Power Systems Lab · 18 modules · all computed in your browser

Five-source network spec

The original Advanced lab: model scope and boundaries.

Lab 02 / Five sources · three buses

Study the whole network.

Two utility infeeds, synchronous DG, solar DG and BESS. Inspect power flow, faults, and the currents each relay actually sees.

PresetAll five online

PresetDER offline

PresetBESS charging

PresetUtility B offline

Each preset starts from the default network. Faults are applied at U · Utility, P · Plant, or F · DER. Source labels are solved MW injection; negative means absorption. The same ideal CT ratio is applied at both displayed relay locations. Positive BESS MW discharges; negative MW charges. Duration uses constant scheduled AC power, present state of charge and the entered one-way efficiency. It excludes auxiliaries, temperature, degradation and voltage-dependent limits.

Study controls, as specified

Base, loads and tap changer. All impedances use one common three-phase MVA base. Buses are nominally 13.8 kV equivalents; utility-side values are already referred to this voltage.
Find closest tap. A static search over 33 positions. No automatic time delay and no hunting.
Transformer, feeder and breakers. T1 is a grounded-wye / grounded-wye equivalent with a zero-sequence path and no phase shift. That is an explicit training assumption.
Faults. ABC is per phase. A–G is phase to ground. B–C is between phases. B–C–G joins B and C, then a common resistance to ground.

What this model does — and where it stops

Balanced power flow

Three-bus complex nodal equations with constant-PQ loads and solar/BESS injections. Two utility equivalents and one synchronous DG are voltage sources behind impedances. A damped Newton method solves six real current-balance equations. Results include convergence residuals and a complex power-balance check. Generator excitation, governors and reactive limits are not simulated. Scheduled inverter P/Q is held constant; low-voltage operation may exceed rated current and is flagged rather than silently clamped.

Sequence fault study

Positive, negative and zero-sequence admittance matrices are formed independently. The solver obtains the selected bus driving-point impedances, connects the sequence networks for ABC, A–G, B–C or B–C–G, then reconstructs bus voltages and branch currents. Loads are omitted from the fault model. Conventional-source internal EMFs remain at their entered values. Fixed positive-sequence inverter fault injections use their rated current multiplier and angle relative to pre-fault local voltage. The fault-network open-circuit voltage is recalculated; it is not the loaded pre-fault voltage.

Tap and storage

T1 has a real off-nominal ratio a = 1 + tap × step/100 at the U end. Yff = y/a², Yft = Ytf = −y/a and Ytt = y. Increasing a reduces the ideal downstream voltage for a fixed upstream voltage; other infeeds alter the system response. BESS state of charge is a static energy calculation. Tap search is a static sweep, not a dynamic OLTC. Grid-following DER alone cannot establish an island voltage; unsupported islands are rejected.

Boundaries

All quantities are steady RMS fundamental-frequency phasors. One common three-phase MVA base and nominal line-to-line kV base apply throughout: Zbase = kV²/MVA and Ibase = MVA × 1,000 / (√3 × kV). Changing the base without rebasing entered per-unit values changes the physical network. The same fixed source Thevenin impedance is used in power flow and the fault network. Source Z₂ = Z₁. Source Z₀ and branch Z₀ use the entered multipliers. All conventional sources have a grounded zero-sequence path. Solar and BESS have no independent negative or zero-sequence injection in this model. There is no load unbalance, harmonics, electromagnetic transients, motor starting, dynamic stability, inverter control model, arc-flash calculation or multi-terminal protection logic. Switches remove paths algebraically; they do not model interrupting duty.

The single-source case you can solve by hand, and check, is Bus fault lab. This five-source study is the specification above: Newton power flow, sequence faults, tap sweep and storage energy. Educational results still need an appropriate model and a review before any real equipment decision.

Learn it

With several infeeds (utility, synchronous DG, inverter-based solar and BESS), the fault current at any point is the sum of every source's contribution. Each relay sees only the part that flows through its own CT.

Inverter-based sources are current-limited to about 1.1 to 1.5 pu, so taking them offline barely changes the fault level, while losing a utility infeed changes it a lot.

Quiz · 0/2

1. Why does taking solar offline barely change the bus fault current?
2. Infeed from a second source at the remote bus makes a distance relay…

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