The accelerating global transition towards sustainable energy systems is fundamentally reshaping electricity distribution networks. Two pivotal technologies driving this change are rooftop photovoltaic (PV) systems, interfaced via solar inverters, and Electric Vehicles (EVs), connected through charging piles. While their proliferation is environmentally imperative, their uncoordinated integration into low-voltage (LV) distribution grids presents significant operational challenges. A primary concern is the exacerbation of three-phase load imbalance, as both residential PV systems and EV chargers are predominantly single-phase connections. This imbalance leads to increased network losses, overloading of distribution transformers, voltage violations, and a general deterioration in power quality, ultimately limiting the hosting capacity of the grid for these distributed resources. This article delves into a novel coordination strategy that leverages the inherent flexibility of solar inverters and EV chargers to actively balance three-phase loads, thereby enhancing grid stability, efficiency, and renewable energy integration.
The core principle of the proposed method is the strategic transfer of active power from heavily loaded phases to lightly loaded ones. Traditional solutions, such as manual phase swapping or the use of dedicated compensating devices like D-STATCOMs, are often costly, inflexible, or require extensive infrastructure changes. The proposed approach is more pragmatic and leverages existing assets. It involves configuring multiple common DC buses within the distribution feeder. Single-phase solar inverters and EV chargers that are geographically proximate but connected to different AC phases have their DC sides linked to this shared bus. This architecture creates a controllable power exchange platform between phases at the DC level, independent of their AC connection point.
We present two distinct hardware implementation schemes with different cost-structures and control capabilities:
Scheme 1: This scheme employs a relay or automatic switch at the output of the AC charger. When an EV is not connected, the switch disconnects the charger from the AC grid and connects its internal DC-link to the common DC bus. The charger’s power electronics can then be used bidirectionally to transfer power between phases. When an EV is plugged in, the switch reconnects the charger to the AC grid for direct charging, and its capacity for phase balancing is temporarily unavailable. The solar inverters connected to the DC bus remain available for balancing at all times.
Scheme 2: This more advanced scheme permanently connects the EV charger’s DC side to the common DC bus via a DC-DC converter. The EV itself is also connected to the bus through another dedicated DC-DC converter. This decouples the EV charging power from the charger’s phase-balancing function. The centralized controller can independently manage the charging power (via the EV’s DC-DC converter) and the phase-balancing power (via the charger’s inverter). This scheme offers greater flexibility as the full capacity of all solar inverters and chargers on the bus is always available for optimization, regardless of EV connection status.
The coordinated control of these assets is formulated as a centralized optimization problem. The objective is to minimize total grid losses while enforcing three-phase balance. It can be shown that minimizing the sum of squares of the total per-phase power is equivalent to minimizing phase imbalance and correlates strongly with loss minimization. For a time horizon \(T\) and a set of phases \(\phi \in \{a, b, c\}\), the objective function for a node \(n\) is:
$$
\min \sum_{t=1}^{T} \sum_{\phi \in \{a,b,c\}} \left( P^{load}_{n,\phi,t} + P^{inv}_{n,\phi,t} + P^{ch}_{n,\phi,t} \right)^2
$$
Where \(P^{load}_{n,\phi,t}\) is the conventional load, \(P^{inv}_{n,\phi,t}\) is the controllable power from solar inverters on the common DC bus (positive for drawing from grid), and \(P^{ch}_{n,\phi,t}\) is the power from coordinated EV chargers. The key constraints for the solar inverters are their capacity limits:
$$
-P^{\text{inv, max}}_{n,\phi} \le P^{inv}_{n,\phi,t} \le P^{\text{inv, max}}_{n,\phi} \quad \text{(for single-phase inverters)}
$$
For a three-phase solar inverter connected to the DC bus, an additional balance constraint is enforced by its control logic:
$$
P^{inv}_{n,a,t} = P^{inv}_{n,b,t} = P^{inv}_{n,c,t}
$$
The power for EVs must satisfy their energy demand constraint within their plug-in window \([t_s, t_e]\):
$$
\eta \sum_{t=t_s}^{t_e} P^{EV}_{k,t} \Delta t = E^{cap}_k – E^{init}_k
$$
where \(\eta\) is charging efficiency, and \(E^{cap}_k\), \(E^{init}_k\) are the battery capacity and initial energy of EV \(k\).
The most critical constraint is the power balance on the \(m\)-th common DC bus, which links all actions together. For Scheme 2, it is:
$$
\sum_{\phi} \sum_{n \in \mathcal{N}_m} (P^{inv}_{n,\phi,t} + P^{ch}_{n,\phi,t}) = \sum_{n \in \mathcal{N}_m} (-P^{PV}_{n,t}) + \sum_{k \in \mathcal{K}_m} P^{EV}_{k,t} + P^{bat,ch}_t – P^{bat,dis}_t
$$
Here, \(\mathcal{N}_m\) is the set of nodes with assets on bus \(m\), \(P^{PV}_{n,t}\) is the PV generation (negative as a source), \(\mathcal{K}_m\) is the set of EVs on the bus, and \(P^{bat,ch/dis}_t\) is the charge/discharge power of an optional stationary battery storage system on the bus. This equation ensures that the net power exchange at the DC bus from all solar inverters and chargers equals the net power from local PV, EVs, and storage.
To validate the proposed strategy, a detailed case study was performed on a real 71-node low-voltage distribution network. The network was divided into several zones, each with a common DC bus. Simulations compared four scenarios: 1) Uncoordinated charging, 2) Classic load variance minimization, 3) Proposed Scheme 1, and 4) Proposed Scheme 2. The optimization models, being linearly-constrained convex Quadratic Programming (QP) problems, were solved rapidly (within 2-3 seconds), demonstrating suitability for online or rolling-horizon control.
The results were conclusive. The proposed schemes successfully achieved nearly perfect three-phase balance throughout the day, as shown by the overlapping per-phase total load curves. This was in stark contrast to the uncoordinated case, which showed severe imbalance, especially during peak PV generation and evening load hours. The objective function’s dual focus effectively reduced peak loads and filled valleys, leading to a flatter net load profile. A key performance indicator is the maximum three-phase voltage unbalance factor (\(\phi_U\)) and current unbalance factor (\(\phi_I\)) over the simulation period. The proposed methods reduced these to negligible levels.
| Scenario | Total Energy Loss (kWh) | Max Current Unbalance \(\phi_I\) | Max Voltage Unbalance \(\phi_U\) |
|---|---|---|---|
| Uncoordinated Charging | 76.79 | 2.16 | 0.113 |
| Classic Load Variance Min. | 56.35 | 1.79 | 0.062 |
| Proposed Scheme 1 | 49.07 | 0.43 | 0.032 |
| Proposed Scheme 2 | 49.02 | 0.43 | 0.031 |
The table summarizes the quantitative benefits. The proposed schemes achieved the lowest network losses (approximately 49 kWh, a 36% reduction vs. uncoordinated charging) and the most balanced operation, as evidenced by the lowest \(\phi_I\) and \(\phi_U\) values. Scheme 2 showed a marginal improvement over Scheme 1 due to its full-time availability of charger capacity for balancing. Furthermore, the integration of a battery energy storage system (BESS) on the common DC bus was tested. The optimization effectively scheduled the BESS to charge during excess PV generation and discharge during high load periods, further enhancing loss reduction and peak shaving capabilities. The state-of-charge (SOC) dynamics followed an optimal pattern, respecting operational limits (\(20\% \le SOC \le 90\%\)).
In conclusion, the coordination of solar inverters and EV chargers via shared DC buses presents a highly effective and practical solution for mitigating three-phase imbalance in active distribution networks. The method transforms potential grid problems—single-phase PV and EV loads—into part of the solution. By enabling power transfer between phases at the DC level, it fully utilizes the existing power electronics capacity of solar inverters and chargers. The formulated optimization model is computationally efficient, ensuring real-time applicability. The benefits are multifaceted: significant reduction in technical losses, complete mitigation of load and voltage imbalance, improved voltage profiles, and enhanced hosting capacity for both PV and EVs. This approach underscores the critical role intelligent solar inverters can play beyond simple maximum power point tracking, evolving into essential assets for grid support and stability. Future work may explore fully distributed control architectures to enhance scalability and robustness.