Relays - Relays are electrically controlled switches that are used to provide logical control to power circuits. Relays come in two main forms, electromechanical and electronic.
The simplest types of relays are electromechanical, using a coil to operate the contacts. When a current is passed through the coil, a magnetic field is created. The force from this magnetic field moves the relay contacts to change the state. Electromechanical relays are still commonly used in automobiles, home appliances, and more.
Small Electromechanical Relays on a Circuit Board
Electronic relays offer more sophisticated control thanks to their technological improvements. Instead of a simple coil-to-contact relationships, electronic relays rely on sensors. These relays often have a variety of inputs that go beyond current, including voltage, temperature, vibration, and more. Depending on the inputs from the sensors and programmed operation, an output signal (digital or analog) is sent out. Electronic relays are very similar to microcontrollers (e.g. Arduino). The difference is that microcontrollers are designed for general applications, while electronic relays are preprogrammed with specific functions like overcurrent or overvoltage protection.
Relays can be used in a normally closed (NC) or normally open (NO) configuration. The diagrammatic representation of these configurations is shown below. Normally open relays will have their contacts separated when the relay's coil isn't energized. Normally closed relays are the opposite, with contacts that are electrically connected without the relay being energized. Most modern relays are designed to have both NO and NC sets of contacts available for the same inputs.
Symbols for Normally Open (NO) and Normally Closed (NC) contacts
Ladder Logic and Controls - Ladder logic is a way of visualizing relay operation and control. The output contacts of relays are shown in a control circuit with their associated relay operation code. The example below shows a simple ladder logic circuit based on an instantaneous (50) overcurrent relay and an inverse-time (51) overcurrent relay contacts. The circle shown is the trip coil for a medium voltage circuit breaker (52T). Coils are often represented as circles with ANSI device codes inside of them.
Trip String Example Circuit
If either overcurrent condition occurs, the circuit will close and the current will flow through to the trip coil of a circuit breaker. Conditions like this are commonly referred to as "trip strings". The conditions that trip the breaker are connected in parallel to ensure that any one action leads to a tripping event. NO contacts from the relay are used to ensure that the circuit only trips when an overcurrent event takes place and energizes the relay coil (or sensor).
A related configuration is show below with the same elements overcurrent elements (50/51) and a breaker close coil (52C). NC contacts are used here in a series connection. Only when all relays are de-energized (no overcurrent events) will the breaker close coil be activated. This series configuration is commonly referred to as a "close string".
Close String Example Circuit
Boolean Algebra - Ladder logic has been around for a long time and is a great visual way to represent the control schemes used in electrical power systems, especially from a circuit point of view. We can also represent the information of a ladder logic diagram with mathematics. Boolean Algebra is a way of taking these control requirements and writing them in a mathematical format instead of a circuit diagram.
Boolean Algebra is a broad mathematical field that has applications well outside the bounds of relaying and controls. Boolean Algebra defines the mathematics of Boolean variables, numbers that can only be in 2 states (e.g. True/False, 0/1, Energized/De-energized, Open/Closed). There are three basic operators that can be used to build up the framework of Boolean Algebra: NOT, AND, OR. These operations are defined as follows:
NOT(0) = 1, NOT (1) = 0
AND(1,1) = 1, AND(1,0) = 0, AND(0,0) = 0
OR(1,1) = 1, OR(0,1) = 1, OR(0,0) = 0
As you can see, the NOT operator simply transforms a Boolean variable into its opposite value. The AND operator takes any two inputs and only produces the positive value if all input values are positive. The OR operator will produce a positive value if any of the input values are positive. Due to the AND operator's similarity to the multiplication operator, they are often used interchangeably. Likewise, the OR operator is often shown as an addition symbol. The NOT symbol is often shown with a bar over the variable or an apostrophe after the variable. Extending the similarity of these operations to traditional algebra, we can define an order of operations:
NOT
AND
OR
Now, we can write algebraic equations that convey the same level of information as a ladder logic diagram. Series connections are made into AND terms and parallel connections are made into OR terms. The NOT operator is used to distinguish between NO and NC contacts.
Example: Convert the following ladder logic diagram to Boolean Algebraic form.
Solution: First, we define the positive state as energized. In other words, z=1 when current flows through the coil.
Start by observing that a and b contacts are in series and NC. This means that z will be 1 only when both a AND b are de-energized (0). These contacts are also in series with a parallel combination of c and d. If either d OR e is energized, there will be a pathway to z. Since c and d are in series with a and b, both of the requirements listed before must be met simultaneously (AND) to ensure that z is energized. Mathematically:
z = a'b'(c + d)
This equation is easily checked. When a and b are 0, then a' and b' are 1. If either c or d is 1, the equation reduces to the following:
z = 0'0'(1 + 1) = 1*1*1 = 1
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