Identifiability of battery fuel savings from sparse diesel engine fuel curves

In the world of heavy industry, massive diesel engines are the workhorses that keep hospitals, data centers, and remote mining operations running when the main power grid fails. These engines burn fuel to create electricity, but they are not equally efficient at every speed. Just as a car gets better gas mileage cruising on a highway than it does idling in traffic, a diesel generator burns less fuel per unit of electricity when it runs at a specific, optimal load. To save money and reduce emissions, engineers often try to pair these engines with large battery banks. The idea is simple: run the engine at its most efficient speed to charge the batteries, then let the batteries power the facility when demand is low, allowing the engine to shut down or run at a steady, efficient pace. This strategy sounds like a guaranteed win for efficiency, but it relies on a critical assumption: that we know exactly how much fuel the engine will burn at any given moment, even at speeds or loads where the manufacturer has not provided specific data.

The core challenge lies in the data itself. Manufacturers provide fuel consumption tables that list how much fuel an engine uses at a few specific, high-power settings. These tables are sparse, meaning they have large gaps between the listed points. Engineers usually fill these gaps by drawing a smooth line through the dots, assuming the engine behaves predictably in between. However, a new analytical study by Mahmoud Abdelfattah Abbas Mahmoud reveals that this common practice can be dangerously misleading. The research asks a fundamental question: if we only know the fuel use at a few specific points, can we mathematically prove that a battery system will actually save fuel at a point in between those measurements? The answer, surprisingly, is often no. The study demonstrates that without additional, specific measurements, the direction of fuel savings—whether the battery saves fuel or wastes it—can remain completely unknown, even when the engine is running within its normal operating range.

The researcher approached this problem by treating the manufacturer's fuel tables not as a complete picture of the engine's behavior, but as a set of strict boundaries. He considered every possible curve that could connect the known data points, provided the curve followed basic physical rules: fuel consumption cannot be negative, and it generally increases as the engine works harder. By calculating the best-case and worst-case scenarios for every possible curve that fits the data, he created a "decision audit." This audit acts as a rigorous test to see if a claim of fuel savings is mathematically certain or if it is merely a guess based on an arbitrary line drawn between two dots. The study applied this method to real-world data from two major engine manufacturers, Cummins and Caterpillar, using their official fuel tables to see if the battery strategy held up under this strict scrutiny.

The findings were stark. When the researcher tested the battery strategy at the exact middle points between the manufacturer's listed data, the results were ambiguous. At a round-trip efficiency of 90.25 percent—a realistic figure for modern battery systems—the analysis showed that for every single test point, it was impossible to say for sure if the battery would save fuel or increase consumption. In some cases, one plausible curve suggested a saving of fuel, while another equally valid curve suggested a waste of fuel. The study found that even though the engine's fuel use was known at the high and low ends of a range, the behavior in the middle remained a mystery. For instance, at a specific low-load point for a Cummins engine, the critical fuel rate that would determine a saving was 31.23 liters per hour. The analysis showed that two mathematically valid extensions of the data could cross this line in opposite directions, meaning the outcome depended entirely on which invisible curve was chosen, not on the actual data provided.

This ambiguity persists even when the target operating point is well within the range of the manufacturer's data. The study examined six specific points located between the known knots for both engine types. In all six cases, the mathematical bounds for fuel savings straddled zero, meaning the sign of the result was unidentified. However, the research did identify specific scenarios where the outcome was certain. For example, in the Caterpillar data, when analyzing two unreported points at 170 and 175 kW simultaneously, the mathematical bounds proved that every admissible curve would increase fuel use, guaranteeing a negative saving. This highlights that while the sparse data alone often fails to guarantee savings, it can sometimes guarantee a fuel increase under specific coupled conditions. The decision to use a battery system often relies on assumptions about the engine's shape that are not supported by the provided numbers. The only way to resolve this uncertainty, the study concludes, is to obtain new, specific measurements. A slope constraint, which limits how quickly fuel use can rise, or a direct measurement of fuel consumption at the specific low-load point, could clear the ambiguity. Without such extra information, the claim that a battery will save fuel remains an unproven hypothesis, not a mathematical certainty.

The implications of this work extend beyond a single engine or a specific battery setup. It serves as a cautionary tale for engineers and facility managers who rely on standard fuel tables to design hybrid power systems. The study does not argue that batteries are useless or that diesel engines are inefficient; rather, it points out that the tools used to predict their performance are often insufficient for making definitive claims. The research provides a reproducible method to audit these claims, showing exactly where the data is strong and where it is weak. It establishes that while the engine's performance at the listed points is exact, the behavior in between is a landscape of possibilities. Until specific measurements are taken at the low-load points of interest, the promise of fuel savings from battery integration remains an educated guess, vulnerable to the specific curve an engineer chooses to draw. The study offers a clear path forward: to move from guesswork to certainty, the industry must measure the fuel consumption at the actual operating points where the savings are expected, rather than relying on the gaps in the manufacturer's tables.