Neighborhood Microgrid Reactive-Power Optimizer

Grid Conditions

Neighborhood load 1.00×

Capacitor bank capacity 6.0 kVAR

Live Readouts

Min bus voltage

1.000 pu

Feeder loss

0.0 kW

Cost J(Q)

0.000

GD iteration

How it works

Ten houses hang off one radial feeder from a substation (the slack bus, held at V₀ = 1.000 pu). Kirchhoff's Current Law fixes the power carried by each branch: the flow into branch i equals the sum of every load beyond it, since current can't accumulate at a node.

Branch flow:   P_i = Σ_{j≥i} P_load,j        Q_i = Σ_{j≥i} (Q_load,j − Q_cap,j)
Voltage drop:  V_i = V_{i-1} − (R_i·P_i + X_i·Q_i) / V_{i-1}
Branch loss:   ΔP_i = R_i · (P_i² + Q_i²) / V_{i-1}²

This is the linearized DistFlow model used for real distribution-feeder studies: real power sags voltage mostly through line resistance R, reactive power through reactance X. Every house also draws reactive power at a lagging 0.94 power factor (inductive loads — motors, compressors), which is exactly what pulls the far end of the feeder below 1.0 pu as load climbs.

Each house's capacitor bank injects positive Q_cap, cancelling reactive demand locally instead of drawing it all the way from the substation. Gradient descent tunes the ten Q_cap values to minimize a cost function balancing voltage deviation against capacitor usage:

J(Q) = Σ_i (V_i − 1)²  +  λ Σ_i Q_cap,i²
Update:  Q_cap,i ← clamp( Q_cap,i − η · ∂J/∂Q_cap,i , 0, Q_max )

The partial derivatives are estimated by finite differences each step (nudge one capacitor, re-solve the feeder, measure the change in J) — the same numerical-gradient idea behind real power-system optimal-power-flow solvers before analytic Jacobians are built.

Neighborhood load — scales every house's real power draw, simulating time-of-day demand.
Capacitor bank capacity — the ceiling Q_max each house's bank can supply; raise it to see how much voltage headroom more compensation buys.
Run gradient descent — steps every capacitor toward the values that flatten the voltage profile; watch the cost J fall each iteration.

Voltage ≥ 0.98 pu Voltage 0.95–0.98 pu Voltage < 0.95 pu

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