Premium Membership

Get access to premium HV/MV/LV technical articles, technical guides & papers. Apply a 20% discount code: 99AF8 for a 1-year plan!

Home / Technical Articles / Six tools you MUST learn before programming numerical protection relays for real

Programming of microprocessor relays

Developing basic setting specifications for numerical relays is a boring process for most electrical engineers, but not for the protection engineers! It requires significant input data but, for the most part, is exciting and relatively straightforward.

6 tools you MUST learn before programming numerical protection relays for real
6 tools you MUST learn before programming numerical protection relays for real (photo credit: Lucy Electric)

A basic understanding of Boolean expressions and methodologies is helpful in developing the required programing to obtain the desired logic and for effectively using the full power that is designed into numerical relays.

The capabilities and power that are built into microprocessor relay designs are continually expanding. In addition to providing an array of protective functions, capability to fulfill most of the control and data acquisition requirements at substations is provided.

Many modern numerical relays possess the power to replace other digital devices that are required within substation control and data acquisition systems such as PLCs, RTUs, meters, and control switches.

An obstacle to the practical use of the expanded power that is made available in microprocessor-based protective devices is the complexity of the programing that is required to use this power.

Protection engineers are not necessarily proficient in programing techniques and, as such, they may be hesitant to apply numerical relays such that their full capability is used.

Programming tools

An understanding of programing techniques is required to effectively use the many features and flexibility that are designed into modern microprocessor-based relays.

Programing tools available for programing modern numerical relays include:

  1. Boolean Algebra
    1. Example
  2. Control Equation Elements
  3. Binary Elements
  4. Analog Quantities
  5. Math operators
  6. Relay settings

Also, let’s mention the enhancements achieved by numerical relays in distribution and transmission system with mentioning of some most typical examples:

  1. Protection Enhancements
    1. Distribution Protection Systems
    2. Transmission protection Systems

1. Boolean Algebra

Knowledge of Boolean algebra and its relationship to logic created by electrical circuits is important to facilitate the task of programing numerical relays.

It is advisable for protection engineers to obtain a degree of fluency in this subject.

Many good texts and courses are available for obtaining knowledge of this subject area. A brief overview of some basic fundamentals follows.

Expressions for Boolean addition — "OR" gate
Figure 1 – Expressions for Boolean addition – “OR” gate

In Boolean arithmetic, terms can only have two states—they can be either a 1 or a 0. Rules for Boolean addition are illustrated in the following equations:

0 + 0 = 0, 0 + 1 = 1,
1 + 0 = 1, 1 + 1 = 1

It does not matter how many terms are added, the sum cannot be any larger than 1 since, as noted earlier, only 1 and 0 can exist:

0 + 1 + 1 = 1,
1 + 1 + 1 + 0 = 1,
1 + 1 + 0 + 1 + 1 + 0 = 1

Boolean addition corresponds to the logical function of an ‘‘OR’’ gate and is representative of parallel contacts in an electric circuit. The basic equations for Boolean addition along with its logical ‘‘OR’’ gate and electric circuit representation are illustrated in Figure 1 above.

Following are the equations that represent the rules for Boolean multiplication:

0 × 0 = 0,
0 × 1 = 0,
1 × 0 = 0,
1 × 1 = 1

Boolean multiplication corresponds to the logical function of an ‘‘AND’’ gate and is representative of series contacts in an electric circuit.

Expressions for Boolean multiplication - ‘‘AND’’ gate
Figure 2 – Expressions for Boolean multiplication – ‘‘AND’’ gate

Figure 2 illustrates expressions for Boolean multiplication. Boolean algebraic variables are denoted by capital letters.

Boolean variable can only have one of two values – a 1 or a 0. Every variable has a complement – the opposite of its value. If a variable A has a value of 1, then its complement has a value of 0. The symbol used for the complement of a variable is denoted by a bar over the associated capital letter.

A complement is referred to as a logical inversion and corresponds to the logical function of a ‘‘NOT’’ gate.

Expressions for Boolean complementation - ‘‘NOT’’ gate
Figure 3 – Expressions for Boolean complementation – ‘‘NOT’’ gate

Electrically, a logical inversion is equivalent to a normally closed contact. Expressions for Boolean complementation are illustrated in Figure 3.

As in mathematics, identities also exist in Boolean algebra. These identities are derived from the unique bi-variable nature of Boolean variables.

Basic Boolean additive and multiplicative identities are illustrated in Figure 4 below.

Basic Boolean identities
Figure 4 – Basic Boolean identities

Boolean algebra also contains cumulative and associative properties.

  • Cumulative property of addition: A + B = B + A
  • Cumulative property of multiplication: AB = BA
  • Associative property of addition: A + (B + C) = (A + B) + C
  • Associative property of multiplication: A(BC) = (AB)C
  • Distributive property: A(B + C) = AB + AC

Some other operators used in Boolean expressions include comparisons (<, >, = , etc.), parentheses, and rising and falling edge triggers. Numerical relays often use symbols to represent Boolean operators (i.e., + = OR,* = AND, ! = NOT).

Truth tables are often used as a first step in the programing process to illustrate exactly what the logic circuit must perform. Truth tables provide a systematic manner for setting up the associated Boolean expressions.

To promote programing efficiency, the initial expressions developed from the truth table should be reduced, using the laws of Boolean algebra, to a simplified form. The required logic circuit can then be developed from the simplified expression.

Figure 5 illustrates truth tables for a variety of logic gates used in logic diagrams.

Logic gates and associated truth tables
Figure 5 – Logic gates and associated truth tables

Go back to contents ↑


The following example illustrates the process of developing logic for control circuits:

Three pilot relaying systems are applied on a very important transmission line. In order to enhance security of the line it is desired that trip outputs from two out of the three pilot systems must be present for a trip of the line to be initiated.

A1 represents a trip output from a pilot scheme and a (0) represents no trip output from a pilot scheme. The associated truth table would look as
shown in Table 1.

A’ will be used to indicate a complement. From the four conditions in the truth table for which an output is indicated, the following Boolean equations can be developed:

Table 1 – Truth Table for ‘Two–Out–Of–Three’ Pilot Logic

Pilot 1 = A Pilot 2 = B Pilot 3 = C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1

Line 4 – A’BC = 1
Line 6 – AB’C = 1
Line 7 – ABC’ = 1
Line 8 – ABC = 1

A Boolean equation could then be developed to cover the conditions given earlier:

Output = A’BC + AB’C + ABC’ + ABC

A logic circuit could be developed to match the Boolean equation stated earlier. However, it would be rather complex. By using rules of Boolean
algebra, the aforementioned equation could be reduced to:

Output = AB + BC + AC

Whereas the logic requirements for this case were more or less intuitively obvious as the required logic was quite simple, for more complex systems it is easy to develop errors when shortcuts are taken and intuition is used instead of a step-by-step process.

It is highly recommended that when developing logic programs, truth tables and a systematic approach be used to facilitate obtaining a valid result.

The associated logic circuit for the aforementioned output equation is illustrated in Figure 6 below.

Logic circuit that satisfies output = AB + BC + AC
Figure 6 – Logic circuit that satisfies output = AB + BC + AC

Go back to contents ↑

2. Control Equation Elements

Control equation elements are a collection of storage locations, timers, and counters that are available in the relay for the user to customize the operation of the relay and to provide logic in data for substation automation.

These elements include control equation variables developed by programed Boolean equations, control equation math variables that are developed by math control equations, latches, and conditioning and sequencing timers.

They also provide storage locations for remote bits that are communicated to the relay to identify the status of other equipment.

Go back to contents ↑

3. Binary Elements

Binary elements are the outputs that are the result of internal relay logic. The logic that controls the binary elements can be pre-programed or programed by the user.

Binary elements can be used in Boolean equations to create other logic or to initiate various actions such as the trip output, close output, triggering of an event report, and so on.

An example of logic diagram for the 50N-1 overcurrent current element (SIPROTEC protection relay 7SJ62/64)
Figure 7 – An example of logic diagram for the 50N-1 overcurrent current element (SIPROTEC protection relay 7SJ62/64)

Go back to contents ↑

4. Analog Quantities

Analog quantities are current and voltage quantities that are received, measured, and calculated. Analog quantities may be instantaneous, average, or RMS values of the associated current or voltage.

Math operators are used to program the analog quantities.

Go back to contents ↑

5. Math operators

Math operators are used for writing mathematical control equations using analog values. Math operators include familiar operations such as addition, subtraction, multiplication, division, square root, logarithms, exponents, trig functions, and so on.

Programing mathematical equations by the user is usually associated with control functions rather than protective functions.

Go back to contents ↑

6. Relay Settings

In addition to programing for logic equations, microprocessor relays require inputs to assign the level and time delay at which various binary elements change state (set points for protective functions, timer setting, etc.) and to enable or disable various functions that are available in the relay.

Inputs are also required to identify phase rotation, current transformer and potential transformer ratios, time-current characteristics that are required for protection functions that operate with inverse time delay, display indications, and so on.

Many numerical relays provide for a wide selection of protective functions that can be selected for use along with a number of setting groups in which different settings can be applied.

Only one setting group can be active at one particular time. The different settings in the groups can be applied to provide the required protection for different operating conditions.

The active setting group can be selected or changed automatically or manually. Protective functions that are not desired to be used should be disabled. With the vast array of features available, numerical relays specifically require a significantly large amount of input data.

In dealing with such large amounts of data, the protection engineer must compile the input requirements with care and due diligence to avoid errors. A simple slip of a digit or an incorrect sign can have serious negative impacts on the reliability and safety of the related power system.

Go back to contents ↑

Protection Enhancements

Significant features of microprocessor-based relays that serve to enhance protection previously available through application of traditional relaying include the following:

  1. Numerical relays allow for a variety of protection systems to be applied with minimal additional cost.
  2. Changes can be made within microprocessor-based relaying systems with ease.

Application of microprocessor relaying systems along with a local area network provides a means to easily modify logic and settings and to easily apply protective schemes that previously could not be justified.

Go back to contents ↑

Distribution Protection Systems

The use of microprocessor-based relaying at distribution substations has allowed for the application of protective schemes that previously were too complex or costly to be justified.

One example is the application of breaker failure relaying. Most numerical relays come equipped with timers incorporated into the software that are available for application as desired by the user. These timers along with some simple programing can be set up to send a signal through the relay’s communication port to trip backup devices, should a feeder breaker fail to interrupt within a prescribed time after operation of an associated protective relay.

Breaker failure relaying has been sparingly applied in the past at the distribution level because of the complexity and cost involved with electromechanical breaker failure schemes.

Basic Breaker Failure Scheme
Figure 8 – Basic Breaker Failure Scheme

With microprocessor-based relaying, it is also a relatively simple matter to provide backup relaying for protection applied on distribution lines.

Backup protection can be obtained by programing the alarm contact of each feeder relay to trip the associated feeder breaker with permission from the operation of a backup overcurrent relay. Closing of the alarm contact occurs when the self-checking mechanism of a relay indicates a problem within the relay.

Overcurrent relaying that is supplied by current flowing through the substation transformer, in many cases, is applied for bus or transformer protection. The overcurrent elements that exist for this relaying can be used for the overcurrent supervision function for the feeder backup protection at minimal additional cost.

The bus relay is programed to trip through an overcurrent relay with a short time delay. The bus overcurrent relay is set to pick up at a level slightly above that of the blocking overcurrent relays on each feeder.

For faults on a feeder, if sufficient fault current exists to pick up the bus overcurrent relay, the blocking overcurrent relay on the faulted feeder will also always operate and block tripping of the bus protection. If the fault is on the bus, none of the feeder overcurrent relays will operate, and the bus scheme will operate after a short time delay.

A time delay of about six cycles will usually be sufficient on the bus scheme.

Larger three-phase motors may be individually protected against unbalances. Smaller three-phase motors and single-phase motors, however, may not be equipped with such protection.

Utilities have received many complaints and lawsuits on account of the motors that have failed when continued operation of a distribution substation with a blown high-side fuse was allowed.

Refrigerator and air-conditioning motors are especially vulnerable under such conditions and one substation may supply many hundreds of such motors.

Application of microprocessor-based relays makes it relatively easy to detect the earlier mentioned blown fuse condition at distribution substations. Microprocessor relays are usually equipped with undervoltage elements that can be programed to detect voltage conditions representative of a blown high-side fuse on a delta–wye connected transformer and to initiate appropriate action to disconnect affected loads.

Typical settings that could be programed into the relay might be such that an output is initiated if, at the same time, any phase-to-phase voltage is less than 40% of nominal AND any phase-to-phase voltage is above 70% of nominal.

Such a setting will detect conditions that exist for a blown high-side fuse condition but will not initiate an output for a blown fuse on the potential transformer that supplies the relay. For a blown PT fuse, two lowside phase-to-phase voltages drop to 58% whereas the other phase-to-phase voltage remains normal.

The ability to automatically change settings on numerical relays can also provide beneficial flexibility at distribution substations. Settings can be reduced at light load conditions to obtain greater sensitivity for fault coverage.

Go back to contents ↑

Transmission protection Systems

The flexibility provided by numerical relays can provide significant benefits for protecting transmission systems. Many of the microprocessor-based relays that are designed for transmission line protection offer a variety of distance characteristics that can be selected by the user.

The best characteristic that fits a particular application can therefore be applied and easily modified if system conditions change.

For example, for a short line, a quadrilateral characteristic might be best to provide the desired arc resistance coverage. For long lines, distance characteristics that are specially designed to provide immunity from operating on load are available on many numerical relays.

If the system is rearranged such that short lines are made longer, long lines made shorter, or multiterminal lines are created, the related distance characteristics can easily be changed to best fit the specific need.

Quadrilateral distance characteristics
Figure 9 – The quadrilateral characteristic basically involves the combination of four measuring units. These units consist of a reactance unit (top line), two resistive units (left and right sides), and a directional element (bottom line).

Higher voltage substations often use a bus tie breaker that can be substituted for any line breaker. The bus tie breaker is ideally used when a breaker is taken out of service for maintenance or on account of a failure of the breaker.

With multiple setting groups that are available on most numerical relays, application of such relays on bus tie breakers allows the settings to be easily changed to match those requirements for the particular line for which the tie breaker currently provides termination.

Transformer differential protection using SEL487E

To implement the differential protection setting on the power transformer in the Digsilent Power Factory environment using SEL487E relay model.

Go back to contents ↑


  1. Protective Relaying Principles and Applications by H. Lee Willis and Muhammad H. Rashid
  2. SIPROTEC protection relay 7SJ62/64 manual

Premium Membership

Get access to premium HV/MV/LV technical articles, electrical engineering guides, research studies and much more! It helps you to shape up your technical skills in your everyday life as an electrical engineer.
More Information

Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.


    Jul 09, 2020

    Dear Respected Engineer,
    Kindly accept my Morning Wishes and Greetings.You deserve for it since you help others by sharing ur Knowledge and Wisdom,thanks for all.
    I want to grade on Instantaneous settings between feeders ,LVs and group control breaker in a sub station.Feeder CT’s have Feeders 4 Nos -400A/11KV,LV’s 1200A/11KV and GC 600A/110KV having all 1A secondary ,TRANSFORMER 16 MVA @110 KV/11 KV with Z 10.05%.
    we need Instantaneous settings with Gradings,If possible Kindly Help
    With Best regards

  2. Mallam Mutti Garba
    Apr 13, 2020

    I will love to have a sound knowledge of control systems, specifically programmable control systems.

    May 21, 2019

    Dear Sir,
    it seems that Fig.3 is not correct.Please check it.
    Best regards

Leave a Comment

Tell us what you're thinking... we care about your opinion!

Subscribe to Weekly Digest

Get email alert whenever we publish new electrical guides and articles.

Experience In LV/MV/HV projects

Join our Premium Membership and get access to advanced articles and papers.