Modelling notes and FAQ

Practical questions that recur when building cases, with answers sourced from the current implementation (some differ from older guidance where BMOPFTools has since added support). Symbols are defined in Notation.

How do I model a constant-impedance or constant-current load?

Use the load model field: constant_impedance ($P\propto|V|^2$), constant_current ($P\propto|V|$), or a full zip mix, with v_nom giving the reference voltage. (Older guidance suggested emulating a constant-impedance load with a shunt; that is no longer necessary now that voltage-dependent load models are supported.)

How do I define a triplex (split-phase service) load?

As one or more single-phase loads across the triplex terminals. For a 1 kW load across legs 1–2 of a triplex bus with terminal_names ["1","n","2"], define a SINGLE_PHASE load with terminal_map ["1","2"] and p_nom [1000.0]. A two-terminal SINGLE_PHASE map is modelled across exactly those two terminals (here line-to-line, 240 V), not phase-to-ground — see Loads.

I converted a wye load to delta with the standard transform and got a different answer. Why?

Because a distribution wye load is four-wire — three phase branches to a neutral return conductor — whereas the textbook delta–wye (Y–Δ) transform assumes a three-wire wye with no return (a graph-theoretic star). The transform is not applicable to a wye-with-neutral load. Model the wye and delta connections directly via the load configuration field; do not pre-transform.

How do I model a three-wire wye load (no neutral return)?

Add a floating midpoint terminal at the bus and connect three single-phase loads (or a wye-with-return whose neutral ties to that floating node) across the phases to it. The floating node carries no external connection, so it enforces the zero-return-current condition of a true three-wire star. There is no dedicated "wye-without-neutral" load subtype.

How do I get center-tap transformer impedances from OpenDSS or Gridlab-D?

OpenDSS specifies the three inter-winding short-circuit reactances $\texttt{Xhl},\texttt{Xlt},\texttt{Xht}$ (% p.u.). These map to the per-winding reactances by the star (T) transform $[\texttt{Xh};\texttt{Xl};\texttt{Xt}] = \tfrac12\,\mathbf{S}\,[\texttt{Xhl};\texttt{Xlt};\texttt{Xht}]$ with $\mathbf{S}=\left[\begin{smallmatrix}1&-1&1\\1&1&-1\\-1&1&1\end{smallmatrix}\right]$, then to ohms via the winding voltage/power base. The transformer page gives the full partitioning (and warns against the common $\texttt{Xhl}/2$ shortcut, which is wrong for center-tap under unbalance).

Gridlab-D gives per-unit primary impedance and secondary impedance1 with a power_rating for the whole transformer. The per-winding SI impedances are

\[\textcolor{brown}{Z_i} = \texttt{impedance}\cdot\frac{3}{1000}\cdot\frac{\texttt{primary\_voltage}^2}{\texttt{power\_rating}}, \qquad \textcolor{brown}{Z_j} = \texttt{impedance1}\cdot\frac{3}{1000}\cdot\frac{\texttt{secondary\_voltage}^2}{\texttt{power\_rating}},\]

where the factor 3 accounts for the total rating being three times the primary-winding power, and 1000 converts the kVA rating to VA.