temperature and energy production, distance out of focus and energy production, and applied this to our results. A highly efficient heatsink will keep temperatures low. However, the increased weight of this heatsink will cause the plate to flex more, putting it out of focus and reducing efficiency, and the increased weight also increases cost. Te best solution is a slightly less efficient heatsink that costs less and weighs less, thereby increasing the “focus efficiency”, as that gives the highest kW/$.’


Making every Watt count PV cells have a non-linear output and ‘no matter how brightly the sun shines, how much power you get from the cell depends on the electrical load,’ according to Peter van Duijsen, R&D programme leader for Simulation Research, which is based in Te Netherlands. Te converter that is the interface between the cell and the rest of the world needs to control the electrical load so as to keep the cell at the maximum power point (MPP) but, as van Duijsen explained, the MPP varies with cloud- cover, intensity of sunlight, and temperature so the controller needs to measure the MPP and try to figure out if there is another point nearby where it can get more power. Te angle of the sun changes through the day, so the MPP is changing all the time, and there is thus an active and continuous control mechanism. Te company’s Caspoc soſtware, originally


intended for electrical drives and power electronics applications, is ideal for the task of simulating the electrical properties of the cell and converter. ‘We have a model for solar cells where you input the light intensity and temperature, the parameters of the cell, with an electrical output, and it is modelled like a physical model. Te output from the solar cell is connected to the converter, which is modelled using discrete components in our simulation. So you can build the complete model with all the semiconductor switches and then you have to define the control part, either by an analogue block diagram, or you can define digital control inside a microchip or a digital signal processor. You can then simulate the electrical behaviour of the converter with the solar cell but also the numerical behaviour of the controller.’ Broadly speaking there are, he said, three


methods of controlling the load so as to keep on the MPP. Te first is a hill-climbing search algorithm, whereby the controller adjusts the voltage by a small amount and measures power from the array; if the power increases, further adjustments in that direction are tried until power no longer increases. It is also called the ‘perturb and observe’ method. It is widely used due to its simplicity. Incremental


www.scientific-computing.com l @scwmagazine


conductance, the second method, obtains the voltage/current graph at fixed time intervals and computes the maximum power point from the curve at the same intervals. Te maximum power method works by taking the derivative of power to voltage and optimising it to zero as this is simply the maximum of the power- voltage characteristic. Although the CFD and structural analysis soſtware may get more attention, among the suite of programmes available from Ansys there are also capabilities to deal with non-linear electronics. Although the Canadian-based Integrated


Engineering Soſtware acts as the main sales agent, Caspoc was developed and is being refined by Simulation Research in Te Netherlands. Like Ron Behee, however, van Duijsen does not see an immediate need to parallelise the code. It is a different sort of problem from finite element analysis, he pointed out. Tere, refining the mesh would yield more accurate answers but, for power electronics, if more detail was needed then it would be at the level of the discrete electronic components within the system – and this was not a compute-intensive task. Tere might be problems of overvoltage or harmonics or other electromagnetic interference that needed simulating, but such modelling needed to be done only for nanoseconds. Caspoc soſtware can also be applied at the


consumption end of the solar power cycle, van Duijsen said, in modelling the power electronics controlling the motors of electric cars. If the number of electrical cars increases then there will be a corresponding increase in electricity demand but, he said, if houses and offices have more PV solar panels then power is produced locally and less is required of the national network (there are always energy losses in a large electricity grid). Tis localised model could help countries maintain some energy independence, and he knows of some pioneers who are already using their domestic and office solar energy to power their electric vehicles.


Further information Ansys www.ansys.com


Integrated Engineering Software www.integratedsoſt.com


Luxon Engineering www.luxonengineering.com


MSC Software www.mscsoſtware.com


Simulation Research www.simulation-research.com


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