To a first approximation the voltage change across a line section is proportional to PR + QX, where P and Q are the active and reactive power transferred and R and X are the resistance and reactance of the section (Kersting, 2017). Low-voltage cables and small overhead conductors have a high ratio of resistance to reactance, so active power dominates the result, and exporting PV raises the voltage almost in proportion to its output. Single-phase connection adds unbalance, since installations are seldom spread evenly across the phases. Passing cloud superimposes changes over seconds to minutes, to which electromechanical tap changers, with their intentional time delays, respond late and repeatedly (Walling et al., 2008).

Whether a voltage is acceptable is decided by the standard in force. In Europe, EN 50160 requires that ten-minute mean values of the supply voltage remain within ±10% of nominal for 95% of each week (CENELEC, 2010). In North America, ANSI C84.1 defines a preferred Range A for service voltage of ±5% of nominal (NEMA, 2020). Measurement methods, including the aggregation intervals on which such limits are assessed, are laid down in IEC 61000-4-30 (IEC, 2015). Inverter behaviour is governed by interconnection rules; IEEE Std 1547-2018 requires distributed resources to be capable of voltage regulation by reactive power and, in its higher performance category, by active power (IEEE, 2018).

Remedies act either at the inverter or on the network. Reactive power absorption by the inverters, at a fixed power factor or according to a volt-var curve, has been analysed by Turitsyn et al. (2011) and Carvalho et al. (2008), and its use through standardised inverter functions is described by Smith et al. (2011). Active power curtailment governed by a volt-watt droop was proposed by Tonkoski et al. (2011). Network measures include revised regulator settings, distribution transformers with on-load tap changers, conductor reinforcement and storage. German experience, where the question arose early and at scale, indicates that inverter-based measures and regulated transformers can defer much conventional reinforcement (Stetz et al., 2013; von Appen et al., 2013). Table 1 summarises the options.

The engineer first records which standard and which interconnection rules apply, and therefore which quantity must stay within which band over which averaging interval. The reported symptoms are then sorted into three classes: sustained over-voltage at times of high generation, rapid fluctuation on partly cloudy days, and excessive operation of regulating equipment. Complaint records, inverter trip logs supplied by customers and the operation counters of regulators and capacitor controllers are the sources. The sorting matters because the first class is a steady-state problem, the second a dynamic one, and the third may be an artefact of control settings.

Measurement precedes modelling. Recorders complying with IEC 61000-4-30 are placed at the substation bus, at each regulator and at a small number of low-voltage points chosen to include the electrically most remote customers and the transformers with the highest PV capacity. Voltage per phase and active and reactive power are logged for a period long enough to contain clear days, overcast days and days of broken cloud at light load. Where smart meters report voltage, their data extend the coverage at no cost. If flicker is among the complaints, short-term flicker severity is recorded as well (Dugan et al., 2012).

A three-phase unbalanced model of the medium-voltage feeder is assembled from the utility's asset records, with the low-voltage networks of the affected transformers represented explicitly and the remainder lumped. Open-source tools such as OpenDSS are adequate for the purpose (Dugan and McDermott, 2011). The model is then run with the measured substation voltage and measured or estimated load and PV profiles, and its voltages are compared with the recordings from Step 2. Discrepancies usually trace to wrong phase assignments, wrong conductor data or incorrect regulator settings, and they are corrected in the model and, where relevant, in the asset records. The model is not used for decisions until it reproduces the measured voltage profile on both a high-generation and a high-load day.

With a calibrated model, quasi-static time-series simulation over representative days answers three questions. Where and for how long does the voltage exceed the limit, and on which phase. How much of the excursion is slow rise attributable to reverse power flow and how much is fast variation with irradiance. And how do the regulators and capacitor banks respond, in particular whether they are operating against one another or against the inverters. The output of this step is a short written diagnosis that assigns each symptom from Step 1 to a cause and a location.

The options in Table 1 are tested in the model roughly in the order listed, stopping at the first that restores compliance with adequate margin at both light and peak load. Settings come first: inverter volt-var and volt-watt functions where the interconnection rules allow the utility to require them, then regulator set-points, bandwidths and time delays. Phase rebalancing is tried where the diagnosis shows marked unbalance. Capital measures follow. For each candidate the engineer records the residual violations, the change in losses and tap operations, the energy curtailed and who bears it, and an estimate of cost. Combinations are considered only when no single measure suffices.

The chosen measure is implemented and the measurements of Step 2 are repeated at the same points for a comparable period. Verification is by measurement, not by the model. If limits are still exceeded, the model is revised in the light of the new data and the procedure returns to Step 4. The file for the feeder should finally contain the diagnosis, the options examined with reasons for rejection, the settings applied and the before-and-after recordings, so that the next engineer to face additional PV on the same feeder starts from a calibrated model.