Overcurrent Relay Coordination Calculator: IEEE & IEC TCC

Let $r=I_{base}/I_{local}$ be each relay’s current referral factor. On a common current base, $M=I_{base}/I_{p,base}$ and $I_{p,base}=r I_{pickup,sec}(CT_p/CT_s)$. The same factor gives $I_{50,base}=r I_{50,local}$ and $I_{L,base}=r I_{L,local}$. Keep CT entries at their nameplate ratings. For balanced through-faults across an ideal transformer, $r=V_{local}/V_{base}$: 22/11 kV gives $r=2$ on the 11 kV current base. Relay operate time is $t=D[A/(M^p-1)+B]$. IEEE uses the full coefficients in SEL (2014), Table I, PDF p. 3; IEC SI/VI/EI use $B=0$, with constants also documented by ABB. LTI follows the legacy ABB manufacturer equation. No standard tables or figures are reproduced.

The faster of inverse-time and enabled instantaneous elements operates. Breaker clearing is added after relay operation. The B–A residual grading margin is $t_B-(t_A+t_{CB,A})$; the A–fuse margin is $t_A-t_{fuse,total}$. The entered residual margin must allow for relay error, overshoot and the study's safety allowance. The 0.30 s default is an illustrative design input, not a mandated value.

Five fuse total-clearing points are interpolated linearly in log current versus log time, with no extrapolation. The screen uses 401 logarithmic currents plus the instantaneous knees, points just below those knees and fuse knots. The minimum is sampled, not a continuous mathematical guarantee.

For fixed B pickup, the minimum multiplier is $D_{req}=\max_I[(t_A+t_{CB,A}+\Delta t)/g_B(I)]$, where $g_B$ is B's operate time at multiplier one. It is rounded upward to the entered increment. If B's instantaneous delay is below the required envelope, no time dial can solve that conflict. The pickup interval is $\max(f_L I_{L,base},I_{max}/M_{hi})\le I_{p,B}\le I_{min}/M_{lo}$. The lower bound is only a candidate: enter an available pickup, then recalculate the dial.

Pickup-interval bounds are common-base amperes. The suggested actual secondary pickup is $I_{p,base}/[r(CT_p/CT_s)]$. Enter an available local secondary setting and recheck. Schneider’s Electrical Installation Guide requires referring MV and LV curves to one equivalent current base.

A negative residual margin means the upstream relay trips before downstream clearing finishes; the downstream relay may still trip first. The critical-current label retains whether its sample lies just below or at an enabled instantaneous threshold; a just-below value must not be read as the exact threshold current.

Radial series path B → A → optional fuse. Both relays see equivalent constant symmetrical RMS through-fault currents on one common base. Each relay has its own local-to-base current referral factor; CT nameplates, local instantaneous thresholds and B’s local load remain unmodified inputs. Voltage-ratio referral assumes balanced three-phase through-faults and an ideal transformer. Ideal CT transformation and ideal instantaneous thresholds. Breaker times are user estimates. Curves represent nominal relay operation; tolerances are covered only by the user's grading allowance. The sweep is a sequence of independent constant-current cases, not integration of relay memory. Zero fuse defaults are empty entry fields, not a fictitious fuse.

Screening and education only; this is not a protection study or a commissioning setting sheet. Equation editions: IEEE C37.112-1996 and IEC 60255-151:2009. LTI is a legacy IEC/BS manufacturer family, not an additional IEC 60255-151 Annex A curve. Enforced inverse-time domains: IEEE MI/VI/EI 1.5–20× pickup, IEC SI/VI/EI 2–20×, legacy LTI 2–7× (ABB REJ523 pp. 19–20). The whole entered range must satisfy these limits even when an instantaneous element is enabled. Behaviour nearer pickup and beyond the domain is not inferred or clamped.

A passing sampled screen does not establish selective coordination. Confirm exact device curve coefficients, time-dial scale, tolerances, minimum operating time, CT performance, interrupting duty, equipment damage, arc-flash constraints and every relevant fault type/topology. Current-limiting fuses require manufacturer energy/selectivity data; fuse-saving and minimum-melting checks are excluded. A qualified protection engineer must check settings against the standard in force; installation and commissioning belong to qualified personnel.

Time-dial trap: some US VI implementations use $A=3.88$, $B=0.0963$ in $D[A/(M^2-1)+B]$, whereas the full IEEE VI coefficients here are $19.61$ and $0.491$. Their operating times differ by roughly 5.1× at the same dial. They are similar fitted shapes, not an exact universal conversion: compare both coefficients and manufacturer conventions, not the curve name. SEL (2014) documents both conventions on PDF pp. 3–4.

Scalar current referral does not establish phase or earth-fault equivalence across transformer vector groups. Use voltage-ratio factors for balanced three-phase through-faults only; unbalanced faults, zero-sequence transfer, taps and inrush require a separate protection study.