Interval analysis applied to the maximum loading point of electric power systems considering load data uncertainties

Comprehensive approach for distribution system planning with uncertainties

“…The IPF is used in the I‐DSEP model to solve the IPF (25) and (26) and to give all interval variables previously defined. The IPF can measure the impact of uncertainties over the system load [26] and generation in a single step, through the reflection of such uncertainties into nodal voltage magnitude and phase angle, as well as into output variables as loss, current and power from substation. IPF starts from the convergence of the deterministic power flow that is solved by using the Newton's method [27] in polar coordinates.…”

“…The interval model is based on the Krawczyk's approach, an efficient technique for solving non‐linear interval systems that stems from the Newton's method [13, 21]. The IPF steps are described in detail in [13, 26].…”

Affine arithmetic‐based power flow algorithm considering uncertainty for hybrid AC/DC grids incorporating VSCs

“…1, the DC‐side power injected from the VSC can be expressed as where denotes the losses of the converter. A detailed calculation model can be found in [27]. Here, are constant loss coefficients.…”

Three‐phase power flow calculation considering probability and interval uncertainties for power distribution systems

“…A technique based on interval arithmetic and forward/backward sweep method for IPF problem was presented in [18], although the hull results cover all the possible value of PF solutions, it is overconservative due to the completely independent natural of interval numbers (INs). In order to improve the accuracy of IPF, many techniques such as iterative interval arithmetic methods [19][20][21][22], optimisation methods [23,24], affine algorithms [25,26], and mixed methods [27][28][29], have been researched and applied to solve IPF problem.…”