Power flow
What it does
A power flow study answers the question that most other studies depend on: with this generation and this demand, what is the voltage at each bus, and how much current is in each branch?
Phasor solves the nodal power balance equations with the Newton–Raphson method. Each bus gives two equations: the real power balance and the reactive power balance. The solver changes the voltage magnitude and the voltage angle at each bus, step by step. It stops when the power mismatch at each bus is below the tolerance.
The solver builds and factorizes the Jacobian matrix again in each iteration, with a sparse LU factorization. Because of this, the solution usually needs only three to five iterations. The size of the network does not change this number by much.
Bus types
Each bus has one of three standard types. If these types are new to you, start with Bus types explained — it has an interactive diagram.
- Slack bus. The voltage magnitude and the angle are fixed. The slack bus supplies the difference between generation and demand, plus the losses. Each electrical island needs exactly one slack bus.
- PV bus. The real power and the voltage magnitude are fixed. The reactive power output is free, up to the generator's Q limit. When the output reaches the limit, Phasor changes the bus to a PQ bus, and the voltage can then move. Phasor reports each change of this type. This report is important: a generator that has no more reactive capability is often the difference between a good voltage profile and a bad one.
- PQ bus. The real power and the reactive power are fixed. Loads and unregulated injections are PQ buses.
How to run a power flow
- Build or open the network. Each branch needs an impedance. Each bus needs a nominal voltage.
- Set the demand scenario. You can define a load as constant power, constant current or constant impedance. You can scale the loads for each scenario — peak, minimum, N-1 — without a copy of the model.
- Set the generation dispatch. Select the slack bus. Set the voltage targets of the PV buses. Enter the reactive power limits of each generator.
- Select how the solver holds the transformer taps. There are two options. Option 1: the solver keeps each tap at its current position. Option 2: the solver moves the tap between iterations to hold a target voltage.
- Run the study. The results color the SLD directly: a voltage heatmap on the buses, the loading on the branches, and a flag on each violation.
- Read the violations list first. The list is in order of severity. Each entry shows the element name that you gave it.
Inputs and outputs
Inputs
| Input | Notes |
|---|---|
| Network topology | Buses, branches, switch states. An open switch can divide the network into islands. |
| Branch impedances | R, X and B, in per unit or in ohms. Phasor multiplies per-km values by the line length. |
| Transformer data | Rating, voltage ratio, impedance, tap range and tap step, vector group. |
| Load definitions | P and Q, or P and power factor, for each scenario. |
| Generation | Dispatch, voltage targets, Qmin and Qmax. |
| Solver settings | Mismatch tolerance, iteration limit, and flat start or warm start. |
Outputs
| Output | Notes |
|---|---|
| Bus voltage | Magnitude in per unit and in kV. Angle in degrees. |
| Branch flow | P, Q, current, and the loading as a percentage of the continuous rating. |
| Losses | For each branch, and the total. Divided into copper losses and shunt losses. |
| Tap positions | The final position of each regulated tap changer. |
| Q limit events | Each PV bus that became a PQ bus, and the limit that caused it. |
| Violations | Each bus outside its voltage band. Each branch above its rating. |
If the study does not converge
Non-convergence is usually a fault in the model, not a fault in the solver. The solver names the bus with the largest remaining mismatch. The cause is usually near that bus.
Check for these causes, in this order:
| Cause | How to find it | What to do |
|---|---|---|
| An island with no slack bus | Open Graph Space. It shows each island. | Close the correct switch, or give the island a source. |
| A branch with zero impedance, or with no impedance | Check the branches near the named bus. | Enter the correct impedance. |
| A load that is too large for the network | Compare the load with the source capacity. | Correct the load value, or accept that the network cannot supply it. |
| A transformer impedance on the wrong base | Check the impedance and its base. | Enter the value on the correct base. |
Notes
Select the voltage band. Do not accept a default. Phasor includes bands in the style of ANSI C84.1 and EN 50160. But the correct band for your network is a policy decision. Set the band on the project. The reason: a 0.95–1.05 pu band and a 0.90–1.10 pu band give very different violation lists from the same results.
Keep the per-unit bases consistent. When you enter an impedance in percent on the equipment rating, Phasor converts it to the project base. But if you enter a value that is already on a different base, no check can find the error. The results downstream will be wrong.
Do not mix loading assumptions
Use one loading basis in each scenario. If one feeder has a high demand estimate and another feeder has a low one, the result is a network state that cannot occur in operation. The fault levels and the grading margins that come from that state have the same problem.