 for time period between t=12 and t=23s. On the contrary GGOV1 does not include overheat control as a sensitive branch and accepts that overheat is practically possible only when fuel flow exceeds nominal levels (Fig, 16). So in this case

there is no active overheating control and fuel system rate limiter limits the rate of mechanical power increase.

0 5 10 15 20 25 30 350.75

0.8

0.85

0.9

0.95

1

time (s)

Tc,

Fd

(pu)

Tc

Fd

Figure 16: Control variables of GGOV1 (step increase of

load)

0 5 10 15 20 25 30 350.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

time (s)

Pm

(pu

)

detailed modelGGOV1

Figure 17: Power generation (step increase of load)

0 5 10 15 20 25 30 35

1

1.05

time (s)

spee

d (p

u)

detailed modelGGOV1

Figure 18: Rotor speed (step frequency decrease)

0 5 10 15 20 25 30 350.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

time (s)

Tc,

Fd(

pu)

Tc

Fd

Figure 19: Control variables of detailed model (step

frequency decrease)

0 5 10 15 20 25 30 350.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

time (s)

Tc,

Fd

(pu)

Tc

Fd

Figure 20: Control variables of GGOV1 (step frequency

decrease)

0 5 10 15 20 25 30 350.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

time (s)

Pm

(pu

)

detailed modelGGOV1

Figure 21: Power generation (step frequency decrease)

The second disturbance is even more severe as the step decrease of frequency generates major transients.

As far as the detailed model is concerned, control loops function in the same way as presented in the first case. Frequency deviation results in a quick increase in fuel flow which results in an increase at exhaust temperature. Overheat control loop is activated and cuts on fuel flow.

GGOV1 produces a power and frequency oscillation of large magnitude which damps relatively slow. This is due

to the analog and integral gain of speed governor where high values are applied. As in the previous case the rate of mechanical power generation is limited by fuel valve rate limiter.

IV. CONCLUSIONS

In this paper we analyzed differences in modeling and dynamic response between detailed and PSS/E models of open cycle and combined cycle plants. The main conclusions can be summarized as follows:

Open cycle modeling is quite similar between PSS/E and detailed model. Dynamic responses are slightly different due to difference in parameter values. PSS/E model includes certain simplifications that do not affect the overall response.

Combined cycle models are quite different. Certain simplifications are made in critical parts of the plant in GGOV1 model.

• Difference between gas and steam turbine time constants is neglected.

• GGOV1 uses simplified equations in order to calculate exhaust temperature which results in different operation of the corresponding control loop.

• IGV's are neglected. Air flow rate is regarded as constant and instead of IGV’s, fuel flow rate limiter is introduced.

• Power generation depends only on fuel flow.

These assumptions result in major differences in combined cycle model dynamic response. Temperature control loop in GGOV1 is almost inactive. In addition difference in speed governor modeling results in high amplititude oscillations in GGOV1 comparing with the ones in the detailed model. Conclusingly GGOV1 is not well tuned for major frequency disturbances.

V. REFERENCES

[1] W. I. Rowen, “Simplified Mathematical Representations of Heavy Duty Gas Turbines”, Trans.Amer.Soc.Mech.Eng., vol. 105, pp.865-869, Oct 1983[2] N. Kakimoto, K. Baba, “Performance of Gas Turbine-Based Plants During Frequency Drops”, IEEE Transactions on Power Systems, vol. 18, No 3, August 2003[3] J. Mantzaris, C. Vournas, “Modeling and Stability of a Single-Shaft Combined Cycle Power Plant”, International Journal of Thermodynamics Vol. 10 (No. 2), pp. 1-9, June 2007 [4] PSS/E-30 Program Operation Manual, Siemens Power Technologies Inc.[5] L. N. Hannett, A. Khan, “Combustion Turbine Dynamic Model Validation from Tests, IEEE, Transactions on Power Systems, Vol.8, 1993[6] L. M. Hajagos, G. R. Berube, “Utility Experience with Gas Turbine Testing and Modeling, IEEE, 2001[7] CIGRE, 2003, “Modeling Gas Turbines and Steam Turbines in Combined-Cycle Power Plants”, International Conference on Large High Voltage Electric Systems, Technical Brochure.