ROBUST PID CONTROLLER DESIGN OF A SOLID OXIDE FUEL CELL GAS TURBINE

Tooran Emami United States Coast Guard Academy

New London, CT, USA

Alex Tsai United States Coast Guard Academy

New London, CT, USA

David Tucker

United States Department of Energy National Energy Technology Laboratory

Morgantown, W.VA, USA

ABSTRACT

The performance of a 300 kW Solid Oxide Fuel Cell Gas

Turbine (SOFC-GT) pilot power plant simulator is evaluated by applying a set of robust Proportional Integral Derivative (PID) controllers that satisfy time delay and gain uncertainties of the SOFC-GT system. The actuators are a fuel valve (FV) that models the fuel cell thermal exhaust, and a cold-air (CA) valve which bypasses airflow rate from the fuel cell cathode. The robust PID controller results for the uncertain gains are presented first, followed by a design for uncertain time delays for both, FV and CA bypass valves. The final design incorporates the combined uncertain gain parameters with the time delay modeling of both actuators. This Multiple-Input Multiple-Output (MIMO) technique is beneficial to plants having a wide range of operation and a strong parameter interaction. The practical implementation is presented through simulation in the Matlab/Simulink environment. INTRODUCTION

There are numerous interests in modeling and control of power generation systems around the world. One of the problems of these power plants is the presence of communication time delays between the processes of the plant. Another issue with practical power systems is that the forward gain of the system can be changed due to internal or external disturbances. This problem is more critical when the processes also face uncertainties in both, the communication time delays and the forward gains. The motivation of the current paper is to apply the robust Proportional Integral Derivative (PID) controller design for a 300 kW Solid Oxide Fuel Cell Gas Turbine (SOFC-GT) pilot power plant in the

presence of communication time delays and forward gain uncertainness.

One of the objectives of hybrid fuel cell gas turbine technology is to produce energy more efficiently [1]. The Department of Energy’s National Energy Technology Laboratory (NETL) has undertaken the majority of work involved in the modeling and control of hybrid systems [3-13].

The system performance of different power plants to various control strategies for the automatic generation control problem is found in the literature [14-17]. Athay [14] introduced a system characteristic of an automatic generation control system related to the current practices of program design and operation. Kothari et al. [15] studied discrete-mode automatic generation control of an interconnected reheat thermal system by looking at a new area of control error based tie-power deviation. The study focused on frequency deviation, time error, and inadvertent interchange. Gogoi et al. [16] applied a graphical design for finding all proportional integral controllers that stabilize a single area of non-reheat steam generation unit for a range of plant operator. Ramakrishna et al. [17] studied an automatic generation control of a two area power system from hydro, thermal, and gas sources, in one area and power generation from hydro and thermal sources in the second area. The scheduled power generation from thermal or gas plants were adjusted to match the system normal operating load. A genetic algorithm to optimize the PID controller gains for various cases was utilized in this work.

The goal of the current paper is to apply a fixed set of robust PID controllers for a 300 kW SOFC-GT pilot power plant simulator to verify the robustness of the system. This problem is solved based on the assumption of three different uncertainties in the systems. The plant has both communication time delays and forward gain uncertainties. The plant actuators are a fuel valve (FV) that model the fuel

Proceedings of the ASME 2016 14th International Conference on Fuel Cell Science, Engineering and Technology FUELCELL2016

June 26-30, 2016, Charlotte, North Carolina

FUELCELL2016-59602

1This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release. Distribution is unlimited.

cell thermal exhaust, and a cold-air (CA) valve, which bypasses airflow rate from the fuel cell cathode. This Multiple-Input Multiple-Output (MIMO) technique is beneficial to plants with a wide range of operation and parameter interaction. The practical implementation of this methodology is presented only through the simulation in the Matlab/Simulink environment.

This paper is organized as follows: first, the facility description is introduced, followed by the problem statement. The results of the robust PID controller for the three main problems of gain uncertainty, time delay uncertainty, and a combination of phase and gain uncertainties are afterwards discussed. FACILITY DESCRIPTION

One objective of the National Energy Technology Laboratory (NETL) is to investigate the design, control, and operation of pressurized SOFC-GT plants. A hybrid prototype known as the Hybrid Performance (Hyper) project was built in 2002 for this purpose, as shown Fig. 1 and 2.

Fig.1 NETL HyPer Test Facility

Fig.2 CAD Rendering of HyPer Hardware Facility

The hybrid system is simulated through the hardware and software. The gas turbine and balance of plant components make up the hardware part, while the fuel cell electrochemistry and thermal dynamics are captured into 1-D high fidelity model [7]. This model calculates the heat overflow a 300 kW-700 kW fuel cell would produce under measured temperature, pressure, and airflow states throughout the physical plant. The model represents the cathode side of the solid oxide fuel cell. The calculated thermal load is then passed unto the plant by a fast acting fuel valve that burns natural gas. The effect of a fuel cell loss or increase in load can be studied as disturbances to the thermal equilibrium of the hybrid system. Descriptions of the plant equipment are summarized below.

Gas Turbine

A120 kW Garrett Series 85 auxiliary power unit is used for the turbine and compressor system, and consists of a single shaft, direct-coupled turbine, operating at a nominal speed of 40500 rpm. A two-stage radial compressor with a gear driven synchronous (400 Hz) generator is attached to the turbine. Isolated 120 kW variable resistors load the electric generator. The compressor is designed to deliver approximately 1.7 kg/s at a pressure ratio of about four. The compressor discharge temperature is typically 475 K for an inlet temperature of 298 K. Fuel Cell Simulator

The thermal characteristic of the effluent exiting the post combustor of an SOFC system is simulated in hardware using a natural gas burner with an air-cooled diffusion flame. The fuel cell dynamics are coupled to the system dynamics through sensor measurements fed to the model. .

Heat Exchangers

The project facility is made of two counter flow primary surface recuperators with a nominal effectiveness of 89 % to preheat the air going into the pressure vessel used to simulate the fuel cell cathode volume. Pressure Vessels

Pressure vessels are used to provide the representative fuel cell air manifold, cathode volume, and the post combustion volume of a solid oxide fuel cell. The total volume of the airside components is approximately 2,000 L. Bleed Air Bypass Valve

The bleed air bypass valve is used to bleed air from the compressor plenum to the atmosphere through the stack as shown in Fig.2. The bleed air valve and associated piping is a nominal 15.2 cm diameter. Cold-air Bypass

The cold-air bypass valve, (15.2 cm nominal diameter), is used to bypass air from the compressor directly into the turbine inlet through the post combustor volume as shown in Fig. 2.

2

Hot-Air Bypass The hot-air bypass valve (15.2 cm nominal diameter) is

used to bypass air preheated by the recuperations into the turbine inlet through the post combustor volume as shown in Fig.2. Load Bank

A 120 kW variable load bank is used to load the turbine electric generator. PROBLEM STATMEMT

Previous work includes the practical derivation of input/output dynamic transfer function in the frequency domain [13]. The dynamic modeling of the system was identified via Bode plots. In these transfer functions each input, CA and FV, was activated in a sinusoidal fashion with a sufficiently frequency spectrum. The outputs were the fuel cell mass flow rate, m kg/s, and the turbine speed, ω rpm. The set of coupled transfer functions are shown in Equations (1-4). The delay components are described by the exponential terms from the frequency phase response.

( )( )

0.510.032 0.085( 0.8) 1.91

ss emCA s s

−+=

+ +

(1)

( )( )( )( )

2 0.6626.68 0.008 0.006

0.077 0.082 2

ss s e

CA s s sω

−+ +=

+ + + (2)

( )( )( )( )( )( )

1.380.041 0.022 0.30.033 0.06 1 4

ss s emFV s s s s

−+ +=

+ + + +

(3)

( )( )( )

0.217.5 0.030.04 0.07

ss eFV s sω −+

=+ +

(4)

The transfer functions in Equations1-4 were approximated

in [13]. These approximations are the result of adjustments made to the facility under new operating conditions. Equations (5-9) are the result of coupled transfer functions based on the adaptive modeling approach in [13]. Note that in this approximation the time delay has been neglected in each system.

( )( )

1m k CA

CA s≈

+ (5)

( )( )

2

3 2

( ) .01 .006

2.2 .32 .013

k CA s s

CA s s sω + +

≈+ + +

(6)

( )( )

6.2 1m k FV

FV s≈

+ (7)

( )( )2

( ) .03.11 .003

k FV sFV s sω +

≈+ +

(8)

In the current paper, new nominal models of the system

transfer functions are a combination of Equations (1-4) and (5-

8) as follows with the presence of different time delays in all the systems:

0.511

0.0156( )1

smG s eCA s

−−= ≈

+

(9)

20.66

226.68( 0.0075 0.0056)( )( 0.077)( 0.082)( 2)

ss sG s eCA s s sω −+ +

= =+ + +

(10)

1.383

0.0214( )6.2 1

smG s eFV s

−= ≈+

(11)

0.24

17.5( 0.03)( )( 0.04)( 0.07)

ssG s eFV s sω −+

= =+ +

(12)

The goal here is to design PID controllers that robustly

stabilize the Solid Oxide Fuel Cell Gas Turbine (SOFC-GT) pilot power plant simulator for the gain and time delay uncertainties to regulate the fuel cell mass flow rate, m , and the turbine speed, ω for both fuel valve and cold-air bypass valves such as:

1

11 1( ) i

c p dK

G s K K ss

= + + (13)

2

22 2( ) i

c p dK

G s K K ss

= + + (14)

where 1 2, ,p pK K 1 2, ,i iK K 1 2, ,d dK K are the proportional, integral, and derivative gains of the PID controllers, respectively. Note that in the simulation modeling the derivative gains are placed in the forward path in parallel with the integral and proportional paths for easy demonstrations of the modeling. It is clear that in the practical realization the derivative term should be placed in the feedback path to avoid actuator saturation.

The target here is to consider the gain and time delay uncertainties for the new modeling of system transfer functions in Equations (9-12). The remodeled transfer functions can be obtained with the gain and phase uncertainties such that:

( )1111 11( ) jmG s K e

CAθ−=

(15)

( )1212 12( ) jG s K e

CAθω −= (16)

( )2121 21( ) jmG s K e

FVθ−=

(17)

( )2222 22( ) jG s K e

FVθω −= (18)

where 11 12, ,K K 21 22, ,K K are the sets of gain uncertainties for fuel valve and cold-air bypass valves , and

11 12, ,θ θ 21 22, ,θ θ are the sets of time delay uncertainties in the process for each system, respectively.

3

RESULTS AND DISCUSSIONS

The simulation diagram of the system transfer functions is shown in Fig. 3 and the subsystems block diagram model is shown in Fig. 4. The target here is to study the gain and phase uncertainties for the system transfer functions in Equations ( 9-12). The remodeling of systems is considered here to include the uncertainty sets in the plants as the following equations:

(19)

(20)

(21)

(22)

Fig. 3 Simulink Model of the System

Fig. 4 The block diagram of controlled MIMO systems

The robust stability results of the system transfer functions with fixed PID controllers are discussed in three parts. First, the time delays are set to zero, i.e. there is no time delays in the systems, and the robustness of the systems with the PID controllers are evaluated for the set of gain uncertainties. Note that the original gains of the systems include the gain uncertainty sets. Second, the gains are selected to be one in the Equations (15-18) and the robust stability results of the system with PID controllers is considered for the sets of phase uncertainties, i.e., time delay uncertainties. Note that the original delays of the system include the phase uncertainty sets. Finally, the robust stability results of the systems with the fixed PID controllers are evaluated for the combination of gain and phase uncertainties.

The robust PID controllers are designed to regulate the

fuel cell mass flow rate, , and the turbine speed, , of SOFC-GT respectively, such as:

(23)

(24)

Note that the two sets of robust PID controller gains here

have been selected via simulation program to meet stability for all the uncertainties in each system.

Gain uncertainties results:

The step responses of the systems in Equations (19-22)

for the uncertain gain sets in the following interval are evaluated here:

,

,

(25) The results of upper and lower bound gains with the fixed PID controllers in Equations (23) and (24) are shown in Fig. 5 and 6, respectively. As can be seen, the step responses are all stable for the fuel cell mass flow rate, , and the turbine speed, . A start step time of 60 seconds in Fig.5a for both fuel cell mass flow rate and turbine speed are stable and have no overshoot and achieve a settling time of less than 30 seconds. Note that in the robust stability condition the goal is the stability of systems under the uncertain conditions. In this work the goal is to look at the response of the system for the upper and lower uncertainty boundaries. To clarify, the effect of each set point on the system, the start time for both actuators have been selected at different times, i.e. such as 20 and 40 seconds, respectively. As can be seen in Fig.5b the step responses of the fuel cell mass flow rate, , started at 20 seconds and the turbine speed, is at 40 seconds. There is no

-

-

-

-

+

+

+

+

4

overshoot for the mass fuel rate response even for 20 seconds of start time, but a delay of 20 seconds for the turbine speed results in an overshoot for m at 40 seconds. However, the fuel cell mass flow rate, m , and the turbine speed, ω , have been stabilized and settled in less than 60 seconds. A similar observation can be seen in Fig. 6a, and 6b for the lower bound uncertainty gains.

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.5a

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.5b

Fig. 5. Step response for the upper bound gains uncertainties in (25) for turbine speed and fuel cell mass flow rate with PID controllers Equations (23),

(24)

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.6a

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.6b

Fig.6. Step response for the lower bound gain uncertainties in (25) for speed and fuel cell mass flow rate with PID controllers Equations (23), (24)

Phase uncertainties results:

The simulation diagram of the system in Fig 3 is used to study the phase uncertainties. The results of the step responses for the turbine speed and fuel cell mass flow rate in Equations (19-22) for the fixed values of all gains equal 1 with the fixed PID controllers in (23), (24) , and the communication time delays are also incorporated in the following intervals:

11 1,K = 11 (0.01,1.25)θ ∈ ,

12 1,K = 12 (0.01,1.5),θ ∈

21 1,K = 21 (0.01,2.8),θ ∈

22 1,K = 22 (0.02,0.2)θ ∈ . (26)

The step responses for the set points of turbine speed and fuel cell mass flow rate for the upper and lower bounds of time delays in the interval of (26) are shown in Figs. 7 and 8. Similar analysis as the gain uncertainties can be discussed for the phase uncertainties. As can be seen from Figs 7 and 8 all

5

the systems are robustly stable for the upper and lower boundary of time delay uncertainties.

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.7a

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.7b

Fig. 7 The results of step responses for upper bound phase uncertainties in (26) for turbine speed and fuel cell mass flow rate with PID controllers in

Equations (23), (24)

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.8a

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.8b

Fig. 8. The results of step responses for lower bound phase uncertainties in (26) for speed and FC mass flow rate with PID controllers in Equations (23),

(24) Gain and phase uncertainties results:

The simulation diagram of the system transfer functions in Fig. 3 is used to test the gain and phase uncertainties. The results of the step responses in Equations (19-22) with the fixed PID controllers in (23), (24) for the upper bound uncertain gains and delays are shown in Fig. 9 and 10 for the following intervals.

11 11( 0.0152, 0.025), (0.01,1.25)K θ∈ − − ∈ ,

12 12(26.68,54), (0.01,1.5),K θ∈ ∈

21 21(0.0214,0.09), (0.01,2.8),K θ∈ ∈

22 22(17.5,36), (0.02,0.2).K θ∈ ∈ (27)

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.9a

6

0 10 20 30 40 50 60 70 80 90 100-500

0

500

1000

Time (Sec)

Am

plitu

de o

f Spe

ed Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.9b

Fig. 9. Simulation for the gain and phase uncertainties in (27) for turbine speed and fuel cell mass flow rate with PID controllers in Equations (23), (24) As can be seen in Fig.9b there is a very high overshoot for the turbine speed step response. To solve this problem the only modification in the nominal plant transfer functions is to adjust the phase delay in the speed over the fuel valve transfer function to 0.1 seconds instead of 0.2 seconds in the original plant with the following intervals:

11 11( 0.0152, 0.025), (0.01,1.25)K θ∈ − − ∈ ,

12 12(26.68,54), (0.01,1.5),K θ∈ ∈

21 21(0.0214,0.09), (0.01,2.8),K θ∈ ∈

22 22(17.5,36), (0.02,0.1).K θ∈ ∈ (28) The step responses of the turbine speed and fuel cell mass flow rate in Equations (19-22) with the PID controllers in (23), (24) and the uncertain gains and delays in (28) are shown in Fig. 10. As can be seen, the step responses all are stable for the fuel cell mass flow rate, m , and the turbine speed, ω . A start step time of 60 seconds in Fig.10a for both fuel cell mass flow rate and turbine speed are stable and have no overshoot and achieve a settling time of less than 30 seconds. To clarify, the effect of each set point on the system, the start time for both actuators have been selected at different times, i.e. such as 20 and 40 seconds, respectively. As can be seen in Fig.10b the step responses of the fuel cell mass flow rate, m , started at 20 seconds and the turbine speed, ω is at 40 seconds. There is an overshoot for the m response for a 20 seconds of starting time, but having a delay of 20 seconds for ω , effects much higher overshoot for m at 40 seconds. However, the fuel cell mass flow rate, m , and the turbine speed, ω have been stabilized and settled in less than 60 seconds.

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.2

0

0.2

0.4

0.6

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.10a

0 10 20 30 40 50 60 70 80 90 100-200

0

200

400

600

Time (Sec)

Am

plitu

de o

f Spe

ed

Step Response of Speed

0 10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

Time (Sec)

Am

plitu

de o

f M*

Step Response of M*

Fig.10b

Fig. 10. Simulation for the gain and phase uncertainties in (28) for turbine speed and fuel cell mass flow rate with PID controllers in Equations (23),

(24) CONCLUSIONS The performance of a 300 kW Solid Oxide Fuel Cell Gas Turbine (SOFC-GT) pilot power plant simulator was evaluated with a fixed set of robust Proportional Integral Derivative (PID) controllers. These designs satisfied the time delay and gain uncertainties chosen in the SOFC-GT system. These controllers were tested for three different stability constraints of the gain and phase uncertainties of the plant consequential actuators. These actuators were a fuel valve that models the fuel cell thermal exhaust, and a cold-air valve which bypasses airflow rate from the fuel cell cathode. The final design incorporates the combined uncertain gain parameters with the time delay modeling of both actuators. The best responses of the combination of phase and gain uncertainties were achieved by decreasing the communication time delay upper bound to half of the nominal model only. The practical implementation of this methodology was presented through the Matlab/Simulink environment. This Multi-Input Multi-Output technique is beneficial to plants

7

having a wide range of operation and strong parameter interaction.

ACKNOWLEDGEMENTS

This work was completed through collaboration between the U.S. Department of Energy Crosscutting Research program, administered through the National Energy Technology Laboratory and the U.S. Coast Guard Academy. We extend many thanks to the reviewers of this paper for their supportive and constructive comments. REFERENCES [1] Tucker, D., Manivannan, A., and Shelton, M. S., “The

Role of Solid Oxide Fuel Cells in Advanced Hybrid Power Systems of the Future,” Interface, Vol.18, Issue 3 2009.

[2] Winkler, W., Nehter, P., Tucker, D., Williams, M., and Gemmen, R., “General Fuel Cell Hybrid Synergies and Hybrid System Testing Status,” Journal of Power Sources, Vol.159, Issue 1, 2006.

[3] Williams, M.C., Strakey, J. and Surdoval, W., “U.S. DOE Fossil Energy Fuel Cells Program”, Journal of Power Sources, Vol.159, Issue 2, 2006.

[4] Tucker, D., Gemmen, R., and Lawson, L., “Characterization of Air Flow Management and Control in a Fuel Cell Turbine Hybrid Power System Using Hardware Simulation” ASME Power Conference, 2005.

[5] Tsai, A., Banta, L., Tucker, D., and Gemmen, R., “Multivariable Robust Control of a Simulated Hybrid Solid Oxide Fuel Cell Gas Turbine Plant” Journal of Fuel Cell Science and Technology, Vol.7, Issue 4, 2010.

[6] Tsai, A., Tucker, D., Groves, C., “Improved Controller Performance of Selected Hybrid SOFC-GT Plant Signals Based on Practical Control Schemes” Journal of Engineering for Gas Turbines and Power, 2010.

[7] Haynes, C., Tucker, D. Hughes, D., Wepfer, W., Davies, K., and Ford, C., “A Real-Time Spatial SOFC Model for Hardware-Based Simulation of Hybrid Systems” Proceedings of ASME 9th Fuel Cell Science, Engineering, and Technology Conference. Washington, DC, 2011.

[8] Hughes, D., Tucker, D., Tsai, A., Haynes C., and Rivera Y., “Transient Behavior of a Fuel Cell/Gas Turbine Hybrid Using Hardware-Based Simulation with a 1-D Distributed Fuel Cell Model” Proceedings of ICEPAG, Costa Mesa, CA, 2010.

[9] Tsai, A., Tucker, D., Perez, E., “Adaptive Control of Balance of Plant Components in a Fuel Cell Gas Turbine Power Plant Simulator” ASME Turbo Expo 2013, San Antonio, TX, 2013.

[10] Restrepo, B., Banta, L. E., Tucker, D., “Characterization of a Solid Oxide Fuel Cell Gas Turbine Hybrid System Based on a Factorial Design of Experiments using Hardware Simulation,” 5th International Conference on Energy Sustainability & 9th Fuel Cell Science, Engineering and Technology Conference, 2011.

[11] Harun, N. F., Tucker, D., Adams, T., “Fuel Composition Transients In Fuel Cell Turbine Hybrid For Polygeneration Applications,” Proceedings of the 2014 Fuel Cell Science, Engineering, and Technology Conference, Boston, MA, 2014.

[12] Pezzini, P., Celestin, S., Tucker, D., “Cold-air as a Function of Pressure Drop in Fuel Cell Turbine Hybrid Systems,” Proceedings of the 2014 Fuel Cell Science, Engineering, and Technology Conference, Boston, MA, 2014.

[13] Tsai, A., Tucker, D., Emami, T., “Adaptive Control of a Nonlinear Fuel Cell-Gas Turbine Balance of Plant Simulation Facility,” ASME DC, The Journal of Fuel Cell Science and Technology, Vol.11, 2014.

[14] Athay, T. M., “Generation Scheduling and Control”. Proceedings of the IEEE, Vol. 75, Issue 12, pp. 1592-1605, 1987.

[15] Kothari, N.L., Nanda, J., Kothari, D.P., and Das, D., “Discrete-Mode Automatic Generation Control of a Two-Area Reheat Thermal System with New Area control Error’’. IEEE Transaction on Power Systems, Vol. 4, Issue 2, pp. 730-736, 1989.

[16] Gogoi, M., Emami, T., and Watkins, J. M., “Robust Stability Design of PI Controllers for a Non-Reheat Steam Generator Unit,” Proceedings of the 2010 ASME Dynamic Systems and Control Conference,” Cambridge, Massachusetts, 2010.

[17] Ramakrishna1, K. S. S., Sharma, P., Bhatti T. S., “Automatic generation control of interconnected power system with diverse sources of power generation,” International Journal of Engineering, Science and Technology, Vol. 2, No. 5, pp. 51-65, 2010.

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