Friday, May 20, 2011

Cost of solar power (10)

Today I’m going to analyse the Levelised Electricity Cost (LEC) for the Ivanpah solar thermal project in California.  As reported by Wikipedia, this is the world’s largest solar thermal project currently under construction.

First, however, I want to make further comments about the methodology for evaluating the LEC.  During the week, I had occasion to read the Garnaut review on the cost of various renewable power generation technologies.  For non-Australian readers, let me mention that Professor Ross Garnaut has been commissioned by the Australian federal government to report on all aspects of the introduction of a tax on Carbon.  His report comes in eight parts covering the following topics:

1.      Weighing the costs and benefits of climate change action
2.      Progress towards effective global action on climate change
3.      Global emissions trends
4.      Transforming rural land use
5.      The science of climate change
6.      Carbon pricing and reducing Australia’s emissions
7.      Low emissions technology and the innovation challenge
8.      Transforming the electricity sector

The Garnaut web site links to 14 commissioned studies, of which I studied “Renewable Energy Technology Cost Review”, prepared by the Melbourne Energy Institute.  I was at first disconcerted by the methodology they used.  This led me further into finance-speak than I wanted to go, but since I have been there, I feel the urge to describe what I found.

Their methodology focuses on Free Cash Flow defined as follows:

FCF = EBIT × (1-T) + DA – CAPEX – WCE

in which all entities relate to the financial year in question.  The notation is

CAPEX = capital expenditure of the business
DA = Depreciation and Allowances
EBIT = Earnings Before Interest and Taxation
FCF = Free Cash Flow
T = rate of taxation
WCE = Working Capital Expenditure

FCF is, in fact, the Present Value of the enterprise for the year in question.  This concept can be used in a discounted cash-flow analysis to evaluate the total Present Value for a business that will operate over a number of years into the future.  Also, the LEC is set so that the correct Working Cost of Capital (WCC) is achieved, be that either paying off debt, paying a dividend to investors, or a combination of the two.

What about my analysis?  Well, in my full analysis (see “LEC – the accountant’s view”, posted 27 April 2011), I concentrate on Net Profit After Tax, NPAT, defined as follows:

NPAT = (EBITDA – DA – I) × (1-T)

in which

EBITDA = Earnings Before Interest, Taxation, Depreciation and Allowances
I = interest on capital

The relationship between these two concepts (NPAT, FCF) can be teased out with a little algebra:

NPAT
= (EBITDA – DA – I) × (1-T)
= (EBIT – I) × (1-T)
= EBIT × (1-T) – I × (1-T)
= FCF – DA + CAPEX + WCE – I × (1-T)
= FCF – {DA-CAPEX} + {WCE - I× (1-T)}

The two expressions in the curly brackets {…} are both very close to zero, depending on the precise basis for the depreciation schedule and interest payments.  Thus my full LEC analysis (see post 27 April 2011) and that used by the Garnaut report are almost equivalent.  The same post also shows that my simplified analysis and my full analysis give similar LEC values provided a Carbon tax is not applied.

The following links have more detail if you are interested:
·         Free Cash Flow
·         Net Profit After Tax

The document commissioned by Garnaut also gave information about industry perspectives on Operations & Maintenance (O&M) costs.  According to these studies, the O&M costs were typically around USD 60-70 per installed kW per year.  Those O&M figures correspond to around one third of what I have assumed.  The evidence is gathering that I should adjust my O&M costs downwards – see discussion in my post “Cost of solar power (3)”, 28 January 2011 – but I won’t do that just yet.

The Ivanpah project is being developed by Bright Source Energy and Bechtel.  It will consist of three separate plants with 347,000 heliostats focussing the sun’s rays on solar receivers atop towers.  The power output will be 392 MW peak and1080 GWhr/yr, with CO2 emission reduction of 400,000 t/yr.  The sun’s energy will be used to generate steam directly without any molten salt storage, and the condensers for the plant will be air-cooled.  The total land area for the project is 16 km^2.  Wikipedia reports the project cost is USD 2.18 billion, with completion in 2013.

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 (3% of the total project cost), and
          government subsidies are neglected.

The results are:

Cost per peak Watt USD 5.56/Wp
LEC                            USD 251/MWhr

The components of the LEC are:
Capital           {0.094× USD 2.18×10^9}/{1080×10^3 MWhr} = USD 190/MWhr
O&M              {0.030× USD 2.18×10^9}/{1080×10^3 MWhr} = USD 61/MWhr

For Ivanpah the cost per tonne of CO2 emissions reduced is {0.094 + 0.03} × USD 2180 million/400000 tonnes = USD 676 / tonne.

To conclude, here are LEC figures for all projects I’ve investigated:

Cost of solar power (2): AUD 199/MWhr (Nyngan, Australia, PV)
Cost of solar power (3): EUR 547/MWhr (Olmedilla, Spain, PV)
Cost of solar power (3): EUR 205/MWhr (Andasol I, Spain, trough)
Cost of solar power (4): AUD 257/MWhr (Greenough, Australia, PV)
Cost of solar power (5): AUD 432/MWhr (Whyalla, Australia, dish)
Cost of solar power (6): USD 177/MWhr (Lazio, Italy, PV)
Cost of solar power (7): AUD 295/MWhr (Kogan Creek, Australia, CLFR pre-heat)
Cost of solar power (8): USD 248/MWhr (New Mexico, CdTe thin film PV)
Cost of solar power (9): EUR 218/MWhr (Ibersol, Spain, trough)
Cost of solar power (10): USD 251/MWhr (Ivanpah, California, tower)

Monday, May 16, 2011

Cost of solar power (9)

It’s a funny world!  Or it would be funny if things weren’t so serious.

Here in Australia, the minority government is struggling to introduce a Carbon tax.  The conservative opposition is going ballistic, whipped along by the right-wing commentariat in newspapers, TV and especially radio.  Public support for the science behind anthropogenic global warming is falling and the AGW deniers seem to be gaining strength.

But things are not necessarily what they seem.  Over the weekend, I attended a launch for the book Climate Change Denial by Haydn Washington and John Cook.  The event was packed to the rafters, mainly with an older audience who looked so prosperous that I would have thought that a majority of them were normally conservative voters.  (Incidentally, John Cook is the founder of the excellent web site http://www.blogger.com/www.skepticalscience.com.) 

In fact, some conservative governments are taking action to lower Carbon emissions.  In the United Kingdom, the coalition government is driving the economy towards a future that is lower in Carbon, albeit with some setbacks along the way.  As reported on 10 May 2011 by Cambridge Econometrics:

“on existing policies including those inherited, endorsed and shortly to be put into effect by the Coalition government, the UK is set to miss the carbon budget targets narrowly in the first two budget periods (2008-12 and 2013-17), but by a wider margin in the third (2018-22)”

“The decline in UK's carbon emissions is set to accelerate after 2020 as power generation makes good progress towards de-carbonisation”.

In Germany, the conservative government has reacted quickly and strongly to the nuclear disaster in Japan, as described in an article No Nukes, No Problem? Germany's Race for a Renewable Future by Arne Jungjohann and Wilson Rickerson, Renewable Energy World, 13 May 2011:

“In advance of the phase out revision, Chancellor Merkel met with the governors of the 16 German states in April of this year and outlined a plan to accelerate Germany’s transition from fossil fuel and nuclear power to renewable energy.  This is a remarkable development because Germany already has one of the fastest growing renewable energy markets in the world.

During the past decade, Germany has fundamentally transformed the way it produces electricity: from 2000 to 2010, Germany increased its share of renewable electricity from 5% to 17%.  The country has consistently met its legislated targets ahead of schedule and appears poised to outdo itself again in the next few years.  The previous target of 30% renewable electricity by 2020 has recently been updated by Germany’s official National Renewable Energy Action Plan (NREAP).  The NREAP reveals that the country expects to actually generate 38% of its electricity from renewables by 2020.”

Such reports on progress towards de-carbonisation get very little traction in the Australian media.  My conclusion is that the public debate in Australia is framed and dominated by vested interests in media, mining, fossil fuels (coal, gas) and power generation.

But, let me come to the topic of today’s post – the cost of power generation from the Ibersol solar thermal power station.  The project leader, Solar Millenium AG, reported on 21 March 2011:

“Die 50 Megawatt Anlage ist das vierte von Solar Millennium in Spanien entwickelte Parabolrinnen-Kraftwerk und nahezu baugleich mit den Projekten Andasol 1-3 in Andalusien, die ebenfalls von der Solar Millennium Gruppe entwickelt wurden.  Die Extremadura ist mit einer jährlichen Direktstrahlung von rund 2.080 Kilowattstunden (kWh) pro Quadratmeter ein ausgezeichneter Standort für Solarenergie.  Laut Prognose auf Basis meteorologisch erhobener Daten soll das Parabolrinnen-Kraftwerk rund 170 Millionen kWh Strom produzieren – … und dabei im Vergleich zu modernen Steinkohlekraftwerken insgesamt rund 150.000 Tonnen Kohlendioxid pro Jahr einsparen.

Dank eines thermischen Speichers wird das Kraftwerk Solarstrom auch nach Sonnenuntergang planbar und zuverlässig bereitstellen.”

Private investors can participate in the project, as Solar Millenium describes:

“Auch Privatanleger können über einen geschlossenen Fonds von den Einnahmen dieses solarthermischen Kraftwerks profitieren.  Mit dem Vertrieb des Fonds hat Solar Millennium federführend das Tochterunternehmen Solar Millennium Invest AG beauftragt.”

There’s a long discussion on Ariva.de about the merits of such an investment.  Buried in that discussion is a comment by oecorentner, post #3225, about the cost of the project:

“ich habe nochmal nachgeschaut, Ibersol kostet 300 Mio €, soll 170 GW/a bringen bei 0,25 €/kwh = 250 €/MW =250000€/GW ist das ein Rohertrag von 42,50 Mio €/a = 14 % brutto.”

So, finally we have the information we need.  Ibersol is almost identical to the earlier Andasol plants, that is the sun’s energy is collected by parabolic troughs, stored in molten salt and drives a Rankine-cycle steam generator.  The plant will produce 50 MW peak and 170 GWhr/yr, save emissions of 150,000 t CO2, and will cost EUR 300 million.

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 (3% of the total project cost), and
          government subsidies are neglected.

The results are:

Cost per peak Watt EUR 6.00/Wp
LEC                            EUR 218/MWhr

The components of the LEC are:
Capital           {0.094× EUR 300×106}/{170×103 MWhr} = EUR 166/MWhr
O&M              {0.030× EUR 300×106}/{170×103 MWhr} = EUR 53/MWhr

The LEC is slightly more than that for Andasol 1, as given in my post “Cost of solar power (3)” (28 January 2011), because the annual output is slightly less.  Back to oecorentner’s comment and the theme of Ariva.de, at EUR 250/MWhr, I predict an annual profit for the project of EUR (250-218) × 170000 = EUR 5.44 million.  That would not be sufficient to sign up investors into a EUR 300 million project, so I suspect my LEC is a little high.  My assumptions are of course only used for comparisons between projects, and taxation implications have not been taken into account.

For Ibersol, the cost per tonne of CO2 emissions reduced is {0.094 + 0.03} × EUR 300 million/150000 tonnes = EUR 248 / tonne.

To conclude, here are LEC figures for all projects I’ve investigated:

Cost of solar power (2): AUD 199/MWhr (Nyngan, Australia, PV)
Cost of solar power (3): EUR 547/MWhr (Olmedilla, Spain, PV)
Cost of solar power (3): EUR 205/MWhr (Andasol I, Spain, trough)
Cost of solar power (4): AUD 257/MWhr (Greenough, Australia, PV)
Cost of solar power (5): AUD 432/MWhr (Whyalla, Australia, dish)
Cost of solar power (6): USD 177/MWhr (Lazio, Italy, PV)
Cost of solar power (7): AUD 295/MWhr (Kogan Creek, Australia, CLFR pre-heat)
Cost of solar power (8): USD 248/MWhr (New Mexico, CdTe thin film PV)
Cost of solar power (9): EUR 218/MWhr (Ibersol, Spain, trough)

Sunday, May 15, 2011

Cost of power - ECET

My last post (12 May 2011) was concerned with the Expansion-Cycle Evaporation Turbine (ECET), in particular how the ECET can be used to provide a 20% boost to the output of an Open-Cycle Gas Turbine (OCGT).  Today I’ll examine the cost of electricity under the OCGT+ECET scenario.  To be specific, I’ll compare the Levelised Electricity Cost (LEC) for the following four generation options:
1.      OCGT
2.      Combined-Cycle Gas Turbine (CCGT, in which the hot OCGT exhaust is used to drive a conventional Rankine-cycle steam turbine)
3.      coal-fired Rankine-cycle steam turbine
4.      OCGT+ECET (see Figure 1 below)
The material in today’s post is taken from www.sunoba.com.au/ECET

Figure 1 shows the OCGT+ECET flow-sheet (click to see original jpg figure).


Figure 1: Flow-sheet for the OCGT+ECET option.  The Expansion-Cycle Evaporation Turbine (ECET) exploits the hot exhaust of the Open-Cycle Gas Turbine (OCGT).  The thermodynamic cycle of the ECET is based on evaporative cooling of hot air at reduced pressure.

A case study has been made (see www.sunoba.com.au/references, article 8) in which the inlet ECET air stream is taken as the exhaust of a 56 MW OCGT that was commercially available in 2007.  The OCGT mass flow-rate is 197 kg/s with exhaust temperature 508°C.  The estimated OCGT dry air flow-rate is 195 kg/s and, assuming the OCGT fuel is natural gas, the estimated ECET inlet partial pressures are 92.5 kPa dry air and 8.8 kPa water vapour.  The specific output of the OCGT is estimated as 287.2 kJ/kg dry air.

The ECET case study used the following parameters:
·         ratio of inlet pressure to pressure in the first-stage evaporator: 6.5
·         number of evaporation/re-compression stages: 4
·         adiabatic efficiency of turbine and compressors: 0.90
·         energy cost for reverse osmosis water purification: 15 kJ/litre
·         energy cost for water injection: 10 kJ/litre
The ECET output was 59.0 kJ/kg dry air, or 20.5% that of the upstream OCGT. 

In the LEC comparison, the OCGT and ECET properties are based on the case study referred to above, except that the adiabatic efficiency of the ECET turbine was increased slightly.  The comparison presented here uses the following parameters:
·         specific capital cost, OCGT:  AUD 750,000/MW
·         specific capital cost, ECET: AUD 750,000/MW
·         specific capital cost, Rankine steam turbine: AUD 1,500,000/MW
·         thermodynamic efficiency, OCGT:  0.34
·         thermodynamic efficiency, Rankine: 0.34 for CCGT supplementary system downstream of OCGT, otherwise 0.39 for coal-fired system
·         ECET output/OCGT output: 0.23 [Note: now assumes adiabatic efficiency for ECET expansion turbine is 0.92]
·         cost of capital: 0.07 × amount owing
·         loan repayment period:  25 years
·         non-fuel O&M costs: 0.015 × capital cost
·         cost of natural gas: AUD 6.00/GJ
·         energy content of coal: 28 GJ/t
·         cost of coal: AUD 80/t
In Figure 2 (click to see original jpg figure), the Capacity Factor (CF) is the fraction of time that the generator is active.


Figure 2: LEC comparisons for the four generation options.

The conventional wisdom (in the absence of the ECET boost) is that coal-fired power is cheapest for base load (CF large), OCGT power is cheapest for peak load (CF small) and CCGT power is cheapest in some middle range (‘shoulder’).  That holds for the parameters used in the economic analysis.

When the ECET boost is applied to the OCGT, the LEC order of merit (from cheapest to most expensive) depends on the Capacity Factor as follows:

0 < CF < 0.14                    OCGT+ECET < OCGT < CCGT < coal
0.14 < CF < 0.23               OCGT+ECET < CCGT < OCGT < coal
0.23 < CF < 0.25               OCGT+ECET < CCGT < coal < OCGT
0.25 < CF < 0.34               CCGT < OCGT+ECET < coal < OCGT
0.34 < CF < 0.44               CCGT < coal < OCGT+ECET < OCGT
0.44 < CF < 1                    coal < CCGT < OCGT+ECET < OCGT

This example indicates there is economic advantage in using the Expansion-Cycle Evaporation Turbine to boost the power of installed OCGTs for peak duty and some shoulder duty in the electricity grid.  The broad features of the interpretation above are robust, although the CF values at which the order of merit changes depend on assigned parameters.

Note that rapid response time is also important for peaking plants.  In that respect, the ECET boost should be as quickly obtainable as OCGT power.  Rankine-cycle steam plants do not have a quick response time.

For more details, see www.sunoba.com.au

Wednesday, May 11, 2011

Research update - ECET etc.

For almost all of 2011, I have been working on a secret project, culminating in today’s launch of the Expansion-Cycle Evaporation Turbine (ECET). 

Let me explain …

I invented the evaporation engine in May 2004 as a device to generate power from hot air collected passively under a transparent insulated canopy.  I quickly realised there were two straightforward ways the thermodynamic cycle (evaporative cooling of hot air at reduced pressure) could be manifested:
·         piston-in-cylinder, and
·         continuous-flow using turbines and compressors. 
I also had a related concept for a Bernoulli heat engine, which excited me enormously, but which seemed to require condensation at reduced pressure.  That was cause for much anguish:  why should some of the engines work on evaporative cooling at reduced pressure, and yet the Bernoulli engine by condensation at reduced pressure?  It took me an embarrassingly long time to work out why – my mathematical model for the Bernoulli device had an error with the pressure calculation during evaporation, which was found by a sharp-eyed reviewer of a manuscript I’d submitted for publication.  Once I’d corrected the error, all three heat engines relied on evaporative cooling at reduced pressure.

After that, the Bernoulli device remained my favourite for a while longer, but since its output was limited by the pressure drop accessible via the Bernoulli effect and since losses in acceleration, evaporative cooling and deceleration were likely to be severe, I eventually stopped working on it.  The continuous-flow version with expansion turbine and subsequent compressor(s) was attractive because of its mechanical simplicity, but I was concerned about losses in expansion and re-compression.  I knew the device could be mounted behind an open-cycle gas turbine to provide a power boost, but I thought the boost wouldn’t be all that substantial and that it was therefore wisest to focus on a piston-in-cylinder version in which losses could be better controlled.

That led me on a four-year journey in which I designed and built a piston-in-cylinder evaporation engine, tested it, and considered what its output would be when the hot air was provided by solar heat collection under a transparent insulated canopy.  Details of that passive solar work are given at www.sunoba.com.au.  Meanwhile, the concept of using an evaporation engine to generate power from the exhaust of internal combustion engines remained attractive, especially for combined heat and power in buildings, but just never got to the top of my priority list.

That all changed at the start of this year when a fellow inventor, Anthony Kitchener, finally persuaded me make a thorough analysis of the use of the continuous-flow evaporation engine to boost the power of open-cycle gas turbines.  Figure 1 shows the ECET layout (click to see original jpg diagram).


Figure 1:  Flow-sheet for a four-stage expansion-cycle evaporation turbine.

My analysis surprised me.  Losses on expansion and re-compression are present of course, but will not be too severe provided the adiabatic efficiencies of the turbines and compressors are high enough.  At www.sunoba.com.au (follow the link to Expansion-Cycle Evaporation Turbine), I provide a case study that shows the ECET can boost the output of a commercially available OCGT by more than 20%.  Now that is useful, and exciting too since the specific capital cost of the ECET, in $/MW for example, should be no greater than the specific capital cost of the upstream OCGT.

So, the ECET can boost the OCGT power by more than 20%, not use any extra fuel, and won’t cost any more per MW to build than the OCGT itself.  That should lead to commercial prospects for the OCGT+ECET combination as peaking plants in the electricity grid, which is a huge market worldwide.

Well, that’s what I’ve been working on for four months.  The concept was launched today with a revision of the website www.sunoba.com.au.

With respect to the passive solar application, I plan to attend the 2011 Solar World Congress in Kassel, Germany, where, provided my submitted abstract is accepted, I’ll present results of my canopy-engine simulations for a sloping canopy.  I also plan to attend the 2011 Conference of the Australian Solar Energy Society at which I hope to report on thermal storage calculations for the passive solar application.  That is work that needs to be done.  I’d better get started.

Acknowledgement: Many thanks to Anthony Kitchener for encouragement, useful information and good ideas.

Tuesday, May 3, 2011

Cost of solar power (8)

After a long search, I’m able to provide an analysis of a recent US-based PV project.  Financial data is not generally publicly provided with US projects, and without such data I can’t estimate the cost per peak Watt and the Levelised Electricity Cost (LEC).

The project is by the Public Service Company of New Mexico (PNM), with solar panels by Arizona-based First Solar.  The first stage opened on 25 April 2011 and is based in Albuquerque, with 2 MW capacity from 30,000 CdTe thin-film panels over a ground area of 8.1 Ha.  None of the press reports I read mentioned anything about tracking of the sun, and the few published photographs I saw indicated that the panels were fixed.

According to press reports, PNM plans to launch four further projects by the end of the year, making five PV plants in total with combined output 22 MW, costing USD 102 million, producing 51 GWhr of electricity per year and "saving 44 million pounds of CO2 emissions”.   This indicates a CO2 emission intensity of 19.96 million kg CO2 per 51 GWhr, or 391 kg CO2 per MWhr.  That’s surprisingly low, but would be consistent with existing generation plant with substantial amounts of natural gas and nuclear, as is the case with PNM:

“PNM is a significant owner of the San Juan generation facility, a coal fired plant located near Farmington, New Mexico, and a 10% owner in the Palo Verde Nuclear Generating Facility near Phoenix, AZ. PNM also owns and operates several natural gas fired plants throughout the state of New Mexico including Reeves Generating Station in Albuquerque, most of which are used to meet additional demand for electricity in the summer months.”

New Mexico state law requires local electricity utilities like PNM to have 10% of the energy output from renewable resources by the end of 2011.  This requirement will increase to 20% by 2020.

The cost metrics are evaluated under my usual 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 (3% of the total project cost), and
·         government subsidies are neglected.

The results are:

Cost per peak Watt USD 4.64/Wp
LEC                            USD 248/MWhr

The components of the LEC are:
Capital           {0.094× USD 102×106}/{51×103 MWhr} = USD 188/MWhr
O&M              {0.030× USD 102×106}/{51×103 MWhr} = USD 60/MWhr

The cost per tonne of CO2 emissions reduced is {0.094 + 0.03} × USD 102×106/19960 tonnes = USD 634 / tonne. That’s high because the existing emissions intensity, as claimed, is low.

By way of comparison, here are my LEC figures for all projects I’ve investigated:

Cost of solar power (2): AUD 199/MWhr (Nyngan, Australia, PV)
Cost of solar power (3): EUR 547/MWhr (Olmedilla, Spain, PV)
Cost of solar power (3): EUR 205/MWhr (Andasol I, Spain, trough)
Cost of solar power (4): AUD 257/MWhr (Greenough, Australia, PV)
Cost of solar power (5): AUD 432/MWhr (Whyalla, Australia, dish)
Cost of solar power (6): USD 177/MWhr (Lazio, Italy, PV)
Cost of solar power (7): AUD 295/MWhr (Kogan Creek, Australia, CLFR pre-heat)
Cost of solar power (8): USD 248/MWhr (New Mexico, CdTe thin film PV)