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Algorithms to the rescue of renewable energy production

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Reducing the use of fossil fuels and increasing the use of renewables is one of the main challenges of the energy transition. Large amounts of greenhouse gases are released into the atmosphere when fossil resources are extracted and transformed into energy (e.g. for fuel or heating). However, the concentration of greenhouse gases in the atmosphere, which has been steadily increasing, is leading to a rise in global temperatures with the feared effects.
However, renewable energy sources are not as predictable or stable as diesel or nuclear.
How many solar panels are needed, for example, to meet a given demand for electricity?
Researchers from ENSTA ParisTech and ENSIIE have found the answer

IThey have in fact designed, in the most optimal way possible, a stand-alone park - not connected to the public electricity grid - consisting of wind turbines, solar panels and batteries. A park that must be able to meet the demand for energy while minimising costs and including the diesel consumed by the substitute generator used in the event of a shortage of other energy sources.

How the park works

When weather conditions are favourable, wind turbines and solar panels are sufficient to meet demand; excess energy is charged into the batteries. These batteries are only used if demand exceeds what the wind turbines and solar panels can provide.

However, the operation of the batteries leads to a loss of energy: not all the kilowatt hours charged can be used. Once they are empty, because the park is not connected to the public grid, a diesel generator can meet the demand no matter what happens, but at great expense - the cost per kilowatt-hour of using the generator is higher than that of a wind turbine.

Wind turbines, solar panels and batteries have been pre-selected by electrical experts, with the type and quantity of each element to be determined optimally to meet a given demand, while minimizing the total cost. This cost includes investment (purchase and installation of equipment, land rental) and operation (maintenance and diesel consumption).

Taking into account weather variations

The problem is complex: many scenarios, depending on uncertainties about demand and production, can occur. The fleet must therefore be robust, i.e. "good enough" regardless of which scenario occurs. The model must therefore take into account the variations in weather conditions over the course of the year (which has been divided into 8760 one-hour periods). Fortunately, the total variation is limited because uncertain data can only vary within a certain limit.

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Researchers first determined an optimal park in the absence of uncertainty: the problem can then be easily solved because it has only three integer variables (the number of wind turbines, solar panels and batteries), nine if different types of equipment are accepted.

When uncertainty is taken into account, the problem becomes much more delicate. The model developed by the researchers then has two levels: the first corresponds to the dimensioning, i.e. the number of pieces of equipment to be installed; the second, called the "recourse problem", seeks to optimize the operation of the system if the worst-case scenario occurs for the park that was chosen at the first level. The researchers thus had to deal with more than 40,000 variables (including 8,000 whole variables) and 50,000 constraints!

A tailor-made algorithm

 

The French energy mix for 2013. Senate Economic Affairs Committee (TEN data).

Scientists have developed an algorithm, combining "separation and evaluation" methods with dynamic programming, which solves the problem of recourse generally much faster than standard algorithms. They tested it on real data from three locations with three different climates: Montana (United States) with a continental climate; an island in the Philippines with a tropical climate; and Dunkirk with an oceanic climate.

In these actual cases, the demand and reference productions of wind and sun are calculated as an average over several years, for each period of time. The scenarios correspond to limited variations around these values. The results show that, if the fleet is sufficient to meet demand during certain critical periods (with respect to demand or production), it can also cover any other period.

In Dunkirk, the algorithm showed that 7 solar panels, 24 wind turbines and 384 batteries can provide year-round production. This result was obtained quickly (160 steps) because the climate is much more regular than in the Philippines (6,000 steps required). For the small island of the Philippines, the optimal park is composed of 10 solar panels, 67 wind turbines and 105 batteries for an annual cost of 31 000 €.

It should be noted that the announced budget is the worst-case scenario that can occur: the actual cost will be between this budget and a minimum, easy-to-calculate cost that corresponds to ideal climatic conditions for the park.

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This type of stand-alone hybrid energy system is particularly useful in islands or isolated regions. But the algorithm can also be applied to other similar problems, such as stock management problems.

Pierre-Louis PoirionPostdoctoral Fellow in Operations Research and Combinatorial Optimization, ENSTA Paris-Tech - Université Paris-Saclay. Alain Billionnet and Marie-Christine Costa are co-authors of this article.

The original text of this article was published on The Conversation.

 

 

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