Tidal Lagoon Plc (TLP) has recently published a document called ‘The New Power Cost League Table’ that compares the cost-effectiveness of different electricity generating technologies according to a new measure they have devised that they call ‘lifetime consumer cost per MWh’. Figure 1 shows the league table.

This gives the impression that tidal lagoons are already one of the cheapest technologies and that after TLP’s initial ‘pathfinder’ project in Swansea Bay has been completed will be *the* cheapest. This is surprising because conventional measures of cost effectiveness, such as plain old LCOE, rank them as one of the most expensive. It is therefore important to try to understand these figures and replicate them if possible.

Although TLP’s document lists its assumptions it doesn’t set out the detail of the calculations and considerable guesswork is required to work out how it was done. I have tried to reconstruct them using the stated assumptions where possible and sensible guesses otherwise. This article explains how.

## Approach and assumptions

From reading TLP’s ‘New Power Cost League Table’ I conclude that their calculation methodology is as follows.

By ‘consumer cost’, they mean the increase in consumer bills that results when you replace one MWh of unsubsidised electricity with one MWh of subsidised electricity. That is, the consumer cost of the *subsidy*, not of the *electricity*. TLP’s document doesn’t make this completely clear, however, and a casual reader could easily think it is the cost of the electricity. RENews must have been under that impression when they wrote ‘Swansea developer claims project will produce power at £25.78/MWh’. Also, I don’t think they take into account the margin added by electricity suppliers, which is obviously part of the cost to the final consumer.

‘Lifetime consumer cost per MWh’ is the present value (PV) of the plant’s subsidy payments over its entire lifetime divided by the PV of the electricity it generates over its entire lifetime. A better name for it would be ‘levelised cost of subsidy’. I agree with TLP that this is indeed a reasonable way to compare the amount of subsidy paid to plants with different lifetimes and which receive subsidy for different lengths of time.

It is, however, debatable whether the cost of subsidy is the best measure of the cost-effectiveness of an electricity generating technology. What counts is the cost to the economy as a whole, not just to the public purse, whether that is defined as taxpayers or bill payers. Private money invested in the project is no longer available to invest in something else that could potentially produce more clean energy or more jobs.

Also, as its name implies, levelised cost of subsidy measures the cost of the *subsidy package* a plant receives, not the generating cost of the technology itself. Consider two plants each using exactly the same technology. If plant A is given an overly generous subsidy package, enabling its owners to make a large profit, and plant B is given a miserly subsidy package, resulting in its owners making a slight loss, then plant B will appear to be ‘cheaper’ than plant A even though common sense would say that their generation costs are exactly the same.

TLP’s league table includes several subsidy packages that may indeed have been too generous and which are no longer available. If the table is be of use to policy makers, rather than just a PR tool, it should reflect each technology’s current generating cost. This means that there should be only one subsidy package per technology and that package should be the most recent one. Ideally, it shouldn’t use actual subsidy packages at all, but a ‘required level of subsidy’ calculated from each technology’s cost and performance data in exactly the same way.

TLP has used the ‘social’ discount rates from the Treasury Green Book. These are the correct ones to use because the public is providing the subsidy in return for public goods, i.e. emission reductions, jobs and industrial development. They are, however, lower than typical commercial interest rates and even lower for very long term projects. LCOE, for example, is conventionally calculated using a discount rate of 10%. A higher discount rate would give less weight to electricity generated further in the future.

In the calculation, subsidy is assumed to be delivered in the form of a feed-in tariff, where the government sets the price a plant receives for its output. The amount of subsidy itself is not explicitly defined but is calculated as the difference between the tariff and a reference price, also set by the government, that is supposed to reflect the price of unsubsidised electricity.

In the UK the reference price is defined as the price of electricity traded on specific markets averaged in specific ways. It would be massive overkill to try to replicate the way this is calculated, not least because it is mind-bogglingly complex. TLP uses a projection of ‘wholesale’ electrcity prices given by BEIS in its Updated Energy and Emission Projections (UEP) 2015 Appendix M. This contains projections to the year 2035. TLP calls this the ‘power curve’, which apparently is city-trader slang for electricity price as a function of time. Several such projections are given but TLP doesn’t say which one it used.

An annoying complication is that, according to the Hendry report, TLP is proposing a ‘partially indexed’ tariff for its project, though what advantage they see in doing that I can’t imagine. Although indexing can easily be taken into account by expressing the tariff in ‘real’ money, in which units it is constant, partial indexing means that the tariff payments are not constant either in real or nominal money. This makes the calculations more complicated. In his report, Charles Hendry says:

‘TLP’s proposal is structured to provide a “Starting Strike Price” that is subject to partial indexation from 2016.’ (page 78)and

‘Taking Cardiff as an example, TLP estimates that this project would require a Starting Strike Price after cost reductions (facilitated by a pathfinder) of £113 per MWh. In “real” terms, the value of this Strike Price would decrease year-on year – falling to £96.1 per MWh by the project’s First Operating Year (2027) and continuing to decrease thereafter.’ (Page 79)

In other words, for the Cardiff project at least, indexation of the strike price starts eleven years before the plant receives its first £1 of subsidy. The figures quoted imply an indexation rate of roughly inflation minus 1.5%. I interpret this to mean that if the plant were to start generating today it would require a strike price of £96.1/MWh in 2016 money to be indexed at inflation minus 1.5%.

You may have noticed that the league table shown in Figure 1 above contains two entries entitled ‘CCGT DECC LCOE’ and that both of them have a positive value, implying that they receive subsidy. They don’t, of course, though the one called ‘20% load factor’ is probably intended to represent a back up station that receives support through the ‘capacity market’. TLP has included them for comparison by feeding their LCOEs into the calculation as if they were feed-in tariffs. While this doesn’t mean that CCGTs are subsidised, it does appear to imply that they are uneconomic, so an explanation is called for. The explanation is that the assumptions that went into the calculation of the LCOEs, for example the prices of gas and carbon permits, are different from the assumptions that went into the calculation of the UEP projections, neither of which are accurate reflections of the real world.

Mention of the capacity market raises the issue of its cost. This is an indirect subsidy that should be taken into account in any calculation of the cost of subsidy to a renewable plant. If we are constructing a league table of the cost of subsidy, then the cost of the capacity market should be allocated to the different renewable technologies according to how much use each technology makes of it. This would be very complicated to do, however, and I don’t know whether anyone has attempted it. It wouldn’t necessarily penalise lagoons compared with other renewables but until someone works out a way of doing it we won’t know.

## Input data

The following tables summarise the input data. Wherever possible they are from TLP’s ‘New Power Cost League Table’

Contract | Strike price (£ _{2012}/MWh) |
---|---|

Solar FiT 2012 | 89 |

Solar FiT 2015 | 59 |

Solar CfD 2017 | 79.23 |

Onshore Wind FiT 2012 | 49 |

Onshore Wind CfD 2019 | 82.5 |

Offshore Wind FIDeR 2017 | 150 |

Offshore Wind CfD 2018 | 119.89 |

Biomass Conversion FIDeR 2016 | 105 |

New Nuclear | 92.5 |

Offshore Wind CfD 2020 | 105 |

Offshore Wind CfD 2025 | 85 |

CCGT DECC LCOE (93% Load Factor) | 80 |

Source: TLP’s ‘The New Power Cost League Table’ Page 13. |

The tariffs referred to in Table 1 as ‘FiT’ are part of the government’s support scheme for small-scale installations. The levels given in Table 1 are sufficiently close to their corresponding ‘Consumer Cost per MWh’ to imply that TLP has assumed a reference price of zero. The ‘FiT’ scheme pays a generation tariff *and* an export tariff. The generation tariff has an enormous array of different levels depending on technology, plant capacity and date of installation. Some of them are extremely high. The export tariff is roughly the same as the wholesale price. The ones stated by TLP are the generation tariffs for stand-alone plants that export all their power. For such plants it would be valid to use the generation tariff with a reference price of zero. For installations that consume some or all of their own power, e.g. domestic solar panels, then this would not be a valid assumption.

Somewhat surprisingly TLP’s ‘New Power Cost League Table’ doesn’t include tariffs for the two tidal lagoon projects listed there, even though they must have specified them in order to calculate the values of ‘lifetime consumer cost per MWh’ that they present.

In his report, Charles Hendry gives a value for the strike price TLP is currently suggesting for the Cardiff lagoon. As discussed above, this is £96.1/MWh in 2016 money beginning on the day the plant starts operating and indexed at inflation minus 1.5%. He also says that TLP’s proposed duration of this tariff is 90 years.

The Hendry report doesn’t discuss the Swansea Bay strike price because it is confidential.

Hough and Delebarre (2016) collect together media references to strike prices proposed by TLP for Swansea Bay. Table 2 lists them:

Date | Price (£/MWh) |
Duration (years) |
---|---|---|

February 2014 | 180 | 90 |

October 2015 | 168 | 35 |

February 2016 | 96.5 | Not reported |

Source: Hough and Delebarre (2016) |

This is quite a large rate of reduction in requested subsidy levels. Interestingly, media reports of its capital cost go in the other direction, from £650M in June 2013, through £850M in February 2014, £1bn in June 2015 to £1.3bn (*double* the 2013 estimate) now. Will it end there, I wonder?

Page 78 of the Hendry report says:

The CFD element of TLP’s proposal for Swansea Bay is for a 90 year contract term with partial indexation of a Strike Price.Reference to ‘The CFD element’ suggests there might be other elements. If there are I think we should be told.

A report written by Pöyry management consultants for TLP in 2014 says:

Our assessment of the central value for the required CfD strike price for the first three lagoons studied on a volume-weighted average basis is £111/MWh (assuming a 35-year CfD duration). Lagoon 1 is £168/MWh, whilst for Lagoons 2 and 3 this falls to £130/MWh and £92/MWh respectively.This agrees with the 2nd estimate reported in Table 2. The Pöyry report says that Lagoon 1 is Swansea Bay, but doesn’t identify Lagoons 2 and 3.

I think it most likely that TLP used the numbers from the Pöyry report, not just because I’ve already done the calculations and found that it gives the best agreement with TLP’s numbers, but also because the League Table pre-dates the Hendry report. I’m therefore going to go with these numbers, which are summarised in Table 3.

Site | Price (£/MWh) |
Duration (years) |
---|---|---|

Swansea Bay | 168 | 35 |

Cardiff | 92 | 35 |

Table 4 lists the durations of the ‘FiT’ tariffs listed in Table 1.

Technology | Duration of tariff |
---|---|

Solar PV | 20 years (25 years for those with an eligibility date before 1 August 2012) |

Wind | 20 years |

Hydro | 20 years |

Anaerobic digestion | 20 years |

Micro-CHP | 10 years |

Source: Ofgem guidance for applicants |

Tariffs referred to in Table 1 as ‘CfD’ or ‘FIDeR’ are part of the government’s support scheme for large scale installations. These all have a duration of 15 years except for nuclear, which has a duration of 35 years.

TLP’s ‘New Power Cost League Table’ also lists its assumptions for the lifetimes of the technologies it covers. Table 5 lists these:

Technology | Plant lifetime (years) |
---|---|

Solar PV | 25 |

Onshore Wind | 24 |

Offshore Wind | 22 |

Biomass Conversion | 22 |

CCGT | 25 |

New Nuclear | 60 |

Tidal Lagoon | 120 |

Source: TLP’s ‘The New Power Cost League Table’ Page 13. |

Figure 2 shows the wholesale electricity price projections from BEIS’s Updated Energy and Emission Projections (UEP). This contains seven scenarios. As mentioned above, TLP doesn’t say which one it used. I think the most likely one is ‘Existing Policies’. However, we are going to simplify the calculation by assuming the reference price is constant. From looking at Figure 2 I suggest that this should be 5p/kWh = £50/MWh.

Table 6 shows the discount rates with which PVs are calculated. These are from the Treasury Green Book, which says that they decline over time.

Period of years | 0–30 | 31–75 | 76–125 | 126–200 | 201–300 | 301+ |
---|---|---|---|---|---|---|

Discount rate | 3.5% | 3.0% | 2.5% | 2.0% | 1.5% | 1.0% |

Source: Treasury Green Book Annex 6 Table 6.1 Page 99 |

This means that for a project with a lifetime of longer than 30 years we need to apply different discount rates to different periods in its life.

Finally, TLP’s document says that they have adjusted downwards by 4% the price of electricity from intermittent sources, and upwards by 27% the price of the ‘20% load factor CCGT’, which is explained as follows:

‘20% load factor CCGT receives a premium of 27% on wholesale market prices captured to reflect high-value period targeting (based on the last 24 months of market data).’These adjustments are shown in Table 7.

Wind/Solar Hourly Price Discount | 4.0% |

CCGT 20% Load Factor Hourly Price Premium | 27.0% |

Source: TLP’s ‘The New Power Cost League Table’ Page 13. |

## Method

The following bit of algebra derives a simplified formula that allows us to avoid constructing a complicated cash-flow projection covering 120 years. The advantage of a simple approximation is that it is more transparent, easier to check and harder to make mistakes, which are easier to find if you do make them.

We start by putting into symbols the definition of ‘lifetime consumer cost per MWh’. This gives a formula that is accurate and general but not suitable for doing calculations except by way of a detailed 120-year cash flow projection, which is what we are trying to avoid. We then assume that more and more of the input parameters are constant, eventually ending up with our desired simplified formula in which all the input variables are constant, including the wholesale price of electricity. Hopefully, when we put numbers into this formula the results will be near enough to TLP’s for us to conclude that our understanding of their calculation is correct. If not, we can try again without assuming the electricity price is constant. In any case, the simplified formula can still serve as a sanity check.

**Notation**

To derive our formula, we need to invent some symbols:

\(PV_{r, \, T}\left( f(t) \right)\) | is the present value, with discount rate \(r\), of the function \(f\) of the time \(t\), evaluated over a time period from the present to \(T\). We are going to use continuous discounting, so it is defined as \(\int_0^T (1+r)^{-t} f(t) dt \) |

\(AEP\) | is the plant’s rate of energy production, in units of MWh/year. Assumed constant for the lifetime of the plant. |

\(T_f\) | is the duration of the feed-in tariff in years. |

\(T_e\) | the duration of electricity production in years. |

\(p_f\) | is the level of the tariff in £/MWh. |

\(p_e\) | is the reference price and the price of unsubsidised or ‘wholesale’ electricity in £/MWh. |

\(g\) | is a dimensionless factor that embodies the price adjustments described in Table 7 above. It is unity for unadjusted technologies, \(1 – 4\% = 0.96\) for wind and solar and \(1 + 27\% = 1.27\) for the ‘20% load factor CCGT’ |

\(R_f\) | is the revenue the plant receives from the tariff in £/year. Equal to \(p_f \times AEP\). |

\(R_e\) | is the revenue, in £/year, the plant would receive if it only got the reference / unsubsidised price. Equal to \(g \times p_e \times AEP\). |

\(C\) | is TLP’s ‘consumer-cost’ measure, in £/MWh. |

## Derivation

As discussed above, TLP’s ‘lifetime consumer cost per MWh’ is defined as the present value of the stream of subsidy payments a plant receives over its entire lifetime, divided by the present value of the electricity it generates over its entire lifetime. Equation \(\eqref{eq:basic_definition}\) states this definition in symbols and Equation \(\eqref{eq:expanded_basic}\) says the same thing in a slightly more detailed way.

\[ \begin{align} C &= \frac{ PV_{r, \, T_f} \left(R_f \, – R_e\right)}{PV_{r, \, T_e} \left(AEP\right)} \label{eq:basic_definition} \\ \notag \\ & \boxed{ = \frac{ PV_{r, \, T_f} \left(AEP \times p_f \, – AEP \times g \times p_e\right)}{PV_{r, \, T_e} \left(AEP\right)} } \label{eq:expanded_basic} \end{align} \]

This is the most general form of \(C\). If \(AEP\) is constant it can come outside the \(PV\) and then it cancels out.

\[ \begin{align} C &= \frac{ AEP \times PV_{r, \, T_f} \left( p_f \, – g \times p_e\right)}{AEP \times PV_{r, \, T_e} \left(1 \right)}\\ \notag \\ & \boxed { = \frac{ PV_{r, \, T_f} \left( p_f\right) – g \times PV_{r, \, T_f} \left(p_e\right)}{ PV_{r, \, T_e} \left(1 \right)} } \label{eq:const_AEP} \end{align} \]

Because \(AEP\) cancels out, load factor does not enter into the calculation, though TLP say they used load factors in theirs. Circumstances in which AEP might not be constant include:

- Plant performance degrades over time due to ageing.
- External factors, such as the market or the grid operator, force the plant to produce less than it could.
- An extremely accurate model of a tidal power plant uses actual tide tables to predict its output, which would lead to different AEP’s in different years.

Of these, the only one that could possibly be used in a calculation such as this one is the first. However, TLP’s report makes no mention of performance degradation rates. I think the most likely explanation of TLP’s use of load factors is that they have used a large complex cash flow model primarily designed for other things, the complexity of which obscures the fact that constant load factors cancel out in this calculation. I think they will find that changing the load factors will have no effect on the results.

If the feed-in tariff is constant (in real terms) then \(p_f\) can also come outside the PV:

\[ \begin{equation} \boxed{ C = \frac{p_{f}\times PV_{r, \, T_f} \left(1\right) – g \times PV_{r, \, T_f} \left(p_e\right)}{ PV_{r, \, T_e} \left(1 \right)} } \label{eq:const_AEP_const_pf} \end{equation} \]

\( PV_{r, \, T} \left(1\right) \) is the present value of a constant flow of 1 unit per year. If we are using continuous discounting it is given by: \[ \begin{equation} PV_{r, \, T_1 \rightarrow T_2}\left(1\right) = \frac{\left(1 + r\right)^{T_2 – T_1} – 1}{\left(1 + r\right)^{T_2} \ln \left(1 + r\right) } \end{equation} \] where \(T_1\) is the start time of the flow and \(T_2\) is its finish time. Usually \(T_1 = 0\)

If the feed-in tariff is ‘partially indexed’ then the situation is slightly more complicated. The term ‘partially indexed’ only means that in nominal money the tariff level increases at a rate somewhere between zero and the actual rate of inflation. Within that constraint there’s an infinite number of ways it could be done. The simplest is to define the indexation rate as ‘inflation minus \(x\)’. In that case, provided that the inflation rate and \(x\) are both small enough that their product is \(\ll1\), the PV of the tariff is given by \[ \begin{equation} PV_{r, \, T}\left(p_f(t) \right) \approx p_f (0) \times PV_{r^{\prime}, \, T}\left(1 \right) \label{eq:partial_indexing} \end{equation} \] where \(r^{\prime} = (r+x)/(1-x) \) and \(p_f(0)\) is the tariff at the start of the project. For this form of ‘partial indexing’ the ‘lifetime consumer cost per MWh’, \(C\), is given by Equation \( \eqref{eq:const_AEP_const_pf} \) but with \(r^{\prime}\) substituted for \(r\) in the first term of the numerator and with \(p_f\) regarded as its value at the start of the project.

If the reference price is constant in real money, then we don’t need to make use of any time series for it. \[ \begin{equation} \boxed{ C = \frac{p_{f}\times PV_{r, \, T_f} \left(1\right) – g \times p_e \times PV_{r, \, T_f} \left(1\right)} { PV_{r, \, T_e} \left(1 \right)} } \label{eq:const_pe} \end{equation} \] This will work with a partially indexed tariff by replacing \(r\) with \(r^{\prime}\) in the first term of the numerator as described above. For technologies that don’t use partial indexing, it simplifies to:

\[ \begin{equation} \boxed{C = \left(p_{f}- g \times p_e \right) \frac{PV_{r, \, T_f} \left(1\right)}{ PV_{r, \, T_e} \left(1 \right)}} \label{eq:simplest} \end{equation} \]

If we are lucky the simple approximation embodied in Equations \( \eqref{eq:const_pe} \) and \( \eqref{eq:simplest} \) might be close enough to TLP’s results that we don’t need to engage in any more serious number crunching. In any case they will serve as a sanity check. They also clearly show that a fundamental driver of performance under this measure is the length of time that a plant can continue generating after its feed-in tariff ends.

## Calculation

So lets start plugging numbers into these equations starting with the most simplified, but least accurate, and, if necessary, gradually working our way up to the most general, but most accurate.

First we need to calculate the values of \(PV_{r, \, T} \left(1\right)\) using the Treasury Green Book discount rates for all the time periods that feature in the calculations. For periods longer than 30 years the Green Book says that we should divide the period up into slices and apply a different discount rate to each slice. Here’s an example calculation of the PV of unity between \(0\) and \(120\) years: \[ \begin{align} PV_{0 \rightarrow 120}\left(1\right) &= PV_{3.5\%, \, 0 \rightarrow 30}\left(1\right) + PV_{3.0\%, \, 30 \rightarrow 75}\left(1\right) + PV_{2.5\%, 75 \rightarrow 120}\left(1\right) \notag \\ \notag \\ &= \frac{1.035^{30} – 1}{1.035^{30} \times \ln \left(1.035\right) } + \frac{1.03^{75 – 30} – 1}{1.03^{75} \times \ln \left(1.03\right) } + \frac{1.025^{120 – 75} – 1}{1.025^{120} \times \ln \left(1.025\right) } \notag \\ \notag \\ &= 18.712 + 24.885 + 27.167 \notag \\ &= 70.764 \notag \end{align} \]

Table 8 shows the values of this for all the time periods used in the calculation. The last column shows the PV corresponding to indexing at inflation minus 1.5%.

\(\dfrac{T}{years}\) | \(PV_{r, \, T} \left(1\right)\) | \(PV_{r^{\prime}, \, T} \left(1\right)\) |

15 | 11.7178 | 10.6866 |

20 | 14.4597 | 12.8471 |

22 | 15.431 | 13.5759 |

24 | 16.3378 | 14.238 |

25 | 16.7683 | 14.5458 |

35 | 23.3601 | 20.3765 |

60 | 38.6051 | 32.66 |

90 | 56.1323 | 47.0438 |

120 | 70.7638 | 56.9885 |

Table 9 performs the calculation using Equations \(\eqref{eq:const_pe} \) and \( \eqref{eq:simplest} \). It can easily be checked by hand using a pocket calculator.

Contract | \(\dfrac{p_f}{£/MWh}\) | \(\dfrac{p_e}{£/MWh}\) | \(\dfrac{T_f}{years}\) | \(\dfrac{T_e}{years}\) | \(g\) | \(PV_{r^{\prime}, \, T_f} \left(1\right)\) | \(PV_{r, \, T_f} \left(1\right)\) | \(PV_{r, \, T_e} \left(1 \right)\) | \(\dfrac{C}{£/MWh}\) | TLP’s value |
---|---|---|---|---|---|---|---|---|---|---|

Solar FiT 2012 | 89 | 0 | 25 | 25 | 0.96 | 14.546 | 16.768 | 16.768 | 89 | 89 |

Offshore Wind FIDeR 2017 | 150 | 50 | 15 | 22 | 0.96 | 10.687 | 11.718 | 15.431 | 77.455 | 74.04 |

CCGT DECC LCOE 20% Load Factor | 123 | 50 | 25 | 25 | 1.27 | 14.546 | 16.768 | 16.768 | 59.5 | 53.73 |

Solar FiT 2015 | 59 | 0 | 20 | 25 | 0.96 | 12.847 | 14.46 | 16.768 | 50.877 | 50.88 |

Offshore Wind CfD 2018 | 118.89 | 50 | 15 | 22 | 0.96 | 10.687 | 11.718 | 15.431 | 53.832 | 50.33 |

Onshore Wind FiT 2012 | 49 | 0 | 20 | 24 | 0.96 | 12.847 | 14.46 | 16.338 | 43.367 | 43.37 |

Offshore Wind CfD 2020 | 105 | 50 | 15 | 22 | 0.96 | 10.687 | 11.718 | 15.431 | 43.284 | 36.39 |

Biomass Conversion FIDeR 2016 | 105 | 50 | 15 | 22 | 1 | 10.687 | 11.718 | 15.431 | 41.765 | 32.99 |

New Nuclear | 92.5 | 50 | 35 | 60 | 1 | 20.376 | 23.36 | 38.605 | 25.717 | 25.78 |

Tidal Lagoon Swansea Bay | 168 | 50 | 35 | 120 | 1 | 20.376 | 23.36 | 70.764 | 31.87 | 25.78 |

CCGT DECC LCOE 93% Load Factor | 80 | 50 | 25 | 25 | 1 | 14.546 | 16.768 | 16.768 | 30 | 21.95 |

Onshore Wind CfD 2019 | 82.5 | 50 | 15 | 24 | 0.96 | 10.687 | 11.718 | 16.338 | 24.744 | 20.07 |

Offshore Wind CfD 2025 | 85 | 50 | 15 | 22 | 0.96 | 10.687 | 11.718 | 15.431 | 28.097 | 19.72 |

Solar CfD 2017 | 79.23 | 50 | 15 | 25 | 0.96 | 10.687 | 11.718 | 16.768 | 21.824 | 18.68 |

Tidal Lagoon Cardiff | 92 | 50 | 35 | 120 | 1 | 20.376 | 23.36 | 70.764 | 9.9858 | 7.8 |

The calculations shown in Table 9 are graphed in Figure 3.

This looks pretty good considering that we have used an extremely simplified formula. I think it is good enough to enable us to conclude that we have understood how TLP has calculated its league table, without needing to indulge in any more serious number crunching. If we were to use Equation \(\eqref{eq:const_AEP_const_pf}\) and one of the time-series of wholesale electricity price from Figure 2 then, no doubt, the agreement would be almost perfect.

Really, though, it shouldn’t have been necessary. TLP should have published its calculations in sufficient detail to allow independent 3rd parties to replicate them. To say:

‘We are publishing the assumptions used in the model. We will be happy to run additional sensitivities in the model on request.’is just not good enough. They should open-source their entire model.

Anyway, all that remains now is to ask what it all means.

## Conclusions

TLP’s ‘The New Power Cost League Table’ is a league table of subsidy packages, not of technologies. ‘Consumer Cost per MWh’ is the cost of subsidy, not the cost of electricity. A better name for it would be ‘levelised cost of subsidy’.

This does seem a reasonable way of comparing the costs of different subsidy packages but not of comparing the cost-effectiveness of technologies. As mentioned above, it is the cost to the economy as a whole that counts, not just the cost to tax or bill payers.

The League Table includes several support packages that are now closed to new applicants. These are red herrings. If TLP wants to compare ‘apples-to-apples’ it should only include support packages that reflect a technology’s *current* cost. If they really want it to be a league table of *technologies*, not of support packages, it should only include one support package per technology, and that should be the cheapest one.

The costs for tidal lagoons used in the league table come from the Pöyry report, with Cardiff = Lagoon 3.

Pöyry’s calculations appear to assume that the only expenditure after the plant becomes operational will be normal operation and maintenance, assumed to be the same in each of the plant’s 120 years. However, although the sea wall may last for 120 years, the turbines and generators probably won’t. The plant will probably need to be repowered at least once during its lifetime. The cost of doing this should be taken into account.

Media reports of the capital cost of the Swansea bay lagoon seem to have been going up, from £650M in June 2013, through £850M in February 2014, £1bn in June 2015 to £1.3bn (*double* the 2013 estimate) now. The Pöyry report (dated March 2014) assumed a capital cost of £913M.

For tidal lagoons, the ‘Consumer Cost per MWh’ is strongly dependent on the plant continuing to operate for 120 years. This is such a long time that the likelihood of unforeseen eventualities must be quite high. 2137 is as far in the future as 1897 is in the past. The world then will be as different from today as today is from the reign of Queen Victoria. We cannot bank on electricity produced that far ahead. If the rationale for doing something today is critically dependent on outcomes in the distant future then that rationale should be treated with caution.

For example, if the plant were to stop generating after 60 years, which could easily occur if the turbines and generators reach the end of their lives and are not replaced for some reason or other, then the league table would look like Figure 4 below:

This moves the Swansea Bay lagoon up near the top of the league table, though not to the very top, but the Cardiff one is surprisingly still at the bottom. If they really can deliver the Cardiff and subsequent lagoons for that cost then maybe it isn’t such a bad option after all. However, the development of the Cardiff lagoon is at the same stage as Swansea Bay was at when its cost was estimated at £650M, and now it’s double that and may not have stopped increasing yet.

Overall, I think that ‘Levelised Cost of Subsidy’—and that’s what it should be called—could be a useful part of a policy analysts toolkit, though only a part, and not the most important one. It gives a particular view of a project’s economics, but not the whole picture, and tells us as much about the subsidy package being modelled as it does about the technology it is applied to. The energy policy community should agree on a transparent methodology for calculating it. But before doing that, others, perhaps in academe, could usefully have a go at replicating TLP’s results and publish their findings. I might have got it wrong! And TLP’s method may not be the right way of doing it either.

© Copyright 2017 Howard J. Rudd all rights reserved.