Thursday, March 29, 2012

Cost of solar power (20)

As an inventor, I’m always interested to hear about new ways to solve old problems, so I was pleased to read recently about a small company in Switzerland, namely Airlight Energy, ALE.

From their web site, ALE

“is a private Swiss company that supplies proprietary technology for large-scale production of electricity using solar power and for energy storage”. 

ALE is active in both Concentrated Solar Thermal (CST) and Concentrated Photovoltaics (CPV), and they are looking to store energy in pebble beds or caverns, respectively by thermal storage and compressed air storage.

Their CST concepts are interesting, especially a one-axis solar concentrator that is built out of flexible fabric mounted on a concrete frame.  Rather than me trying to describe the concept, it’s best to obtain the details directly from their web site.  The essence of course is to collect the sun’s heat at a high temperature and as cheaply as possible.  They think they have the best combination of technologies for the task.  The thermal energy is then converted to electrical energy with a Rankine-cycle steam turbine.

How will this work out in practice?  Well, it turns out that ALE is building a modest plant in Morocco, which they describe as follows:

“Airlight Energy will build its first CSP solar park in Ait Baha in Morocco.  From September 2012, the plant will supply green energy to the cement factory of the Italcementi Group.  By installing three solar modules, combined with the existing system for recovering residual heat in the cement factory, an electric power of 150 kW will be generated continuously, 24 hours a day.  The project, which involves an investment of 2.7 million Euros, will produce a saving of around 800 tonnes of CO2 every year.”

That’s enough for me to make an estimate of their Levelised Electricity Cost of Electricity (LCOE).

First I need to calculate the annual output, which, assuming a Capacity Factor of 97% after allowing for maintenance, will be 0.97*150 kW*365*24 hours/yr = 1,274,580 kWhr/yr = 1,275 MWhr/yr.

I now evaluate the LCOE using my customary assumptions
          there is no inflation,
          taxation implications are neglected,
          projects are funded entirely by debt,
          all projects have the same interest rate (8%) and payback period (25 years), which means that the required rate of capital return is 9.4%,
          all projects have the same annual maintenance and operating costs (2% of the total project cost), and
          government subsidies are neglected.

For further commentary on my LCOE methodology, see posts on Real cost of coal-fired power, LEC – the accountant’s view and Cost of solar power (10).  Note that I am now using annual maintenance costs of 2% rather than 3% as in posts during 2011.

The results are:

Cost per peak Watt              EUR 18/Wp
LCOE                                     EUR 241/MWhr

The components of the LCOE are:
Capital           {0.094 × EUR 2.70 × 10^6}/{1,275 MWhr} = EUR 199/MWhr
O&M              {0.020 × EUR 2.7 × 10^6}/{1,275 MWhr} = EUR 42/MWhr

By way of comparison, LCOE figures (in appropriate currency per MWhr) for all projects I’ve investigated are given below.  The number in brackets is the reference to the blog post, all of which appear in my index of posts with the title “Cost of solar power ([number])”:

(2)        AUD 183 (Nyngan, Australia, PV)
(3)        EUR 503 (Olmedilla, Spain, PV, 2008)
(3)        EUR 188 (Andasol I, Spain, trough, 2009)
(4)        AUD 236 (Greenough, Australia, PV)
(5)        AUD 397 (Solar Oasis, Australia, dish, 2014?)
(6)        USD 163 (Lazio, Italy, PV)
(7)        AUD 271 (Kogan Creek, Australia, CLFR pre-heat, 2012?)
(8)        USD 228 (New Mexico, CdTe thin film PV, 2011)
(9)        EUR 200 (Ibersol, Spain, trough, 2011)
(10)      USD 231 (Ivanpah, California, tower, 2013?)
(11)      CAD 409 (Stardale, Canada, PV, 2012)
(12)      USD 290 (Blythe, California, trough, 2012?)
(13)      AUD 285 (Solar Dawn, Australia, CLFR, 2013?)
(14)      AUD 263 (Moree Solar Farm, Australia, single-axis PV, 2013?)
(15)      EUR 350 (Lieberose, Germany, thin-film PV, 2009)
(16)      EUR 300 (Gemasolar, Spain, tower, 2011)
(17)      EUR 228 (Meuro, Germany, crystalline PV, 2012)
(18)      USD 204 (Crescent Dunes, USA, tower, 2013)
(19)      AUD 316 (University of Queensland, fixed PV, 2011)
(20)      EUR 241 (Ait Baha, Morocco, 2012)

[Note: all estimates made using 2% annual maintenance cost.]

I calculate the cost of CO2 abatement as (1,275 MWhr/yr) * (EUR 241 / MWhr) / (800 t/yr) = EUR 384/t.

The cost per peak Watt at Ait Baha is very high, but that is to be expected with a system that operates 24/7 with energy storage.  For LCOE comparisons, the nearest European equivalent would be Gemasolar, for which the LCOE is 24% higher.

To conclude, these figures must be interpreted with caution since ALE is using “the existing system for recovering residual heat in the cement factory”.  It’s not clear whether all the required heat comes from the solar collectors or whether some comes from the cement kilns.

Thursday, March 15, 2012

Thermal storage simulations

If you have visited this blog before, you’ll know that I have been working on a new concept for passive solar thermal power generation.  The concept involves a thermodynamic cycle based on evaporative cooling of hot air at reduced pressure.  The energy to power the engine is provided by sunshine and collected passively under a transparent insulated canopy.

Details can be found at www.sunoba.com.au.

Thermal energy can be stored in a bed of rocks simply by blowing hot air from the canopy through the bed during the day.  At night, cool air is drawn through the bed by the engine, heating up in the process, and then the reclaimed thermal energy is converted into electrical power.

That highlights the need to develop simulation tools so that important questions can be answered.  For a given rock mass in the bed, how much energy is stored?  What size should the rocks be, and how much energy is required to pump air through the bed?  How sharp is the interface between hot rocks and cold rocks?  How does one simulate a charge/discharge cycle?

I started to think about these issues in early 2011 and wrote down the elements of a mathematical model for the storage simulations. Subsequently my focus switched elsewhere and I made no further progress on the work until early 2012, at which point I discovered an important paper by Hänchen et al. [1]  Their work contained a comprehensive literature review, model equations, numerical algorithms, validations, and computer simulations of various storage scenarios.

The mathematical model in [1] is different to mine.  They assume the air has constant density, the pressure is constant, rock particles heat and cool instantly (as fast as heat can be supplied/removed at the particle surface), and there is no diffusion in the air but some inter-particle diffusion in the rock bed.  The relevant equations are solved by a finite difference technique.

In my model, air is an ideal gas with variable density but constant pressure and constant specific heat capacities.  I allow heat to diffuse radially in the rock particles.  I include diffusion in the air but no inter-particle diffusivity.  And I solved my equations by a finite volume procedure.

The variation in air density with temperature is significant: my engine will operate over a range of say 20-140°C, for which the density ranges between 1.20 and 0.85 kg/m^3.  In [1], the maximum temperature considered was 550°C, for which the air density is 0.43 kg/m^3.  So you can imagine my surprise when I found that my simulations gave the same answer as [1] for a validation test.

Why is this so?  It turns out that the chosen coefficient for heat exchange between air and rock particles depends on the mass flow-rate of air, and not separately on the air density or bulk flow speed.  As the air temperature goes up, the density goes down and the bulk air speed goes up, so that the mass flow-rate stays approximately constant.  Moreover, the crucial feature of the thermal storage simulations is the heat exchange between particles and air.  So that’s the nub of the explanation.

My simulation codes need tweaking to control wiggles and instabilities, but that can be managed by attention to the timestep and spatial resolution.  It also helped to ensure that the initial and boundary data for simulations is specified in a consistent way.

I hope to publish this work later this year, so I won’t provide further mathematical or computational details here.   I do however provide below a 16-hour simulation of a charge-discharge cycle, as appropriate for my evaporation engine.  A pdf file that gives a coarse movie of the simulations can be found at www.sunoba.com.au (look for the link to “Thermal storage simulations” in the panel on the right-hand side).

I’m excited about possible applications for these new simulation tools.  If you would like to have a conversation about air-blown thermal storage, please get in touch.
Fig 1:  Simulation of air-blown thermal storage in a bed of steatite rocks.  Inlet temperatures 140°C (charge, 0 to 8 hrs) and 20°C (discharge, 8-16 hrs), initial bed temperature 20°C, inlet bulk air speed 0.4 m/s, particle diameter 0.040 m, bed height 5 m.  The air temperature is shown as a function of depth at each hour.  [Click to enlarge.]

Reference
[ 1]  M Hänchen, S Brückner & A Steinfeld, “High-temperature thermal storage using a packed bed of rocks – heat transfer analysis and experimental validation”, Applied Thermal Engineering 31 (2011), 1798-1806.

Saturday, March 10, 2012

Cost of solar power (19)

In this series of blog posts, I like to analyse the cost of solar power for projects at utility scale, say around 100 MW.  Every now and then, however, a smaller project comes along, which is suitable for my analysis and might have some public interest.

One such case is the University of Queensland’s solar array on the rooftops of four of the largest buildings at UQ.  The whole system is rated at 1.22 MW peak output from 5,004 polycrystalline silicon panels on a total rooftop space of 8,200 square metres.  The panels were supplied by Trina Solar.

This project was officially opened on 15 July 2011.  Engineering, procurement and construction cost AUD 4.85 million, and UQ spent (or I should say invested) a further AUD 2.65 million on a visitor centre, viewing platform, additional ground works, and the development of a public user interface. 

Let’s use the AUD 4.85 million figure for the cost of power generation, and not the combined figure of AUD 7.5 million.

A feature of the project is that Brisbane-based RedFlow has supplied a prototype 200kW zinc bromine battery bank that is connected to a 339kW section of panels.  The outcomes of this installation will be interesting to monitor, since the zinc bromine concept offers the promise of relatively cheap storage of electricity.

At the time of writing, a full year’s output has not been measured, but UQ says the system is on track to deliver 1.75 GWhr per annum and save emissions of 1,600 tonnes of CO2 annually.  (Note that much of the electricity generated in Queensland is from black coal, at around 900 kg CO2 per MWhr.)

I now evaluate the Levelised Electricity Cost (LEC) using my customary assumptions
          there is no inflation,
          taxation implications are neglected,
          projects are funded entirely by debt,
          all projects have the same interest rate (8%) and payback period (25 years), which means that the required rate of capital return is 9.4%,
          all projects have the same annual maintenance and operating costs (2% of the total project cost), and
          government subsidies are neglected.

For further commentary on my LEC methodology, see posts on Real cost of coal-fired power, LEC – the accountant’s view and Cost of solar power (10).  Note that I am now using annual maintenance costs of 2% rather than 3% as previously.

The results are:

Cost per peak Watt             AUD 3.98/Wp
LEC                                        AUD 316/MWhr

The components of the LEC are:
Capital           {0.094 × AUD 4.85 × 10^6}/{1,750 MWhr} = AUD 261/MWhr
O&M              {0.020 × AUD 4.85 × 10^6}/{1,750 MWhr} = AUD 55/MWhr

By way of comparison, LEC figures (in appropriate currency per MWhr) for all projects I’ve investigated are given below.  The number in brackets is the reference to the blog post, all of which appear with the title “Cost of solar power ([number])”:

(2)        AUD 183 (Nyngan, Australia, PV)
(3)        EUR 503 (Olmedilla, Spain, PV, 2008)
(3)        EUR 188 (Andasol I, Spain, trough, 2009)
(4)        AUD 236 (Greenough, Australia, PV)
(5)        AUD 397 (Solar Oasis, Australia, dish, 2014?)
(6)        USD 163 (Lazio, Italy, PV)
(7)        AUD 271 (Kogan Creek, Australia, CLFR pre-heat, 2012?)
(8)        USD 228 (New Mexico, CdTe thin film PV, 2011)
(9)        EUR 200 (Ibersol, Spain, trough, 2011)
(10)      USD 231 (Ivanpah, California, tower, 2013?)
(11)      CAD 409 (Stardale, Canada, PV, 2012)
(12)      USD 290 (Blythe, California, trough, 2012?)
(13)      AUD 285 (Solar Dawn, Australia, CLFR, 2013?)
(14)      AUD 263 (Moree Solar Farm, Australia, single-axis PV, 2013?)
(15)      EUR 350 (Lieberose, Germany, thin-film PV, 2009)
(16)      EUR 300 (Gemasolar, Spain, tower, 2011)
(17)      EUR 228 (Meuro, Germany, crystalline PV, 2012)
(18)      USD 204 (Crescent Dunes, USA, tower, 2013)
(19)      AUD 316 (University of Queensland, fixed PV, 2011)

[Note: all estimates made using 2% annual maintenance cost.]

The Capacity Factor for the UQ installation is 1,750 / (1.22 × 24 × 365) = 0.164, about what one would expect from fixed panels in a sunny location that had average daily exposure of 19.3 MJ/m^2 in 2011.

The LEC for the UQ installation is a little high compared to other recent projects such as the recently-opened Meuro project and the yet-to-start Moree Solar Farm (which at last report was having trouble securing finance so that construction could start).  It is, of course, a small project built on top of existing infrastructure, so it could not be expected to deliver the world’s best LEC.