Wind farm optimization algorithms

I have always been amazed by the number of published papers, master thesis and documents focusing on the use of algorithms to optimize the layout of a wind farm. Some of them were proposed more than 25 years ago, showing a continuous, sustained interest in the topic.

I guess that the reason for such abundance is the stimulating difficulty of the problem and the fact that there are huge investments behind a wind farm.

From a mathematical perspective the problem is complex due to the type of variables involved, both discrete (you can have 30 or 31 turbine but not 30.5) and continuous (for instance, the length of cables). Additionally there are strong links between variables (for instance higher turbines = higher tower and foundation cost) so finding the “sweet spot” that maximize earnings is not a simple task.

Generally speaking, these algorithm try to maximize the profitability of the investment, usually expressed in terms of Net Present Value (NPV). Basically they compare the value of all expenditures during the life of the project “in today money” with all the earning “in today money” using a certain discount rate for cash flows in the future.

Expenses belong to two categories, capital expenses (CAPEX) and operational expenses (OPEX), while net earnings are function of the amount of power produced, the price of electricity and the electrical losses.

Therefore even a simplified model should try to minimize these expenses:

  • Wind turbine
    • Model (power curve)
    • Tower
    • Installation
  • Civil works
    • Foundations
    • Roads
  • Electrical works
    • MV cables
    • Substation
  • Operation & Maintenance

While maximizing the production, a mainly a function of:

  • Wind
  • Wind shear (of the speed of the wind increase with height)
  • Wake effect (how turbine interact with each other creating turbulences)

The interaction between all these variables is what makes the problem interesting.

To give a few examples,

  1. Packing the turbines densely in a small area will lower the cost of roads and cables but will create huge production losses due to the turbulences inducted by the turbines upwind.
  2. Using a higher tower should increase the production – unless the wind shear is low, in which case the additional tower and installation costs would off weight the benefits
  3. A certain position could be extremely productive – but it could be very far away from the substation (increasing the electrical losses ) or on the top of a steep hill (increasing the earthworks cost)

Additionally you have to decide the level of complexity of the model. For instance the foundation cost can be considered as:

  • A lump sum, equal for all turbine models. Under such assumption, you would see a benefit decreasing the number of turbines but not switching to a different WTG model.
  • A function if the wind turbine model (greater loads = greater foundation).
  • A function of wind turbine model, geotechnical parameters of the soil and unit cost of concrete of still. This latter option, although more precise, would probably make the model very difficult to handle.

I believe that a reasonable compromise between complexity of the model and quality of the result can be achieved using nested algorithms as proposed by these researchers.

In the first steps, only the variables related to the turbines (power curve, wind resource, availability and cost) are considered. Once the turbine model and the layout are fixed the civil and electrical works can be considered, defining the optimum position of the substation (to minimize cable length) and the shortest roads connecting the wind turbines.

How much does it cost a wind turbine?

Onshore wind turbines - price per MW (Millions Euro)

The easy answer to this question is “Today it costs less then yesterday. And probably tomorrow it will cost less than today”.

Today (April 2019) the average price is around 700.000€ per MW – that is, expect to pay around 3 ML€ for a 4 MW wind turbine. That’s a huge reduction when you consider that some years ago the easy to remember formula was 1MW = 1ML€

If you are working in the wind industry you are probably aware of the huge pressure on wind turbine prices, driven by several factors and resulting in turbines cheaper than ever.

It is interesting to observe that, in the current market condition where wind turbines are very cheap, the majority of the main wind turbine manufacturers are reporting very solid order intake figures. However, net profit is still elusive and EBIT margin are very low.

For instance, Vestas reported 9.5% for 2018 while Siemens/Gamesa 7.6% (pre PPA and I&R costs) for the same period, with a guiding range for 2019 between 7% and 8.5%.

It looks like manufacturers are having more luck in the maintenance side of the business: margins there are significantly better.

One of the consequences of this situation is that several players are leaving the market (Senvion declared bankruptcy some weeks ago) and the consolidation of the sector continue: there are rumours about a possible purchase of Suzlon (heavily indebted) by Vestas, while Enercon absorbed the Dutch manufacturer Lagerwey some time ago.

In case you are wondering about the origin of the figures in this post I’ve taken the numbers for this post from the official annual statements of Siemens/Gamesa and Vestas and not from my friends working there 😉

Invest in wind energy option #1 – buy wind turbines

This is the first of several post that I’d like to write in the next weeks about investing in wind energy.

There are several possible alternatives to invest in wind energy, or more broadly in renewables: stocks, managed funds, ETFs or even direct investment in the development of a project.

The option described in this post (buy your own turbines) is probably the most extreme but it’s not unseen. I’ve been personally involved in several projects owned not by utilities, mega corporations or professional developers but by private investors or small companies willing to pay out of their balance sheet.

Additionally, it has to be considered that the banks are usually willing to finance a relevant portion of projects. The percentage that can be financed is somewhere around 60% to 70%, in some cases even more.

The capital cost of wind projects are dominated by the cost of the turbine. In this blog you will find quite a lot of post detailing the other costs associated with the project, usually called “Balance of Plant” (BoP).

As a rule of thumb I would say that the turbines, fully installed and operational (that is, including transportation, installation and commissioning costs) will be somewhere between 60% to 80% of the total investment.

How much does an industrial, multi megawatt wind turbine cost?

It’s obviously not easy to answer this question as it’s dependant on several variables such as number of turbines purchased, transportation costs (marine and overland), financing, insurance and warranties, etc. Actually is so critical that companies in the wind business have usually specialized departments devoted to the gentle art of Pricing.

However several reliable sources (Bloomberg in primis - they are the source for the image above) are concordant on the fact that the cost per megawatt is steadily decreasing.

When I joined the wind industry (2010) a MW was somewhere around 1.4 to 1.6 million dollars -  that is, you could expect to pay around 3 ML$ for a 2 MW wind turbine.

Today (end of 2018) prices have dropped dramatically. Buying a turbine today, with delivery at the end of the next year, will probably cost around 1 M$ per MW.

There are several reasons behind this price drop. I believe that the main 2 are scale factor (today, 3 to 4 MW wind turbines are the norm while in the past the standard was 1.5 to 2 MW) and market pressure in the majority of developed markets (USA and Europe).

To summarize, to invest in wind energy building your own small wind farm (1 turbine around 3MW, no substation or other substantial BoP costs) you would need probably between 0.5 and 1 ML$. This very rough estimate consider a total cost of the project between 3.5 and 4 ML$, with the banks financing around 70%.

 

Invest in wind energy option #2 – stocks and ETFs

A second alternative to invest in wind energy is given by stocks and ETFs of companies in the energy.

There are many “renewable energies” ETF and a bunch of solar ETFs.

However the choice for wind ETF is much more limited.

There used to be one ETF form Invesco (PWND) specialized in pure wind players but it has been delisted due to very low trading. Yes, that is not a good sign.

So, as far as I know today (2018) the only wind ETF is First Trust ISE Global Wind Energy Index Fund (FAN – a very appropriate name).

Not all the companies in this ETD are 100% wind: for instance, the biggest share (almost  10%) is Ørsted (or Dong, if you prefer the old name like me: Dansk Olie og Naturgas).

You will, however, find the big players, including  Longyuan Power (probably the biggest wind power producer in Asia) and all the usual suspects such as Vestas, Siemens Gamesa, etc.

What you will buy is very high volatility today, but probably also long term growth.

An alternative is to do some cherry picking and select the stocks one by one. Almost all players are traded (with some exceptions, for instance Enercon).

Target Price for BoP: a basic introduction to a complex topic

There is an old joke that say something like “What happens when you put 10 economists in a room? You'll get 11 opinions.”

My experience with Target Price is similar: I’ve heard many opinions in favour and against it and probably in general it’s not “right” or “wrong", but it's a strategy that, depending on the context, can be more or less appropriate.

Basically, the idea is to share with the subcontractors the price level that they are supposed to reach – or if you want to see it the other way around how much you can afford to pay to build the wind farm.

On a smaller scale the idea is not new. It is what happen when you ask someone if they can meet a certain budget, for instance asking to an artist “Can you do me a portrait for 100$?”. The answer could be for instance something like “Yes, but the dimensions will be 20x20 cm”

There are indeed some arguments I can see in favour of it:

  • BoP is (partially) a custom service with certain technical specifications that in some cases can be changed.

The implication is that the input of the subcontractor can be requested to hit the target, or some initial requirements can be changed. A classic example is the level of redundancy of the substation: fail proof solutions are not cheap.

  • Material costs can be clearly identified (in some cases).

This is for instance the case when items like medium voltage cables are purchased - a key driver in the cost of cables is the spot price of the raw materials (copper, steel, aluminium) so it’s relatively easy to calculate how much you should pay.

However, it’s also easy to find arguments against it:

  • To give a target price, the buyer should understands the cost structure.

This is not so easy as sit might seem: people dealing with BoP are usually operating in different markets, interacting with companies of different sizes and with different business models. Therefore having a clear view of the seller costs structure can be a daunting task.

  • Price volatility should be low.

This is true in certain markets where it’s easy to find a steady supply of bidders. However, overheated markets with several competing projects executed at the same time can create price volatility: basically, the resources that you need to build the wind farm (for instance the crane, or the mobile batching plant) will go to another project – another wind farm nearby, or possibly something totally different.

Google: powered by wind

One interesting fact that you might not know is that the Big G (that is, Google) decided several years ago to power 100% of its activities using renewable energy.

They reached their objective in 2017: what is surprising is that they started only in 2010, with a wind farm in the USA. Basically the strategy is to close Power Purchase Agreements with developers, aiming at investing in “additional” production.

“Additional” means that they don’t want only to buy renewable energy: they want to add this MW to the grid, building new plants and lowering the carbon footprint.

Another interesting fact is that they buy renewable plants connected to the same grid were the data centres are.

For instance their very first PPA was for a 114 MW windfarm in Iowa, one of the states with a data centre, while their 72 MW wind project in Sweden (2013) was intended to  “feed” the data centre in Finland.

The next step is to sell power to the grid at the spot price. Here is where the magic happen: Google is willing to sell it at a loss in case the spot price is lower than the price indicated in the PPA. The idea is that they wanted to use their financial power to give developers a steady cash flow, assuming the risk of fluctuations in prices.

They also get the famous “renewable energy credits”, and they use them to offset  the carbon footprints of the data centres.

A legitimate question would be “Why don’t you buy directly the renewable energy credits?”. The position of Google, as mentioned before, is that they want to help developers to create more and more renewable energy plants. They believe that the best way to do it is to  use their deep pockets to make more projects reality - "bankability", the possibility to get the money to finance a project from a panel of bank, is usually one of the critical point that kills many developments.

The good news, at least for people like me in the wind business, is that the vast majority of the investments (>95%) are in wind farms. The same apply to other business giants following Google on the renewable path, such as Amazon, Microsoft and Facebook.

The quest for scale: mergers and acquisitions in the wind industry

Mergers and acquisition are not a recent phenomenon in the wind business. My former manager Luis Miguel still remember vividly the merger in ’97 between Nordtank Energy Group (NEG) and Moerup Industrial Windmill Construction Company (Micon) – and the subsequent merger between NEG Micon and Vestas in 2004.

While in ’97 I was still enjoying the Golden Age of University, I had myself the pleasure of experiencing first-hand the merger between Nordex and Acciona Windpower 2 years ago. The same year Siemens merged with Gamesa, creating a new giant in the business. And that was not all, because GE’s completed the acquisition of Alstom.

What’s next?

Well, if you want my two cents on the topic the trend is going to continue in the next years. Wind turbine prices are free falling, and quite a lot of MW are awarded with an auction system were the cheaper takes all.

Every wind turbine manufacturer is working hard to lower the cost of energy, and for sure economies of scales help in the effort. I would say that Senvion is a good candidate for the next M&A: owned by the private-equity firms Centerbridge and Rapid Partners could be a good target for a Chinese manufacturer, for instance.

The acquisition can also be “vertical” in the value chain – turbine manufacturers are purchasing companies producing blades, blade moulds (Nordex with SSP Technology), or even providing Service (Vestas with the Operation and Maintenance company UpWind Solutions).

I see a consensus in the industry that this consolidation process will continue during the next years, somehow similar to the automotive industry.

Payment Security: an overview

In another post I have presented several types of financial securities. In this post I would like to describe more in detail an important subcategory, the Payment Securities.

A Payment Security is usually requested by the seller from the buyer of wind turbines. It is a mechanism to compensate the seller, entirely on partially, if the payments are not completed as per the contractual payment schedule.

Payment securities such as Letters of Credit can have a financial impact – their cost can range from 0.5 to more of 2% of the amount covered, and they usually use lines of credit.

The 2 main types of Payment Securities are:

  • Letter of Credit (full or partial)
  • Parent Company Guarantee (with or without download trigger)

Other 2 possible types of project finance mechanism (without Payment Security) are:

  • Balance Sheet Financing
  • Direct payment from lenders

A Letter of Credit from the point of view of the seller is the strongest alternative. Usually is “unconditional” and “irrevocable”, meaning that it can be used almost as cash: the seller can go to the bank who issued the Letter of Credit and ask for its full amount without explaining what is happening (it is “unconditional”) and at any time (it is “irrevocable”). It is not linked to the contract – that is, the seller does not have to proof that the buyer is defaulting on its obbligations.

A Partial Letter of Credit is simply a Letter of Credit that cover only a percentage of the total contract price (for instance, 30% or 40%).

A Parent Company Guarantee means that the performance of the contractual obligation of the company purchasing the turbines (usually a SPV, a “Special Purpose Vehicle” created only for the project) are guaranteed by a bigger, financially solid parent company owning the SPV.

The Parent Company Guarantee has a Download Trigger if there is a mechanism in place that can force the buyer to replace it with a Letter of Credit. The “download” refers usually to a credit rating downgrade of the parent company or some kind of deterioration of the balance sheet.

The Balance Sheet Financing is not frequent, at least in my experience. It happens when big companies (for instance State utilities) decide to pay for a project “out of their pocket”, without recurring to lenders. As this companies are usually huge, at least in terms of turnover compared to the other players in the business, they can be allowed to buy without providing a Payment Security. Basically they are (or should be) too big to fail.

In the last scenario, Direct Payment from Lenders, the seller doesn’t provide a Payment Security. However, the money flows directly from the lenders (usually a consortium of banks) to the seller, effectively lowering the risk. Obviously the seller will perform a due diligence to check all conditions of the project financing agreement.

Financial securities: what's that all about?

A financial security is an instrument to give a party (for instance, the buyer of a wind turbine foundation) an assurance that the seller (in this case, the company that build the foundation) will perform according to his obligation (that is, will comply with the technical and commercial requirements).

They can have different names – the most usual are “Bonds” and “Guarantees”.

The main difference between the 2 is that a bond is stronger – you can draw upon a bond simply asking the money to the bank, while with a guarantee you need to demonstrate that there is a breach of contract before getting the money.

An additional problem with guarantees is that they are linked to the specific contract in place. Therefore changes to the contract (and changes during construction happen really often) could potentially invalidate the guarantee.

There are quite a few bonds / guarantees that are usually used in a wind farm construction contract.

The most frequents are usually linked to the following  topics

  • Advance Payment: the subcontractor receive money upfront to start the works, but he has to give a bond in exchange.
  • Performance: this bond is draw upon if something goes wrong during the execution of the contract.
  • Warranty: this will cover the obligation of the subcontractor after the execution of the project.

There are other Guarantees frequently seen in the business – one is the Parent Company Guarantee, that  you are going to ask if you are working with a small company that belongs to a greater industrial group with a more solid mother company and the other is the Letter of Credit, that you are normally asking to a bank to confirm that the buyer of your product (for instance, expensive wind turbines) will pay for it.

Bonds, warranties and similar stuff are not free – you have to ask them to your bank and they will cost money, and obviously the bigger the bond the higher the price. Therefore the value of each security, normally expressed as a percentage of the contract, is usually subject of never ending discussions and negotiations between the parties.

Key milestones in wind farm development

The development of a wind farm project is characterized by several milestones linked to contractual obligations of the parties.

The most relevant milestones are marked below. They are in chronological order, and some of them could not appear in a specific project (for instance, not all projects have a limited notice to proceed or the payment milestones can vary a lot from project to project).

Limited notice to proceed (LNTP): in this milestone an agreement is reached between the party to perform some works (for instance, to purchase some long lead time item, such as the substation main transformer). It makes sense when it’s necessary to accelerate the project for some reason.

Advance payment: this is a down payment paid by the customer before the start of the works. It is usually done to secure the production slot of the turbines

Commencement date: in this milestones, all condition precedents are met and the contract is activated.

Payment milestones: every contract has different payment milestones (and different percentage of payment associated with each milestone). However, some “standard” milestones are marked below to give you an idea of how they could look like:

  1.                WTG ex works
  2.                WTG shipped
  3.                WTG erected
  4.                WTG commissioned

Mechanical completion: in this milestone, a certificate is issue stating that the wind turbine has been erected following the relevant technical specifications and it’s ready to start Commissioning

Commission certificate: at the end of commissioning (a set of test done to confirm that the turbine is ready for production) the turbine is ready to start trial operations. A certificate is issued to formalize this fact.

Taking over certificate (TOC): this milestone is usually linked to transfer of risk and beginning defects liability period for a specific turbine (the “defects notification period”).

Provisional acceptance: from this point in time, usually an Operation and Maintenance contract for the wind farm start.

Final acceptance: in this milestone the customer formally accept that the wind farm is complete, fully operational and compliant with the relevant technical specifications.