New Multi-Stage Method Boosts Solar Hosting Capacity in Low-Voltage Grids
In an era defined by urgent climate action and rapid electrification, the integration of distributed energy resources—particularly rooftop solar photovoltaics (PV)—into low-voltage distribution networks has become both a necessity and a challenge. While solar adoption surges across residential neighborhoods, grid operators face mounting pressure to accommodate unprecedented levels of reverse power flow without compromising reliability or safety. A groundbreaking study published in Southern Power System Technology offers a robust, multi-stage solution that could redefine how utilities assess and expand the hosting capacity of distribution substations under high solar penetration.
Led by Zijun Liu and Huaying Zhang from the New Smart City High-Quality Power Supply Joint Laboratory at Shenzhen Power Supply Bureau Co., Ltd., in collaboration with researchers from Hunan University—including Yifang Jin, Ziao Su, Yihong You, and Bin Zhou—the team has developed a novel methodology that simultaneously addresses three critical pain points in modern distribution systems: reverse overloading, voltage violations, and three-phase imbalance. Their approach doesn’t just evaluate capacity—it actively enhances it through intelligent coordination of distributed resources.
The problem is not hypothetical. In many regions, especially in China’s rapidly urbanizing zones like Shenzhen, household solar installations have outpaced local electricity demand. During midday hours, when sunlight peaks but residential consumption dips, excess solar generation flows backward through distribution transformers toward the sub-transmission network. This “reverse power flow” can overload transformers, inflate voltages beyond statutory limits, and—when single-phase PV systems are unevenly distributed across phases—induce severe three-phase imbalance. Such conditions degrade transformer performance, accelerate insulation aging, and risk catastrophic failures.
Traditional methods for calculating available capacity often rely on simplistic rules, such as capping solar interconnection at 80% of a transformer’s rated capacity. But as the research team demonstrates, this static approach ignores dynamic interactions between generation, load, and grid topology. Worse, it fails to account for constraints at the upstream 35 kV or 110 kV substation level, where cumulative reverse flows from dozens of low-voltage feeders can trigger overloads far removed from the point of interconnection.
The proposed solution introduces a three-phase, multi-stage assessment framework that operates in sequence: phase-aware PV allocation, virtual capacity expansion via flexible resources, and system-level verification with corrective feedback.
The first stage tackles three-phase imbalance at its root. Instead of allowing new PV systems to connect arbitrarily to any phase—often based on installer convenience or homeowner preference—the model optimizes the phase assignment of each new installation. By strategically distributing additional PV capacity across phases A, B, and C, the algorithm minimizes the imbalance index over the evaluation period. This isn’t just about fairness; it directly enhances the transformer’s reverse loading capability. The team incorporates a physics-based relationship showing that as imbalance increases, the transformer’s effective capacity drops due to hotspot heating in overloaded windings. By keeping phases balanced, the same physical asset can safely handle more reverse power.
The second stage leverages flexibility from two rapidly growing end-use technologies: electric vehicles (EVs) and smart thermostats. Here, the innovation shifts from passive assessment to active management. The model treats EV charging and air conditioning loads as controllable resources that can be dispatched to absorb excess solar generation during peak production hours. Rather than merely curtailing solar output—a costly and inefficient solution—the system encourages “virtual capacity expansion” by reshaping demand to match supply.
For EVs, this means optimizing not only when they charge but also which phase they connect to. A fleet of 50 EVs, for instance, can be dynamically assigned across phases to further balance the net load. Simultaneously, air conditioning systems—modeled using first-order thermal dynamics—are allowed to slightly reduce power consumption during solar peaks, provided indoor temperatures remain within user-defined comfort bands. This dual approach reduces both the magnitude and asymmetry of reverse power flow, effectively creating headroom for more solar without hardware upgrades.
Critically, the model accounts for uncertainty. Solar irradiance varies with weather, EV usage depends on unpredictable human behavior, and outdoor temperatures fluctuate daily. To ensure reliability under worst-case scenarios, the team formulates a robust optimization problem that identifies the most adverse combination of these uncertainties and guarantees constraints are satisfied even then. This conservative yet practical design aligns with utility risk management protocols.
The third and final stage closes the loop at the system level. Even if individual substations appear capable of hosting more solar, their collective impact on the upstream 110 kV or 35 kV substation must be verified. The method aggregates the proposed capacity increases from all connected low-voltage feeders and checks whether the total reverse flow exceeds the substation’s safe limit. If it does, the algorithm proportionally scales back the allowable capacity for each feeder—ensuring grid-wide integrity without penalizing any single neighborhood unfairly. It also deducts pending interconnection applications (“in-process capacity”) to reflect real-world queue dynamics.
To solve this complex, multi-layered problem, the researchers employ a sophisticated algorithm known as the Nested Column-and-Constraint Generation (N-C&CG). This technique decomposes the original problem into three interlinked sub-problems: PV phase configuration, flexible resource dispatch, and upstream capacity verification. These sub-problems are solved iteratively, exchanging information until convergence is achieved. The result is a globally optimal solution that balances local transformer constraints with system-wide stability.
The team validated their method using real-world data from a typical Shenzhen distribution substation equipped with a 500 kW transformer and 300 kW of existing PV (75 kW on phase A, 105 kW on B, 120 kW on C). They compared four scenarios: (1) their full method; (2) phase allocation without imbalance-aware transformer modeling; (3) imbalance-aware modeling without flexible resources; and (4) flexible resources without upstream verification.
The results were striking. Compared to the baseline, the full method increased available capacity by 9.84%, reduced peak three-phase imbalance by 66.67%, and boosted the transformer’s reverse loading capability by 34.24%. Scenario 2, which ignored imbalance effects, overestimated capacity and risked transformer overload. Scenario 3 improved safety but left capacity untapped. Scenario 4 maximized local capacity but pushed the upstream substation into reverse overload—highlighting the necessity of the final verification stage.
From a utility perspective, these gains translate directly into operational and financial benefits. A 10% increase in hosting capacity means fewer grid upgrades, shorter interconnection queues, and faster solar adoption—all while maintaining reliability. For regulators, the method provides a transparent, physics-based framework for setting fair and safe interconnection limits. For homeowners, it means fewer denials and delays when applying to go solar.
Moreover, the approach is future-proof. As EV penetration grows and smart thermostats become ubiquitous, the pool of flexible resources will expand, further increasing the “virtual” capacity of existing infrastructure. The model is designed to incorporate these trends organically, turning potential grid stressors into assets.
The implications extend beyond China. While the study uses Shenzhen as a testbed, the underlying challenges—reverse flow, voltage rise, phase imbalance—are universal in grids with high residential solar penetration. Utilities in California, Australia, Germany, and elsewhere face similar constraints. The methodology’s modular design allows adaptation to local regulations, transformer standards, and resource availability.
Critically, the research adheres to engineering best practices. It builds on established models for transformer thermal behavior, three-phase power flow, and thermal dynamics of buildings. It respects statutory voltage limits (±7% in China) and transformer loading guidelines (80% continuous load). And it uses real-world data for EV travel patterns and weather profiles, ensuring practical relevance.
This work also aligns with global trends toward distribution system operator (DSO) functions, where utilities actively manage distributed resources rather than treating them as passive injections. By framing demand response and phase balancing as capacity-enhancing tools, the study provides a blueprint for the next generation of grid planning.
In conclusion, the multi-stage assessment method developed by Liu, Zhang, Jin, Su, You, and Zhou represents a significant leap forward in distribution grid integration. It moves beyond static, component-level limits to a dynamic, system-aware approach that unlocks hidden capacity through intelligence rather than investment. As the world races to decarbonize, such innovations will be essential to building grids that are not only cleaner but also smarter, safer, and more equitable.
Authors: Zijun Liu¹, Huaying Zhang¹, Xiaorui Liang¹, Yifang Jin², Ziao Su², Yihong You¹, Bin Zhou²
Affiliations:
¹ New Smart City High-Quality Power Supply Joint Laboratory of CSG, Shenzhen Power Supply Bureau Co., Ltd., Shenzhen, Guangdong 518020, China
² College of Electrical and Information Engineering, Hunan University, Changsha 410082, China
Published in: Southern Power System Technology, Vol. 18, No. 5, May 2024
DOI: 10.13648/j.cnki.issn1674-0629.2024.05.013