Archive for September, 2011

Optimizing CPV Systems


Optimizing CPV Systems

Concentrating Photo-Voltaic (CPV) systems have some competitive advantages, for example,

  • CPV uses land efficiently, i.e., MW/acre is excellent for CPV
  • CPV does well when ambient temperatures are very high, e.g. in excess of 110 degrees Fahrenheit (43°C).
  • CPV needs no water to operate and very minimal water for maintenance work.
  • CPV seems to have very minimal ecological impact – better than wind and other forms of solar power generation.

Thus CPV works well in deserts where there is a nearby connection to the grid, and where the regional electric company can take all the power that a CPV farm generates and can put up with no power at night and slightly irregular power due to occasional clouds.  (Today CPV systems tend not to have energy storage mechanisms to smooth out the energy delivery to the grid.) This defines the CPV “niche.”

CPV systems have the disadvantage in that they are complex.  Starting with three layer multi-junction photovoltaic cells, which are expensive in their own right and somewhat complicated to wire into arrays and panels, they need a Fresnel lens to concentrate sunlight onto (or more precisely into) these cells.  They require that the sunlight rays be orthogonal to the plane of the panel, and this means that the panel must track the sun using a two axis system that adjusts both the azimuth and polar angles of the panel.  Large panels need to be mounted relatively high so that the panel clears ground objects as it “tracks” during the day.  A robust structure is needed to support the system weight and the  forces of wind on the system.  Depending on the locality, service roads and fencing might have to be installed.  Finally each CPV structure needs an inverter to convert DC to AC, and a connection to the grid.  The cost of each of these components is, of course, the first point of attack in optimizing CPV systems.  These are the capital costs that need to be optimized.

There are of course non-trivial, non-capital installation, calibration, maintenance, and operational costs.

The capital, installation, and operational costs of a CPV system can be mitigated in the near future by a favorable regional government-dictated Feed-in Tariff (FiT), which guarantees a grid connection, a long term contract, and rates that take into account these costs and that guarantee an operational profit. Italy’s FiT is particularly advantageous, since it has a special tariff table for CPV. [1]  Now if competition weren’t enough motivation for CPV vendors to drive costs down, most Feed-in Tariffs reduce the guaranteed rates by a small percentage each year to motivate the vendors to take advantage of technology improvements and reductions in operating costs.

As mentioned in an earlier post on Levelized Cost of Energy (= a system’s lifetime future costs divided by the lifetime energy it will produce) there are many components to lifetime costs, each of which needs to be consciously and systematically driven down by the CPV vendor. What is needed here is a company-specific model for these costs and a continuous improvement program to drive each cost component down.  NREL’s System Advisor Model (SAM) is a very nice start (and its earlier versions motivated the definition of LCOE), but a company needs more detail to optimize costs.

For example, a CPV system is particularly sensitive to being aligned precisely (to a small fraction of a degree) to the sun.  This necessitates high precision in its two axis tracking system.  In addition to its additional capital cost, a tracker has additional installation and maintenance costs.  Mounting a tracker on a high pedestal created additional weight and hence wind force factors.  Each of these details (accuracy, capital cost, installation cost, maintenance cost, weight, and required structural support to address wind forces) must be optimized by the CPV vendor.

LCOE isn’t the only useful metric for a CPV vendor to consider.  Now marketing folks and the press like big numbers, and hence the peak power or Watts-Peak (Wp) makes a lot of headlines. It is the maximum power that can be generated by the system.  Sometimes this number is tempered (no pun intended) by NREL’s Standard Test Conditions (STC) to get a “name plate” rating.  Probably a little more interesting is the Energy to Peak Power ratio.  Define:

SI = Site Irradiation (kWh/m2/yr)

RI = Rating Irradiance (kWp/m2)

PCE = DC to AC power conversion efficiency

ATE = Average temperature efficiency

EPP = Energy to Peak Power Ratio = SI*PCE*ATE/RI

The Site Irradiation, SI, is really the actual energy produced by the CPV system per unit area, say over a year.  Since the energy produced varies with time, this needs to be a sum over time-intervals small enough so that the energy produced in each time-interval is approximately constant.  Similarly the ATE varies with time, since the device will heat up during the day causing increased degradation.  One then uses time-intervals small enough so that the temperature during the time-interval is approximately constant.  PCE is just the inverter efficiency.  The EPP ratio is a little flawed in that the numerator has the factor of hours per year in it.  A mathematician would divide it out, but the industry tends to leave it in.  Oh well, …

While LCOE has most of the EPP terms in its ultimate calculation, it is none-the-less instructive to track this ratio as well as to optimize each term.  Note that the Energy to Peak Power ratio is a function of locality as is LCOE.

The significant improvement in solar cell efficiencies has driven CPV’s LCOE down in past years due primarily to increased energy production.  PV, on the other hand, has had its capital costs driven down dramatically by massive Chinese government investments.  This has driven down fixed thin film PV’s LCOE.  The net result of these two trends is to make thin film PV more attractive EXCEPT in the niche described earlier for CPV dominance.  This race of technology and manufacturing improvements will, of course, continue.  Unfortunately, the three major CPV vendors, Amonix, Concentrix, and SolFocus are all going after smaller numbers of large “utility sized” sites.  This doesn’t lend itself to cost or manufacturing efficiencies as compared to the goal of putting thin film PV on every rooftop in the world. CPV vendors will need to invest to compensate for this.  It will be a challenge.



[2] “LCOE For Concentrating Photovoltaics (CPV)” by Warren Nishikawa, Steve Horne, Jane Melia,, SolFocus Inc., 510 Logue Ave., Mountain View, CA 94043 International Conference on Solar Concentrators for the Generation of Electricity (ICSC – 5), November 1619, 2008, Palm Desert, CA USA ( )


Levelized Cost of Energy (LCOE)


Levelized Cost of Energy

For any power generating system, one can compute the “levelized cost of energy” (LCOE) over the predicted lifetime of the system.  It is the ratio of the present value of the total cost of operation or ownership (TCO) to the total energy generated (TEG) over the predicted lifetime of the system.  This ratio, LCOE =TCO/TEG, looks simple, but the devil is in the details (as my mother used to say.)

LCOE does have a simple interpretation.  First note the units:  Today’s cents, dollars, Euro’s, etc. are in the numerator, and kilo-watt-hours (or mega-watt-hours) are in the denominator.  Usually it is cents per kWh or dollars per MWh.  If you want to build a power plant, you definitely want to sell the power you put onto the grid at a price greater than your LCOE, or you will lose money.

You can also compare the cost efficiency of various systems, and indeed, of various types of systems.  Here’s a table of such from a respected government source [1]. It indicates how LCOE can vary by region.  E.g. Transportation charges for coal, amount of sunlight and incidence angles for solar, amount of wind for windmills all vary by region.  However interesting these tables are, there is no guarantee that the LCOE was calculated fairly in each case.  Thus before making any decisions based on LCOE numbers, be sure you really understand how they are computed.  The text after the table is a start.

Regional Variation in Levelized Cost of New Generation Resources, 2016.

Plant Type Total System Levelized  Costs
(2009 $/MWh)




Conventional Coal




Advanced Coal




Advanced Coal withCCS




Natural Gas-fired
Conventional Combined Cycle




Advanced Combined Cycle




Advanced CC with CCS




Conventional Combustion Turbine




Advanced Combustion Turbine




Advanced Nuclear








Wind – Offshore




Solar PV1




Solar Thermal
















Energy Information Administration, Annual Energy Outlook 2011,
December 2010, DOE/EIA-0383(2010)

For example, this table indicates that wind is comparable to natural gas.  This surprises me.  Also note how much more offshore wind costs.  This is particularly surprising given the large investment that is under weigh along the east coast of the U.S.  Hydro is a winner, but as my son Sam pointed out to me, it is unlikely that these numbers compute the damage done to the fishing industry (esp. salmon fishing) by these dams (environmental damage can be modeled as uninsured costs, see below).  This is another devilish detail.

Now, let’s look at the devilish details:

First the predicted or expected lifetime of the system assumes excellent maintenance and reasonable upgrades.  At the beginning of the lifetime, there is the original (capital) cost of construction and of the hook-up to the grid, and at the end of the lifetime there is the decommissioning and waste management of all the remaining materials.  The original cost needs to include things like access road improvements, right of way purchases, the installation’s fair share of grid improvements necessary for the hookup, etc.  Some towns, knowing that all the construction vehicles passing over its roads will wear on those roads, may want compensation in order to repair or refurbish them after the construction.  This should be included in the original cost.  Here the cost of financing needs to be carefully included.  The decommissioning cost is often (fraudulently in my opinion) excluded.  It must include tear down costs, land fill costs for the debris, and the safe storage of chemicals, fuels, and radioactive material.  It might include, instead, the cost of a complete refurbishing of the system to make a totally new power generation plant.  In this case, one must fairly separate the decommissioning and waste management cost of the old system from the original cost of the new system.  The residual value of the old system needs to be subtracted from its TCO.  Similarly, if waste steel is recycled, its residual value needs to be subtracted from the old system’s TCO.

Note:  Some people believe that if nuclear power plant LCOE included the total decommissioning and cost of nuclear waste removal and storage, then nuclear simply wouldn’t look very attractive economically.  As a boy, I used to think that waste nuclear fuel should be put into rockets and shot into the sun.  Sadly, this quite reasonable idea is not feasible economically.

Now during the lifetime of the system, there is a lot of operational cost, maintenance, repairs, and upgrades.  There are many of these.  Here are some:

  • Land lease costs.
  • Labor, travel, fuel, materials, etc. costs for operations and maintenance.  Note that some fuel prices, e.g. nuclear and petroleum, might have difficult-to-predict cost variations due to political considerations.
  • Large, infrequent upgrades or replacements.  A ten year replacement for inverters is often mentioned.
  • Insurance costs.
  • Property tax costs (but not income tax as that speaks to profitability not cost).
  • Utility costs, e.g. water, sewage, network communications, telephone charges.
  • Uninsured liability, theft, vandalism, disaster, and ecological damage costs.
  • Future green-house gas GHG charges.

These all have to be estimated over time and space (region), the present value of these costs needs to be calculated, and added up, we get the total cost of ownership, TCO.  As mentioned above, these costs will vary by region and of course over time. Some costs are correlated to an appropriate conflation index, and others need to be modeled.  All assumptions need to be carefully documented.

Finally, the economic assumptions for the present value calculation of all these costs must be documented.

Let’s turn to the denominator, the total energy generated over the predicted lifetime of the system.  For very stable sources of energy, e.g. nuclear, hydro, coal, natural gas, etc., one can reasonably assume a policy of steady consistent energy production, e.g. a certain number of kWh per day.  For wind, solar, geothermal, tidal, etc, there are simple models for energy generated, say per year, and there are more detailed models that would depend on weather and warming trends.  These latter can be quite sophisticated.  There are some additional subtleties to consider.  For example, not all of the power rating of the system gets onto the grid as energy, i.e. as electricity.  Some of this difference is standard due to energy conversions and efficiency of equipment.  For wind and solar farms, not all of the equipment is 100% operational; for example, some of it may be down for routine maintenance or repairs.  (PV systems need to be cleaned regularly, and the system will degrade as its solar cells or lenses slowly get dirty.)  Some reasons are more subtle, e.g. time shifting energy production via the use of an energy storage mechanism (CAES, liquid salt, MgH2, batteries, etc.)  Conversion both to and from the storage mechanism produces an energy loss.  Thus the algorithm for time shifting needs to be considered in the calculation for LCOE.

Given that some of the variable components of both TCO and TEG are “random”, i.e., depend on random events such as weather and politics over time, it is often appropriate (and easier) to make assumptions on these random event distributions and run Monte Carlo simulations for the calculations.  Argonne Laboratories has written a paper on this.

Note that the calculation of LCOE avoids (except for the reasons for time shifting) what the electric companies will pay for energy put onto the grid.  LCOE is one massive average over a long (20-30 year) lifetime.  Electrical rates are quite another thing.

Electrical rates vary across the day, with utilities charging commercial enterprises more for electricity during “peak hours” than during “off hours”.  The differences can be considerable.  Solar systems generate most of their power during peak hours.  If a solar system is directly substituting for utility company power during peak hours, then the value to the owner of that system will be, during these hours at least, equal to the peak rate the electric company charges. This type of logic is not directly factored into LCOE calculations; however, a favorable power provider agreement (PPA) between the generator owner and the utility can improve the deal for financing charges.  Residential and most commercial installations of solar power will not get a favorable agreement with the utility company.  Per the California Public Utility Commission, excess electricity generated and not used, i.e. put back onto the grid, is to be compensated annually at the average spot rate for the year – better than nothing, but far less than peak rates and not a real incentive to install solar power on your roof for the purpose of making money by selling the excess energy.

As explained before in these notes (here) irregular sources of utility scale energy such as wind and solar may well be more profitable with local energy storage.  This would allow a base level of energy to be put onto the grid, and also some additional energy for peak times.  To model this, a revenue model needs to be created in parallel with the LCOE model.  This can be done in a spreadsheet, but it can also be done with Monte Carlo methods.  These models need to be part of the pro forma economic analysis done at site selection and system design time.  The PPA negotiation with the utility company needs to conform with the model results.

Finally, NREL publishes a simple LCOE calculator here, which can be used to test any LCOE calculation for reasonableness.


[1] Levelized Cost of New Generation Resources in the Annual Energy Outlook 2011