Simulation of a Stirling Engine Solar Power Generation System Using Simulink Mehdi Zareian Jahromi∗ , Mohammad Mehdi Hosseini Bioki† , and Roohollah Fadaeinedjad‡ , Member IEEE ∗† Electrical
and Computer Engineering Department, Kerman Graduate University of Technology, Kerman,Iran. and Computer Engineering Department, Kerman Graduate University of Technology, Kerman,Iran. Telephone: +98-3426226517, Fax: +98-3426226618, Email:
[email protected] ‡ International Center for Science, High Technology and Environmental Sciences, Kerman, Iran.
‡ Electrical
Abstract—In order to fully study a Stirling engine based solar power generation system, a detailed model that considers all thermal, mechanical, and electrical aspects of the system should be used. Research in the area of Stirling engine systems has been performed either without considering the electrical parts, or with a simple model for the electrical parts. Hence, the effects of interactions between electrical and mechanical components are neglected. In this paper, simulation of a solarpowered Stirling engine system is proposed that considers all thermal, mechanical, and electrical aspects of the system. The system is mainly composed of two parts that are the mechanical and electrical parts. The mechanical part includes the Stirling engine that is modeled using thermal and mechanical equations in Matlab/Simulink environment. The electrical part consists of a synchronous generator, an ac/dc converter, a battery, and an electrical dc load that are simulated using Simulink blocks.
I. I NTRODUCTION Environmental concerns and growing energy demand have increased interest in the use of the renewable energy, especially solar energy that can be used as an input source for heat engines like Stirling engines. It is astonishing when we realize that the amount of sunlight reaching the earth’s surface continuously is 1.05×105 TW. If only 1% of this power could be converted into electricity with a 10% efficiency, it would provide about 4 times of the total global energy needs for 2050 that are projected to be about 25 − 30 TW [1]. Different technologies including conventional photovoltaic (PV), solar power tower, solar parabolic trough, and solar dishengine can be used to harvest the solar energy [2]. The cost of the produced energy is the main limiting factor in the use of these technologies. The Stirling engine was reported to be the cheapest for solar electric generation in the range of 1 to 100 KW [3], [4]. The Stirling engines have been developed to improve the deficiencies over a period of time [2], [4], [5]. Nowadays, the Stirling engines are highly reliable and efficient and these are keys to a cost effective solar power generator system. With average efficiencies of over 20% and the record measured peak efficiency of nearly 30%, dish/Stirling systems currently exceed the efficiency of any other solar conversion technology. Direct solar-powered engines may be of great interest to countries where solar energy is available in a vast quantity such as Iran. Potential markets include small-scale portable power systems for battery charging and other off-grid applications. They
978-1-4673-5003-7/11$26.00©2011 IEEE
could be especially useful in developing countries since they will run on any fuel, including biomass; or when incorporated in parabolic dish systems, they can use solar energy. Cogeneration is possible using the cooling water that maintains the cold sink, so heat-and-power systems for homes are provided. With higher efficiencies, their quiet vibration-free operation, very low emissions when burning natural gas, simplicity, and potentially high reliability could make the Stirling engines an attractive alternative in the near future [6]. Simulation and modeling can be used to evaluate the operation of the solar Stirling engine based power generation systems. Considerable research has been performed on the modeling and control of Stirling engine systems. Most of this research, however, has been done using mechanical and thermal models of Stirling engines that neglects the electrical parts of the system [5], [7], [8]. In this research, however, a model is developed that considers the thermal, mechanical, and electrical aspects of the Stirling based power generation system. II. S YSTEM C ONFIGURATION For this research, a typical solar-powered Stirling engine power generation system is modeled and studied that is shown in Fig. 1. The solar heat is converted into the electricity by the proposed energy conversion system in two stages that are the thermal to mechanical and mechanical to electrical conversion stages. As can be seen in Fig. 1, the system consists of different parts including: a solar-powered Stirling engine, a permanent magnet synchronous generator, an ac/dc converter, a battery, and an electrical dc load. The effect of solar radiation concentrated by a dish is considered as a constant temperature collector in the system. The modeling of the system is basically performed in Matlab/Simulink environment [9]. As shown in Fig. 1, the system includes mechanical and electrical parts that are explained in further details in the following sections. III. T HERMO - MECHANICAL PART (S TIRLING E NGINE ) As mentioned before the Stirling engine is the main part of the energy conversion system that can be used to convert the delivered heat by a solar collector into mechanical power. In this research, a constant temperature is assumed for the
676
Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey
Fig. 1.
The study system configuration.
solar collector (hot end in the Stirling engine) that is subjected to the solar radiation. The modeling of the Stirling engine is performed based on some thermal and mechanical equations that are given in this section. The operation procedure of the Stirling engine is also described. A. Stirling Engine Operation Concept Stirling engines are external combustion thermodynamical machines working theoretically on the Stirling cycle, or its modifications, in which compressible fluids (such as air or Helium), are used as working fluids [4]. Stirling engines are powered by the expansion of a gas when heated, followed by the compression of the gas when cooled. The Stirling engine contains a fixed amount of gas that is transferred back and forth between two cold and hot ends. As shown in Fig. 2, the Stirling engine includes a displacer piston (shown in red) and a smaller piston (shown in blue) that is named the power piston. The displacer piston (bigger one) moves the gas between the two ends and the power piston (smaller one) changes the internal volume as the gas expands and contracts. Air in the engine is cyclically heated and expands to push the power piston to the right. As the power piston moves to the right, the yellow linkage forces the loose-fitting and moves the red piston to displace air to the cooler side of the engine. By losing the heat on the cooler side, the air contracts and pulls the power piston to the left. The air is again displaced, sending it back to the hotter region of the engine, and the cycle repeats. The power piston acts upon the linkage to a flywheel and the back and forth motion of the power piston is converted to the rotational motion of the flywheel [7]. B. Stirling Engine Modeling In order to model the Stirling engine, the operational procedure of the Stirling engine should be implemented using a set of relations that are explained in this part. The heat source is modeled as a constant temperature effort source, Th . The heat source (solar collector) transfers entropy, Sh , to the air in the cylinder through a variable resistance. Similarly, the heat sink is considered as a constant temperature effort source, Tc , which also transfers entropy, Sc , from the air in the cylinder through a different variable resistance.
Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey
Fig. 2.
Schematic of Stirling engine [7].
The air in the cylinder is modeled as a multi-port capacitor. To consider the leakage from the cylinder, one port on the multi-port capacitor tracks the mass loss through a resistance to ambient conditions, modeled as a constant pressure effort source. The entropy variations is considered by a second port on the capacitor. The variations are caused by mass flow, entropy flow from heat source, and entropy flow to heat sink. The final port on the capacitor is associated with the volume change. The pressure in the cylinder acts upon the power piston which is modeled as a constant transformer. The piston then acts upon the linkage to the flywheel, modeled as a modulated transformer. The flywheel is modeled as an inertia, while all of the friction losses in the system are modeled as a resistor with damping b. The major modeling assumption used in this model are [7]: • uniform temperature for air in engine; • lumped friction element to govern engine speed; • no power transfer through the heat piston; • mass-less pistons; • uniform constant temperature sources; • all leakage from engine through power cylinder; • motion of heat piston is sinusoid 90 degrees ahead of power piston. For this research, the Stirling engine is modeled using the following set of algebraic and differential equations that are implemented in Simulink environment [7], [10], [11].
677
where θ θ˙ θ¨ Se Sh Sc Ne Re Asc Ppc Ah Ac Te Al Ap Vc m R s¯o To Pa Po Cv τe τelec b I µ
x = Re (1 + sin θ) Ah = Asc (1 + cos θ)
(1)
Ac = Asc (1 − cos θ) + Ppc x Ah µ(Th − Te ) S˙ h = Te A µ(T c e − Tc ) S˙ c = Te N˙ e = −Al 2ρe (Pe − Pa ) Se ˙ S˙ a = Na Ne S˙ e = S˙ h − S˙ c + S˙ a Ve = Vc + Ap x Ve v¯e = mNe v¯ −R s¯e − s¯o e Cv exp Te = To v¯o Cv v¯ − −R s¯e − s¯o Cv +1 e exp Pe = Po v¯o Cv Fe = (Pe − Pa )Ap τe = Fe Re cos θ τe − τelec = bθ˙ + I θ¨
(3)
The thermo-mechanical operation of the Stirling engine is presented through equations (1) to (13). Equation (14) shows the generated mechanical torque of the Stirling engine as a function of the radius of linkage pivot on the flywheel. It is important that the interaction between the mechanical and electrical dynamics of the system be accurately considered in the model, as the Stirling engine and the synchronous generator are coupled through a mechanical shaft. The Stirling engine torque, τe , and the generator torque, τelec , are applied to the same shaft and equation (15) can be used to calculate the rotation velocity. This equation also represents the mechanical dynamics of the electrical generator.
(2) (4) (5) (6) (7) (8)
IV. E LECTRICAL PART
(9)
As can be seen in Fig. 1, the Stirling engine drives the permanent magnet synchronous generator that converts the mechanical power to the electrical power. In this paper, Simulink is used to simulate the electrical dynamics of the generator that are based on d-q equivalent model [9], [12]. The generator output voltages are applied to the three phase controlled rectifier that converts the three phase ac voltages to a dc voltage. The dc voltage is used to supply the dc load and energize the battery. The battery is used to store the energy to supply the dc load when the solar energy is not available.
(10) (11) (12) (13) (14) (15)
A. The Permanent Magnet Synchronous Generator
the angular position of the flywheel; the angular velocity of the flywheel; the angular acceleration of the flywheel; the total entropy of the air in the cylinder; the heat source transferred entropy to the air; the heat sink transferred entropy from the air; the number of mols of air in the cylinder; the radius of linkage pivot on the flywheel; the heat transfer surface area of the cylinder; the perimeter of the power piston; the heat transfer area; the cold heat transfer area; the air temperature in the engine; the area of leak; the area of the power piston; the volume of the air cylinder; the molar mass of the air; the mass gas constant air; the specific entropy of air at T=300 K; starting temperature of air in the cylinder; the ambient pressure; the air pressure in the cylinder; constant volume specific heat; the mechanical torque of Stirling engine; the electromagnetic generator torque; the damping constant (total mechanical friction); the inertia of flywheel; the heat transfer constant of the cylinder, this was calculated as the thermal conductance of steel with the cylinder wall thickness.
The main advantage of permanent magnet synchronous generators is that any external excitation current is not required by these machines. A major cost benefit in using the permanent magnet synchronous generator is the fact that a diode bridge rectifier may be used at the generator terminals since no external excitation current is needed. Different research has been performed using the diode rectifier [13], [14]. In the studied system, the permanent magnet synchronous generator converts the mechanical power to the electrical power. The electrical dynamics of the generator are represented by a second-order state-space model. The sinusoidal model assumes that the flux established by the permanent magnets in the stator is sinusoidal, which implies that the electromotive forces are sinusoidal. In order to model the electrical system of the generator the following equations which are expressed in the rotor reference frame (q-d frame) are used [15]. It should be mentioned that all of quantities are referred to the stator side. 1 R Lq d id = vd − id + P ωr i q (16) dt Ld Ld Ld 1 R Ld λP ωr d iq = vq − iq − P ωr i d − (17) dt Lq Lq Lq Lq (18) τelec = 1.5P [λiq + (Ld − Lq )id iq ] where iq , id v q , vd L q , Ld R ωr
678
q- and d-axis current components; q- and d-axis voltage components; q- and d-axis inductances; resistance of stator windings; rotor angular velocity;
Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey
P τelec λ
number of pole pairs; electromagnetic generator torque; amplitude of the flux induced by the permanent magnets of the rotor in the stator phases.
B. The Controlled Rectifier The three phase controlled rectifier is used to convert the three phase ac voltages to a dc voltage that is used to supply the dc load and energize the battery. The controlled rectifier consists of two parts: a three phase full bride diode rectifier that rectifies the generator output voltages and a boost converter that controls the output dc voltage of the rectifier. The three phase diode bridge rectifiers are commonly used for high and low power applications because they are very efficient and popular wherever both dc voltage and current requirements are high. In many applications, no additional filter is required because the output ripple voltage is very low. Even if a filter is required, the size of the filter is relatively small [16]. The Boost converter is used to convert the diode rectifier output voltage into a regulated dc voltage against load and input voltage variations. It also reduces the ac voltage ripple on the dc output voltage below the required level and provide isolation between the input source and the load [16]. The boost converter is controlled by a PID controller which stabilizes and regulates the output dc voltage at 110V. The schematic of the boost converter and the PID controller is shown in Fig. 3. All of the diode rectifier, boost converter, and PID controller are implemented and modeled in Simulink environment. C. The dc Load and Battery The output dc voltage of the controlled rectifier is used to supply the dc load and energize the battery. The load is a 60 Ohms resistance. The battery is used to store the energy to supply the dc load when the solar energy is not available. The battery is charged when the Stirling engine is normally driving by solar energy and is discharged when supplying the load in the lack of solar energy. The initial state of charge of the battery is 70% at the beginning of the simulation and increases to 100% as the solar energy is adequate to charge it up and decreases to lower than 70% if the solar energy becomes unavailable and the battery is used to supply the load. V. S IMULATION R ESULTS Using the developed model, the performance of the Stirling engine power generation system is evaluated in different operating conditions. Some of the simulation results are given in this section. The rotation speed and generated torque of the Stirling engine are shown in Fig. 4. When the system is subjected to a load step change at 0.04 sec. To change the dc load, the output resistance is switched from 60 Ohms to 10 Ohms. As can be seen in Fig. 4, the rotation speed is decreased while the Stirling engine tries to keep it constant by increasing the torque. It should be mentioned that the Stirling output power is almost constant and the required dc load power is
Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey
Fig. 3. The Boost converter with PID controller scheme implemented in Simulink environment.
supplied from battery. As shown in Fig. 4, some oscillations are visible on the rotation speed and generated torque. These oscillations are related to normal operation of the Stirling engine which is a reciprocating engine. As the Stirling engine and the synchronous generator are coupled through the mechanical shaft, the oscillations on the engine torque may cause oscillations on the generator voltages. The effect of these oscillations on the output dc voltage can be eliminated by PID controller that control the boost converter. The amplitude of torque oscillations is decreased by increasing the output dc load, as shown in Fig. 4. Fig. 5 shows the load current, the battery current, and the summation of the load and battery currents. It should be mentioned that the summation of the load and battery currents represents the boost converter output current. The boost converter supplies the dc load and charges the battery before 0.04 sec, when the the currents are respectively about 2 A and 3.75 A. After switching the load resistance to 10 Ohms, the load current is rapidly changed to around 12 A, when the battery current is decreased to about -8.75 A. This means that the battery is discharging for the load resistance of 10 Ohms. Fig. 6 shows the output voltage of the dc converter which is about 110 V. As can be seen in this figure, the load step change causes variation less than 5% on the output dc voltage. Moreover, no oscillation is observable on the dc voltage that shows the effectiveness of the PID controller. The generated voltages and currents of the generator are depicted in Fig. 7. As can be seen, the load step change causes a small variation on the generator currents and voltages. The variation in the generator voltages may cause variation on the diode bridge output dc voltage that is applied to the boost converter.
679
Fig. 4.
Fig. 5.
The rotation speed and the Stirling engine generated torque.
The load current, the battery current, and the summation of the load and battery currents.
Fig. 6.
The output dc voltage.
680
Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey
Fig. 7.
The synchronous generator output voltage and currents.
VI. C ONCLUSION In the paper, a relatively comprehensive model that considers the thermal, mechanical, and electrical aspects of the Stirling engine based power generation system was developed. The simulation results verified that the system shows a realistic representation of the real model when the system is subjected to the load variation. The interaction between mechanical and electrical part was also considered and it was shown that normal operation of the Stirling engine can cause oscillatory effect on the rotation speed and generated torque and as a result oscillations on the synchronous generator rotation speed and torque. The boost converter controller can eliminate the oscillations on the output dc voltage. The proposed system can be used as an off grid generation system which can supply a dc load taking the advantage of the efficient Stirling engine and the sustainable solar energy as the heat source. ACKNOWLEDGMENT The authors would like to thank Kerman Graduate University of Technology and International Center for Science and High Technology for support during the course of this work.
[8] S. Bittanti, A. D. Marco, M. Farina, and S. Spelta, “Modeling and simulation of a dish stirling solar engine,” in 16th IFAC World Congress,, Prague (The Czech Republic), 2005. [9] The Mathworks Inc., Power System Blockset for use with Simulink(User’s guide), The Mathworks Inc., 3 Apple Hill Drive, Natick, MA 017602098 USA, 2004. [10] F. White, Heat and Mass Transfer. Addison-Wesley Publications, 1988. [11] G. Van Wylen and R. Sonntag, Fundamentals of Classical Thermodynamics, 3rd ed. John Wiley and Sons, 1986. [12] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, 2nd ed. IEEE Press, 2002, pp. 111125. [13] Y. Higuchi, N. Yamamura, M. Ishida, and T. Hori, “An improvement of performance for small-scaled wind power generating system with permanent magnet type synchronous generator,” in 26th Annual Conference of the IEEE Industrial Electronics Society, vol. 2, Oct. 2000, pp. 1037–1043. [14] K. Tan and S. Islam, “Optimum control strategies in energy conversion of PMSG wind turbine system without mechanical sensors,” IEEE Trans. On Energy Conversion, vol. 19, no. 2, pp. 392–399, June 2004. [15] D. Grenier, L. Dessaint, O. Akhrif, Y. Bonnassieux, and B. LePioufle, “Experimental nonlinear torque control of a permanent magnet synchronous motor using saliency,” IEEE Transactions on Industrial Electronics, vol. 44, pp. 680–687, 1997. [16] M. H. Rashid, Power Electronics Handbook. Academic Press, 2001. TABLE I S YSTEM PARAMETERS
R EFERENCES [1] S. Kalogirou, Solar Energy Engineering: Processes and Systems. Elsevier, 2009. [2] A. D. Minassians and S. R. Sanders, “Multiphase stirling engines,” ASME Journal of Solar Energy Engineering, vol. 131, May 2009. [3] W. Stine, The CRC handbook of mechanical engineers, F. Kreith, Ed. Boca Raton: CRC Press, 1998. [4] B. Kongtragool and S. Wongwises, “A review of solar-powered stirling engines and low temperature differential stirling engines,” Renewable and Sustainable Energy Reviews, vol. 7, pp. 131–154, 2003, elsevier Science Ltd. [5] F. Nepveu, A. Ferriere, and F. Bataille, “Thermal model of a dish/stirling systems,” Elsevier Solar Energy, vol. 83, pp. 81–89, 2009, available online at www.sciencedirect.com. [6] G. M. Masters, Renewable and Efficient Electric Power Systems. John Wiley and Sons, 2004. [7] D. P. Hart, “Stirling engine analysis,” Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 2.670 Course notes, 1999.
Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey
Stirling engine
Re =1.25cm, Asc =40cm2 , Ppc =4.9cm, Ah =variable, Ac =variable, µ=10000W/m2 , Al =0.06mm2 , Ap =1.9cm2 , Vc =40cm3 , m=29kg/kmol, R=287J/kg, s¯o =2800J/K.kg, To =300K, Po =Pa =1e5P a, Cv =717J/kg.K, b=0.7e − 3N/rad/s, I=4kg.cm2
Permanent magnet synchronous generator
Lq =0.02682H, Ld =0.02682H, λ=0.1717wb, R=18.7Ω, P =2
Boost converter
L=250µH, C=1056µF , Mosfet: Ron =15Ω, Rd =0.001Ω, Rs =1e5Ω, Cs =∞, PID controller: KP =100, KI =10, KD =0.1,
Battery
Battery T ype:nickel-metal-hydride, nominal voltage=110V , rated capacity=1.5Ah, initial state-of -charge=70%.
681
