- Email: [email protected]
Control of grid-connected fuel cell plants for enhancement of power system stability
Renewable Energy 28 (2003) 397–407 www.elsevier.com/locate/renene
Control of grid-connected fuel cell plants for enhancement of power system stability K. Ro a,∗, S. Rahman b a
Department of Electrical Engineering, NPTC, Dongguk University 26 Phil-dong 3-ga, Joong-gu, Seoul 100-715, South Korea b 206 N. Washington St., Suite 400, Alexandria Research Center, Alexandria, VA 22314, USA Received 2 October 2001; accepted 4 March 2002
Abstract This paper presents a methodology for effective control of fuel cell devices connected to an electric utility distribution network. A controller is developed for a fuel cell power plant to assist the conventional generators to damp out oscillations, which is possible by utilizing the fast response characteristic of fuel cells. It achieves the objective by generating appropriate switching signals to the DC–AC inverters and modulating both active and reactive powers. Computer model of the controller is developed and its effectiveness is proved by a sample test. Fuel cell devices, therefore, can be used to improve power system stability when these are applied to a power distribution system. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fuel cells; Power system control; Power system stability; Rotor oscillation; DC–AC inverter
1. Introduction As the increase in world population requires definitely more electrical energy, more usage and the resultant less reserve of fossil fuels may stop or delay future development of technology. Nuclear power generation, considered once as an unlimited energy source, is now proved being a technology that is not easily accepted. Renewable energy sources are still of low economy and unrealistic, so the energy problem has worldwide been a difficult issue to solve. The tasks to resolve the energy ∗
Corresponding author. Tel./fax: +82-2-2260-3346. E-mail address: [email protected] (K. Ro).
0960-1481/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 2 ) 0 0 0 4 2 - 3
398
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
problem include (i) more efficient utilization of fossil fuels, (ii) more secure use of nuclear energy, and (iii) development of new technologies for utilization of renewable energy sources including solar, wind, tidal, and fuel cell power. In recent years, fuel cell power supply in addition to solar power is spotlighted as a part of environmentally benign technology as the world’s environmental concern about global warming and acid deposition grows. A fuel cell is an electrochemical device that directly converts the free-energy change of an electrochemical reaction into electrical energy. Due to its great features such as high efficiency, fast loadresponse, modular production and fuel flexibility, the fuel cell technology is going to be largely applied to dispersed power plants and transportation vehicles. The feasibility of a fuel cell system in coordination with a photovoltaic system has been successfully demonstrated for a grid-connected application [1,2]. Owing to its fast ramping capability, the fuel cell system can smooth out the photovoltaic cell’s inherent problem of intermittent power generation. Yamaguchi et al. [3] have developed 1-MW phosophoric acid fuel cell plant simulator and load-following and shutdown operation characteristics were examined by comparing the simulation results with the process and control test results. A computer model for simulating a transient operation of a tubular solid oxide fuel cell was proposed [4]. The transient model includes the electrochemical and thermal aspects of cell operation that affect the output power produced, which is achieved by stepping back and forth between the two parts. Lukas et al. [5] have reported a nonlinear mathematical model of an internal reforming molten carbonate fuel cell plant for its control application. The model can be used to evaluate the cell responses to varying load demands and to define transient limitations and control requirements. Another approach to fuel cell modeling is found in Ref. [6] where an electrical equivalent circuit of a fuel cell generation system was developed for system control and the system is tested using a fuzzy logic controller. Several test results for operation of the phosphoric acid fuel cell plant installed in Germany are reported by Hoelzner et al. [8], where the response time for load change from 25% of the rated power to full load is 1 min. This paper focuses the application of a fuel cell device to power system control. As its utilization in a power system increases, it is quite required to obtain a strategy for efficient control of the fuel cell system. The paper proposes a controller for the fuel cell system to enhance the overall power system stability, which is possible by utilizing the fast response characteristic of fuel cells. It achieves the objective by generating appropriate switching signals to the DC–AC inverters and modulating both active and reactive powers. Computer simulations will prove effectiveness of the models for the fuel cell system and the controller.
2. System description The configuration of a grid-connected fuel cell power plant is illustrated in Fig. 1. A model for a single cell is described separately in Appendix A. The fuel cell system consists of three major subsystems:
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 1.
399
Configuration of a grid-connected fuel cell system.
(i) a reformer subsystem to process raw natural gas through desulfurization, steam reforming and carbon monoxide (CO) shift to produce a hydrogen-rich fuel; (ii) a power production subsystem to provoke the electrochemical reaction inside fuel cell stacks with the reformed fuel and oxidant to generate DC power; (iii) a power conditioning subsystem (PCS) to fulfill DC–AC power conversion by turning on and off switches according to a certain switching scheme. The capacitor in parallel with the fuel cell stacks operates to limit the change of the fuel cell voltage, Vfc. The PCS, consisting of a 6-switch 3-phase bridge inverter, converts the DC power from the fuel cell stacks into regulated AC power useful to a utility distribution network at the 66.9 kV level. The PCS is thought as an active AC source connected to the utility grid through a transformer and reactors. The parallel outputs of the PCSs go into two different primary sides of the transformer. That kind of transformer setup incurs the voltages behind the primary sides phase-shifted each other by 30° so that it reduces harmonics involved in the inverter output voltage. The series reactors between the transformer and the utility grid feed the transformer output power into the utility grid. The inductive impedance is required for active and reactive power control, and it also functions to limit the rate of increase of the inverter current caused by the grid line disturbances. The feedback controller receives as inputs the grid bus voltage magnitude and system frequency variations. Then it sends out optimal switching signals to the PCSs in order to supply the appropriate active and reactive power to the utility grid so that it can assist the conventional generating unit to damp out oscillations caused by an outside disturbance.In addition, excellent operating features can be achieved through reactive power handling with a leading or lagging power factor. Fig. 2 illustrates a control range of the active and reactive power that the fuel cell system can produce. Effective control of reactive power is important because it is strongly related to the transmission losses and voltage stability.
400
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 2.
Fig. 3.
Active and reactive power range of the fuel cell system.
Logic diagram of the fuel cell system including feedback controllers.
3. Voltage and frequency control loops Fig. 3 shows a logic diagram of the fuel cell system including two feedback controllers; the lower loop is for active power control and the upper one is for reactive power control. The swing equation part represents the dynamics of the conventional generating units as illustrated in Eq. (1). d2di ddi Mi 2 ⫹ Di ⫹ PGi ⫽ PMi dt dt
(1)
where PGi ⫽
1 E V sindi Xi i ti
(2)
Mi is the inertia constant of generator i, di the rotor angle of generator i relative to the reference axis, Di the damping coefficient of generator i, PGi the active power output of generator i, PMi the active power input of generator i, Ei the internal voltage of generator i, Vti the terminal voltage of generator i, and Xi is the reactance between internal and terminal voltage of generator i. The power flow analysis part describes solving the power flow equations denoted
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
401
in Eqs. (3) and (4), where the shunt capacitances of transmission lines were not included.
冘
兩Vi兩兩Vk兩(Gikcosqik ⫹ Biksinqik)
(3)
冘
兩Vi兩兩Vk兩(Giksinqik⫺Bikcosqik)
(4)
n
Pi ⫽
k⫽1 n
Qi ⫽
k⫽1
where Pi is the active bus power at bus i, Qi the reactive bus power at bus i, Vi the voltage magnitude of bus i, qik the voltage angle difference between buses i and k, Gik the line conductance between buses i and k and Bik is the line susceptance between buses i and k. A change in load demand (⌬PD, ⌬QD) causes corresponding changes in both bus voltage magnitudes (⌬PGi) and active power outputs of the conventional thermal generating units (⌬PGi). These values are calculated in the power flow analysis block. The change in the generator’s active power output results in system frequency variations (⌬f) through the swing equations. The frequency variations are monitored continuously at the grid bus and a control signal proportional to the frequency variations is used. The switching control signal (⌬Vf)for the inverter is generated through a PI-type controller to adjust the phase difference between the voltage of the grid bus and the voltage of the inverter. It then supplies more or less active power to the utility grid so that it compensates for the change in system loading. On the other hand, the upper feedback loop for control of the inverter’s output voltage is very similar to that of the frequency control. The change in load demand also causes a change in bus voltage magnitudes, which is carried out in the power flow analysis block. A control signal proportional to the voltage change activates the angle controller through the PI controller. Then an appropriate switching signal (⌬Vd) is generated to modulate the amplitude of the inverter output voltage in relation to the grid bus voltage, thus implementing reactive power control.
4. Computer model of the control loops Fig. 4 illustrates a computer model for overall dynamics of the fuel cell power plant and feedback control loops. The operation of the fuel cell system can be explained by appropriate transfer functions, so the angle and phase controllers are modeled as first-order transfer functions individually. The state equations for system dynamics analysis can be explicitly represented from the transfer functions in Fig. 4. The characteristic equations of a fuel cell are expressed in Eqs. (A.1) and (A.2) in Appendix A. According to Fig. 1, the variations of the fuel cell voltage, Vfc, across the capacitor, Cd, depend mainly on the difference between the fuel cell current, Ifc, and the DC inverter current, Id. This relationship can be denoted as the following differential equation.
402
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 4.
Computer model of the fuel cell system and feedback control loops.
1 d V ⫽ (I ⫺I ) dt fc Cd fc d
(5)
The following development is for use in D/A inverter block in Fig. 4. The voltage behind the secondary transformer in Fig. 1 can be derived as Vfn ⫽
4冑2 NVfcVdcos15ⴰ p
(6)
where N is the turn ratio of the transformer, Vfc the output voltage of the fuel cell stacks, and Vfn the voltage behind the secondary transformer. Vd in Eq. is the control variable to the inverter and is generated from the angle controller. When we define the outputs of the angle and phase controllers as Vd ⫽ cosd
(7)
Vf ⫽ cosf
(8)
the active and reactive powers supplied to the grid bus from the fuel cell system are calculated as in Eqs. (9) and (10), respectively, using the control signals. 1 Pac ⫽ (VsVfnsinf) X 1 Qac ⫽ (V2fn⫺VsVfnVf) X
(9) (10)
where X is the interconnecting reactance and Vs is the grid bus voltage magnitude connected to the fuel cell system. Then, assuming the inverter is lossless, the inverter DC current (Id) can be represented as the following equation since the fuel cell DC output should be same as the inverter AC output.
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Id ⫽
1 2 (P ⫹ Q2ac)1/2 Vfc ac
403
(11)
The power flow program calculates an initial steady-state operating point before a disturbance. The mechanical input power to the generator is assumed to be constant during a short time after the disturbance. The power flow program is used to compute the changes in grid bus voltage and active power output of the conventional generators.The change in the active power output, through the angle controller, generates the inverter’s switching signals for control of phase angle of the inverter voltage. Adjusting the phase angle difference between the inverter AC voltage and grid bus voltage carries out active power control. The inverter’s switching signals for control of the inverter voltage magnitude is generated through the phase controller. The magnitude of the inverter output voltage relative to the bus voltage is manipulated to control reactive power flow.
5. Case study This section describes simulation results to verify effectiveness of the proposed controller, showing variations of the rotor angle and rotor speed of the conventional generating unit. The computer model of the fuel cell system described in Section 4 is applied to a sample 5-bus power system shown in Fig. 5. The sample system comprises a fuel cell power plant with a rating of 26 MW, transmission lines, and a conventional generating unit without functions of frequency and voltage control. The fuel cell power plant comprises 100 sets (10 in series, 10 in parallel) of a 260kW phosphoric acid fuel cell (PAFC) stack. Each stack is composed of 516 single cells connected in series. Appendix B illustrates the system’s line data, and result of initial power flow analysis prior to a disturbance. A sudden increase in load demand to 20 MW and 10 MVAR at bus 2 causes oscillations of the rotor angles (i.e. active power) of the thermal generating unit. Fig. 6 shows variations of system parameters: (a) the generator’s rotor angle, (b) the rotor speed, (c) the generator’s active power, (d) the generator’s reactive power, and (e) the fuel cell plant’s power. The thin dotted line and the thick line represent the parameter variations without and with operation of the controller, respectively. In the case without operation of the controller, the load increase results in the
Fig. 5.
A sample autonomous power system.
404
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 6.
Transient responses of the system parameters for the load change.
rotor angle down after several oscillations for more than 2 s. This phenomenon takes place because the conventional generating unit does not have a capability of frequency control. The fuel cell system’s power does not change in this case. However, in the case with operation of the controller, the controller reacts the
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
405
load increase to adjust the fuel cell power to 21.27 (MW). This control action reduces the rotor angle and rotor speed oscillations significantly by the fuel cell system’s providing an appropriate damping to the oscillating dynamics of the generating units. Consequently, the controller of the fuel cell system contributes to system stability enhancement in dynamic behaviors of the conventional generating unit. 6. Conclusion This paper discusses the need for effective control of fuel cell devices connected to an electric utility distribution network. The control scheme utilizes the fast response characteristic of fuel cells to damp out oscillations of the conventional generators. The main contributions of the paper are thought as designing the controller of the fuel cell system and developing its computer model. Satisfactory dynamic responses, as can be seen from the simulation results, verify effectiveness of the developed controller. Therefore, fuel cell devices with the controller can be applied to improve stability of a large power system. The fuel cell plant equipped with appropriate control devices can be thought to provide a high-quality power by enhancing system stability.
Acknowledgements This work was sponsored by Next-Generation Power Technology Center supported by Ministry of Science and Technology and Korea Science and Engineering Foundation, and by Electrical Engineering and Science Research Institute (EESRI) that is supported by Korea Electric Power Corporation (KEPCO). (EESRI-99-015) Appendix A. Model of a fuel cell A typical cell voltage versus current density plot, which is shown in Fig. A.1 [7], illustrates the performance of a fuel cell that operates at low and intermediate
Fig. A.1 Cell voltage versus current density of a fuel cell.
406
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
temperatures of 25–200 °C. The following relation may represent the relating equations from a current density of zero to the end of the linear region. Efc ⫽ Efc0⫺blogIfc⫺RIfc
(A.1)
where Efc0 ⫽ Er ⫹ blogIfc0
(A.2)
Efc is the terminal voltage of a fuel cell (V), Ifc the cell current density (A/cm2), b the tafel slope (0.1), Ifco the exchange current density for oxygen reduction reaction (0.012), R the Internal resistance of a fuel cell (0.093) and Er the reversible potential of the cell (1.0 V)
Appendix B. Sample data This section gives the necessary data of the 5-bus sample power system illustrated in Fig. 5, for simulation of the controller in the fuel cell system. 1. System’s line data Line From
To
1 1 1 2 2 3
2 3 5 4 5 5
R (pu)
X (pu)
1/B (pu)
0.031 0.024 0.040 0.005 0.026 0.028
0.205 0.115 0.175 0.080 0.125 0.155
0.0045 0.0065 0.0055 0.0020 0.0035 0.0100
2. Result of initial power flow analysis prior to a load change Bus #
Voltage magnitude Voltage angle Active power Reactive power (MW) (MW) (MW) (MVAR)
1 2 3 4 5
1.050 1.009 1.025 0.996 1.012
0.0 ⫺2.409 ⫺1.673 ⫺3.005 ⫺2.463
85.008 10.0 20.0 30.0 40.0
57.768 5.0 10.0 15.0 20.0
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
407
References [1] Rahman S, Tam K. A feasibility study of photovoltaic-fuel cell hybrid energy system. IEEE Trans Energy Convers 1988;3(1):50–5. [2] Ro K, Rahman S. Two-loop controller for maximizing performance of a grid-connected photovoltaicfuel cell hybrid power plant. IEEE Trans Energy Convers 1988;13(3):276–81. [3] Yamaguchi M, Saito T, Izumitari M, Sugita S, Tsutsumi Y. Analysis of control characteristics using fuel cell plant simulator. IEEE Transactions on Industrial Electronics 1990;37(5):378–86. [4] Hall DJ, Cloclaser RG. Transient modeling and simulation of a turbular solid oxide fuel cell. IEEE Trans Energy Convers 1999;14(3):749–53. [5] Lukas MD, Lee KY, Ghezel-Ayagh H. Development of a stack simulation model for control study on direct reforming molten carbonate fuel cell power plant. IEEE Trans Energy Conversion 1999;14(4):1651–7. [6] Kim YH, Kim SS. An electrical modeling and fuzzy logic control of a fuel cell generation system. IEEE Trans Energy Convers 1999;14(2):239–44. [7] Blomen LJ, Mugerwa MN. Fuel cell systems. New York: Plenum Press, 1993. [11] Hoelzner K, Schimph G, Szyszka A. Test operation of phosophoric acid fuel cell plant. Power Eng J 1988;:252–60.
Control of grid-connected fuel cell plants for enhancement of power system stability K. Ro a,∗, S. Rahman b a
Department of Electrical Engineering, NPTC, Dongguk University 26 Phil-dong 3-ga, Joong-gu, Seoul 100-715, South Korea b 206 N. Washington St., Suite 400, Alexandria Research Center, Alexandria, VA 22314, USA Received 2 October 2001; accepted 4 March 2002
Abstract This paper presents a methodology for effective control of fuel cell devices connected to an electric utility distribution network. A controller is developed for a fuel cell power plant to assist the conventional generators to damp out oscillations, which is possible by utilizing the fast response characteristic of fuel cells. It achieves the objective by generating appropriate switching signals to the DC–AC inverters and modulating both active and reactive powers. Computer model of the controller is developed and its effectiveness is proved by a sample test. Fuel cell devices, therefore, can be used to improve power system stability when these are applied to a power distribution system. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fuel cells; Power system control; Power system stability; Rotor oscillation; DC–AC inverter
1. Introduction As the increase in world population requires definitely more electrical energy, more usage and the resultant less reserve of fossil fuels may stop or delay future development of technology. Nuclear power generation, considered once as an unlimited energy source, is now proved being a technology that is not easily accepted. Renewable energy sources are still of low economy and unrealistic, so the energy problem has worldwide been a difficult issue to solve. The tasks to resolve the energy ∗
Corresponding author. Tel./fax: +82-2-2260-3346. E-mail address: [email protected] (K. Ro).
0960-1481/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 2 ) 0 0 0 4 2 - 3
398
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
problem include (i) more efficient utilization of fossil fuels, (ii) more secure use of nuclear energy, and (iii) development of new technologies for utilization of renewable energy sources including solar, wind, tidal, and fuel cell power. In recent years, fuel cell power supply in addition to solar power is spotlighted as a part of environmentally benign technology as the world’s environmental concern about global warming and acid deposition grows. A fuel cell is an electrochemical device that directly converts the free-energy change of an electrochemical reaction into electrical energy. Due to its great features such as high efficiency, fast loadresponse, modular production and fuel flexibility, the fuel cell technology is going to be largely applied to dispersed power plants and transportation vehicles. The feasibility of a fuel cell system in coordination with a photovoltaic system has been successfully demonstrated for a grid-connected application [1,2]. Owing to its fast ramping capability, the fuel cell system can smooth out the photovoltaic cell’s inherent problem of intermittent power generation. Yamaguchi et al. [3] have developed 1-MW phosophoric acid fuel cell plant simulator and load-following and shutdown operation characteristics were examined by comparing the simulation results with the process and control test results. A computer model for simulating a transient operation of a tubular solid oxide fuel cell was proposed [4]. The transient model includes the electrochemical and thermal aspects of cell operation that affect the output power produced, which is achieved by stepping back and forth between the two parts. Lukas et al. [5] have reported a nonlinear mathematical model of an internal reforming molten carbonate fuel cell plant for its control application. The model can be used to evaluate the cell responses to varying load demands and to define transient limitations and control requirements. Another approach to fuel cell modeling is found in Ref. [6] where an electrical equivalent circuit of a fuel cell generation system was developed for system control and the system is tested using a fuzzy logic controller. Several test results for operation of the phosphoric acid fuel cell plant installed in Germany are reported by Hoelzner et al. [8], where the response time for load change from 25% of the rated power to full load is 1 min. This paper focuses the application of a fuel cell device to power system control. As its utilization in a power system increases, it is quite required to obtain a strategy for efficient control of the fuel cell system. The paper proposes a controller for the fuel cell system to enhance the overall power system stability, which is possible by utilizing the fast response characteristic of fuel cells. It achieves the objective by generating appropriate switching signals to the DC–AC inverters and modulating both active and reactive powers. Computer simulations will prove effectiveness of the models for the fuel cell system and the controller.
2. System description The configuration of a grid-connected fuel cell power plant is illustrated in Fig. 1. A model for a single cell is described separately in Appendix A. The fuel cell system consists of three major subsystems:
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 1.
399
Configuration of a grid-connected fuel cell system.
(i) a reformer subsystem to process raw natural gas through desulfurization, steam reforming and carbon monoxide (CO) shift to produce a hydrogen-rich fuel; (ii) a power production subsystem to provoke the electrochemical reaction inside fuel cell stacks with the reformed fuel and oxidant to generate DC power; (iii) a power conditioning subsystem (PCS) to fulfill DC–AC power conversion by turning on and off switches according to a certain switching scheme. The capacitor in parallel with the fuel cell stacks operates to limit the change of the fuel cell voltage, Vfc. The PCS, consisting of a 6-switch 3-phase bridge inverter, converts the DC power from the fuel cell stacks into regulated AC power useful to a utility distribution network at the 66.9 kV level. The PCS is thought as an active AC source connected to the utility grid through a transformer and reactors. The parallel outputs of the PCSs go into two different primary sides of the transformer. That kind of transformer setup incurs the voltages behind the primary sides phase-shifted each other by 30° so that it reduces harmonics involved in the inverter output voltage. The series reactors between the transformer and the utility grid feed the transformer output power into the utility grid. The inductive impedance is required for active and reactive power control, and it also functions to limit the rate of increase of the inverter current caused by the grid line disturbances. The feedback controller receives as inputs the grid bus voltage magnitude and system frequency variations. Then it sends out optimal switching signals to the PCSs in order to supply the appropriate active and reactive power to the utility grid so that it can assist the conventional generating unit to damp out oscillations caused by an outside disturbance.In addition, excellent operating features can be achieved through reactive power handling with a leading or lagging power factor. Fig. 2 illustrates a control range of the active and reactive power that the fuel cell system can produce. Effective control of reactive power is important because it is strongly related to the transmission losses and voltage stability.
400
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 2.
Fig. 3.
Active and reactive power range of the fuel cell system.
Logic diagram of the fuel cell system including feedback controllers.
3. Voltage and frequency control loops Fig. 3 shows a logic diagram of the fuel cell system including two feedback controllers; the lower loop is for active power control and the upper one is for reactive power control. The swing equation part represents the dynamics of the conventional generating units as illustrated in Eq. (1). d2di ddi Mi 2 ⫹ Di ⫹ PGi ⫽ PMi dt dt
(1)
where PGi ⫽
1 E V sindi Xi i ti
(2)
Mi is the inertia constant of generator i, di the rotor angle of generator i relative to the reference axis, Di the damping coefficient of generator i, PGi the active power output of generator i, PMi the active power input of generator i, Ei the internal voltage of generator i, Vti the terminal voltage of generator i, and Xi is the reactance between internal and terminal voltage of generator i. The power flow analysis part describes solving the power flow equations denoted
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
401
in Eqs. (3) and (4), where the shunt capacitances of transmission lines were not included.
冘
兩Vi兩兩Vk兩(Gikcosqik ⫹ Biksinqik)
(3)
冘
兩Vi兩兩Vk兩(Giksinqik⫺Bikcosqik)
(4)
n
Pi ⫽
k⫽1 n
Qi ⫽
k⫽1
where Pi is the active bus power at bus i, Qi the reactive bus power at bus i, Vi the voltage magnitude of bus i, qik the voltage angle difference between buses i and k, Gik the line conductance between buses i and k and Bik is the line susceptance between buses i and k. A change in load demand (⌬PD, ⌬QD) causes corresponding changes in both bus voltage magnitudes (⌬PGi) and active power outputs of the conventional thermal generating units (⌬PGi). These values are calculated in the power flow analysis block. The change in the generator’s active power output results in system frequency variations (⌬f) through the swing equations. The frequency variations are monitored continuously at the grid bus and a control signal proportional to the frequency variations is used. The switching control signal (⌬Vf)for the inverter is generated through a PI-type controller to adjust the phase difference between the voltage of the grid bus and the voltage of the inverter. It then supplies more or less active power to the utility grid so that it compensates for the change in system loading. On the other hand, the upper feedback loop for control of the inverter’s output voltage is very similar to that of the frequency control. The change in load demand also causes a change in bus voltage magnitudes, which is carried out in the power flow analysis block. A control signal proportional to the voltage change activates the angle controller through the PI controller. Then an appropriate switching signal (⌬Vd) is generated to modulate the amplitude of the inverter output voltage in relation to the grid bus voltage, thus implementing reactive power control.
4. Computer model of the control loops Fig. 4 illustrates a computer model for overall dynamics of the fuel cell power plant and feedback control loops. The operation of the fuel cell system can be explained by appropriate transfer functions, so the angle and phase controllers are modeled as first-order transfer functions individually. The state equations for system dynamics analysis can be explicitly represented from the transfer functions in Fig. 4. The characteristic equations of a fuel cell are expressed in Eqs. (A.1) and (A.2) in Appendix A. According to Fig. 1, the variations of the fuel cell voltage, Vfc, across the capacitor, Cd, depend mainly on the difference between the fuel cell current, Ifc, and the DC inverter current, Id. This relationship can be denoted as the following differential equation.
402
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 4.
Computer model of the fuel cell system and feedback control loops.
1 d V ⫽ (I ⫺I ) dt fc Cd fc d
(5)
The following development is for use in D/A inverter block in Fig. 4. The voltage behind the secondary transformer in Fig. 1 can be derived as Vfn ⫽
4冑2 NVfcVdcos15ⴰ p
(6)
where N is the turn ratio of the transformer, Vfc the output voltage of the fuel cell stacks, and Vfn the voltage behind the secondary transformer. Vd in Eq. is the control variable to the inverter and is generated from the angle controller. When we define the outputs of the angle and phase controllers as Vd ⫽ cosd
(7)
Vf ⫽ cosf
(8)
the active and reactive powers supplied to the grid bus from the fuel cell system are calculated as in Eqs. (9) and (10), respectively, using the control signals. 1 Pac ⫽ (VsVfnsinf) X 1 Qac ⫽ (V2fn⫺VsVfnVf) X
(9) (10)
where X is the interconnecting reactance and Vs is the grid bus voltage magnitude connected to the fuel cell system. Then, assuming the inverter is lossless, the inverter DC current (Id) can be represented as the following equation since the fuel cell DC output should be same as the inverter AC output.
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Id ⫽
1 2 (P ⫹ Q2ac)1/2 Vfc ac
403
(11)
The power flow program calculates an initial steady-state operating point before a disturbance. The mechanical input power to the generator is assumed to be constant during a short time after the disturbance. The power flow program is used to compute the changes in grid bus voltage and active power output of the conventional generators.The change in the active power output, through the angle controller, generates the inverter’s switching signals for control of phase angle of the inverter voltage. Adjusting the phase angle difference between the inverter AC voltage and grid bus voltage carries out active power control. The inverter’s switching signals for control of the inverter voltage magnitude is generated through the phase controller. The magnitude of the inverter output voltage relative to the bus voltage is manipulated to control reactive power flow.
5. Case study This section describes simulation results to verify effectiveness of the proposed controller, showing variations of the rotor angle and rotor speed of the conventional generating unit. The computer model of the fuel cell system described in Section 4 is applied to a sample 5-bus power system shown in Fig. 5. The sample system comprises a fuel cell power plant with a rating of 26 MW, transmission lines, and a conventional generating unit without functions of frequency and voltage control. The fuel cell power plant comprises 100 sets (10 in series, 10 in parallel) of a 260kW phosphoric acid fuel cell (PAFC) stack. Each stack is composed of 516 single cells connected in series. Appendix B illustrates the system’s line data, and result of initial power flow analysis prior to a disturbance. A sudden increase in load demand to 20 MW and 10 MVAR at bus 2 causes oscillations of the rotor angles (i.e. active power) of the thermal generating unit. Fig. 6 shows variations of system parameters: (a) the generator’s rotor angle, (b) the rotor speed, (c) the generator’s active power, (d) the generator’s reactive power, and (e) the fuel cell plant’s power. The thin dotted line and the thick line represent the parameter variations without and with operation of the controller, respectively. In the case without operation of the controller, the load increase results in the
Fig. 5.
A sample autonomous power system.
404
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
Fig. 6.
Transient responses of the system parameters for the load change.
rotor angle down after several oscillations for more than 2 s. This phenomenon takes place because the conventional generating unit does not have a capability of frequency control. The fuel cell system’s power does not change in this case. However, in the case with operation of the controller, the controller reacts the
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
405
load increase to adjust the fuel cell power to 21.27 (MW). This control action reduces the rotor angle and rotor speed oscillations significantly by the fuel cell system’s providing an appropriate damping to the oscillating dynamics of the generating units. Consequently, the controller of the fuel cell system contributes to system stability enhancement in dynamic behaviors of the conventional generating unit. 6. Conclusion This paper discusses the need for effective control of fuel cell devices connected to an electric utility distribution network. The control scheme utilizes the fast response characteristic of fuel cells to damp out oscillations of the conventional generators. The main contributions of the paper are thought as designing the controller of the fuel cell system and developing its computer model. Satisfactory dynamic responses, as can be seen from the simulation results, verify effectiveness of the developed controller. Therefore, fuel cell devices with the controller can be applied to improve stability of a large power system. The fuel cell plant equipped with appropriate control devices can be thought to provide a high-quality power by enhancing system stability.
Acknowledgements This work was sponsored by Next-Generation Power Technology Center supported by Ministry of Science and Technology and Korea Science and Engineering Foundation, and by Electrical Engineering and Science Research Institute (EESRI) that is supported by Korea Electric Power Corporation (KEPCO). (EESRI-99-015) Appendix A. Model of a fuel cell A typical cell voltage versus current density plot, which is shown in Fig. A.1 [7], illustrates the performance of a fuel cell that operates at low and intermediate
Fig. A.1 Cell voltage versus current density of a fuel cell.
406
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
temperatures of 25–200 °C. The following relation may represent the relating equations from a current density of zero to the end of the linear region. Efc ⫽ Efc0⫺blogIfc⫺RIfc
(A.1)
where Efc0 ⫽ Er ⫹ blogIfc0
(A.2)
Efc is the terminal voltage of a fuel cell (V), Ifc the cell current density (A/cm2), b the tafel slope (0.1), Ifco the exchange current density for oxygen reduction reaction (0.012), R the Internal resistance of a fuel cell (0.093) and Er the reversible potential of the cell (1.0 V)
Appendix B. Sample data This section gives the necessary data of the 5-bus sample power system illustrated in Fig. 5, for simulation of the controller in the fuel cell system. 1. System’s line data Line From
To
1 1 1 2 2 3
2 3 5 4 5 5
R (pu)
X (pu)
1/B (pu)
0.031 0.024 0.040 0.005 0.026 0.028
0.205 0.115 0.175 0.080 0.125 0.155
0.0045 0.0065 0.0055 0.0020 0.0035 0.0100
2. Result of initial power flow analysis prior to a load change Bus #
Voltage magnitude Voltage angle Active power Reactive power (MW) (MW) (MW) (MVAR)
1 2 3 4 5
1.050 1.009 1.025 0.996 1.012
0.0 ⫺2.409 ⫺1.673 ⫺3.005 ⫺2.463
85.008 10.0 20.0 30.0 40.0
57.768 5.0 10.0 15.0 20.0
K. Ro, S. Rahman / Renewable Energy 28 (2003) 397–407
407
References [1] Rahman S, Tam K. A feasibility study of photovoltaic-fuel cell hybrid energy system. IEEE Trans Energy Convers 1988;3(1):50–5. [2] Ro K, Rahman S. Two-loop controller for maximizing performance of a grid-connected photovoltaicfuel cell hybrid power plant. IEEE Trans Energy Convers 1988;13(3):276–81. [3] Yamaguchi M, Saito T, Izumitari M, Sugita S, Tsutsumi Y. Analysis of control characteristics using fuel cell plant simulator. IEEE Transactions on Industrial Electronics 1990;37(5):378–86. [4] Hall DJ, Cloclaser RG. Transient modeling and simulation of a turbular solid oxide fuel cell. IEEE Trans Energy Convers 1999;14(3):749–53. [5] Lukas MD, Lee KY, Ghezel-Ayagh H. Development of a stack simulation model for control study on direct reforming molten carbonate fuel cell power plant. IEEE Trans Energy Conversion 1999;14(4):1651–7. [6] Kim YH, Kim SS. An electrical modeling and fuzzy logic control of a fuel cell generation system. IEEE Trans Energy Convers 1999;14(2):239–44. [7] Blomen LJ, Mugerwa MN. Fuel cell systems. New York: Plenum Press, 1993. [11] Hoelzner K, Schimph G, Szyszka A. Test operation of phosophoric acid fuel cell plant. Power Eng J 1988;:252–60.