🎓 Lesson 18
D5
Hosting Capacity Estimation: Voltage & Reverse Power Limits
Hosting capacity estimation tells us how much solar or wind power a local part of the grid can safely absorb without causing voltage problems or sending too much power backward into the system.
🎯 Learning Objectives
- ✓ Calculate voltage rise at a DG connection point using simplified load-flow principles
- ✓ Analyze reverse power flow magnitude relative to utility interconnection limits (e.g., IEEE 1547-2018)
- ✓ Explain how transformer thermal limits and feeder X/R ratio influence hosting capacity
- ✓ Apply sensitivity-based methods to rank feeder segments by hosting capacity potential
📖 Why This Matters
As mines increasingly deploy solar PV, battery storage, and diesel-replacement microgrids, engineers must ensure new generation doesn’t destabilize aging medium-voltage distribution feeders. Overvoltage during low-load/high-generation periods—or reverse power tripping protective relays—can halt operations, damage equipment, or trigger unplanned blackouts. Hosting capacity estimation is the first engineering gate before any DG project gets approved.
📘 Core Principles
Hosting capacity hinges on two dominant physical constraints: (1) Voltage rise — caused by reactive and active power injection into impedance-limited feeders (ΔV ≈ (R·P + X·Q)/V₀); and (2) Reverse power flow — where DG export exceeds local load, risking relay misoperation and violating utility anti-islanding rules. Additional factors include harmonic distortion, fault current contribution, and dynamic stability under load transients. Modern estimation uses quasi-static time-series simulations (e.g., 15-min load/generation profiles over a year), but analytical approximations remain essential for rapid screening—especially in remote mining sites with limited modeling resources.
📐 Voltage Rise Approximation (Single-Phase Equivalent)
This simplified formula estimates worst-case voltage rise at the DG point of connection due to active power injection—assuming unity power factor and negligible upstream voltage regulation. It’s used for preliminary screening before detailed load-flow studies.
Approximate Voltage Rise (Per Unit)
ΔV_pu ≈ (R·P_gen + X·Q_gen) / V₀²Estimates steady-state voltage change at point of common coupling due to DG active/reactive power injection.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| ΔV_pu | Voltage rise | pu | Per-unit voltage deviation from nominal |
| R | Line resistance | Ω | Total series resistance from substation to PCC |
| X | Line reactance | Ω | Total series reactance from substation to PCC |
| P_gen | Net active power injection | W | DG output minus local load at PCC |
| Q_gen | Net reactive power injection | VAR | Reactive power supplied by DG (positive = capacitive) |