Amount Of Stored Energy Research Articles

Robust Predictive Control of High-Density Cascaded DC Voltage Link Power Converters

Cascaded dc voltage link power converters typically employ a significant amount of energy storage at the intermediate link. The dc bus voltage is assumed to be stiff enough to provide decoupling between the source and load, allowing dynamic regulation functions to be implemented at the load and source terminals independently. In these cases, the size of the dc bus capacitance is dictated by requirements of steady-state ripple voltage, ripple current rating, ride-through considerations, and, more importantly, voltage overshoot during source and load transients. Design tradeoffs in realizing a stable system with acceptable transient performance often place a lower bound in the value of dc bus capacitance. In this paper, a robust predictive controller based on integrated and coupled control at the intermediate dc link, source, and load terminals is presented. The approach permits the use of a small amount of intermediate energy storage compared to conventional decoupled designs. The predictive control aspect of the proposed approach features cost function minimization and accurate duty ratio calculations based on converter model that accounts for small values of dc link capacitance. Although this allows stable operation of the system, it leads to persistent steady state error and transient overshoot voltages. The robust aspect of the proposed approach is based on the theory of variable structure systems. It introduces a capacitor charge restoration function that overcomes the drawbacks of the predictive control by squarely addressing uncertainty of model parameters and operating conditions. The resulting significant reduction in size of the capacitive reactive components opens the prospect of replacing electrolytic capacitors that have a limited life span with film capacitors with much longer life in emerging applications. The proposed approach is presented in a step-by-step manner using a dc-to-dc converter example and further extended to a dc-to-ac inverter case. Extensive computer simulations and experimental results from a laboratory-scale prototype of an example system are used to demonstrate the viability of the proposed controller.

Mountain Gravity Energy Storage: A new solution for closing the gap between existing short- and long-term storage technologies

The world is undergoing an energy transition with the inclusion of intermittent sources of energy in the grid. These variable renewable energy sources require energy storage solutions to be integrated smoothly over different time steps. In the near future, batteries can provide short-term storage solutions and pumped-hydro storage can provide long-term energy storage with large generation capacities. However, none of these technologies can provide long-term energy storage in grids with small demand. This paper proposes a new storage concept called Mountain Gravity Energy Storage (MGES) that could fill this gap in storage services. MGES systems move sand or gravel from a lower storage site to an upper elevation. The higher the height difference the greater the amount of stored energy in a given installed capacity, as this technology is constrained to the topography of the location. MGES cost varies from 50 to 100 $/MWh of stored energy and 1–2 M$/MW of installed capacity. MGES could be a feasible option for micro-grids, for example, small islands and isolated areas, and power systems where electricity costs are high, demand for energy storage is smaller than 20 MW with monthly or seasonal storage requirements.

Effects of wavy wall and Y-shaped fins on solidification of PCM with dispersion of Al2O3 nanoparticle

In current modeling, solidification process within a three-dimensional triplex tube was numerically studied. In two sides, the cold water flow is used while the middle tube contains RT82. The purpose of the current article is investigating the impacts of using nanoparticles, fin, and the combination of both of them on thermal characteristics during solidification in an energy storage unit. Also, the amount of stored energy has been investigated over time, and the influences of temperature and water velocity were scrutinized. The results revealed some substantial improvements in the solidification rate by adding fins or nanoparticles. It was indicated that using a combination of these two heat transfer enhancement methods presents a better enhancement compared to when either of these two methods is employed alone.

Superior Doped Olivine Cathodes for Fast Charge/Discharge Lithium Batteries

In recent years, the lack of high-performing electrical energy storage systems is seriously bottlenecking the operation of appliances in several fields, that include portable electronics, electric automotive, and stationary devices [1]. Until now, lithium batteries (LiBs) are the highest-performing systems that could address satisfactorily all the requirements of such appliances [2]. Indeed, LiBs show a high specific capacity, a high efficiency, and a long lifespan [3]. However, improvements are still needed in the operating potential (that influences the specific energy and power of the LiBs) and in the rate capability properties of the cathodes. Indeed, electric vehicles need high power during acceleration, and a large amount of stored energy to achieve a sufficient mileage. Herein we describe the synthesis and the study of an innovative family of high-energy and high-rate cathodes for application in LiBs. The structure of a high-performing olivine material of the type LiMPO4 (M = Fe, Ni, and Co) [4] has been doped with high-valence transition metal ions (V(V), Nb(IV), or Ta(IV)). In a first step, the synthesis procedure has been optimized. Five different materials have been obtained, as follows: (i) LFNCVP is a vanadium-doped olivine obtained under oxidizing conditions; (ii) LFNCVP/C is a vanadium-doped olivine obtained under partially reducing conditions (graphite is added during the pyrolysis); (iii) LFNCVP/H is a vanadium-doped olivine obtained under reducing conditions (pyrolysis is carried out under a hydrogen atmosphere); (iv) LFNCNP is a niobium-doped olivine obtained under oxidizing conditions; and (v) LFNCTP is a tantalum-doped olivine obtained under oxidizing conditions. The effects of the different synthesis protocols and ion insertion on the structural, morphological, and electrochemical properties of the cathodes have been thoroughly investigated. The composition of the cathodes has been evaluated by means of Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES), the morphology and size distribution have been gauged by Scanning Electron Microscopy (SEM) and High-Resolution Transmission Electron Microscopy (HR-TEM); the structure has been revealed through powder X-Ray Diffraction (XRD) and IR spectroscopy techniques. The electrochemical performance has been investigated by Cyclic Voltammetry (CV), Electrochemical Impedance Spectroscopy (EIS), and coin battery charge/discharge tests at different current rates. As expected (see Figure 1), the proposed materials reveal a high performance in terms of working potential (4.0÷5.0 V vs. Li/Li+), specific capacity (149 mAh∙g-1), and specific energy (656 mWh∙g-1). Moreover, the insertion of high-valence transition metals is able to boost the rate capability of the cathodes, allowing for fast charge and discharge processes without depleting the cathodes.

Characterization of heat load profiles in buildings and their impact on demand side flexibility

A data set of heat load measurements for 197 buildings from different building categories (apartment blocks, hotels, nursing homes, offices and schools), have been analysed to evaluate the potential for peak shaving. A moving average filter is applied to investigate how smoothening of the load profiles can reduce the peak loads. It is shown that for short term peak shaving, apartment blocks and hotels have the highest potential (around 8% for a two hour period), while for longer term peak shaving, the results are more even for all the building categories. Schools stand out, with a large difference in heat consumption between inside and outside opening hours, leading to a large flexibility potential on daily basis, but this would require a large amount of stored energy. As it is difficult to control, and thereby reduce the peaks for unknown loads, a prediction model is applied to the data, to analyse the predictability. It is shown that the peak shaving potential is reduced 90-30 % when analysing only the predictable loads. The biggest difference is in the short-term potential for apartment blocks and hotels, while difference is smaller in the long-term (24-hour) peak shaving potential.

Compression–Expansion Processes for Chemical Energy Storage: Thermodynamic Optimization for Methane, Ethane and Hydrogen

Several methods for chemical energy storage have been discussed recently in the context of fluctuating energy sources, such as wind and solar energy conversion. Here a compression–expansion process, as also used in piston engines or compressors, is investigated to evaluate its potential for the conversion of mechanical energy to chemical energy, or more correctly, exergy. A thermodynamically limiting adiabatic compression–chemical equilibration–expansion cycle is modeled and optimized for the amount of stored energy with realistic parameter bounds of initial temperature, pressure, compression ratio and composition. As an example of the method, initial mixture compositions of methane, ethane, hydrogen and argon are optimized and the results discussed. In addition to the stored exergy, the main products (acetylene, benzene, and hydrogen) and exergetic losses of this thermodynamically limiting cycle are also analyzed, and the volumetric and specific work are discussed as objective functions. It was found that the optimal mixtures are binary methane argon mixtures with high argon content. The predicted exergy losses due to chemical equilibration are generally below 10%, and the chemical exergy of the initial mixture can be increased or chemically up-converted due to the work input by approximately 11% in such a thermodynamically limiting process, which appears promising.

The role of energy storage in deep decarbonization of electricity production

Deep decarbonization of electricity production is a societal challenge that can be achieved with high penetrations of variable renewable energy. We investigate the potential of energy storage technologies to reduce renewable curtailment and CO2 emissions in California and Texas under varying emissions taxes. We show that without energy storage, adding 60 GW of renewables to California achieves 72% CO2 reductions (relative to a zero-renewables case) with close to one third of renewables being curtailed. Some energy storage technologies, on the other hand, allow 90% CO2 reductions from the same renewable penetrations with as little as 9% renewable curtailment. In Texas, the same renewable-deployment level leads to 54% emissions reductions with close to 3% renewable curtailment. Energy storage can allow 57% emissions reductions with as little as 0.3% renewable curtailment. We also find that generator flexibility can reduce curtailment and the amount of energy storage that is needed for renewable integration.

Investigation of chaos and memory effects in the Bonhoeffer-van der Pol oscillator with a non-ideal capacitor

In this paper, the voltage fluctuations of the Bonhoeffer van der Pol oscillator system with a non-ideal capacitor were investigated. Here, the capacitor was modeled, using a fractional differential equation in which the order of the fractional derivative, α, is also a measure of the memory in the dielectric. The governing fractional differential equation was derived using two methods, namely a differential and integral approach. The former method utilized a hierarchical resistor-capacitor (RC) ladder model while the latter utilized the theory of the universal dielectric-response. It was found that the dynamical behavior of the potential across the capacitor was affected by the parameter α and, therefore, the memory of the system. Additionally, findings indicate that an increase in the memory parameter was associated with an increase in the energy stored in the dielectric. Furthermore, the effects of the dynamical behavior of the voltage on the capacity of the dielectric to store energy was examined. It was found that oscillation death resulted in a higher amount of stored energy in the dielectric over time, as compared to behavior, which displayed relaxation oscillations or chaotic fluctuations. The relatively-lower stored energy resulting from the latter types of dynamical behavior appeared to be a consequence of the memory effect, where the present accumulation of energy in the capacitor is reduced by previous decreases in the potential. Hence, in this type of scenario, the dielectric material can be thought of as “remembering” the past behavior of the voltage, which leads to either a decrease, or an enhancement in the stored energy. Moreover, an increase in the fractional parameter α, under certain conditions, led to the earlier onset of the chaotic voltage oscillations across the capacitor. On the other hand, the corresponding phase portraits showed that the chaotic behavior was heightened, in general, with a decrease in α. The non-ideal capacitor was also found to have a transitory nature, where it behaves more like a resistor as α → 0, and conversely, more like a capacitor as α → 1. Here, a decrease in α was linked to an enhanced metallic character of the dielectric. Finally, a possible link between the complexity of the voltage noise fluctuations and the metallic character of the non-ideal capacitor will be discussed.

Influence of Multiwalled Carbon Nanotubes as Additives in Biomass-Derived Carbons for Supercapacitor Applications.

Glucose-derived carbon/carbon nanotube (CNT) hybrid materials were prepared by hydrothermal carbonization of glucose in the presence of CNTs and subsequent carbonization, physical activation, or chemical activation. The proportion of CNTs added during the hydrothermal polymerization of glucose was varied to ascertain the optimum dose to maximize the performance of the carbon hybrids in supercapacitor applications. Both the thermal treatment applied and the addition of CNTs lead to changes in the textural and chemical properties of the activated carbons. It was observed that samples bearing CNTs exhibit higher number of nucleation centers for glucose oligomers to polymerize, and consequently, the behavior of the hydrothermal carbon toward activation differs according to the activating agent employed. Moreover, the initial chemical speciation dominated by acidic groups shifts to more basic functionalities (quinones and carbonyl groups) with the addition of CNTs. The effect of the different physicochemical properties of the prepared carbons on their electrochemical behavior was evaluated. The addition of 2 wt % of CNTs and subsequent chemical activation leads to electrode materials yielding 206 F g-1 and 78% of capacitance retention up to 0.8 V and 20 A g-1 and high rate cyclability (97% after 5000 cycles). The outstanding performance is ascribed to the high surface area, narrow mesopores, and phenol/carbonyl surface functionalities, which enhance molecular diffusion, the amount of stored energy, and electronic transportation, respectively.

Design and construction of the Cadet-M unmanned marine platform using alternative energy

Environmental monitoring has become an urgent task in recent years in connection with the deterioration of the environmental situation caused by industrialization [1]. Usually, manned vessels with measuring equipment and personnel serving it on board were used for these purposes, but with the development of technology, full automation of this process became possible. The problem of the need to use human resources is solved by applying an autonomous vessel control system. However, the big problem remains, which is the need to refuel the vessel in connection with the finite amount of stored energy. This problem is solved by using renewable energy, an example of which is solar energy, on measuring platforms. This article will discuss methods for developing platforms controlled by the autopilot and using solar energy, using the Cadet-M platform as an example.

Critical Phenomena in Portevin–Le Chatelier effect during compression of aluminium-magnesium alloy and stored energy evolution

This work was inspired by works of Gianfranco D’Anna (2000) where the Portevin-Le Chaˆtelier effect (PLC) was investigated by compressing Al-Mg alloy specimen in a very large deformation range and the results were interpreted from the viewpoint of phase transitions and critical phenomena. Two critical points where deformation process changes from “laminar” to jerky flow and back were noticed. We found that the second critical point where the rate of the serrations is decreased before the macroscopic fracture is not reachable for some alloys even with proposed geometry. We have tested 2 sets of specimens made of the same AMG6 alloy (~6% of magnesium) but with different amount of Si obtained from different producers. Specimens with a higher amount of Si tends to fracture before reaching the second point.Also, we have measured the amount of stored energy which can be recovered as heat during the annealing process. We used the differential scanning calorimeter STA "Jupiter" 449. We found that the amount of this energy sharply increases with the beginning of PLC serrations (first critical point) and drops at a second critical point or at macroscopic fracture. This can be related to a special type of critical phenomena—structural scaling transitions in mesodefect ensembles and associated structural relaxation mechanisms Naimark (2016)

Stored energy release in neutron irradiated silicon carbide

The purpose of this investigation is to experimentally quantify the stored energy release upon thermal annealing of previously irradiated high-purity silicon carbide (SiC.) Samples of highly-faulted polycrystalline CVD β-SiC and single crystal 6HSiC were irradiated in a mixed spectrum fission reactor near 60 °C in a fluence range from 5 × 1023 to 2 × 1026 n/m2 (E > 0.1 MeV), or about 0.05–20 dpa, in order to quantify the stored energy release and correlate the release to the observed microscopic swelling, lattice dilation, and microstructure as observed through TEM. Within the fluence of this study the crystalline material was observed to swell to a remarkable extent, achieving 8.13% dilation, and then cross a threshold dose for amorphization at approximately 1 × 1025 n/m2 (E > 0.1 MeV) Once amorphized the material attains an as-amorphized swelling of 11.7% at this irradiation condition. Coincident with the extraordinary swelling obtained for the crystalline SiC, an equally impressive stored energy release of greater than 2500 J/g at the critical threshold for amorphization is inferred. As expected, following amorphization the stored energy in the structure diminishes, measured to be approximately 590 J/g. Generally, the findings of stored energy are consistent with existing theory, though the amount of stored energy given the large observed crystalline strain is remarkable. The overall conclusion of this work finds comparable stored energy in SiC to that of nuclear graphite, and similar to graphite, a stored energy release in excess of its specific heat in some irradiation conditions.

Numerical investigation of melting in a cavity with vertically oriented fins

This paper investigates the effect of vertical fins, as an enhancement technique, on the heat transfer rate and energy density of a latent heat thermal energy storage system. This contributes with knowledge on the interaction of heat transfer surface with the storage material for optimizing storage capacity (energy) and power (heat transfer rate). For the assessment, numerical modeling is employed to study the melting process in a two-dimensional rectangular cavity. The cavity is considered heated isothermally from the bottom with surface temperatures of 55 ˚C, 60 ˚C or 70 ˚C, while the other surfaces are insulated from the surrounding. Aluminum and lauric acid are considered as fin/enclosure material and phase change material, respectively. Vertical fins attached to the bottom surface are employed to enhance the charging rate, and a parametric study is carried out by varying the fin length and number of fins. Thus, a broad range of data is provided to analyze the influence of fin configurations on contributing natural convection patterns, as well as the effects on melting time, enhanced heat transfer rate and accumulated energy. The results show that in addition to increasing the heat transfer surface area, the installation of vertically oriented fins does not suppress the natural convection mechanism. This is as opposed to horizontal fins which in previous studies have shown tendencies to reduce the impact of natural convection. This paper also highlights how using longer fins offers a higher rate of heat transfer and a better overall heat transfer coefficient rather than increasing the number of fins. Also, fins do not only enhance the heat transfer performance in the corresponding melting time, but also maintain similar total amount of stored energy as compared to the no-fin case. This paper discusses how this is the result of the enhanced heat transfer allowing a larger portion of sensible heat to be recovered. For example, in the case with long fins, the relative mean power enhancement is about 200% with merely 6% capacity reduction, even though the amount of PCM in the cavity has been reduced by 12% as compared to the no-fin case. Although the basis for these results stems from the principles of thermodynamics, this paper is bringing it forward with design consideration. This is because despite its importance for making appropriate comparisons among heat transfer enhancement techniques in latent heat thermal energy storage, it has not been previously discussed in the literature. In the end, the aim is to accomplish robust storage systems in terms of power and energy density.

Numerical Study of Latent Heat Thermal Energy Storage Enhancement by Nano-PCM in Aluminum Foam

Thermal storage system (TES) with phase change material (PCM) is an important device to store thermal energy. It works as a thermal buffer to reconcile the supply energy with the energy demand. It has a wide application field, especially for solar thermal energy storage. The main drawback is the low value of thermal conductivity of the PCM making the system useless for thermal engineering applications. A way to resolve this problem is to combine the PCM with a highly conductive material like metal foam and/or nanoparticles. In this paper a numerical investigation on the metal foam effects in a latent heat thermal energy storage system, based on a phase change material with nanoparticles (nano-PCM), is accomplished. The modelled TES is a typical 70 L water tank filled with nano-PCM with pipes to transfer thermal energy from a fluid to the nano-PCM. The PCM is a pure paraffin wax and the nanoparticles are in aluminum oxide. The metal foam is made of aluminum with assigned values of porosity. The enthalpy-porosity theory is employed to simulate the phase change of the nano-PCM and the metal foam is modelled as a porous media. Numerical simulations are carried out using the Ansys Fluent code. The results are shown in terms of melting time, temperature at varying of time, and total amount of stored energy.

Online Learning Schemes for Power Allocation in Energy Harvesting Communications

We consider the problem of power allocation over one or more time-varying channels with unknown distributions in energy harvesting communications. In the single-channel case, the transmitter chooses the transmit power based on the amount of stored energy in its battery with the goal of maximizing the average rate over time. We model this problem as a Markov decision process (MDP) with transmitter as the agent, battery status as the state, transmits power as the action and rate as the reward. The average reward maximization problem can be modeled by a linear program (LP) that uses the transition probabilities for the state-action pairs and their reward values to select a power allocation policy. This problem is challenging because the uncertainty in channels implies that the mean rewards associated with the state-action pairs are unknown. We therefore propose two online learning algorithms: linear program of sample means (LPSM) and Epoch-LPSM that learn these rewards and adapt their policies over time. For both algorithms, we prove that their regret is upper-bounded by a constant. To our knowledge this is the first result showing constant regret learning algorithms for MDPs with unknown mean rewards. We also prove an even stronger result about LPSM: that its policy matches the optimal policy exactly in finite expected time. Epoch-LPSM incurs a higher regret compared with the LPSM, while reducing the computational requirements substantially. We further consider a multi-channel scenario, where the agent also chooses a channel in each slot, and present our multi-channel LPSM (MC-LPSM) algorithm that explores different channels and uses that information to solve the LP during exploitation. MC-LPSM incurs a regret that scales logarithmically in time and linearly in the number of channels. Through a matching lower bound on the regret of any algorithm, we also prove the asymptotic order optimality of MC-LPSM.

Condition and reproductive strategy of the Argentina sphyraena, a cold-water species in the Mediterranean Sea

We evaluate the condition and reproductive status of the lesser silver smelt, Argentina sphyraena in the north-western Mediterranean Sea. We describe for the first time several life history traits of this species, i.e. condition, reproductive cycle, fecundity, breeding strategy, oocyte recruitment and egg quality, and evaluate the links between these traits. We also contrast condition and reproduction parameters in two study areas with different environmental conditions: the Gulf of Lion and the Balearic Sea. Our results indicate that A. sphyraena is a capital breeder with group-synchronous oocyte development and determinate fecundity. Energy requirements for reproduction are mostly met by lipids stored in the mesentery which is the main fat deposit and a good indicator of condition; this means that condition can be estimated visually and easily using a fat scaling technique. Our results show that, in terms of condition and reproduction, this species performs better in the colder and more productive Gulf of Lion than in the warmer and less productive Balearic Sea, as evidenced by the amount of stored energy and reproductive strategy. These findings suggest that suboptimal environmental conditions may have a negative impact on the condition and reproduction strategy of cold-water species, which will ultimately affect their abundance and distribution.

Energy Storage by Melting Commercial Change Phase Materials in Hexagonal-Shaped Heat Exchangers

A two-dimensional melting of a technical-grade phase-change material is modeled. The phase-change material is placed in the annular space formed by an outer regular hexagonal tube and an inner tube. A nonorthogonal boundary fitted coordinate method is implemented on a staggered grid arrangement. The mushy region of the impure phase-change material has been accommodated through the enthalpy-porosity scheme. A set of parametric studies is carried out. Selected results are presented as a function of time for the velocity and temperature fields, the cumulatively stored energy, the total melt fraction, and the average Nusselt number on the inner tube. The oblate-shaped inner tube results in the highest melting rate and stores the maximum energy among the studied units irrespective of the shape and vertical position of the inner tube. Among the three vertical positions of the inner circular tube, when the center of the inner tube is placed at one-third height from the base of the outer tube, it shows the greatest thermal efficiency, and the worst performance is obtained for the upper position of the inner tube at the two-thirds height of the outer tube. With the increase in the Rayleigh number (wall temperature), the amount of energy storage is enhanced.

New roles of metal–organic frameworks: Fuels for aluminum-free energetic thermites with low ignition temperatures, high peak pressures and high activity

Aluminum-based thermites are widely used in gas generators, propulsions, explosives, and welding because these materials can release a large amount of stored energy on combustion. However, one of the biggest problems in the traditional aluminum-based thermite systems is excessive oxidation of the aluminum particle before combustion, resulting in a decrease of the active aluminum content. Here, we report a new-concept aluminum-free thermites based on an energetic metal–organic framework [Cu(atrz)3(NO3)2]n (MOF(Cu), atrz = 4,4′-azo-1,2,4-triazole) as a fuel. Compared with the traditional aluminum-based thermites, these new thermites exhibit superior performances such as low electrostatic discharge sensitivities, low ignition temperatures, high heats of reaction, high peak pressures, high activity, and production of very few solid residues. It is anticipated that this work will open a new field for the application of MOFs, while laying the groundwork for the development of new energetic materials.

Initiation of the Decomposition of a Semi-Transparent Mixture of Energetic Materials

In this paper, we propose a model for the heating and decomposition of a binary mixture of energetic materials by a short laser pulse which takes into account melting and the formation of a two-phase zone and the decomposition reaction of the individual components of the mixture. A binary solution of furazanotetrazine-dioxide (C2N6O3) and dinitrazapentane (C3H8N4O4) was studied as a model system. The pressure change in the reaction zone was calculated, and the effect of pressure on the rate of decomposition reactions was examined. Numerical investigations were performed to study the dynamics of the process and determine the main stages of the process: melting, the propagation of reaction zones in the mixture, the rapid development of an explosion or the termination of reactions, depending on the amount of stored energy. The influence of the optical properties of the mixture on the initiation dynamics was demonstrated.

Probabilistic siting and sizing of energy storage systems in distribution power systems based on the islanding feature

Distributed storage systems embedded in distribution power systems could complement renewable generation and improve their operation, reducing peak power levels and providing supply support to island zones in the cases of outages. This paper proposes a multi-objective optimisation, which takes advantage of the possibility of operating in an island mode. The optimisation considers the siting and sizing of storage systems placed on power distribution systems with radial topology. The objectives to be minimised are: the amount of energy storage, power losses and expected energy not supplied (EENS). Loads and generators are uncertainty variables, and a probabilistic power flow based on the point estimate method helps with assessing the electrical parameters.The optimisation uses the IEEE-34 and IEEE-123 test feeders. The Monte Carlo simulation benchmarks some results. The final results show that storage systems could reduce the peaks of power required from the central network and improve other electrical parameters. In addition, those systems with higher interruption probabilities or those working near their operation limits could benefit from storage systems.This point of view is different from other authors’. Here, storage energy systems and the island mode of operation are defined by a probabilistic point of view. The siting and sizing of storage energy systems is decided from data obtained on the probabilistic power flow and the universal generating function.