Modeling and Simulation for Solar and Wind Energy
Peter van Duijsen
1, Pavol Bauer
2, Frank Chen
31Simulation Research, The Netherlands, p.vanduijsen@caspoc.com
2Technical University Delft, The Netherlands, p.bauer@ewi.tudelft.nl
2PitoTech, Taiwan, pitotech@mail.pitotech.com.tw
Abstract - The application of Modeling and Simulation in the
design and verification process for Renewable and Green Energy is the focus of this paper. The scope will be solar and wind energy. First the role of electrical energy is discussed and second samples are given where modeling and simulation can be applied. A brief discussion is given on the model of the wind turbine and the models for the generators. The second part of the paper is concerned with the estimation of losses in the power electronic converters. Here a model in Caspoc will be presented for fast loss prediction in an IGBT inverter.
Keywords: Modeling, Simulation, Renewable, Green Energy,
Solar, Wind Power, Losses IGBT, Doubly Fed
I. INTRODUCTION
Green Energy will effect the quality of our life in the near future. With limited fossil energy resources available, it is only a matter of time when we will change our focus on renewable and clean green energy.
There are many discussions going on about the type of energy storage and transportation. The two main candidates for storage and transportation are hydrogen and electricity. Since electrical energy is the most practical to generate and transport, it is favored over hydrogen. However storage of electrical energy is more difficult and requires other physical means for storage. For high energy levels, water storage on different altitudes is a proven technology. For automotive and mobile applications, batteries, super capacitors, or mechanical flywheels become more practical. Fuel cells for automotive applications and even for small mobile apparatus are in development.
A combination of efficient energy storage in the form of hydrogen and generation of electricity by fuel cells seems to be the most promising alternative to fossil energy resources. However the practical question remains, where
do we get the power to produce H2
Focus of the paper
The main focus in this paper on electrical energy is on the generation of electrical energy by solar cells and wind turbines. Samples are given for solar power as well as for generator modeling. The loss estimation in an IGBT is discussed in the second part of this paper as well as modeling the thermal aspects of power electronics.
What is Green Energy?
Every now and then, new buzzwords start to appear and this is also true for electrical engineering. The term Green Energy can be associated with environment-friendly generation, transport, storage and use of energy. If we
compare the use of electrical energy for railway applications with a steam locomotive, the advantage of electrical energy for preserving the environment is evident. However, where is this electrical energy produced? You can not simply get it like other natural energy resources like coal or oil. Remember that burning coal, oil and methane produces a substantial part of the electrical energy that we use today. And we are not so fond of nuclear power, mainly to its waste problem! These are all fossil energy resources that are not part of our definition of Green Energy. Solar power, wind power, and the natural flow of water are resources that comply with our definition of Green Energy. Since the natural fossil energy resources are limited on this planet, we have to put our focus on green power generation like solar and wind power.
Taking into consideration the environment-friendly character of electrical energy, we can state that at least for transport, storage and use, electrical energy is our favorite. In the next sections we will discuss the generation, transport storage and use of electrical energy.
Generation of electrical energy
If we look at electrical energy, we can state that it is Green Energy, when it comes to transport storage and use. Only the generation of electrical energy with using natural energy resources such as solar or wind power can be considered Green Energy. Also a Fuel Cell is considered as Green Energy, but remember that somewhere the hydrogen has to be produced.
Transport of electrical energy
Transport of electrical energy seems to be very simple, just use some cables, and the job seems to be done. This seems to be true on short or medium distances, but transporting electrical energy from one continent to another is a major challenge and losses during transport become significant.
Storage of electrical energy
Storage of electrical energy is possible for low power. For example, batteries are common in use, but have serious limitation when it comes to power level, life time, production and pollution due waste. Also the energy density/ weight ratio is far less compared to fossil energy resources. As an example, a liter of gasoline will get you much further than a fully charged battery if 1Kg.
On a larger scale, hydrogen could be stored more easily and could be generated from electrical energy. Storage in the form of mechanical power such as with a flywheel for automotive applications only found serious use in public transport. Super capacitors are a promising component, but still partly in the development stage. Storage in the form of
2006第五屆台灣電力電子研討會
hydrogen seems to be the most promising candidate for the future.Use of electrical energy
The use of electrical energy is straightforward and well accepted. There are exceptions in certain areas, for example such automotive, aeronautics, space exploration, industrial heating and welding and heating of buildings, where due to storage and the high power level requirements, electrical energy for propulsion is not very practical.
Control of electrical energy
Today, controlling the flow of electrical energy is mainly done by power electronics. Solid state electronics have a good reliability and a high MTBF. However thermal stress on power electronics, is the main cause of failure. Therefore a thorough investigation of the thermal stresses on power electronics is required that can be done via modeling and simulation. Here modeling the semiconductor switches is crucial. The model on one side should be able to predict the on state and switching losses and the parameters should be temperature dependent. On the other side, the simulation should be as fast as possible, requiring simple models. The presented semiconductor models allow loss prediction while maintaining a high simulation speed [7].
II. SOLAR POWER
Solar Power seems to be the most efficient way of generating energy from the sun, but the production of solar cells is expensive and environment-unfriendly. Furthermore, the efficiency of the solar cell is low. In this sample the non-linear characteristic of the solar cell is simulated, showing the current dependency of the output voltage. The solar cell is a current source up to its nominal power. As soon as the maximum power is reached, the current drops to lower levels. In this sample, current levels up to 3A are possible, up to 120 Watt.
Figure 1: Solar Cell characteristics.
To make the electrical energy from the solar panel useable for home appliances, it has to be converted into AC, preferably 240V RMS for European households. This can be done using an inverter with transformer as indicated in figure 2.
Temperature of the Solar Cell TEMPERATURE Intensity of the sunshine
SUN SCOPE4 SCOPE3 VAC50HZ1 325.2691 + -SCOPE1 R1 1000 CON 25 C1 1mF CON 500 SCOPE2 L2 10u L1 40mH 0 0 T 50 1 20 SUNDENSITY
Figure 2: Solar panel with inverter.
In the most right scope the output from the inverter is compared with the utility voltage. A phase shift can be observed and therefore a control is required to synchronize the phase between the utility voltage and the output from the inverter.
III. WIND POWER
Wind power was popular in the old days and is still very popular nowadays, because of the high power that can be achieved in an efficient way, see figure 3. If we model the energy produced by wind power, we have to model all components in the system. First the wind turbine has to be modeled, including the mechanical drive train, such as shafts, gearboxes and bearings. Second the electrical machine, mostly a synchronous machine, is modeled in detail and connected to a model of the power electronics, such as AC-DC or back to back converters (AC-DC-AC with variable frequency). The control of the wind turbine needs special attention. The pitch control is important, since the efficiency is greatly influenced by the pitch of the rotor blades.
Figure 3: Modern and classical wind power in Holland. There are various types of generators possible. Squirrel cage induction machines, doubly fed induction machines and directly driven synchronous machines.
The most common is the synchronous generator that is driven by the wind turbine via a gearbox and is connected to the mains by power electronics. The squirrel cage induction machine requires a capacitive load in order to operate as a generator. The doubly fed induction machine can be operated a various drive speeds, while maintaining a very low slip.
Synchronous Generator
In the simulation shown in figure 4, the wind power is converted into electrical energy by a synchronous generator and rectifier. The scope shows the DC link voltage and the load current. The Synchronous generator is modeled by using a detailed two-phase model in the stator reference frame (1),
(1) where (all quantities in the rotor reference frame are referred to the stator)
Lq, Ld q and d axis inductance's
R Resistance of the statorwindings
iq, id q and d axis currents
vq, vd q and d axis voltages
ωr Angular velocity of the rotor
λ Amplitude of the flux inducedby the permanent magnets of
the rotor in the stator phases
p Number of pole pairs
Te Electromagnetic torque
The power electronics is modeled by ideal switch models. Use can be made of dynamic models for the diodes, or models including the reverse recovery effect. The load is modeled by a series RL impedance.
Figure 4: Wind Energy, The scope shows the DC Link Voltage and Current.
Doubly Fed Induction Generator
The induction machine applied as a generator is more difficult to understand than a synchronous generator, because in reality the induction machine is a rotating transformer. Where a synchronous generator has a rotating magnetic field from which the voltage in the winding is
induced, in the induction machine the rotating field first has to be created.
It is easier to understand the principle of the induction generator from the doubly fed induction machine. In figure 5 the doubly fed induction generator is fed by an inverter. A simple six-step modulation scheme is applied to feed the rotor windings. w V_ANGULARSPEED1 40 SCOPE3 SCOPE1 0 c b a 40 iim 0
Figure 5: Doubly fed induction generator
The shaft is rotating with a constant angular speed of 40 [Rad/s]. The inverter frequency is 40Hz. Depending on the slip s of the machine, the frequency of the induced voltage in the stator will therefore approximate 40Hz+40/2pi. The shape of the rotor voltage defines the shape of the voltage on the stator. Also the ratio in windings between the rotor and stator influences the induced voltage. Needless to say that the higher harmonics of the rotor voltage do not improve the efficiency of the generator. The high amounts of harmonics in the rotor and induced in the stator poles result in high eddy current and hysteresis losses in the machine. An unwanted rise of temperature in the machine will be the result. Therefore an inverter with a high switching frequency and a low-pass filter has to be applied in order to reduce the higher harmonics.
Squirrel Cage Induction Generator
A squirrel cage induction machine can be used as a generator, provided that there is some remanent magnetic field in the induction machine. This remanent magnetic field will cause an induced voltage that in turn will create a larger magnetic rotating field. This process will continue until a stable operation point is reached. Figure 6 shows the start up of an induction generator, where the remanent energy is modeled by an initial voltage on one of the capacitors. SCOPE2 C4 140u C6 140u T I_TORQUE1 1000 R_BEARING1 1 C5 140u 0
Figure 6: Induction machine with capacitor compensation as generator
Wind Turbine
The wind turbine model should include the effects of wind speed and pitch of the rotor blades. A general equation for the output power of the wind turbine is given by (2)
(2)
where
Pm Mechanical output power of the turbine (W)
cp Performance coefficient of the turbine
Ρ Air density (kg/m3)
A Turbine swept area (m2)
vwind Wind speed (m/s)
Λ Tip speed ratio of the rotor blade tip speed towind speed
Β Blade pitch angle (deg)
The parameter cp is given by the manufacturer of the wind
turbine and is either modeled by a function, or by a
look-up table. Figure 7 shows the parameter cp for various pitch
angles dependent on the tip speed ration.
Figure 7: Parameter cp as function of the Pitch angle and
Tip Speed Ratio.
The turbine model is included in the simulation in figure 4, where wind speed and pitch are the external variables.
IV. POWER ELECTRONICS
Major power semiconductor manufacturers present regularly improved new versions of their successful semiconductors. They claim that using their new semiconductors, the on state losses, switching losses and EMI/EMC are reduced. However the losses of the semiconductors are highly dependent on chip temperature and power circuit operation. In order to choose between the various semiconductors offered and to optimize the design, one needs some help in the form of a simulation tool. Using the simulation tool [4], [5], the temperature dependent losses for a typical semiconductor in the particular power circuit can be estimated. Unlike complex semiconductor simulation models required for the first generation of circuit simulators, modern multilevel simulation tools include models that are based on manufacturer data sheet information.
Modeling requirements
To simulate the losses in the semiconductors during switching, the most obvious choice for modeling would be a model that is as detailed and complex as possible and is based on a large number of parameters coming from the fabrication process. However the main goal is to predict the on and off times during switching and the thereby
associated switching losses, see the section on the Mosfet Model. The correct waveform during switching could be simulated using a detailed model with verified parameters under certain conditions such as:
• Correct 3D thermal model allowing the non-linear temperature distribution on the junction.
• Parameters are fabrication process dependent and known for the used semiconductor
• Correct 3D electromagnetic model for the surroundings of the semiconductor
Even taking into account these conditions, still one has to cope with uncertainties like:
• Varying ambient temperature
• Components from a different fabrication line or factory
• External electromagnetic influences
• Mechanical stress influencing the thermal conductivity
Taking into account these uncertainties it seems a tremendous effort to get reliable simulation results. Simulation time is not even discussed here, but is seems obvious that such a detailed analysis leads to long simulation times.
The goal for many designers is however to get some prediction on how the power electronics will perform under a wide range of conditions. For example:
• The ambient temperature varies from -40 to +120 degrees Celsius
• Because of mechanical stress the thermal conductivity to the heat sink can over time reduce by a factor 2
• Parameters for parts coming from various manufacturers vary several percent
Also the simulation time is of concern. To perform simulation studies for a wide range of parameter variations, the simulation has to be as fast as possible. This gave rise to the development of methods that would predict losses in semiconductors during switching. There are two important design criteria that have to be predicted during the simulation:
• Switching losses • EMI/EMC
Instead of using detailed models, manufacturers provide measurement data for switching losses, dependent on the most important conditions such as temperature and power level. EMI/EMC is mainly dependent on the electromagnetic properties of the circuit, such as lead wire inductance and bus bar inductance impedance.
Mosfet Model
In Caspoc the spice compatible model for the Mosfet [9][10] is adapted where:
• In the Caspoc Mosfet model, the capacitance CGD is depending on the voltage VDG across it [6].
• In the Caspoc Mosfet model RDS(on) and KP are temperature dependent [8].
Figure 8 shows a simulation of single Mosfet with simple thermal model and ideal diode model for the freewheeling of the coil current
Figure 8: Spice compatible IRF730 Mosfet Model in Caspoc
Figure 9 shows the gate voltage and the relation to the turn
on and turn of shown by VDS and IDS in case that snubber
circuits are added and the diode includes a reverse recovery model. 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 45.000 -600.000m 50.000 1000.000n 1100.000n 1200.000n 1300.000n 1400.000n 1500.000n 1600.000n 1700.000n 1800.000n 1900.000n 2000.000n VGS IDS VDS VDS
Figure 9: Mosfet Switching in Caspoc; Gate voltage VGS
(red trace) versus VDS (green trace) and IDS(blue trace)
Although the dynamics of the mosfet are modeled and the conduction and switching losses are simulated, the total simulation time would be too long, when a complete wind power system has to be simulated. Therefore fast loss predicting models are required, see section VI.
V. THERMAL MODELING
Thermal modeling is required both for the detailed models and for the fast-lost predicting models. Important is to identify the layers of material that have different thermal conductivity [8]. The ambient temperature will be nearly constant and the temperature on the heat sink will vary very slowly. However the temperature on the junction will rise much faster because of the switching losses. The example in the last section of this paper shows the temperature fluctuations directly on the junction compared to the slowly varying heat sink temperature. In the following figure the various layers of the chip, solder, lead frame and case are shown. Thermal resistors model these layers. The model of the semiconductor is dependent on the temperature of the junction. Therefore the losses are
injected in the thermal model and the temperature of the junction is used to change the semiconductor parameters.
Rtn dA C C dA tn = λ ρ = tn Rth6 Rth5 Rth4 Rth3 Rth2 Rth1 Cth6 Cth5 Cth4 Cth3 Cth2 Cth1 case lead frame solder chip TC
Figure 10: Layers and the thermal model of a semiconductor.
The following figure shows the dependence of the transconductance and on-resistance of a power mosfet on the junction temperature from the thermal model.
C R G th1 thha Ta Rth1 D S RD(T) Vt0(T) Kp(T) P
Figure 11: Coupling between the semiconductor model and the thermal model.
For simple thermal structures this model is a good approximation. However when components are spaced close to each other their thermal models will also be coupled, see figure 12.
Figure 12: Thermal dependency between components on a PCB modeled in Ansys/Workbench
In that case the entire mechanical structure has to be modeled and the thermal model for this structure has to be approximated. There are two options for coupling the thermal model with the semiconductor simulation:
• Coupled simulation
• Thermal model approximation
A coupled simulation can be carried out between Caspoc [4] and Ansys/Workbench [11]. In this case the switching losses are injected in the 3D thermal model in Ansys/Workbench, where the temperature is calculated each time step. The temperature is then send back to Caspoc to adapt the temperature dependent parameters in the semiconductors.
Another method is to first calculate a thermal model using any FEM package such as [11] or [12] that can be included directly in the system simulation. The disadvantage here is that non-linear temperature-dependent thermal conductivity parameters are neglected. In the coupled simulation, these effects are taken into account.
VI. FAST LOSS PREDICTING MODELS
To predict the losses in a drive system, the simulation has to run for many cycles. With the ever-increasing switching frequency, the total simulation time would be too long for a simulation employing dynamic Mosfet, IGBT or GTO models. Therefore the ideal switch model, with conduction and switching losses modeled are used to calculate the losses in the inverter.
Figure 13: Modules for the Mosfet, GTO and IGBT with loss prediction
The figure above shows the modules in CASPOC [4] for the fast loss prediction models. Besides the electrical nodes, each module has a thermal node that can be connected to a thermal model.
Figure 14: Single-phase IGBT inverter with thermal model In case of a Mosfet, the transconductance and drain-source on-resistance are dependent on the temperature. In the fast loss prediction modules also a forward voltage drop for the mosfet is included in the model, although mostly the temperature dependent drain-source on-resistance is the
design parameter of interest. For the IGBT, both VCEon and
RCeon are temperature dependent. The switching losses are
given in the manufacturer data-sheet and are specified for 25˚ Celsius and 125˚ Celsius. The junction temperature has to be calculated during the simulation and is used to adapt the parameters for the semiconductors.
Using the fast loss prediction model enables the prediction of the system behavior and prediction of the losses of the
component. In an IGBT, the temperature dependent VCEon
and RCeon model the conduction losses. The switching
losses are calculated from the data-sheet parameters Eon and Eoff. The temperature on the heat sink is dependent on the losses. The losses are temperature dependent because
VCEon and RCeon are temperature dependent.
The simulation in figure 14 shows the start up (first 10ms) with a switching frequency of 10kHz and runs only a couple of seconds.
The heat sink is modeled and the temperature on the case is shown and compared to the heat sink temperature. The red trace shows the junction temperature.
50.000 100.000 150.000 0 200.000 0 5ms 10ms TJunction THeatSink
Figure 15: Junction temperature (red trace), versus heat sink temperature (blue trace)
VII. CONCLUSIONS
A complete Solar or Wind power system can be modeled and simulated including detailed models for the solar cell, wind turbine, generator and power electronics.
The crucial parameters and equations to be included are: • Non-linear current dependency in a solar cell.
• Non-linear wind speed and pitch dependency in a wind turbine, with a models of the flexible shaft, and inertia of the turbine and gearbox. • The minimum model for the generator should be able to model the basic harmonic existing in the machine and should be coupled to the power electronics models.
• An ideal switch model should model the power electronics, to include the generation of harmonics by the switching sequence.
• EMI/EMC, losses and thermal stress are modeled by using the fast loss predicting models where a high simulation speed is maintained.
VIII. References
[1] Bauer P. Understanding the Power Quality Problems and Compensators, Proceedings PCIM 2004, page 50508, ISBN 3-928643-39-8
[2] Sasaki S., Sato E., Okamura M., The motor Control Technologies for the Hybrid Electric Vehicle, PCIM 2004, page 1-10, ISBN 3-928643-39-8
[3] Bauer P., Duijsen P.J. van, Simulation Software with Open Interface, Power Electronics Europe, page 29-31,
[4] Simulation Research, Simulation program Caspoc 2005, www.caspoc.com
[5] Bauer, P., and Duijsen P.J. van, "Challenges and Advances in Simulation," Proceedings of PESC '2005 Conference, Recife (Brazil), 2005.
[6] Dudrík J., "New Methods in Teaching of Power Electronics Devices", I. Journal Of Electrical And Computer Engineering, Vol. 4, No. 2, Summer-Fall 2005
[7] Van Duijsen P.J., Bauer P., Lascu D., "Selection of Semiconductor Models in Power Electronics Simulation", Proceedings of the PCIM 2003
[8] P.J. Van Duijsen, P. Bauer, U. Killat, "Thermal Simulation of Power Electronics", PCIM 04, Nurnberg, May 25-27, ISBN 3-928643-39-8, pp.881-886
[9] Dudrík J., Power Semiconductor Devices and their Protection, LdV, 2001, ISBN 80-89061036
[10] Ramshaw R.S., Power Electronics Semiconductor Switches, Chapman & Hall, 1993
[11] Ansys/Workbench Multiphysics, Ansys Corp., www.ansys.com [12] Comsol multiphysics , Comsol , www.comsol.com
