Transmission & Grid calculator
Load Flow Calculator: AC Power Flow & Bus Voltages
Solve a small AC power-flow network for bus voltages, branch MW/MVAr and losses. Includes an editable five-bus example and Newton–Raphson iteration.
GridBasis: AC nodal power balance · Newton–Raphson
Results
- Enter values to calculate
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How to use this calculator
Load flow calculates a steady operating point. Start with the example, then replace the bus and branch rows using one consistent MVA base. A slack bus fixes magnitude and angle; a PV bus fixes active power and magnitude; a PQ bus fixes active and reactive power.
Read voltage magnitude first, then source injections and branch loading. A converged solution only means the power-balance equations were solved; it does not mean the system meets operating limits. Negative net injection is consumption. A branch result includes its sending-end charging contribution.
Formula
I = Ybus V; Sᵢ = Vᵢ conj(Σ Yᵢⱼ Vⱼ)
Pᵢ = |Vᵢ| Σ |Vⱼ| [Gᵢⱼ cos(θᵢ−θⱼ) + Bᵢⱼ sin(θᵢ−θⱼ)]
Qᵢ = |Vᵢ| Σ |Vⱼ| [Gᵢⱼ sin(θᵢ−θⱼ) − Bᵢⱼ cos(θᵢ−θⱼ)]
J Δx = [Pspec−Pcalc; Qspec−Qcalc]; xnew = x + Δx
Here Ybus = G + jB, x contains non-slack angles and PQ voltage magnitudes. P equations apply to PV/PQ buses; Q equations apply to PQ buses. Numerical derivatives form the Jacobian; a damped step reduces mismatch.
y = 1/(R+jX); Yff = (y+jBline/2)/tap²; Yft = Ytf = −y/tap; Ytt = y+jBline/2
Sfrom = Vfrom conj(Yff Vfrom + Yft Vto) × Sbase. Sum sending/receiving-end branch powers for losses.
Worked example
The example uses a 100 MVA base, slack bus 1 at 1.04 p.u., PV bus 2 generating 50 MW at 1.01 p.u., and three loads totaling 145 MW and 45 MVAr. The solver calculates generator reactive output and transmission losses from the listed impedances. This is an original teaching network, not an IEEE benchmark case.
The sample solution gives bus 5 approximately 0.969520 p.u. at −5.760°, and total active branch loss of 3.3515 MW.
Assumptions and standards
- Balanced positive-sequence AC model; up to 30 buses and 100 branches, one slack bus, one connected network.
- Constant-PQ loads; real taps and π-line charging included. Phase-shifting transformers, PV reactive limits and equipment thermal limits are not enforced.
- Mismatch tolerance is 10⁻⁹ p.u.; maximum 40 Newton steps. Failed convergence produces an error instead of solved results.
Calculation model checked: November 4, 2026
Frequently asked questions
What is the difference between load flow and fault current?
Load flow solves normal steady-state voltage and power balance. Fault-current analysis solves the network during a specified fault using the relevant source and sequence models.
Why is there a slack bus?
The slack bus supplies the real and reactive mismatch left after loads, generator schedules and network losses are accounted for.
Can this solve transmission networks?
It solves small balanced networks within the stated model. A utility study additionally needs verified equipment models, limits, controls, contingencies and independent validation.
Can I use these results for final design?
Use them for preliminary design and checking. Final designs must be verified by a qualified engineer against the code edition and standards adopted where the work is installed.
Is my data sent anywhere?
No. Every calculation runs in your browser. Nothing you type is uploaded or stored on our servers.
References and further reading
Power system calculations: formulas and model guide