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Off-Grid Load-Carrying Capability

Detailed Explanation of PCS Off-Grid Load-Carrying Capability

This document describes the boundaries of a PCS (Power Conversion System / energy storage inverter) for directly switching in transformers and motors when operating in off-grid / islanded mode, as well as the capacity sizing rules when multiple loads coexist. Each rule is broken down below.

1. Terminology Prerequisites

  • Grid-Following PCS (GFL): Requires the grid voltage as a reference, does not establish voltage on its own, and has limited overload capability (typically 1.1~1.2× rated, long-term 1.0~1.1×).
  • Grid-Forming PCS (GFM): Can establish its own voltage and frequency reference, can be regarded as a "virtual generator", and has strong overload capability (instantaneously up to 3× rated, returning to 1.5× within 3~10 seconds).
  • Pn / In: PCS rated power / rated current.
  • PA / PB / PC: Power ratings of the already steady-state running load, the newly switched-in transformer, and the newly switched-in other inrush load, respectively.

2. Rule 1 — Direct Transformer Switching by Off-Grid PCS

2.1 Physical Background: Transformer Magnetizing Inrush Current

At the instant of no-load closing of a transformer, due to the superposition of core residual flux and an unfavorable voltage phase, the winding enters deep magnetic saturation, producing an inrush current whose amplitude can reach 6~8× the rated current, lasting 0.5~2 seconds. This is the so-called "closing inrush current / magnetizing inrush".

The inrush is not real load power but reactive current (magnetizing current); however, its amplitude is extremely large and can trip PCS protections or pull down the bus voltage.

2.2 Interpretation of the Rule

PCS Type Directly Switchable Transformer Capacity Principle
Grid-Following PCS ≤ 0.5 Pn The magnetizing inrush of a 0.5Pn transformer is estimated at ≈ 6~8×0.5×In ≈ 3~4×In, which falls within the 1.1~1.2× overload window
Grid-Forming PCS (3× overload) ≤ Pn The full-load magnetizing inrush of a Pn transformer is 6~8×In, which is still within the 3× overload window (3×In / 6~8 = sufficient margin but cannot be larger)

Practical implication: During off-grid commissioning, if the on-site transformer is ≥ 0.5Pn, a grid-forming unit must be used, or a switching scheme with pre-magnetization / soft-start devices must be adopted (such as a closing switch with resistor pre-insertion, or a soft-start transformer).

3. Rule 2 — Direct Motor Switching by Off-Grid PCS

3.1 Physical Background: Motor Direct-On-Line Starting Surge

When an asynchronous motor is direct-on-line started (DOL, Direct-On-Line): - At the instant of starting, the slip s=1 and the rotor equivalent resistance is extremely small; - The starting current is typically 6~10× the rated current; - The starting torque is also very large (about 1.5~3× rated torque); - The duration is 1~3 seconds.

This section uses a conservative 10× factor for the surge calculation.

3.2 Interpretation of the Rule

Requirement:

Isurge=10×In,motor≤In,PCS \boxed{I_{\text{surge}} = 10 \times I_{n,\text{motor}} \le I_{n,\text{PCS}}}

That is, 10×0.1Pn≤Pn10 \times 0.1 P_n \le P_n drives the upper limit exactly to the PCS rated current. Therefore the capacity of a single motor must be ≤ 0.1 Pn.

Example: A 1000 kW PCS (with grid-forming capability) can direct-start at most a 100 kW single motor. Larger motors must use VFD soft start / soft starter / star-delta reduced-voltage starting, etc.

4. Rule 3 — Combined Multi-Load Scenarios

The PCS sizing rule when an existing load PA is already running stably and a new load is added.

4.1 Adding a Directly Switched-in Transformer (PB)

PPCS≥1.5⋅PA+2×2⋅PB=1.5PA+4PB \boxed{P_{\text{PCS}} \ge 1.5 \cdot P_A + 2 \times 2 \cdot P_B = 1.5 P_A + 4 P_B}

Meaning of each term:

Term Coefficient Meaning
1.5 × PA 1.5 Safety margin for the already running load (to handle bus voltage/frequency disturbances and short-term overloads)
2 × PB 2 Equivalent capacity factor of transformer magnetizing inrush (6~8×, taking a conservative value and converting to a power multiplier)
× 2 2 A second safety margin (because the inrush is a dual-axis power/current impact, an additional 2× protection is overlaid)

Why is the transformer given an additional 2× factor? Because transformer inrush is a reactive impact — it consumes no active power yet heavily occupies the current channel — so sufficient margin must be reserved according to current capability rather than average power.

4.2 Adding Other Inrush Loads (PC)

PPCS≥1.3⋅PA+PC \boxed{P_{\text{PCS}} \ge 1.3 \cdot P_A + P_C}

Applicable scenarios: direct-on-line fan starting / VFD soft start / series-reactor soft start / capacitor compensation switching / large rectifier equipment, etc.

Term Coefficient Meaning
1.3 × PA 1.3 A milder margin for the already running load (these loads have surge factors ≤ 6, lower than the 6~8× transformer inrush)
× PC 1.0 Directly take the maximum surge power without an additional multiplier (because the surge factors of these loads have already been limited by the wind turbine / VFD / series reactor to a level the PCS can just tolerate)

Reference DOL surge factors: Large axial-flow fans direct-on-line 5~7×; VFD soft start 1.5~2×; series-reactor soft start 3~4×. Since the surge has already been limited, the derating implied by the control strategy is embedded within PC, and PC can simply be added directly.

5. Parallel Derating Coefficient

When multiple PCSs operate in parallel, circulating currents / current-sharing imbalance exist (even for the same model, IGBT voltage drop, sampling accuracy, and modulation delay all have slight differences), and derating is mandatory:

Integration Method Derating Coefficient Equivalent Note
2 PCSs in parallel 0.95 Reserve 5% for current-sharing imbalance losses
≥3 integrated units 0.90 Reserve 10% for multi-unit compounded imbalance and communication jitter

The final sizing formula becomes:

PPCS,total≥1.5PA+4PB (or 1.3PA+PC)kparallel P_{\text{PCS,total}} \ge \frac{1.5 P_A + 4 P_B \text{ (or } 1.3 P_A + P_C\text{)}}{k_{\text{parallel}}}

where kparallel=0.95k_{\text{parallel}} = 0.95 or $0.90$.

6. Comprehensive Example (Consolidating Understanding)

Scenario: Grid-forming PCS, single unit 1000 kW, already carrying a stable load of 300 kW, about to switch in a 200 kVA transformer and a 90 kW direct-on-line motor.

  1. Can the transformer be directly switched in? 200 kVA > 0.5 × 1000 = 500 ❌ — that's the single-unit capacity; here, the ratio is 200 / 1000 = 20%, which is within the limit and can be directly switched in.
  2. Can the motor be direct-started? 90 kW / 1000 = 9% < 10% ✅ — can be direct-started.
  3. Total capacity check (using the transformer rule):

PPCS≥1.5×300+4×200=450+800=1250 kW P_{\text{PCS}} \ge 1.5 \times 300 + 4 \times 200 = 450 + 800 = 1250 \text{ kW}

That is, a single-unit PCS is insufficient and must be upgraded to 1250 kW / 2 units in parallel, with 0.95 derating:

PPCS,total≥12500.95≈1316 kW P_{\text{PCS,total}} \ge \frac{1250}{0.95} \approx 1316 \text{ kW}

→ Select 2 × 800 kW = 1600 kW PCS, leaving more safety margin.

7. Key Takeaways

  1. An off-grid PCS is not the grid — it has no "infinite bus" to absorb surges, so the switched-in capacity must be calculated for the worst case;
  2. Transformers are the largest hidden surge source (inrush 6~8×), so a separate 4× factor is applied;
  3. Direct-on-line motor starting is the second surge source, but its capacity is capped at 10%Pn, and is often paired with VFDs / soft starters in engineering practice;
  4. Parallel operation always requires derating — not because current-sharing algorithms are inadequate, but because physical devices are inevitably mismatched;
  5. These numbers all carry conservative engineering margins, reserved as a buffer for abnormal field conditions — they are not textbook theoretical values.