Electrical Transducers Theory of Operation
The AYA Electrical Transducers are designed for accurately measuring electrical parameters of electric networks. They measure the incoming voltage and current signals and provide analog outputs for use with external recorders and loggers with a high voltage input/output isolation. True RMS AC voltage and current transducers provide output signals that are TRUE RMS values of the input parameters independent of the signal waveform. The AC WATT transducers provide output signals that represent REAL ACTIVE POWER for any power factor.
Other transducers measure KVAR, KVA, FREQUENCY, POWER FACTOR, WATT-HOURS and other parameters. The transducers provide analog outputs of 0-1, 0-5, 0-10 Volts DC or 0-1, 0-20, 4-20 Milliamperes DC. Other outputs are available as well as customized products. The AYA transducers are packaged in enclosures that can easily be mounted on DIN-Rails or on flat surfaces
WHAT IS A TRUE RMS TRANSDUCER?
The voltages and currents in AC power lines, when not affected by a complex non-linear load, are basic sine-wave signals produced by rotating generators. The average value of a sine wave voltage is 70.7% of its peak value. In non-linear loads, such as adjustable speed drives or switching power supplies, the waveforms of the voltage and the current are distorted and they include harmonics. The diagram on the right shows a pure sine-wave with a pure third harmonic.
This diagram shows the waveform of a sine wave that is distorted by the presence of a third harmonic. If the load is a rotating machinery, the energy generated by the third harmonic may cause overheating of the motor without contributing to the torque.
The true value of a distorted wave is not its average, but rather its TRUE ROOT MEAN SQUARE value, known as RMS. A TRUE RMS computation is a process of measuring the incoming voltage or current signal, amplifying it, multiplying its value by itself, computing the mean value of this product and computing the square root value of the mean, which results in the true RMS value of the input signal.
ELECTRICAL TRANSDUCERS with ANALOG OUTPUTS
AC voltage and current transducers that provide an analog output are very common in the process industry and in electrical switchboard systems. Such transducers provide either a DC voltage or a DC current that can be read by monitoring meters, loggers, oscilloscopes and recorders. A 4-20 Milliampere DC output signal is commonly used in control systems.
ISOLATION
To protect the operator and the equipment connected to a transducer from the high voltages present in electric networks, electrical transducers incorporate means of isolating the output wires and the enclosure from the line voltage. Isolating the input from the output can be achieved either by means of transformers or by optical isolating circuits.
Electrical transducers can be connected directly to a power line or they can be connected to voltage reducing transformers and current reducing transformers. Voltage reducing transformers, known as Potential Transformers (PT’s), reduce the high voltage of a power line to a level that is compatible with the input range of the transducer being used. Current transformers, sometimes referred to as CT’s, reduce the high current in a power line to a level that is compatible with the transducer range or common industrial meters and relays. The output of many installed metering CT’s is 5 Amperes at full scale.
WHAT ARE POWER TRANSDUCERS?
Monitoring the power delivered to a load provides important information on the power line. When dealing with a purely linear resistive load, the power consumed by the load can be obtained by multiplying the voltage by the current. In actual practice, however, loads are rarely purely resistive. Practical loads contain capacitive or inductive components which cause a phase shift between the voltage and the current. The phase shift and the distortion are taken into consideration by the AYA power transducers.
The Active Power consumed by a load is:
W = E x I x COSINE O (1)
Where W = Real Power in WATTS
E = Voltage in VOLTS
I = Current in AMPERES
O = Phase Angle
The Apparent Power is the product of the voltage and the current:
VA = E x I (2)
The Reactive Power is expressed in VARS as:
VAR = E x I x SINE O (3)
The Power Factor
The Cosine of the phase angle is referred to as the Power Factor. The Real (Active) Power can, therefore, be obtained by:
W = E x I x PF (4)
Where PF is the Power Factor
WHAT ARE CURRENT TRANSFORMERS?
The CURRENT ratio of a standard magnetic-core transformer, ignoring losses, is defined by the equation:
I2 = (N1/N2) x I1
Where I1 = Input current, I2 = Output current
N1 = Number of turns of primary coil
N2 = Number of turns of secondary coil
An AC current transformer is a special kind of transformer which does not have a primary coil. The conductor, whose current is to be measured, acts as the primary coil when it is placed inside the magnetic path of the core. The signal obtained from an AC current transformer has the same wave-shape as the current being measured. However, current transformers introduce measurement errors of amplitude, phase and wave-shape due to frequency range limitations.
A current transformer converts the primary current of the conductor to a current output whose value depends on N2. Using equation (1), the output current can be computed if N2 is known. If N2 is 1000 turns, the output current is 1/1000 of the primary current, which can be expressed as 1 Milliampere per Ampere. Such a current transformer has a turns-ratio of 1000:1. The output of this CT can be read by any AC ammeter whose input impedance is compatible with the specifications of the current transformer.
APPLICATIONS
Current transformers are used in current metering installations for use with current meters, current transducers, power transducers and power analyzers. The current monitoring of time varying electrical loads, such as electric motors, is of prime importance to plant engineers, maintenance engineers and design engineers.
AYA offers an extensive line of current transformers. Closed core current transformers are designed for permanent installation in high precision electrical applications. They are available with primary currents ranging from 5 to 4000 Amperes with burdens ranging from 1.25 VA to 60 VA. Many models can be supplied with either a 1-Ampere or a 5-Ampere output.
MEASURING POWER
The active power in Watts in a single-phase electric network with a linear load can be obtained by the following equation:
W = E x I x PF
For a resistive load, the Power Factor is 1.0. For reactive loads, such as motors and compressors, the voltage and the current are not in phase, and the power factor is always less than 1.0. The AYA transducers and power line monitors perform this computation internally. They measure the voltage either directly or by the use of a step-down transformer. The current is measured either directly or by using a current transformer.
In a balanced three-phase WYE network, where all three loads are identical, only one current clamp or current transformer is needed, and the power is given by the following equation:
W = 3 x Va x I1 x PF
Where Va = Vb = Vc = Phase-to-Neutral voltage
I1 = I2 =I3 = Phase current
If the loads are unbalanced, three current transformers are required, and the following equation applies:
W = (Va x I1 x PF1)+(Vb x I2 x PF2)+(Vc x I3 x PF3)
In a balanced DELTA network, again only one current transformer is needed, and the power is:
W = 3 x Va-b x I1 x PF
Where Va-b = Vb-c = Vc-a = Phase-to-Phase voltage
I1 = I2 = I3 = Phase current
If the load is unbalanced, either two or three current transformers are required. The power of each phase must be computed and summed to obtain the total network power.
Non-linear loads, such as SCR control circuits and switching power supplies, cause distortion of the currents and the voltages, and they introduce harmonic frequencies to the power line. Under these conditions, PTs and CTs must have a wide frequency response so that the harmonics of the line frequency are not eliminated from the power computation. In addition, the power transducers must be capable of processing distorted waveforms caused by non-linear loads.
GLOSSARY OF TERMS
Ampere: The unit of measuring alternating (AC) or direct (DC) electric current.
Volt: The unit of measuring alternating (AC) or direct (DC) electric potential force (voltage).
RMS: Root Mean Square is the square root of the sum of the squares of instantaneous amplitudes of a waveform. It is the effective value of an AC waveform that produces heat equivalent to a DC of the same value.
Power: Electrical energy expended per unit time.
Apparent Power: (in VA) is the product of the voltage and the current delivered to a load.
Real Power: (in Watts) is the component of the apparent power that represents true work.
Reactive Power: (in VAR) is the component of the apparent power which performs no real work.
Frequency: (in Hertz) the number of periods of a waveform that occurs in one second.
Power Line Frequency: The fundamental frequency of a power system (60 Hz in the US, 50 Hz in many other countries).
Transformer: A device that transfers a voltage (PT) or a current (CT) using a coupling of electromagnetic flux fields of its windings.
Power Factor: The ratio of Real Power to the Apparent Power (W/VA).
Single-Phase: Electric network in which only one phase of current is available in a two-conductor or a three-conductor circuit.
Delta Connection: Electric network using a 3-phase transformer where the windings form an electrical triangle whose corners are the connections to the 3-phase load.
Wye (“Y”) Connection: Electric network using a 3-phase transformer with all phase windings connected to a common (Neutral) point.
Accuracy Class: The percent of the reading of an instrument plus a constant.
THE IMPORTANCE OF POWER FACTOR
A power factor is actually the Cosine of the angle between the voltage and the current. When the voltage and the current are in phase with each other, the angle is ZERO, the Cosine is ONE and the POWER FACTOR is ONE. A power factor of 1 is an ideal situation and the power delivered to the load is just the voltage multiplied by the current (V x I). In this case the APPARENT POWER is the same as the ACTIVE POWER..
If the current lags or leads the voltage, the angle is not zero and the power factor is LESS THEN ONE. In most industrial applications the load is INDUCTIVE which causes the current to lag the voltage. This results in a "LAGGING POWER FACTOR”. Under such conditions, the ACTIVE POWER delivered to the load is lower then the APPARENT POWER. It is the voltage multiplied by the current and them multiplied by the POWER FACTOR.
Capacitors, which have the opposite effect, are generally placed on the load to compensate for the inductive motor windings. Some industrial sites have large banks of capacitors just for the purpose of correcting the power factor back toward one to save on utility company charges.
POWER FACTOR TRIANGLE
The power triangle shown above demonstrates the effects of the relationship between the active (real) and reactive (imaginary) power. The active power in WATTS (represented by the horizontal leg) is the actual power that produces real work. It is the energy transfer component. The reactive power (represented by the vertical leg of the upper or lower triangle) is the power required to produce the magnetic fields to enable the real work to be done. Reactive power is normally supplied by generators, capacitors and synchronous motors. The longest leg of the triangle (on the upper or lower triangle), labeled total power, but commonly known as APPARENT POWER, represents the vector sum of the reactive power and real power components. Mathematically, this is equal to:
AC POWER RELATIONSHIPS
The relationships between voltage, current, resistance and power in a single-phase AC network with a resistive load is shown in the diagram on the right, where
- W = Active power in WATTS
- E = Voltage in VOLTS
- I = Current in AMPERES
- R = Resistance in OHMS.
For non-resistive loads, the Power W = V x I x PF, where PF = Power Factor (or Cosine of the angle between the voltage and the current)
The three-phase calculation is:
- W = E x I x 1.773 x PF
Where E = Phase-to-Phase voltage
