How a 40% Drop in Battery Losses Could Supercharge Renewable Energy

A single lithium-ion battery, when paired with a redox-flow battery in a hybrid energy storage system, reduces total energy losses by up to 40% compared to conventional dispatch methods—especially during low-power operations, where inefficiencies typically spike. This isn’t due to brute-force engineering, but to a quiet mathematical insight: leveraging the Karush–Kuhn–Tucker (KKT) conditions to make real-time, optimal power-sharing decisions without relying on computationally heavy solvers. In a world racing to integrate volatile renewable sources like solar into stable grids, such efficiency gains aren’t just technical wins—they translate directly into longer battery lifespans, lower operating costs, and more reliable clean energy delivery.

The finding emerges from a new controller design tested on a simulated 10 MW solar photovoltaic (PV) plant equipped with a 5 MW hybrid energy storage system (HESS), split evenly between lithium-ion and redox-flow batteries, each with 5 MWh of capacity (Rios-Peñaloza et al., 2026). Unlike most existing approaches that assume constant battery efficiency, this method accounts for how efficiency changes with power output—revealing that small, seemingly negligible losses at low power can compound into major system inefficiencies. By minimizing these losses through an analytical optimization framework, the researchers demonstrate not only improved performance but also real-time feasibility, validated on hardware-in-the-loop systems.

This matters because as nations push wind and solar past 50% grid penetration, the role of storage shifts from backup to backbone. Solar farms are no longer just producers—they’re expected to provide ancillary services like frequency regulation and reserve power. But solar output fluctuates. Clouds pass. The sun sets. To smooth these variations and meet grid commitments, storage must respond rapidly and efficiently. A poorly managed battery system wears out faster, wastes energy as heat, and risks failing when the grid needs it most. The cost of such failure isn’t just financial—it’s a blow to grid reliability and public confidence in renewables.

Enter the hybrid energy storage system. The idea is simple: combine technologies with complementary strengths. Lithium-ion batteries (LIBs) respond quickly and efficiently at high power, making them ideal for sudden grid demands. Redox-flow batteries (RFBs), while slower and less efficient at peak output, offer long-duration storage, endure thousands of cycles, and decouple power from energy—meaning you can scale storage duration independently. Together, they promise flexibility. But only if you know how to share the load wisely.

The Science

The core challenge in managing a HESS is power sharing: how much of the required charge or discharge should go to each battery? Most current methods use rules of thumb—equal splitting, state-of-charge weighting, or fixed thresholds. Some employ complex optimization models, but these often require iterative numerical solvers too slow for real-time use, especially when ancillary service signals arrive on sub-second timescales.

Rios-Peñaloza, Prodanovic, and Roldán-Pérez propose a different path: instead of solving an optimization problem numerically, they solve it analytically by enforcing the Karush–Kuhn–Tucker (KKT) conditions—necessary criteria for optimality in constrained optimization. The goal is straightforward: minimize total energy losses across the HESS over each time step.

The loss in each battery depends on its efficiency, which in turn depends on the power it’s delivering or absorbing. The authors model this explicitly. For the lithium-ion battery, efficiency drops linearly with power:

$${\eta }_{\text{LIB}}(P)={\eta }_0-\kappa \cdot P$$

where $\eta_0$ is peak efficiency and $\kappa$ is a decay constant. For the redox-flow battery, efficiency is more complex, shaped by auxiliary loads like pumps and cooling systems:

$${\eta }_{\text{RFB}}(P)=c_1-c_2\cdot e^{-\alpha \cdot P}-c_3\cdot P$$

These curves, derived from experimental data (Rios-Peñaloza et al., 2026, citing [35] for RFB and [37] for LIB), reveal a critical insight: RFB efficiency is poor at low power. Why? Because even at idle, pumps must run. So at low output, the RFB’s fixed overhead dominates, dragging efficiency down. At higher power, it improves—peaking around a specific power level $P_o$—before declining again due to resistive losses.

The optimization problem becomes:

$$\min \sum _{i=1}^N{\ell }_i\text{subject to}\sum _{i=1}^N{P}_i=P^{\ast },P_{i,\min }\le P_i\le P_{i,\max }$$

where $\ell_i = (1 - \eta_i) P_i \Delta t$ is the energy lost in battery $i$ over time $\Delta t$, and $P^*$ is the total power reference from the grid or plant controller.

Using the Lagrangian:

$$\mathcal{L}=\sum _{i=1}^N{\ell }_i(P_i)+\lambda \left(P^{\ast }-\sum _{i=1}^N{P}_i\right)+\sum _{i=1}^N{\underline{\mu }}_i(P_i^{\min }-P_i)+\sum _{i=1}^N{\overline{\mu }}_i(P_i-P_i^{\max })$$

the KKT conditions yield a solution where, in the interior case, the marginal losses $d\ell_i/dP_i$ are equalized across active units. If a unit hits its power limit, it’s clamped, and the marginal loss equality no longer holds.

But here’s the catch: the RFB’s marginal loss curve isn’t monotonic. It dips at low power, violating strict convexity. That could mean multiple local minima—bad news for optimality. Yet the authors argue, and numerically confirm, that in practice, the LIB is so much more efficient in that low-power zone that the global optimum still favors using it exclusively there. The non-convexity doesn’t break the solution.

To handle on/off decisions (since starting a battery incurs a fixed loss), the algorithm evaluates three cases: both batteries active, only LIB active, only RFB active. It computes total losses for each and picks the minimum. This enumeration is feasible because the system has only two storage units.

What They Found

The researchers tested their KKT-based controller in MATLAB/Simulink and on a real-time OPAL-RT hardware-in-the-loop (HIL) setup. The simulation scenario involved a 10 MW PV plant participating in day-ahead and secondary reserve markets, with a 5 MW HESS (2.5 MW each from LIB and RFB, 5 MWh capacity each).

The key metric: energy losses in the storage system. The proposed method was compared against a conventional approach that equalizes state-of-charge (SOC) between the two batteries.

The results were striking. Across a range of power demands, the KKT-based controller reduced total losses by up to 40%. The biggest gains occurred at low power outputs—precisely where the RFB’s inefficiency is most pronounced.

Energy Loss Reduction Across Power Levels

Label	Value
0.1 MW	42
0.5 MW	38
1.0 MW	28
1.5 MW	18
2.0 MW	12
2.5 MW	8

Source: Simulated performance data from Rios-Peñaloza et al. (2026). Greatest savings occur at low power outputs where redox-flow battery inefficiency is highest.

Figure 1 shows the variation in losses when substituting the LIB with the RFB. The 3D surface reveals a sharp increase in loss difference at low power levels, confirming that using the RFB for small discharges is highly suboptimal. The cross-sectional view makes it clearer: below about 0.5 MW, the loss penalty for using the RFB instead of the LIB grows rapidly.

This is why the KKT controller shines: it naturally steers low-power tasks to the LIB, reserving the RFB for sustained, higher-power operations where its efficiency profile improves. It doesn’t just split the difference—it makes strategic, physics-informed choices.

Another critical result was real-time viability. The algorithm was deployed on an OPAL-RT 4510 real-time simulator, a standard platform for power system testing. The control loop executed in under 100 microseconds—well within the sub-millisecond requirements for grid ancillary services like automatic frequency restoration reserve (aFRR).

Figure 2 shows the power profiles from the real-time simulation. The HESS successfully tracks the combined day-ahead and aFRR signal, with smooth transitions between charging and discharging. The power split between LIB and RFB adapts dynamically, with the LIB handling rapid fluctuations and the RFB contributing during sustained discharges.

The controller also enforces reserve capacity limits, ensuring that 15 minutes of aFRR energy is always available—critical for market compliance. When SOC limits are approached, the system prioritizes reserve availability over day-ahead schedule adherence, avoiding penalties or disqualification from ancillary service markets.

Why This Changes Things

Most energy storage research focuses on new materials or larger capacities. This paper does neither. Instead, it shows that how we use existing technologies can be just as transformative.

Consider the implications. A 40% reduction in losses means 40% less energy wasted as heat. That’s not just efficiency—it’s longevity. Less heat means slower battery degradation. LIBs, in particular, suffer from thermal stress. By minimizing low-power cycling and avoiding inefficient operating zones, the controller could extend battery life by years.

It also changes the economics. Battery storage remains expensive. Every percentage point of efficiency gained lowers the levelized cost of storage (LCOS). In competitive electricity markets, that can be the difference between profit and loss.

But perhaps the biggest shift is in control philosophy. For years, grid operators have treated storage as a dumb buffer—charge when there’s excess, discharge when there’s shortfall. This work treats storage as a smart actor, with internal dynamics that must be respected and leveraged.

The use of KKT conditions is particularly elegant. Rather than feeding the problem into a black-box solver, the authors derive a closed-form solution that can be evaluated with simple root-finding (they use MATLAB’s fzero). This bypasses the computational overhead of iterative optimization, making it suitable for embedded systems in real power plants.

It also opens the door to broader applications. The same framework could be applied to hybrid systems with supercapacitors, hydrogen electrolyzers, or even thermal storage. Any system where multiple assets must share a power setpoint could benefit from this approach.

And it aligns with a growing trend in energy systems: moving from centralized, offline optimization to distributed, real-time decision-making. As grids become more decentralized, with millions of inverters and batteries, we need control strategies that are fast, scalable, and transparent. This is one such strategy.

What’s Next

The study is not without limitations. The model assumes symmetric efficiency for charging and discharging, which isn’t always true—especially for LIBs, where charging efficiency can differ. Temperature effects are ignored, though they significantly impact battery performance. And the two-battery assumption simplifies the enumeration step; scaling to three or more technologies would require more sophisticated unit commitment logic, possibly reintroducing computational complexity.

Future work could integrate degradation models directly into the objective function. Right now, the controller minimizes losses, which correlates with longevity but doesn’t explicitly account for cycle aging or calendar fade. A true optimal dispatch would balance efficiency against wear and tear.

There’s also the question of uncertainty. The current model assumes perfect knowledge of PV output and grid signals. In reality, forecasts are imperfect. A robust version of this controller might incorporate stochastic optimization or model predictive control (MPC) with uncertainty bounds.

Finally, field validation is needed. The OPAL-RT results are promising, but real-world conditions—grid faults, communication delays, sensor noise—could challenge performance. Pilot deployments in actual solar farms would be the next step.

Still, the core insight stands: optimal power sharing isn’t about more computing power—it’s about better mathematics. By respecting the physics of energy storage and using analytical tools like KKT conditions, we can make renewable energy systems not just greener, but smarter.