How to calculate THD and PF?
Total Harmonic Distortion (THD) Analysis and Power Factor Evaluation Within this discussion, we'll explore methodologies for gauging total harmonic distortion alongside computations for power factor.
Total Harmonic Distortion (THD) is a metric reflecting the amalgamation of harmonic frequencies juxtaposed against the primary frequency—such as 60Hz—on a circuit. It encompasses all harmonic frequencies present. THD can be associated with current or voltage harmonics. To quantify the distortion in line voltage, apply the following formula:
Figure 1. Measurement of THD ought to be conducted at the transformer, not adjacent to the load.
Where Vn_rms is the RMS voltage of the nth harmonic, and Vfund_rms denotes the RMS voltage of the fundamental frequency. A pure sine wave, devoid of higher harmonics, like an impeccable voltage source, showcases a THD of 0%. Any THD value exceeding zero indicates distortion of the sine wave. THD figures are typically presented as percentages, e.g., 5% or 50%. THD can be assessed for both current and voltage signals.
Harmonic currents arise from non-linear loads that draw current in pulses. Voltage harmonics stem from these currents traversing through diverse system resistances. Transformer current induces a voltage drop across its coils. When current is pulsed, voltage mirrors this pulsation. Excessive voltage distortion is detrimental since it serves as a conduit for harmonics towards linear loads, such as electric motors. Voltage harmonics introduce additional heating into power distribution systems and connected devices.
In troubleshooting circuits for harmonics, ascertain to measure both voltage THD and current THD. Ideal outcomes ensure voltage THD does not surpass 5%, and current THD remains beneath 20% of the base frequency. THD should be evaluated at the transformer level for precise system-wide THD calculation (as depicted in Illustration 1). Load-side THD readings offer the loftiest values since harmonic cancellation hasn't occurred throughout the system.
When measuring THD current under full load conditions, the THD is akin to total demand distortion (TDD). TDD is the quotient of current harmonics to the ultimate load current. A THD measurement is executed when diagnosing or testing systems. TDD diverges from THD because TDD is benchmarked against the peak current measurement over time. THD solely measures current at the instant of measurement. TDD's role is to account for instances where THD is elevated, yet the aggregate load is relatively low. Under such circumstances, TDD is modest, minimizing overheating.
Power factor delineates the ratio of authentic power to apparent power in a circuit or distribution network. Every AC circuit is comprised of real, reactive, harmonic, and apparent (aggregate) power. True power, in watts or kilowatts, is expended by motors, lighting, and other apparatuses to execute functional tasks. Reactive power, in volt-amperes reactive or kilovolt-amperes reactive, is stored and discharged by inductors and capacitors. Reactive power materializes as phase displacement between current and voltage waveforms. Harmonic power, in volt-amperes or kilovolt-amperes, is dissipated due to harmonic distortion. Apparent power, in volt-amperes or kilovolt-amperes, is the vectorial sum of true power, reactive power, and harmonic power. Apparent power isn't a simple accumulation but a vector summation.
Displacement Power Factor
The displacement power factor is the ratio of genuine power to apparent power attributable to phase displacement between current and voltage (as shown in Illustration 2). Capacitors can frequently be integrated into a circuit or distribution network to rectify the displacement power factor. Its computation is as follows:
PF = cos(θ)
where PF signifies displacement power factor and θ is the discrepancy between voltage and current phases in degrees. Note: DPF or PFD may occasionally substitute PF to denote displacement power factor.
Figure 2. Displacement power factor enables calculation of the power genuinely accessible for a load.
The presence of harmonics introduces complexity into the discussion of power factor. The distortion power factor, defined as the ratio of true power to apparent power due to Total Harmonic Distortion (THD), cannot be mitigated simply by adding capacitors to a circuit. This is because the impedance of capacitors decreases with an increase in frequency, potentially turning them into sinks for high-frequency harmonics rather than effective compensators.
To address the distortion power factor, specialized solutions are employed. These include special types of transformers designed to handle harmonic loads or tuned harmonic filters that consist of a combination of capacitors and inductors. Such filters are specifically engineered to resonate at harmonic frequencies, effectively absorbing or cancelling out these distortions.
The calculation of the distortion power factor involves assessing the impact of harmonic content on the overall power factor, reflecting the diminished efficiency caused by the presence of these higher-order frequencies in the electrical system.
The distortion power factor is calculated as follows:
.
where
PFTHD = distortion power factor
THD = total harmonic distortion
The total power factor is the product of the displacement power factor and the distortion power factor and is calculated as follows:
PFTot = PF × PFTHD
where
PFTot = total power factor
PF = displacement power factor
PFTHD = distortion power factor
For example, what is the total power factor when the displacement between voltage and current is 25°, and the THD is 49% (0.49)? The displacement power factor is calculated as follows:
PF = cos(θ)
PF = cos (25°)
PF = 0.906
The distortion power factor is calculated as follows:
.
The total power factor is calculated as follows:
PFTot = PF × PFTHD
PFTot = 0.906 × 0.898
PFTot = 0.814
Understanding the total power factor is crucial as it directly correlates with apparent power, which is fundamental in sizing components within a power distribution system. Apparent power serves as a key metric for ensuring that all elements in the system are appropriately rated to handle the electrical load without being overloaded.
Current Crest Factor
The current crest factor, defined as the ratio of the waveform's peak value to its RMS value, serves to indicate the extent of distortion in the waveform. Its calculation provides insights into the waveform's quality, with higher factors pointing to greater levels of distortion. The formula for determining the current crest factor is as follows:
.
where
CCF = current crest factor
Ipeak = peak value (in A)
Irms = root mean square value (in A)
For example, what is the current crest value of a perfect sine waveform? In a perfect sine waveform with a peak value of 1, the rms value is 0.707.
.
An elevated current crest factor can result in excessive heat generation within circuits and devices. For instance, on a 120V circuit powering digital equipment such as computers, a distorted current waveform might display a crest factor ranging from 2 to 6 (consult Figure 3). Typically, circuits with a higher current crest factor contain a greater proportion of energy in their higher harmonics.
A power source is obligated to provide the peak power needed by the circuit, matching the specified voltage and current demands. A conventional backup power system, such as an uninterruptible power supply for computers, is capable of delivering a current crest factor of 3 when operating at full capacity but may experience augmented crest factors under lighter load conditions.
Figure 3. The current crest factor comparison
Source Impedance
The source impedance impacts the crest factor generated by non-linear loads. Upon reaching a specific voltage threshold, the power supply initiates the charging of a smoothing capacitor. When the source impedance is minimal, the current surge into the capacitor is substantial, resulting in a brief charging duration. Conversely, higher impedance constrains the current flow, thereby elongating the capacitor's charging period. This prolonged charge interval effectively diminishes the crest factor. One can augment the source impedance through the incorporation of line reactors or drive isolation transformers.
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