Power flow & voltage

This page solves the network load flow and reports the voltage, current, loss and loading picture of the scheme. The engine is engines/loadflow.js: a nodal admittance (Ybus) build with constant-power load iteration. One run issues three /api/design/loadflow calls (full load 1.0, half load 0.5, no load 0) plus one /api/design call that returns the cable schedule, the transformer loss and the tap position. The slack node is an ideal voltage source behind the upstream grid impedance Zg, which is derived from Ssc and X/R, so a weak supply shows a real voltage dip. Results are per-node voltage magnitude and angle, per-branch current / power / loss / loading, total network loss, power factor, the violation list and the warnings. The three load levels it solves are the operating points the rest of the simulator reads, and the cable schedule keeps the authoritative loading figure and the load-flow figure side by side instead of mixing the two bases.

This is the page that answers "does the scheme hold its voltage". It decides whether a transformer tap has to be moved, whether compensation is needed, whether a section has to be increased, and whether a PV or storage connection point sits above the allowable voltage. It is also the physical basis of every money number downstream: the loss allocation, the annual energy cost and the life-cycle cost are all built on this solution rather than on a rule of thumb, and the voltage violation list is the first thing a grid-connection reviewer looks at.

Input: nodes and edges with section / length / material / cores, load kW, cos φ and load type (static, motor, nonlinear), transformer Sn / uk / no-load loss P0 / load loss Pk / tap position, external Ssc and X/R, capacitor bank kvar → chain: branch impedances are put in per unit (Sbase = 1 MVA, Vbase per voltage level, so the transformer ratio normalises away and impedances across voltage levels can be summed) → Ybus is assembled and parallel branches handle loops without any loop-breaking input → the slack node becomes ideal source E behind Zg → constant-power loads, compensation injections and motor starting are converted into shunt admittances and the complex system is solved iteratively until max|ΔV| ≤ 1e-8 pu → node voltage and angle, branch current / power / loss / loading, total loss = line I²R + transformer P0 + Pk×(S/Sn)² → violation list (below 0.95 pu or above 1.05 pu, with a separate severe alert below 0.90 pu) → output. Linkage: enlarging a section lowers the resistance, so the voltage drop and the I²R loss fall while the fault current rises, which in turn raises the protection sensitivity and the Icw the switchgear must be rated for. Moving a tap changes the secondary voltage and the transformer loss at the same time. Adding capacitor kvar raises the voltage and cuts the network loss but can push a resonance point towards a dominant harmonic, which is why the volt-VAR recommendation re-runs the resonance scan before it accepts a capacitor step. Approximations, all disclosed: positive-sequence, balanced three-phase, constant-power loads computed at the three load levels; ampacity values are engineering typical values (copper YJV on a tray at 30 °C); cable earth capacitance is included as a π equivalent from cable-library typical values and can be switched off for a bit-identical legacy result.

1000 kVA transformer, 400 kW load at cos φ 0.9 (= 0.9 pf, 194 kvar) fed by 200 m of 240 mm² copper: the far end of the feeder sits at 0.9185 pu and the network loss is 24.3 kW (6.1% of load, transformer loading 48%). Changing that feeder to 400 mm² raises the far-end voltage to 0.9352 pu and cuts the loss to 15.2 kW (3.8%); halving the length to 100 m gives 0.9512 pu and 12.7 kW.

Voltage drop and ampacity from IEC 60364-5-52 / GB 50054 and GB/T 16895 series, load-flow formulation per IEC 60909 network reduction, power-factor limits per GB/T 14549 / IEEE 519 context, transformer losses per GB 20052-2020 efficiency grades.

Why does the voltage drop so much on a 200 m feeder?

Because the load current of about 642 A through a 240 mm² copper conductor produces a resistive and reactive voltage drop of roughly 8% at full load. Doubling the cross-section or halving the length both reduce it — the table above shows the exact numbers for this scheme.

Is the power flow solved or estimated?

Solved. The engine builds the network admittance matrix and iterates node voltages (Newton-Raphson, with PV buses for generators and inverters that hold a voltage set point) until the mismatch is below 1e-8; if it does not converge the solver falls back and the response says so.

What do the four alarms mean?

Overload: a cable or transformer above its ampacity / rating. Undervoltage and overvoltage: a loaded node outside the allowable band. Low power factor: the network pf below the usual 0.9 requirement, which is also what the capacitor-bank sizing on the power-quality page reacts to.