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Home / TechnologyConvergence Issues with Newton-Raphson Method

In the animation below, weve developed an example to visually show the issues with the Newton-Raphson Method. Weve chosen a twobus model primarily because in such a simplified model, the mathematical solutions can be calculated directly. In this idealized scenario,we see several of the key problems. These include: the existence of both a physical and virtual solution to the quadratic equation, thefractal nature of the solution, solutions that are sometimes incorrect, sometimes correct with wrong phase angle, and increasingly along thevoltage collapse curve, provide no resolution. Our direct HELM based algorithms suffer none of these issues. HELM always providean accurate physical solution to the load-flow or advise when one does not exist. Reference files are to the left.

version 0.6

Antonio Trias IEEE Paper 2012 (Pdf)

Antonio Trias Presentation To EEI 4-2012(Pdf)

Two Bus Model Mathematical Proof (Pdf)

United States Patent N 7,519,506 B2-System And Method For Monitoring AndManaging Electrical Power TransmissionAnd Distribution Networks (Pdf)

United States Patent N 7,979,239 B2-System For Monitoring And ManagingElectrical Power Transmission AndDistribution Networks (Pdf)

Move your mouse along the voltage collapse curve (topright). For each point along the curve, weve generated forover a million starting points, the load flow solution shownin the circular image (bottom left). The stacked histogram(bottom right) provides details of the frequency of eachsolution class.

No convergence The iterations have not convergend after the cut-off limit.

Anomalousconvergence

The iterations have converged to a point that is neither one of the two knownsolutions.

Unstable: wrongwinding

The iterations have converged to the unstable solution, but the angle is shiftedby possibly large multiples of 2.

Unstable: rightwinding

The iterations have converged to the unstable solution, and the angle isnormalized within -, .

Stable: wrongwinding

The iterations have converged to the correct operational solution, but the angleis shifted by possibly large multiples of 2.

Stable: rightwinding

The iterations have converged to the correct operational solution, and theangle is normalized within -, .

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