Load variability, not storage tech, decides when hybrid energy storage pays off

Hybrid energy storage systems, which pair two storage technologies with complementary strengths such as a battery with a supercapacitor, are widely promoted as a way to cut losses and shrink system dimensions. Yet a new systematic study suggests that the celebrated benefits of these hybrids depend far less on the storage technologies themselves than on one deceptively simple property of the electricity demand they must serve: how much the load fluctuates. The dominant predictor of both loss savings and sizing gains, the researchers report, is the variation coefficient of the load profile, defined as its standard deviation divided by its mean, with Pearson correlation coefficients of approximately 0.9.

The study, published in the journal Energy Informatics by Sebastian Günther, Astrid Bensmann and Richard Hanke-Rauschenbach, tackles a long-standing weakness in the hybrid storage literature. Previous case studies had reported loss savings mostly between 0 and 30 percent, and in some cases up to 70 percent, but those numbers are hard to generalize because each study used different applications, load profiles, dispatch strategies, reference systems and modeling assumptions. More importantly, the authors argue, case studies entangle two distinct mechanisms: the way a load is distributed across two storage units during operation, and the simple fact that one technology may have intrinsically better efficiency or lower self-discharge than the other.

To disentangle these effects, the team employed the concept of loss-equivalent storage units. Two storage units are loss-equivalent if they produce the same total energy losses when operated independently over a given load profile, even if one loses more energy through conversion inefficiency and the other through self-discharge. By constructing hybrid pairs from parameter tuples that are individually equivalent to a reference single storage system, any advantage the hybrid shows can be attributed to its systemic operational behavior rather than to a trivially superior parameter set. The authors had previously shown theoretically that a hybrid cannot outperform a correctly sized single storage system when both units share identical efficiency and self-discharge parameters, and that outperformance requires distinct loss characteristics; the new study confirms this empirically, with gains exactly zero when the two units are parameterized identically.

The technical machinery behind the results is a linear storage model formulated as a cascaded, bi-level quadratic programming problem. Each storage unit is characterized by constant rated power limits, an energy capacity, constant charge and discharge efficiencies, and a linear self-discharge rate. Conversion losses are proportional to instantaneous storage power, while self-discharge losses are proportional to the stored energy content. For each load profile, an inner optimization finds the minimal energy and power dimensions a single storage system needs, while an outer level searches for loss-equivalent parameter tuples that achieve defined total losses with a defined ratio of efficiency-related to self-discharge-related losses. A second optimization then minimizes the operational burden of the base storage while holding the hybrid’s dimensions fixed. Dispatch is determined by offline optimization rather than a real-time energy management system, which the authors note keeps the results untangled from the behavior of specific control strategies.

The scale of the parameter study is considerable. The researchers drew on 1024 distinct load profiles from the n1024 dataset of the Energy Systems Time Series Suite, a collection derived from diverse real-world energy systems including photovoltaic installations, wind farms, residential, commercial and industrial loads, microgrids, machine tools, production plants, electric vehicles and rail transport, supplemented by semi-artificial profiles generated to increase diversity. Half of the profiles change sign, representing discharge with intermittent charging events. Varying the reference efficiency across three values, the reference loss ratio across six values, the deviation between the two storage units across five levels, and the specific power pairing across nine combinations produced 829,440 distinct hybrid optimizations, more than 800,000 parameter configurations in total, each recorded alongside 119 time-series features of the load profiles.

The headline finding concerns what drives the gains. Across the densely populated range of variation coefficients up to approximately 5, the relationship between load variability and relative sizing gains is well represented by a linear trend, with a Pearson correlation coefficient of 0.89. Higher variability means stronger differences between sustained and transient demands, giving the dispatch optimizer more room to allocate operating regimes to whichever storage unit has the more favorable loss characteristic. Low-variability profiles, by contrast, offer little potential, because there is simply not enough temporal structure to exploit. The strength of the loss-parameter deviation between the two units is the second key driver: sizing gains fall linearly as the deviation ratio decreases, vanishing entirely when both units are parameterized identically. Higher total reference losses also raise gains proportionally, since losses then contribute more to the installed capacity needed to meet the same load, but the internal composition of those losses, whether they stem from self-discharge or conversion inefficiency, turns out not to matter, and neither does the specific power pairing of the two units under ideal dispatch.

Here the study delivers its most sobering practical message. Although the statistical relationships are strong, sizing gains within realistic parameter ranges are limited and rarely exceed 3 percent, surpassing that threshold only for variation coefficients above 5, a level reached by only a limited fraction of the real-world-derived profiles in the dataset. The reason lies in the physics of storage sizing: required system dimensions are primarily driven by the energy throughput the system must handle, and losses make up only a limited slice of that throughput. A saturating relationship of the form 1 minus e to the minus x connects loss savings to sizing gains, meaning that even substantial loss reductions translate into only small reductions in installed capacity. The fitted curve in the low-sizing-gain range, where most practically relevant configurations sit, carries substantial scatter and should be read as a global statistical trend rather than a precise predictor for individual cases.

Loss savings themselves are a different story. Relative loss savings are substantial across most scenarios, often exceeding 20 percent, and remain above that level even for variation coefficients in the range of 1 to 3. Because conversion and self-discharge losses directly affect operational cost and heat generation, the authors argue that a hybrid may still be justified by operational loss reduction even when dimensional savings are negligible, particularly for applications with high energy throughput, relevant electricity costs or strict thermal constraints. Whether such a justification holds economically depends on balancing the reduced losses against the added cost, complexity and control effort of running two storage technologies instead of one. The regression models constructed to substantiate these trends achieved a coefficient of determination of 0.86 for sizing gains and 0.82 for loss savings, with the combined model indicating that loss savings are governed predominantly by load-profile variability rather than by the absolute level of total losses.

For practitioners, the variation coefficient offers a cheap first screening tool. If a candidate application’s load profile has a low variation coefficient, substantial loss-induced sizing gains should not be expected, even with strongly heterogeneous storage pairings, and relevant gains may be restricted to applications with strongly intermittent or peak-dominated demand. For sizing-related benefits, the authors conclude, matching the specific power ratios of the storage units to application requirements matters more than tailoring loss characteristics, since other mechanisms dominate the dimensional side of the design problem.

The authors are careful to delimit the scope of their claims. The study is application-independent and abstracts specific technologies to their mathematical core, which precludes direct assertions about individual real-world installations but enables general design dependencies to be identified. The storage model omits nonlinear efficiency behavior, temperature effects, degradation and transient constraints; costs are not explicitly considered, so the results support physical and operational interpretation but do not determine economic optimality. The offline optimal dispatch establishes an upper bound, and real-time energy management implementations may yield lower gains due to forecast errors or additional control constraints. The loss-equivalence framework also intentionally suppresses the intrinsic superiority of one storage unit, so the observed gains may not represent the full practical benefit of combining two real technologies. The regression relationships summarize trends within the investigated parameter space and should not be treated as exact design equations replacing application-specific simulation or techno-economic assessment. Future work, the authors suggest, should address techno-economic evaluation, technology-specific storage models, real-time energy management strategies and the prevalence of relevant load-profile characteristics in specific application domains. The data and analysis code are openly available via Zenodo and GitHub.

Subject of Research: Parameterization effects of efficiency and self-discharge on hybrid energy storage system sizing and loss savings

Article Title: The effect of efficiency and self-discharge parameterization on the sizing of hybrid energy storage systems

Article References: Günther, S., Bensmann, A., & Hanke-Rauschenbach, R. (2026). The effect of efficiency and self-discharge parameterization on the sizing of hybrid energy storage systems. Energy Informatics, 9(1), Article 72. https://doi.org/10.1186/s42162-026-00676-z

Image Credits: AI Generated

DOI: 10.1186/s42162-026-00676-z

Keywords: hybrid energy storage systems, loss-equivalent storage units, self-discharge, conversion efficiency, load profile variability, variation coefficient, sizing gains, loss savings, bi-level optimization, quadratic programming, battery-supercapacitor, Energy Informatics