Virtual Machine and Passivity Control Tame Dangerous Voltage Swings in DC Power Converters

Power electronics rarely make headlines, yet a quiet revolution inside the converters that shuttle electricity through data centers, electric aircraft, and fuel-cell systems could determine whether the grids of the future stay stable or collapse into oscillation. Researchers in Chongqing, China, have now unveiled a control strategy that borrows the physics of old-fashioned spinning machines and the mathematics of energy dissipation to keep a modern DC-DC converter rock-steady under conditions that would destabilize conventional controllers. In experiments on a gallium nitride-based prototype rated at 3 kilowatts, the new approach slashed worst-case bus-voltage deviations by as much as 91.7 percent compared with standard industrial control.

The work, published in Frontiers in Electronics by a team from the State Grid Chongqing Economic Research Institute and Chongqing University of Science and Technology, tackles one of the most stubborn problems in DC power distribution: the constant power load. When a downstream converter is tightly regulated to deliver a fixed power regardless of voltage, it behaves like a negative resistance on the bus. If the bus voltage dips, the load draws more current to keep its power constant, dragging the voltage down further. This positive-feedback-like interaction erodes the natural damping of the system and can amplify oscillations after sudden disturbances, sometimes to the point of outright instability.

Modern converters compound the problem because, unlike the rotating generators of the twentieth century, they possess no inherent electromechanical inertia. When a load steps abruptly or an input source fluctuates, the mismatch between incoming and outgoing energy has nowhere to go except into the small output capacitor. The bus voltage can then overshoot or undershoot severely, potentially tripping overvoltage or undervoltage protection and shutting the system down. The research team, led by Wenzuo Tang and Shuaicheng Hou, argued that a truly robust controller must do two things at once: counteract the negative damping of constant power loads and supply sufficient virtual inertia to soften transient excursions.

Their testbed is a two-phase interleaved Boost converter, a topology prized in medium- and high-power applications because the parallel phases share current stress and partially cancel input-current ripple. Interleaving means the two switching stages operate half a cycle out of phase, smoothing the current drawn from the source. The team derived an averaged mathematical model of the converter in continuous conduction mode, then recast it in Euler-Lagrange form, a framework that describes the system in terms of stored and dissipated energy. This energy-based description is the key that unlocks passivity-based control.

Passivity theory treats a converter as an energy-handling network: energy flows in from the source, accumulates in the inductor’s magnetic field and the capacitor’s electric field, and drains away through dissipation. If the dissipated energy always exceeds the difference between supplied and stored energy, the system is strictly passive and inherently stable. The researchers exploited this by defining an error-energy function measuring the gap between actual and desired inductor current, then injecting artificial damping to drive that error energy to zero. The convergence rate is set directly by the damping coefficient, giving the controller a clear physical tuning knob. Because the Boost converter is a non-minimum-phase system, direct voltage control would produce unstable internal dynamics, so the team selected the current-regulating equation as the duty-ratio law, guaranteeing global stability of the current loop.

An additional wrinkle arises in interleaved operation: the two phases must share current equally. The final control law incorporates a current-sharing term, so that when one phase’s inductor current exceeds its reference, the duty cycle shrinks, shortening the charging interval and pulling the current back. This creates a self-correcting, energy-dissipating feedback loop in hardware, not merely on paper. Yet the passivity-based inner loop alone cannot solve the voltage-side problem, because a conventional proportional-integral outer loop would still convert a sudden bus-voltage error into an aggressive current reference, slamming the converter through large transients.

Enter the virtual DC machine. The outer voltage loop deliberately emulates the external behavior of a DC motor, complete with an armature circuit, a virtual back electromotive force, a virtual moment of inertia, and a virtual damping coefficient. The measured bus-voltage error is processed through a PI stage to yield mechanical power, from which a virtual torque is computed. The mechanical equation of motion, with its inertia and damping terms, then filters the response, producing a virtual armature current that becomes the reference for the passivity-based inner loop. The result is that a sudden voltage error is no longer translated instantaneously into a current command; the virtual rotor must ‘spin up’ first, exactly as a physical machine would.

Small-signal analysis of this virtual machine reveals it behaves as a first-order inertial element whose time constant equals the virtual inertia. Bode plots show that increasing the inertia coefficient lowers the cutoff frequency and improves smoothing of high-frequency noise, at the cost of slower tracking, while raising the damping coefficient boosts low-frequency gain and improves phase margin, strengthening disturbance rejection. The trade-off is explicit and quantifiable: more inertia and damping buy stability but slightly delay recovery. The team’s frequency-domain study lets engineers choose those coefficients deliberately rather than by trial and error.

The experimental verification is where the approach becomes genuinely striking. The prototype, built with GaN power devices switching at 500 kilohertz, converts a 96-volt nominal input, spanning 80 to 120 volts, to a regulated 270-volt bus. Its volume of roughly 0.335 liters yields a power density of about 9 kilowatts per liter, a figure that underscores why gallium nitride matters: the higher switching speeds and lower losses of GaN allow the small inductors and capacitors that make such density possible. The converter was tested across no-load, half-load, and full-load conditions, holding output-voltage fluctuation within 1 percent across the entire power range.

The dynamic tests delivered the headline numbers. When input voltage stepped from 80 to 120 volts under full load, conventional PI plus PI control produced an 8.9 percent overshoot with a 9-millisecond settling time. Replacing only the current loop with passivity-based control halved the deviation to 3.7 percent. Adding the virtual DC machine on top cut the deviation to just 1.5 percent, an 83.1 percent reduction versus the conventional benchmark. Load steps proved even harsher, and the contrast starker: dropping the load from 3000 watts to 100 watts produced a 13.3 percent excursion under PI plus PI control, but only 1.1 percent under the composite scheme. In extreme simulations where load power suddenly tripled, the PI current loop descended into limit-cycle oscillation and lost stability, while the passivity-based loop still restored the rated voltage. The virtual-inertia approach did concede a millisecond or two of recovery time in some cases, but the authors argue this is a bargain: a modest slowdown in exchange for eliminating the voltage excursions that trigger protective shutdowns. For fuel-cell supplies, DC microgrids, and motor drives, where converters must survive wide operating ranges and violent load swings, the combination of energy-based damping and machine-like inertia may prove to be the stabilizing handshake that high-density power systems have been waiting for.

Subject of Research: Stability enhancement of interleaved boost converters with constant power loads using virtual DC machine and passivity-based control

Article Title: Stability enhancement method for interleaved boost converter based on virtual DC machine and passivity-based control

Article References: Tang, W., Li, B., Hou, S., Shao, X., & Yu, H. (2026). Stability enhancement method for interleaved boost converter based on virtual DC machine and passivity-based control. Frontiers in Electronics, 7, Article 1909575. https://doi.org/10.3389/felec.2026.1909575

Image Credits: AI Generated

DOI: 10.3389/felec.2026.1909575

Keywords: DC-DC converter, interleaved boost converter, constant power load, passivity-based control, virtual DC machine, gallium nitride, DC bus stability, power electronics, fuel cell power supply, control theory, power density, Euler-Lagrange model