Accueil > Recherche > Equipes > HMCIS > Thèmes de Recherche > Variabilité Climatique et Energies Intermittentes > Augmentation de la pénétration des énergies renouvelables variables en combinant l’énergie hydraulique au fil de l’eau avec les énergies solaire et éolienne


OSUG - Terre Univers Environnement

Augmentation de la pénétration des énergies renouvelables variables en combinant l’énergie hydraulique au fil de l’eau avec les énergies solaire et éolienne

12 avril 2018, par Brice Boudevillain

Le taux de pénétration des énergies liées au climat, comme les énergies solaire, éolienne et hydraulique, est potentiellement faibles en raison de la grande variabilité spatiale et temporelle des variables climatiques les pilotant. Le taux de pénétration peut être augmenté en combinant différentes sources d’énergie. Plusieurs études ont définit les meilleures combinaisons pour différentes régions du monde. Cependant, elles n’ont uniquement considéré les énergies éolienne et solaire. A partir de 33 années de données quotidiennes (1980-2012), nous avons ré-estimé la combinaison optimale en tenant compte de l’énergie hydraulique au fil de l’eau dans deux régions européennes au climat contrasté. La nature de la combinaison optimale se trouve être très dépendante du climat de la région pour laquelle elle est obtenue, mais présente toujours une forte fraction d’énergie hydraulique au fil de l’eau (40 et 50% pour les régions France et Finlande, respectivement). Une fraction importante d’énergie solaire (45%) est obtenue pour la France alors que seulement 15% est obtenu pour la Finlande. La fraction d’énergie éolienne est plus élevée en Finlande (35%) qu’en France (15%). Ces résultats mettent en perspective la combinaison optimale 60% éolien- 40% solaire actuellement utilisé pour l’Europe dans de nombreuses études. Pour les deux régions, y compris au fil de la rivière dans le mélange permet d’augmenter le taux de pénétration de la CRE d’environ 6%.


In Europe, installed power capacity of Variable Energy Sources (VRE), i.e. wind-power, solar-power and hydro-power, is growing quickly. The European Climate Foundation actually states that 100 % renewable is an objective to be achieved by 2050 [ECF, 2010]. Such a scenario is physically realistic, even at the global scale, since the technical potential of renewable energies covers several times the energy demand [Hoogwijk and Graus, 2008]. However, it is well-known that this available potential is not equally distributed over space [von Bremen, 2010]. In Europe, solar power potential is much lower in Northern countries than in the southern ones. For wind power, it is the opposite with higher potential in the North and along the shores. The space distribution of hydropower potential is linked with the mountain ranges in Europe : higher is the altitude, the higher the hydropower potential [Lehner et al. 2005].

For a 100 % scenario at the European scale, von Bremen [2010] shows that the mix composed by 60 % of wind and 40 % of Photo-Voltaic (PV) minimizes the monthly energy balance variance which governs the balancing costs related to energy transport and storage. In some ways, hydropower is never explicitly included in the mix computation but considered as a storage facility for balancing production and load mismatches. Less attention is paid to small run-of-the-river power (hereafter denoted as RoR power), even if the amount of energy produced is important [François et al. 2016b].

This study investigates how the use of RoR hydropower coming from uncontrolled river flows may increase the global penetration of VREs under the hypothesis that only solar, wind and RoR power are used to meet the demand. We use two European regions representing two different climates. Neither storage nor transport among regions is considered in this study.

2.1 Case study

A French and a Finnish regions of about 40 000 km² are selected for this study (Figure 1). Although the areas do not match country border, they will be referred for convenience with country. These regions represent two different climates in Europe : nordic and oceanic clmimate.

Figure 1 : Location map of the two studied regions.

Solar and wind power generation are estimated at a daily time step from mean daily solar radiation, temperature and wind speeds. Run-of the river hydropower is estimated for each region from simulated water discharges within each region. Energy load time series are simulated from temperatures. All power time series are normalized so that their average equals to the energy demand average over the study period (i.e. 1980-2012). More details about the model and the data bases used are given in François et al. [2016a].

2.2 Analysis Framework

For a given region, an energy mix scenario can be generated using a weighted sum of the three normalized power time series obtained for each of the three energy sources, respectively :
where Pmix is the energy generated from the energy mix (Wh), pPV, pW and pRoR are the normalized time series of solar (photovoltaic), wind and run-of-the river power (Wh), and sPV, sW, sRoR the related sharing coefficients (no dimension). We only consider these three different energy sources to supply the energy load L, so the sum of the sharing coefficients sPV, sW, sRoR equals 1. The factor γ (no dimension) represents the average VRE production factor and corresponds to the ratio between the energy produced by the energy mix and the energy demand over the considered period. The penetration of the energy mix is given by :
where max [ ] is the maximum operator. In other words, the penetration rate corresponds to the percentage of the instantaneous load that can be satisfied by the mix, on average, without any storage or backup facility. In the present analysis, the maximum possible value of the penetration ratio is 100%. When γ equals 1, a penetration ratio equal to 100 % would be obtained for a configuration where the temporal organization of the load is exactly the same than the one of the production. If the temporal organization of the load and the production differ, such a ratio is obtained when the production exceeds the load at any time and can only be obtained with an average VRE production factor γ higher than 1. In the following, the penetration function will refer to the function PE(γ), defined with PE values obtained for different values of γ.

3. Results
3.1 Variavbility of seasonal power generation patterns

For illustration only, the seasonal patterns of the energy load, solar-power, wind-power and run-of-the river power are presented for the France and Finland regions in Figure 1.

Figure 2 : Normalized inter-annual average cycle of VRE power generation (solar- (red), wind- (black) and RoR hydro- (blue) power) and load (green) in France (a) and Finland (b) over the period 1980-2012 (see equation 6 for the normalization procedure) ; For information only, light shaded areas show the distance between the 25th and 75th percentiles of the variable obtained for the 1980-2012 period for each calendar day ; the x-axis gives the initial letters of the months of the year ; the value of each variable on the y-axis is given in percentage of the average load.

Solar power presents in all regions a similar seasonal pattern with a high production period during the summer (Figure 2). The patterns have larger amplitude in Finland due to the important daylight time changes along the years. Table 1 illustrates how the time variability of solar power decreases with decreasing the latitude (see the Coefficient of Variation, hereafter denoted as CV, of daily data ranging from 0.89 to 0.57, Table 1). Seasonal wind power pattern is anti-correlated with the seasonal solar power pattern (Figure 2). On average, high wind power generation is observed during winter and low generation during summer. Wind power time variability is more homogeneous in space than solar power (CV ranging from 0.88 to 0.90, Table 1). Run-of-the river power seasonal patterns result from precipitation seasonality and snow pack dynamics. The latter is influenced by both the altitude and the latitude. RoR seasonal patterns in regions with either high altitudes or located at high latitudes show important production during the snowmelt period from spring to early summer and low production during winter (Figure 2b). For other regions where the hydrological regime is rainfall dominated (Figure 2a), the RoR seasonal patterns follow more or less the rainfall seasonality, with, in this part of the world, higher values during winter.

RegionPV PowerWind PowerHydro Power60% wind 40% solar Energy load
Finland 0.89 (6) 0.88 (6) 0.55 (3) 0.58 (4) 0.16
France 0.57 (7) 0.90 (11) 0.60 (8) 0.51 (6) 0.08

Table 1 : Coefficient of variation (CV) of the daily power time series from each VRE (CV = standard deviation / mean) and for the von Bremen solar/wind optimal mix (von Bremen, 2010). CV of daily energy load in last column. Numbers within brackets give the ratio values between CV from each VRE and the load ‘s CV.

3.2 Penetration functions for solar, wind, and RoR power

Figure 3 shows penetration functions for France and Finland regions and for solar, wind and RoR power. For low production factors (i.e. from 0 to 0.4), the daily power generation from all VREs never exceed the daily energy demand (not shown). In such a case, there is no waste of energy and the penetration rate equals the factor γ. When increasing the power capacity, i.e. increasing the γ factor, the power generation can exceed the energy load during some time periods. If no storage facility is available, the fatal generation is next wasted or simply not produced by shutting down the plants for security reasons. As a consequence, the penetration rate becomes lower than the average VRE penetration. For very high values of γ, the penetration rate of a given VRE reaches a sill corresponding to the configuration where the generation is always higher than the load.

The penetration rate function can be significantly different for one energy source to another (Figure 3). In France for instance, wind penetrates the least and RoR penetrates the most. We note that the VRE penetration rates are ordered regarding the time variability of the VRE power generation (illustrated with the CV on Table 1). This result is due to the almost nil time variability of the energy load (CV = 0.08 and CV=0.16 for France and Finland, respectively). It would not be valid anymore if the load were fluctuating with a similar magnitude than the VRE power. In such a case, a high correlation would be required for matching the demand, which is not the case here (not shown).

In Figure 3, we additionally note that the penetration rate also differs from one region to another. As discussed previously, wind power penetrates the least in France which is not the case in Finland. Solar power penetrates the least in Finland but its penetration is somehow high in France. It is interesting to note that in Finland solar and wind powers have similar time variability in term of CV (i.e. 0.89 and 0.88 respectively). However, we observe a higher penetration rate for wind than for solar power, especially for high VRE production factor γ. This might be explained looking at the significant anti-correlation of solar with the energy load (the patterns are in opposition in Figure 2b). In such a case, it seems such a significant anti-correlation handicaps the solar power penetration.

Figure 3 : Evolution of the penetration rate PE with the average VRE generation factor γ for a) France and b) Finland and for solar (red), wind (black), hydro (blue) VREs and the von Bremen optimal mix (60% wind, 40% solar, orange).

As a first conclusion, we can note that, considering a low variable energy load (Table 1), time variability of VRE power generation seems to be the main driving factor of the penetration rate.

Looking now at the optimal mix suggested by past studies such as the one of von Bremen [2010], namely 40 % of solar power and 60 % of wind power, we note that the penetration of this mix exceeds the penetration rates obtained with a single energy source (Figure 3). This results from lower time variability of the generation produced by the mix (Table 1) and from the reduced anti-correlation obtained from solar power (not shown).

3.3 Increasing penetration with RoR hydropower integration

We now focus on the 100 % generation scenario (i.e. considering an average VRE production factor γ equal to 1). Figure 4 shows the penetration rate for each possible mix among wind, solar and RoR hydro power in France and Finland. It highlights that in these regions, the penetration rate significantly increases when integrating RoR hydropower with solar and wind. The black arrow in Figure 4 goes from the optimal wind-solar power mix to the optimal wind-solar-RoR power mix. The orientation of the arrows indicates whether RoR replaces more solar than wind power, or conversely. An angle between the arrow and the horizontal axis (i.e. the axis showing a constant share of wind power) lower than 30°, means that RoR hydro power substitutes more solar power than wind power (and conversely when this angle is greater than 30°). For instance, Figure 3a shows for France that the optimal integration of RoR hydro power would replace more wind than solar power and Figure 3b.

Figure 4, we first note that the optimal wind-solar mix penetrates more in France than in Finland. Table 2 gives the penetration rates obtained with the “optimal” wind-solar mix for the different regions. These optimal shares maximize the penetration rate and thus differ from the one obtained by von Bremen [2010] the latter being obtained minimizing the monthly residual load variance (the von Bremen optimal share was also obtained considering Europe as a whole and for a much smaller time period). We note that the optimal share obtained for each region may have higher time variability than the one suggested by von Bremen [2010], as it is the case for Finland for instance. However in such a case, the optimal share allows to limit the significant anti-correlation brought by solar power (not shown).

Table 2 : Optimal shares and corresponding CV, correlation coefficient r and penetration rate PEopt for a wind / solar mix and for a wind / solar / hydro mix. Shares are given for solar (SPV), wind (SW) and RoR (SRoR) power for the 12 regions. The numbers in brackets give the penetration increase when integrating RoR hydro power into the solar/wind mix.

Figure 4 : VRE penetration rate (%) for all wind/solar/hydro mix configurations in France (left) and Finland (right) when a 100 % VRE production scenario is considered (the average VRE generation factor for the 1980-2012 period is γ=1). The x-axis gives the share of solar power (sPV [%]), the left axis gives the share of RoR power (sRoR [%]), and the right axis gives the share of wind power (sW [%]). Red, black and blue bullets correspond respectively to a 100% solar, 100% wind and 100% hydro mix scenario. Horizontal gray lines show mix with the same wind share. 60° increasing (resp. decreasing) gray lines show mix with the same solar power share (resp. RoR power share). The black square corresponds to an equal share of each energy source. The black arrow shows the shift of the optimal VRE share and of the corresponding penetration rate when replacing a fraction of solar and wind power by RoR hydro power. It goes from the optimal wind-solar mix to the optimal wind-solar-RoR mix (i.e. the mix giving the highest penetration rate). The orientation of the arrows indicates what RoR replaces more wind than solar or conversely. For instance, a horizontal arrow indicates that RoR only replaces solar power (with no change in the wind rate). Conversely, an angle of 60° between the arrow and the wind axis indicates that RoR only replaces wind power (with no change in the solar rate).

Not surprisingly, the optimal combination of wind and solar power obtained for France and Finland regions are different.. Thanks to its low time variability, the share of solar power is high in France, such (i.e. sPV = 60 %). It is lower in Finland (sPV = 35 %) where wind power is more favorable (indeed, in Northern countries solar power is highly variable and significantly anti-correlated with the energy load).
When integrating RoR hydropower, the global penetration rate increases for both regions by about 6 % (Table 2). The benefit from integrating RoR power into the power mix actually depends on the different complementarity in time between RoR hydropower and wind and solar power, i.e. the way RoR power integration may decrease the time variability of the power generation and to improve the correlation with the energy load. As a result, the optimal share of RoR hydropower into the energy mix differs from one region to another. Its fraction is quite high (40 % in France and 50 % in Finland).


At the European scale, several past studies looked at the potential advantages of combining solar and wind power. Other renewable energies such as biomass and hydropower were considered, either directly or not, as storage facilities able to balance the mismatches between load, wind and solar power generation. The literature shows that the optimal share between wind and solar power varies according to the time scale. For Europe and at daily time scale, it is usually considered as a mix composed by 60 % of wind power and 40 % of solar power. In this study, we integrated run-of-the-river (RoR) power with solar and wind power. We analyze RoR power integration over 2 different regions located in France and Finland.

This work has been extended to twelve regions in Europe (Figure 5) [François et al. 2016a]. The penetration rate is computed for all the possible combination of the three considered CREs. Taking into account a 100 % renewable scenario (i.e. an average CRE generation factor γ=1), we show that RoR power integration increases the overall CRE penetration (about 6+ percentage points for both regions, Table 2). Increasing penetration rate actually appears to result from a trade-off between i) decreasing the difference in time variability between generation and load, and ii) improving the generation-load correlation (which often means limiting the anti-correlation coming from either solar or RoR hydro power).

Figure 5 : Similar to Figure 4 for 12 European regions

The optimal solar-wind-RoR mixes show a high rate of RoR power for both regions (40 % in France and 50 % in Finalnd). One could rightly point out that such a high share of RoR hydropower is not realistic in some areas, for some technical and/or economic reasons. However, our results show that i) it is worth integrating even a small amount of RoR hydropower into a solar-wind mix since the penetration always increase and ii) it is possible to optimize the RoR hydropower integration for each climate region by ‘replacing’ more solar or wind power contribution.


This work is part of the FP7 project COMPLEX (Knowledge based climate mitigation systems for a low carbon economy ; Project FP7-ENV-2012 number : 308601 ;

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