Even here in Britain, the sun sometimes shines. But my wife and I were surprised to discover that the photovoltaic solar panels newly installed on the roof of our house don’t reach as high a peak power output on hot summer days as in spring and autumn.
Sunshine is free and there is a lot of it: more than 86,000 terawatts of solar power reaches the Earth’s surface each year (although a lot more hits the upper atmosphere). In principle, this would be enough to satisfy current global demand a thousand times over. But making use of the sun’s bounty is more complicated than it seems, as our little domestic example shows. So it is no surprise that simulation and optimisation plays a critical role in ensuring that green energy is also efficient energy.
Even when it shines, the sun is a problem. It radiates light, which photovoltaic (PV) cells convert to electricity, but it also radiates heat. The efficiency of PV cells decreases as their temperature rises. Then the sun moves (or, as Galileo pointed out, it appears to move), and so the angle of incidence and the total flux of radiation changes as the day wears on.
In Britain and elsewhere, the sun seldom shines from a cloudless sky, so part of an array may be shaded while another part is in full sun – can the load across all the panels be balanced for maximum efficiency? The winter may bring snow – again partially shading some, but not other parts, of the array. But snow has a mechanical effect as well as electrical. Will the panels stand the extra weight and does it matter how that is distributed? It rains a lot in Britain, and the wind blows, producing stress in the panels and their support structures.
In addition to the temperature effect, PV cells have a non-linear response to variations in solar radiation flux. They also produce direct current, whereas most of the world is set up to use alternating current. The output from the panels needs to be stored if not immediately needed, and converted to AC before being sent out for consumption.
Roof-top PV cells are not the only way of harvesting energy from the sun. But the problems of thermal stress and distortion, and seasonal and diurnal variability, apply just as much to industrial-scale concentrated power plant systems where moving mirrors track the sun across the sky and concentrate the reflected radiation to a central point into a heat-transfer fluid, feeding either a steam turbine or a Stirling engine. Many of the issues apply even to the ‘intelligent’ design of buildings that tries to take advantage of solar thermal radiation to heat the building when needed, and bring down shutters or blinds to keep it cool in the summer.
Thermal analysis
Software for thermal analysis is what animates Ron Behee, director of development for MSC Software, headquartered in California. The company’s thermal analyser package, Sinda, has a distinguished pedigree – it can trace its roots back to NASA’s Apollo programme in the early 1960s, Behee said – and in its modern guise it has found successful application in space programmes such as Astra, ERS 1-2, Gomos, Mars Express, Silex, and Soho, as well as more down to earth applications in the aircraft, automotive, and electronics industries. According to Behee, one important characteristic of solar power is that the sun radiates both in the visible and the infrared areas of the spectrum; and engineers have to model these two fluxes separately, something which traditional finite-element analysis codes do not easily do. ‘You need a ray-tracing code to model sunlight bouncing off shiny surfaces, and the spacecraft people have been doing that for years.’ With the experienced gained by developing the software for aerospace applications, he said: ‘We have all the right elements to model heat transfer on earth’.
But MSC Software felt it was missing one terrestrial dimension – the weather. So the company hired a graduate student from Arizona State University, which has an impressive solar energy programme. He pointed out that, for decades, at virtually every airport around the world, virtually every day, someone has been noting down the temperature, wind speed and direction, cloud cover, and precipitation. Later this year, therefore, MSC Software will release a GUI ‘that makes it very user-friendly. You just grab a file off the internet for an airport near you and you can simulate a house for solar cooling or heating’. The availability of such weather data, neatly integrated with the thermal analyser, allows engineers to conduct simulations that have two divergent purposes. A solar power company may wish to use the real data to get a realistic projection of the likely output of its installation. But others may want to choose a best and worst case – the hottest day and the coldest – to gauge how the constraints that the weather might place on their equipment.
Behee sees applications for the simulation software in the concentrated power plant arena – both thermal solar power and arrays of PV cells – and in the design of PV solar panels for roof-tops. The US Government has a programme to promote concentrated solar power plants. He pointed out that there was growing interest in hybrid power plants – when available, sunlight would be used to turn water to steam to drive a turbine but, when the sun was not out, gas or other fuel could be used. ‘We can model that concept, where you use the same turbine and pipework,’ he said. Other concepts that the software has been applied to were flat-plate mirrors that were etched with a grating so as to focus on a parabolic collector made of glass that had the heat-transfer fluid at its focus. Unfortunately the heat distorted the glass, making it de-focus. The solution was to design the collector so that it was out of focus when cold but thermal distortion brought it into focus as it operated.
Behee also noted that ‘PV is big in Arizona too, and tends to be more popular because it has fewer moving parts’. There is a lot of scope for optimisation, he said, in trying to keep the cells cool, so as to maximise their energy conversion efficiency. Concepts have included cooling fins on the underside of the panels and heat exchangers on the back of the panels, so it might even be possible to get warm water out of a PV panel set-up.
It is, Behee said, ‘an exciting recycling of technology’ that the thermal analysis software that owes its origins to aerospace – often military projects – should now be being applied to the supply of ‘green thermal’ energy. With the new ability to incorporate real data on weather conditions with an easy-to-use GUI, the industry will be able to make realistic projections. Aerospace modelling, he said, tended to focus on best/worst case scenarios – how would my military airplane react to a day parked out in the full sunshine of a desert airfield or a winter’s day in Alaska? But now, MSC Software had found a way to do realistic simulations and modelling for the energy sector using realistic data.
Modelling the chemistry of making solar cells
A similar concern with performing real-life simulations for the solar energy sector was evident from Ahmad Haidari, global industry director (energy and process) for Ansys, which has its headquarters south of Pittsburgh in Canonsburg, Pennsylvania. Energy is one of seven industrial sectors that Ansys serves, he said. Although solar is currently a relatively small part of the business, it is growing and Haidari expects faster growth in Asia, where much of the manufacturing is being done, and Europe, where a lot of innovative research and design work is being carried out, than in the USA. He sees two main areas where Ansys simulations can make a difference. The first is in the manufacturing process; for example, multi-phase fluid mechanics of the design of the chemical reactor in which the silicon is processed to make PV cells, modelling such factors as species transfer and, at a later stage in the process, surface deposition of the silicon onto the substrate of the cells. Such simulations may involve multiphase calculations – which are very compute-intensive, he warned.
The aim is to change manufacturing processes so that less material is used. Independently, research is going on to improve the composition of the cells so that they convert more of the sun’s radiation to electricity and waste less as heat. Alternative ways of making PV cells to increase conversion efficiencies to 30 per cent are at the heart of the US Department of Energy’s ‘SunShot’ programme, launched in February 2011, which aims to reduce the total costs of PV systems by three quarters to roughly $1 a watt (corresponding to about six cents per kilowatt-hour) which would make them cost competitive at large scale with other forms of energy.
Optimising structures
The second area is more conventional structural engineering. Ansys has a suite of programs that can be used to calculate stresses and loads in mechanical engineering but, in addition, he pointed out, solar loading – shade calculations and the best location with respect to the sun – and, especially for commercial structures, wind-loading and mobility of the mirrors need to be factored in. ‘On the mechanical side of things, reliability is important – structural integrity and reliability. What happens to that system on the rooftop over 25 years? It’s not a simple linear structure,’ he asked. As with Ron Behee and MSC Software, the issue for Haidari is the weather and fluctuating conditions. Though some of this can be tested empirically, he said: ‘Engineering simulation tests the real-life reliability of a panel across various operating events. More goes into the design of these panels to make sure they’re there for 25 years. That’s where computational technology comes into play – to really test the real life variability of a panel across many applications.’
Concentrated power plant installations present further challenges for simulation and optimisation. The mirrors tend to be flat and smooth, and their supports have to be relatively stiff so they do not flex when the wind blows or other loads are placed on them. The mirrors have to track the sun as it moves overhead, and this presents issues of simulating the control circuitry that keeps them pointing in the right direction.
Some of these calculations can be very compute-intensive. Ansys has been concentrating on parallelising all its code, across all applications and sectors ‘to create an environment for our customers that offers realistic system design’. He sees high-performance computing (HPC) as ‘one of the enabling tools to create an environment where people can do real-life simulations.’ The company was also looking at the programming challenges and opportunities presented by GPUs to make simulations faster.
For Luxon Engineering, a mechanical engineering consulting firm located in San Diego, California, however, Altair’s HyperWorks was the package of choice when it came to optimising a large-scale industrial panel system where components also rotate to track the sun. Luxon’s brief was to lower the manufacturing costs, and also to model wind and snow loading, so the system could be deployed in a wider range of geographical locations. The system consisted of lenses focused on photovoltaic cells separated over a large distance; if the focal distance between cell and lens shifted, the panel lost efficiency. Luxon, therefore, worked to increase the stiffness of the plates that hold the cells in place. By optimising the topology of the drive mechanism, Luxon improved its structural performance at the same time as cutting its cost by eight per cent. Luxon also replaced the steel crank arm with cast-iron, reducing cost by 38 per cent and mass by 52 per cent.
According to Billy Wight, president of Luxon: ‘In general, we wanted to reduce mass as much as possible, subject to constraints on stress and stiffness. The customer wanted a “one size fits all” solution. There are areas of the world where the product would not be subject to very intense loads, which opens up the opportunity to further reduce cost. However, the extra work and complexity involved in managing multiple product configurations would likely offset any cost advantage.’
He said: ‘We use HyperWorks for 95 per cent of our analysis work. For CAD we use SolidWorks, which includes a basic, linear, static finite-element solver – SolidWorks Simulation. It is, he said, easy to set up a basic analysis in SolidWorks, but harder to control mesh quality. So Luxon tries to interest its customers in applying HyperWorks. They mainly use the structural finite-element solutions – from simple, linear, static, implicit solutions to highly complicated, non-linear explicit solutions, the CFD capabilities, and the optimisation capabilities. ‘Most parts of the suite talk well with one another,’ he continued and ‘The optimisation capabilities were another huge selling point for us. No other package offers this diversity of solution types under one licence scheme.’
Trying to reduce the heating effect of the sun was an issue in this project too, and Luxon had to optimise the heatsinks (size, shape, number of fins, and so on) mounted on each solar cell: ‘We used both an assumed convection coefficient model to iterate quickly through a few designs, then moved to a CFD model to refine the promising designs.’ Ultimately, as in most engineering projects, the optimisation is not just about the physical, thermal and electrical but also about the financial constraints. According to Wight: ‘The goal was to maximise energy production per cost (kW/$). We knew the relationships between 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. The 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 The Netherlands. The 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. The 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.
The company’s Caspoc software, 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. The 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. The 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 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. The 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 software 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 Software acts as the main sales agent, Caspoc was developed and is being refined by Simulation Research in The 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. There, 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. There 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 software 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). This 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.
