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 😉

Wood towers for wind turbines

I always believed that wood towers for wind turbines were a solution possible only in small, domestic WTGs (somewhere around 10 kW to maybe maximum 100 kW). There are several example available, for instance this product of InnoVentum.

Well, I was wrong: I see that some years ago (2012) a Vensys 77 1,5 MW turbine has been installed on a 100 meters tower. That is quite a number: a 77 meters rotor is considered small for today standard, however it fully qualify as a “utility scale” solution.

This full scale prototype followed a 25 meters test tower built by the same companies some years before.

Developed by 2 German companies (TimberTower & TiComTec) it has been built near Hannover. The foundation is standard (concrete) and the connection between the tower and the foundation is made trough 4 meters long steel rods.

With a somehow unusual octagonal cross section the tower diameter is comparable to a standard concrete or steel solution. I see however that other geometries are possible (hexagonal or dodecagonal).

The life span of this solution looks similar to the steel alternative (20 years). Unfortunately I haven’t been able to find information regarding the cost. For the sake of clarity it is not 100% wood – few steel elements are used inside the tower.

 

Wind farm project management: PRICE2 vs PMP

In another post I have discussed my experience with the PMP certification and its (somehow weak) relationship with wind farm project management.

In a nutshell, several processes and concepts are not directly applicable given the peculiarity of our industry. Said that, I believe that the PMP has a value, because it explain in detail a lot of tools and ideas that are used daily – for instance dependency types in Gantt charts, how to handle risk management or the “stakeholder management” concept.

Some days ago I have made another PM certification, the British de facto standard PRINCE2. The main reason for that has been my curiosity to see another point of view on a very broad topic such as project management.

Both certifications are trying to live together and differentiate themselves:

  • PMP define itself as a “standard” and comes with a mountain of processes and techniques.
  • PRINCE2 define itself as a “methodology”, coming with models and templates but very few techniques.

My personal impression is that the role of the Project Manager in PRICE2 is less relevant compared to the PMP idea of the same role – basically he has some decision margins, but he’s somehow squeezed between the Project Board making the big decisions and the teams doing the actual job. As soon as one of the tolerance levels is exceeded, he need to escalate the problem to the Project Board (that in the wind industry, if it exist, is usually called “Steering Committee” or something similar).

This image is strikingly different from the one that my mentor Luis Miguel gave me when he told me that, in the infancy of the wind industry, the PM was basically “the God of construction site”. Possibly the image is a bit strong but it makes the concept crystal clear.

Said that I also had the feeling that PRINCE2 was much easier to follow in the definition of the workflow, with less processes (seven) clearly linked between them and few key concepts (“Themes” and “Principles”). Understanding the relationship between the 49 processes of PMP is not that easy: I had to print them in a huge A0 and spend a lot of time staring at it to make a sense of them.

An interesting argument that I want to mention against PRINCE2 is that it is “unfalsifiable”, in the scientific sense defined by Karl Popper. This basically means that PRINCE2 has to be tailored (that is, adapted) to the specific project to work properly. If something goes wrong, you cannot proof that the problem is PRINCE2 (because possibly the tailoring you have made was wrong).

In conclusion I would recommend both certification to people interested in knowing more about project management, even if some tools, techniques and processes are not used in wind farms construction.

Concrete tower assembly in Chile

 

An interesting video on the use of concrete towers in Chile. Among the benefits of this solution the creation of local jobs (several hundred for factory) and the increase of local content (the amount of goods and services provided locally, an important parameter in some tenders).

Concrete towers are especially cost effective when the hub height is over 100 meters. Additionally they are less prone to price variation - steel prices, at least in Europe, dropped in 2016 to rebound in 2018.

Finally transport cost are usually lower, at least if the factory is located near the wind farm as it is usual.

Long term instrumented monitoring of wind turbine foundations cracks evolution

Fiber Bragg grating sensors (Image copyright fbgs.com)

Some weeks ago I have discovered that, as I am currently enrolled as a university student (getting “slowly but steady” a second degree in Economics) I have full access to the Elsevier database.

This is an enormous amount of information, including all the best scientific papers and technical articles published by industry journals.

I am using this possibility to learn more and stay updated on several niche topics that I found interesting – from recycling of wind turbine to bird strikes to foundations pathologies.

Browsing the database, I recently stumbled upon an interesting article published by Jack McAlorum et al. from the University of Strathclyde (Glasgow).

The paper is called “Deterioration of cracks in onshore wind turbine foundation”.

The authors instrumented an octagonal slab foundation (sometimes called “star foundation” or “wall foundation”) to monitor the evolution of existing cracks.

I already wrote a couple of posts on foundation cracks: they can be due to a variety of root causes, such as:

  • Design mistakes
  • Errors in the composition of concrete mix
  • Extreme temperatures
  • Errors in the execution of the wind turbine (for instance, concrete poured in different batches creating construction joints)
  • Failures due to the use of an embedded can (this is a frequent failure reason for older wind turbines)

The paper does not specify the reason for the cracks. However, as typical, the most severe cracks were in the side of the wind turbine facing the wind (as the concrete is in tension there).

What it is interesting is the fact that the behaviour of the foundation has been monitored for a very long period (over 9 months) and under standard operating conditions. This is very unusual: while other key component of the turbine like the gearbox are constantly monitored and the data is collected trying to detect problems and predict failures, I have never heard of such monitoring for the foundation.

Additionally it is interesting the type of sensor used: instead of standard accelerometers or strain gauges the researchers used a strain sensor based on fibre-optic called “fibre Bragg gratings” (FBGs).

Basically it is a sort section of optical fiber treated in a way that some specific wavelengths are reflected and some are transmitted. They can be used as a strain sensor because when they are deformed the transmitted and reflected wavelengths shift, allowing a calculation of deformation.

Cracks can evolve with 3 different displacement type:

  1. Opening (the crack becomes wider)
  2. Sliding (one face of the crack slides on top of the other)
  3. Tearing

Through the monitoring period no significant evolution of cracks was observed. Basically, the wind turbine owner was lucky: cracks did not deteriorate and no intervention was needed.

Unfortunately, the cost associated with the monitoring are not shared, so it is difficult to make a business case (cost of immediately repairing the cracks with grouts or epoxy resins vs. cost of monitoring to see if the intervention is needed).

I also see that this solution only allow monitoring visible cracks. This is a strong limitation, as several failures originate in a non-visible area of the foundation.

Said that the idea is certainly interesting and useful, above all considering that some turbine are kept in operation for a very long time, even exceeding the design life of the foundation (usually 20 years).

 

Over and over and over again: serial defect clause

The serial defect clause is a warranty frequently requested by customers.

It belongs to a classic “tryptic” of warranties allocating risk on the turbine suppliers:

  • General warranty, for defect in design, manufacturing, installation, etc.
  • Power curve warranty
  • Serial defect warranty

Generally speaking, a serial defect is a component defective on a significant number of turbines. If there is a certain percentage of defective components, the warranty force the turbine seller to replace it on all the turbines.

As you will imagine, the tricky part is the specific definition of the clause.

Among the key point to be defined these are specially important:

  1. The definition of defect / defective.
  2. The time-frame for the defect to appear. How many years?
  3. The reason for the defect. Is the root cause the same? You can have for instance many blade failures caused by different problems.
  4. The percentage of failures needed to declare a serial defect. Is it 10%, 20%, more?
  5. The population of turbines used to calculate the percentage of failure. Only the wind turbine in the wind farm, all the turbines of the same model owned by the customer, all existing turbines of the same model?
  6. Who should confirm the existence of the defect. A reasonable compromise for this point can be an independent third party.

The reason behind this clause is that such serial defects happened in the past - not only in the infancy of the wind industry, but also in more recent years when components have been replaced on massive numbers of turbines, even of Tier 1 manufacturers.

Without this clause the buyer can be left in a very uncomfortable situation where maybe he is aware of the (latent) problem but only if the components that fail during the Warranty or Service period are replaced.

Transfer of title & transfer of risk

Transfer of title and transfer of risk are 2 key concepts in wind farms contracts (and, presumably, in many other comparable businesses). They appear in both EPC and Supply Only agreements.

This is what they usually means:

Transfer of title (ToT): the ownership (of the entire turbine or of one of the component of the wind farm, such as the foundation) is transferred to the buyer.

Transfer of risk (ToR): risk of damages and losses is transferred to the buyer.

Although it may look counterintuitive they do not have to happen at the same point in time: for instance, an EPC contract could have transfer of title when a certain percentage of the wind turbine is paid -for instance, 80%- and transfer of risk only after commissioning (that is, the turbine is installed, tested and ready for production).

When the relevant percentage is paid is defined in the projects cash flow. In general, it could happen that the transfer of title happen many months before wind turbine installation.

The percentage of the wind turbine price to be paid to have transfer of title is usually one of the key negotiation topics. For the sake of clarity, the wind turbine seller would retain some case of security (e.g. a bank bond) until the equipment is paid in full in case the buyer stop the payments after the transfer of title.

It is worth to notice that one party (or both) might be interested in an early ToT or ToR, for instance if they are linked to revenue recognition. For instance, in some Supply Only or Supply and Install contracts revenue recognition is at ToR, so the turbine seller want to have it as soon as possible.

For a variety of reasons, it could be the buyer interested in an early ToT or ToR, possibly even before the completion of the wind farm balance of plant (basically, when the wind farm is not ready for installation). In a similar scenario the turbines would be delivered to a temporary storage area where the ToT and ToR would happen.

One more interesting point is that, in some jurisdictions, a sales tax could become applicable when the ownership of the turbines is transferred. This could be a good reason for an early or late transfer of title in a different jurisdiction.

 

Wind turbines defective parts warranty

Lately I’ve been spending some time trying to learn something more about quality. Although I see that there is no consensus on the business effectiveness of some of these technique I’ve decided to take a certification (ASQ Six Sigma Green Belt) to have a first-hand experience.

One of the first concept I’ve learnt is the difference between defect and defective. This is the standard definition in the wind industry:

“Defect” is defined as a non-conformity, a failure to comply with the Technical Specifications, a flaw in design, manufacturing, workmanship or damage.

“Defective” is defined as a part that has one or more defects and fail due to it.

The key concept here is that in principle it is possible to have one or more defect on a component without having safety or operational problems.

Wind turbines warranties (and presumably other similar equipment) usually are based in the concept of defective – that is, of failure of the component to operate correctly.

The logic is that a failure is usually a black or white concept: either the gearbox is working or it is broken.

However, seen from the perspective of the customer, this definition is not reassuring: a component could have a defect that, even if it’s not preventing the turbine to work, is making it underperforming, unreliable, deteriorating quicker than usual, etc.

Basically the concern of the customer is that the turbine seller will simply “try to keep the turbine alive” until the defect warranty expire (usually after 2 years). Afterwards, it will become a problem of the customer.

For this reason the clause with the definition of defect and defective is usually extensively negotiated. Some possible wording, from the least to the most favourable to the customer, are:

  1. Defective is a part that fails due to a defect
  2. Defective is a part that has a defect that could reasonably cause adverse effects on production or safety
  3. Defective is a part that doesn’t match the Technical Specifications
  4. Defective is a part that contain a defect

Obviously the last one is very onerous for the company who has to mantain the turbine, while the second can offer a reasonable level of protection to both parties.

Why wind turbine blades are made of composite materials?

I’ve received a question regarding material selection for wind turbines blades. The reader asked why there is a predominance in the use of composite materials for the blades instead of wood, steel and aluminium and other materials used in the first glorious, pioneering years of wind energy.

Please note that I’m by no mean an expert so the only intention of this post is to give a very general introduction to the subject. This is a very broad topic involving different engineering branches.

In general the 2 design drivers are weight and stiffness.

A blade should be as light as possible for a variety of reasons:

  • To lower gravity induced fatigue loads
  • To be easily transported and installed
  • To have a better performance

However, it should also be stiff (that is, rigid) for several other reasons:

  • To withstand loads (both wind loads and gravity loads). Wind loads are function of wind speed and length of the blade, and increase from the root to the tip of the blade. Gravity loads are function of the material density.
  • To prevent collision between the blade and the tower under extreme wind
  • To prevent instability (local or global buckling) maintaining its shape

For these reasons blade designers try to minimize the mass for assigned stiffness levels – it is to find a balance between aerodynamic and structural requirements.

So we want less weight (that is lower density) and more stiffness.

Stiffness is expressed by the Young’s modulus of the material – basically the relationship between force and deformation. In general blades are very flexible, stronger in the flapwise direction and weaker in the edgewise direction.

And here is the reason for the use of composite materials. For a given Young Modulus, the material with the lower density is the composite (resin plus glass fiber).

You can see graphically this relationship in a type of graphic called “Ashby Plot” (I attach a version stolen online from a document of the University of Cagliari.

Ashby plot for a wind turbine blade