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An algorithm to improve the renewable energy production

To manage renewable energy efficiently, all weather variation need to be taken into account. Greg Clarke/Flickr, CC BY-SA

Relying less on fossil fuels and more on renewable energy is one of the key challenges of energy transition. Large quantities of greenhouse gases are released into the atmosphere when fossil fuels are extracted and transformed into energy (to be used as motor fuel or for heating, for example). The steadily increasing concentration of greenhouse gases in the atmosphere is causing a rise in global temperatures that could have disastrous effects.

The trouble is, renewable energy sources are not as predictable or stable as diesel or nuclear power.

For example, how many solar panels does it take to meet a given demand for electricity? Researchers from ENSTA ParisTech and ENSIIE have found the answer. They have optimized the design of a stand-alone hybrid energy system – stand-alone meaning not connected to the public electricity grid – composed of wind turbines, solar panels and batteries. Such a system must be able to meet the demand for electricity while minimizing costs, including the cost of the diesel generator that provides backup power if the other energy sources fall short.

How the system works

When weather conditions are favorable, the wind turbines and solar panels are enough to meet demand and the excess energy is stored in batteries. These batteries are only used if the demand exceeds what the wind turbines and solar panels can supply.

Unfortunately, battery operation results in energy loss; not all the kilowatt-hours stored can be used. As the system is off-grid, a diesel generator is used to satisfy demand once the batteries are empty. But this is expensive – the cost per kilowatt-hour of generator usage is higher than that of a wind turbine.

A few types of wind turbine, solar panel and batteries were preselected by electricity specialists. The type and quantity of each component has to be optimally determined to meet a given demand while minimizing the total cost, which includes the cost of investment (land rental and the purchase and installation of the components) and the operating costs (maintenance and diesel).

Taking weather variations into account

This is a complex problem, since uncertainties about demand and production mean that many scenarios are possible. The system must be robust, which means “good enough” whichever scenario plays out. The model has to take into account variations in weather conditions over the year (which was divided into 8,760 periods of one hour). Fortunately, the total variation is limited because the uncertain data can only vary between given bounds.

First, the researchers designed the optimal system without uncertainties. At this stage, the problem is easy to solve because it has only three integer variables (the number of wind turbines, solar panels and batteries), or nine if different types of materials can be used.

When uncertainties are taken into account, the problem gets a whole lot trickier. To cope with this complexity, the researchers developed a model with two levels. The first corresponds to sizing, or the number of components to be installed. The second, called the “recourse problem”, seeks to optimize the system’s performance if the worst-case scenario should occur for the system selected at the first level. The researchers had to deal with more than 40,000 variables (including 8,000 integer variables) and 50,000 constraints.

A custom algorithm

French energy mix, 2013. Commission des affaires économiques du Sénat.

The scientists developed an algorithm combining branch-and-bound methods with dynamic programming, and which solves the recourse problem much faster than standard algorithms in most cases. They tested it with real data from three locations with different climates: Montana, USA, with a continental climate; an island in the Philippines with a tropical climate; and Dunkirk, France, with an oceanic climate.

In these real cases, the demand and the reference values for wind and solar production are average values over several years for each time period. The scenarios are limited variations around these values. The results show that if the system is capable of meeting demand at certain critical periods (critical in terms of demand or production), it can also cover any other period.

In Dunkirk, the algorithm showed that seven solar panels, 24 wind turbines and 384 batteries could ensure sufficient production capacity all year round. This problem was quick to solve (160 steps) because the climate is much more stable than in the Philippines (6,000 steps required). For the small island in the Philippines, the optimal system consists of 10 solar panels, 67 wind turbines and 105 batteries, for an annual cost of 31,000 euros.

Note that the budget corresponds to the worst-case scenario. The real cost will fall somewhere between this budget and an easily calculated minimum cost reflecting the ideal climate conditions for the system.

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

This article was originally published in French

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