A grid operator can't watch every rooftop solar inverter and battery in real time, but a new paper shows how to set device controls in advance so that no matter how those devices behave, voltage stays close to where it should be. The trick is to treat the problem as a worst-case game: the operator picks reactive power settings first, and an adversary — modeling anything from normal solar variability to a compromised or hacked device — then picks the active power injections that would do the most damage.
The setting is distributed energy resources, or DERs: rooftop solar panels, batteries, and other small generation and storage units connected throughout a distribution network. These devices inject active power (the power that actually does work, measured in watts) and can also inject or absorb reactive power (which doesn't do work directly but helps control voltage). Voltage regulation matters because too much deviation from nominal voltage can damage equipment, trip protective devices, or degrade power quality for everyone on the circuit. As more DERs get added to a feeder, their fluctuating active power output — whether from a cloud passing over a solar farm or from a malicious dispatch instruction — becomes a bigger source of voltage swings than utilities have traditionally had to manage.
IEEE Standard 1547-2018, the industry rulebook for how DERs interconnect with the grid, gives operators a specific tool for this: constant power factor control. Under this mode, each device's reactive power output is locked to a fixed ratio of its active power output — the device can't reveal or exploit its own reactive power output independently, but the operator can pick that fixed ratio in advance for each device before knowing what active power the device will end up injecting. That timing detail is what makes this a genuine game-theoretic problem: the operator moves first and has to commit to a strategy that performs reasonably well across every active power scenario the device might realistically produce, including adversarial ones.
The paper formalizes this as a minimax problem using a standard linearized voltage model, in which voltage deviation at a bus is approximately a weighted sum of nearby active and reactive power injections. Writing $p$ for the vector of active power injections and $q$ for reactive power injections tied to $p$ through power factor ratios $q_i = k_i p_i$, the operator wants to choose the ratios $k_i$ that solve $$\min_{k} \max_{p \in \mathcal{P}} \; \left| \sum_i R_i \left( p_i + k_i p_i \right) \right|$$ where $\mathcal{P}$ is the feasible set of active power injections (bounded by device ratings) and $R_i$ captures each device's sensitivity coefficient to the bus voltage of interest under the linear model. In plain terms: the operator is picking, ahead of time, how much reactive power each device should produce for every unit of active power it produces, so that even the worst possible combination of active power injections leaves the aggregate voltage deviation as small as possible.
The authors solve this by splitting the payoff according to whether the resulting voltage deviation lands above or below nominal voltage, and show that under a particular condition — when every feasible voltage outcome stays on the same side of nominal it started on — the optimal ratios have a clean closed-form expression that exactly cancels each device's contribution to the worst-case deviation. That's a meaningful practical result: it means that for DERs within certain realistic rating ranges, a simple, computable power-factor rule can fully neutralize the adversarial or unpredictable component of voltage swings, without needing real-time communication or control.
Not every DER falls into that easy regime, though. The paper also identifies the realistic device ratings for which the clean cancellation strategy applies, and — just as usefully — quantifies how much regulation capacity is lost when a device's power factor range is restricted, as IEEE 1547-2018 requires for smaller DERs. That gap matters for utilities deciding equipment specifications or negotiating interconnection agreements: a narrower allowed power factor range is easier to certify and cheaper to implement, but it comes at a measurable cost in how much voltage protection the operator can guarantee.
To check the approach holds up outside the idealized linear model, the authors validate their minimax strategy against full nonlinear AC power flow simulations at a representative DER rating, alongside directly solving the complete minimax problem numerically rather than relying only on the closed-form shortcut. This puts the work in the same family as recent research modeling DER voltage control as a robust or adversarial optimization problem against compromised or attacker-controlled injections, and as parallel proposals like 'volt-PF' control that blend power factor and voltage feedback — suggesting power-factor-based defenses against active power volatility are becoming a genuine subfield within grid optimization rather than a one-off idea.
The bigger takeaway for utilities and DER integrators is that voltage regulation doesn't have to mean choosing between simple, cheap control modes and robust protection against bad actors or bad weather. A minimax formulation gives a principled way to size that trade-off explicitly, telling an operator exactly how much protection a given power-factor range buys and where it stops being enough — a useful input as interconnection standards keep evolving alongside DER penetration.
Sources: Primary source: 'Zero-Sum Power Factor Games', arXiv:2608.20298 · NLR, 'Clause-by-Clause Summary of Requirements in IEEE Std 1547-2018', https://www.nlr.gov/grid/ieee-standard-1547/clause · NREL, 'An Overview of Issues Related to IEEE Std 1547-2018 Requirements Regarding Voltage and Reactive Power Control', https://docs.nrel.gov/docs/fy21osti/77156.pdf · Zhang, Lam, Domínguez-García, Tse, 'An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems', arXiv:1204.5226 · 'Volt-PF Control Mode for Distribution Feeder Voltage Management Under High Penetration of Distributed Energy Resources', arXiv:2405.18305 · Purdue CERIAS, 'Adversarial Attacks to Distributed Voltage Control in Power Distribution Networks with DERs', https://www.cerias.purdue.edu/assets/symposium/2018-posters/BF0-B7A.pdf · 'Utilizing Adversarial Training for Robust Voltage Control: An Adaptive Deep Reinforcement Learning Method', arXiv:2603.23648
