CT Sizing Calculator

The CT Sizing Calculator is an online based engineering calculator tool designed for power system protection engineers.

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It automates the sizing verification of Current Transformers (CTs) connected to the neutral of a power transformer secondary winding.

The calculator evaluates two important protection functions:

• Core I – 51NS: Definite Time Ground Overcurrent Protection

• Core II – 64R: Restricted Earth Fault (REF) Protection

Terms

Term	Definition
CT	Current Transformer – a measuring transformer that produces a reduced secondary current proportional to the primary current.
51NS	ANSI device number for a time-overcurrent relay applied to the neutral-to-ground current (ground overcurrent, definite or inverse time).
64R	ANSI device number for a Restricted Earth Fault relay that operates for internal transformer winding faults.
REF	Restricted Earth Fault – a high-impedance or low-impedance differential protection scheme sensitive to earth faults within a defined zone.
Knee Point Voltage (Vk)	The point on the CT magnetization curve at which a 10% increase in voltage results in a 50% increase in magnetizing current. Required parameter for Class PS/PX CTs.
Class PS / PX	IEC accuracy class for protection CTs defined by Vk and Rct, rather than accuracy at rated burden. Used for differential and REF schemes.
Rct	Secondary winding resistance of the CT, measured at 75°C. A key parameter in knee point voltage calculations.
Through Fault Current	The maximum fault current that flows via the CT primary without the fault that is being in the protected zone. Used for stability calculations.
Loop Resistance (RL)	The total resistance of the pilot cable circuit including outgoing and return conductors.
%Z	Transformer impedance expressed as a percentage of base impedance. Used to calculate maximum through-fault current.

Core I: 51NS Definite Time Ground Overcurrent

Purpose

The 51NS function provides definite time overcurrent protection against ground faults by measuring the residual current at the transformer neutral.

The CT should be adequately rated to accurately regenerate the fault current under maximum via fault conditions without saturating.

Input Parameters

Parameter	Unit	Description	Default
CT Primary Ratio	A	Primary current rating of the CT	900 A
CT Secondary Ratio	A	Secondary current rating of the CT	1 A
Accuracy Class	–	IEC accuracy class of the CT (e.g., 5P10, 5P20)	5P10
CT Rated Burden	VA	Nameplate rated burden of the CT	15 VA
IDMT Relay Burden	VA	VA burden of the overcurrent relay at rated secondary current	0.1 VA
Cable Length (one-way)	m	One-way cable route length from CT to relay panel	150 m
Cable Size	mm²	Cross-sectional area of pilot cable conductors	4 mm²
Resistivity at 75°C	Ω/km	Conductor resistivity at 75°C operating temperature	5.41 Ω/km

Calculation Procedure

Step-1: Loop Resistance

Loop Resistance Formula:

R‹L› = 2 x L(m) x ρ(Ω/km) ÷ 1000

Factor of 2 accounts for the outgoing and return conductors of the pilot cable loop.

Step-2: Loop Burden

Loop Burden (at rated secondary current):

Loop Burden (VA) = R‹L› (Ω) x I²‹sec›

At rated secondary current (e.g., 1 A or 5 A) and this is the VA drop across the cable resistance.

Step-3: Total Burden & Safety Check

Total Connected Burden:

Total Burden = Loop Burden + Relay Burden

The CT rated burden must be ≥ Total Burden for the CT to operate within its accuracy class

Condition	Result
CT Rated Burden ≥ Total Burden	✔ SAFE – CT is adequately rated
CT Rated Burden < Total Burden	✘ NOT SAFE – Select a higher-rated CT or reduce burden

Core II: 64R Restricted Earth Fault Protection

Purpose

The 64R (Restricted Earth Fault) scheme provides high speed, sensitive protection against internal earth faults in the transformer winding zone bounded by the differential current transformers. 

It uses Class PS (or PX) CTs which must meet a minimum Knee Point Voltage (Vk) to maintain stability under maximum through-fault current.

Input Parameters

Parameter	Unit	Description	Default
CT Primary Ratio	A	Primary current rating of the CT	900 A
CT Secondary Ratio	A	Secondary current rating of the CT	1 A
Primary Voltage	kV	Transformer primary (HV) winding voltage	33 kV
Secondary Voltage	kV	Transformer secondary (LV) winding voltage	6.6 kV
Transformer Rating	MVA	Transformer nameplate MVA rating	8 MVA
Transformer Impedance	%Z	Positive sequence impedance as percentage	8.35%
Accuracy Class	–	Must be Class PS or PX for REF schemes	PS
REF Relay Burden	VA	VA burden of the REF relay	1.0 VA
Cable Length (one-way)	m	One-way pilot cable route length	150 m
Cable Size	mm²	Pilot cable conductor cross-section	4 mm²
Resistivity at 75°C	Ω/km	Conductor resistivity	5.41 Ω/km
CT Secondary Resistance Rct	Ω	Internal winding resistance of CT secondary	2 Ω

Calculation Procedure

Step-1: Maximum Through-Fault MVA

Through-Fault MVA:

Fault MVA = (Transformer MVA x 100) ÷ %Z

Represents the maximum short-circuit power that can flow through the transformer.

Step-2: Through Fault Current at Primary

Primary Fault Current:

I‹f› = (Fault MVA x 10⁶) ÷ (√3 x V‹primary›)

Three phase fault current referred to the transformer primary (HV) side.

Step-3: Fault Current Referred to CT Secondary

Secondary Fault Current:

I‹fs› = I‹f(primary)› ÷ CT Ratio

Cross-check: (Fault MVA x 10⁶) ÷ (√3 x V‹secondary› x CT Ratio)

Step-4: Loop Resistance

Loop Resistance:

R‹L› = 2 x L(m) x ρ(Ω/km) ÷ 1000

Step-5: Required Knee Point Voltage

Knee Point Voltage Formula (IEC 60044-1 / BS 3938):

V‹k› ≥ 2 x I‹fs› x (R‹ct› + 2 x R‹L›)

The factor of 2 provides stability margin. 

The factor 2xR‹L› accounts for the outgoing and return leads.

Step-6: Governing Vk

The governing (adopted) Vk for CT procurement is the higher of:

• The calculated Vk from Step 5, and
• The project minimum specification (typically ≥ 500 V)

Governing Vk = max(Calculated Vk, Project Minimum Vk)

Vk‹govern› = max(V‹k(calc)›, 500 V)

The CT should be procured with a Vk equal to or > the governing value.

Input Parameters Quick Reference

Symbol	Description	Unit
Rp	CT primary ratio (rated current)	A
Rs	CT secondary ratio (rated current)	A
ρ	Conductor resistivity at 75°C (Cu: 5.41 Ω/km; Al: 8.93 Ω/km)	Ω/km
L	One-way cable length from CT to relay	m
R‹L›	Pilot cable loop resistance = 2 × L × ρ / 1000	Ω
Rct	CT secondary winding resistance (Class PS requirement)	Ω
V‹k›	CT knee point voltage (Class PS specification parameter)	V
MVA	Transformer nameplate MVA rating	MVA
%Z	Transformer positive sequence impedance	%
V‹p›	Transformer primary (HV) voltage (line-to-line)	kV
V‹s›	Transformer secondary (LV) voltage (line-to-line)	kV
I‹f›	Maximum through-fault current at primary	A
I‹fs›	Maximum through-fault current at CT secondary	A

Applicable Standards & References

Standard	Title	Relevance
IEC 60044-1	Instrument Transformers: Current Transformers	CT accuracy classes 5P, 10P, PS
IEC 61869-2	Additional requirements for current transformers	Class PX definition (replaces IEC 60044-1)
BS 3938	Specification for Current Transformers	Class X (Knee Point Voltage) definition
IEC 60255	Measuring relays and protection equipment	Relay burden and performance
ANSI/IEEE C37.110	Guide for the Application of CTs used for PRM	CT sizing methodology
IEEE C37.91	Guide for Protecting Power Transformers	REF protection philosophy