AC POWER BASICS AND MECHANISMS OF POWER MEASURING INSTRUMENT
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- 1. Overview
- 2. Principles of Power Measurement
- 2.1. Basic Principles of AC Signals
- 2.2. Power of Distorted Waves: Active Power Is the Sum of the Products of Voltage, Current, and Phase of Each Frequency Component
- 2.3. Three-Phase Power
- 3. Mechanisms of Power Measuring Instruments
- 3.1. Benchtop vs. Portable Powermeters
- 3.2. High Voltage Measurement: Be Watchful of Heat Emissions from Input Circuits and the Voltage Coefficient
- 3.3. Current Input Circuit: Shunt Resistance
- 3.4. Calculation Section
- 3.5. Harmonic Measurement Function: PLL Circuits and FFT Calculation for Power Measurement and Evaluation of Power Quality
- 4. Actual Measurement Example: Inverter Power Consumption
- 5. Conclusion
1. Overview
Power measuring instruments are tools that measure power consumption in electronic devices and power facilities. They are used in a wide range of applications including R&D for home electronics and lighting equipment, and in industrial applications such as manufacturing lines and electrical receiving and distributing equipment.The demand for energy-saving electronic devices has increased due to recent emphasis on global environmental issues and effective use of energy resources. As engineers meet this demand with more efficient and compact equipment, the result has been an increase in devices with high-frequency–driven power converters. Such an increase calls for power measurement across wider frequency bandwidths and with higher accuracy.
To achieve these higher efficiencies, power converters must control power with a greater sophistication that requires detailed measurement of the power consumed at each of the conversion processes in the power conversion circuits.
Moreover, there is a requirement for energy management measures to comply with ISO14001- (environment management systems) certification standards and energy-saving laws.
2. Principles of Power Measurement
2.1. Basic Principles of AC Signals
Active power equals the products of the instantaneous voltages and currents, averaged over a period of time.With AC power, a phase difference occurs between the voltage and current if a capacitive or inductive load is introduced. If the instantaneous voltage u(t) and instantaneous current i(t) are sinusoidal and expressed as
, instantaneous AC power p is expressed as follows:
U: Voltage RMS I: Current RMS φ: Phase difference between voltage and current.
p is the sum of time-independent terms UIcosφ and the AC component of twice the frequency of the voltage or current -UIcos(2ωt-φ).
Since the power P consumed by the load per unit of time represents the average value of multiple instances of p, the AC component of p [-UIcos(2ωt-φ)] is 0, and the power P is P=UIcosφ[W]. Combining these findings, power per unit of time can be found using the expression below.
T: Input Cycle
Figure 1: Relationship between load type and voltage/current phase
Active, Reactive, and Apparent PowerEven given the same voltage and current, the power consumed varies depending on the phase difference φ. Figure 1 shows the relationship between voltage and current when the load is resistive, inductive, or capacitive. The product of RMS voltage and RMS current, UI, is called the apparent power S (units: VA). Apparent power is used to express the electric capacity of the device. Within apparent power there is active power (or effective power, units: W), which is the power consumed by the load mentioned above, as well as reactive power (units: var) which is not part of the consumed power.
The following equation expresses the relationship between apparent, active, and reactive power.
Here, cosφ represents the proportion of the apparent power that is actually consumed by the load, and is called the power factor (λ).
Figure 2: Relationship between apparent, active, and reactive power
2.2. Power of Distorted Waves: Active Power Is the Sum of the Products of Voltage, Current, and Phase of Each Frequency Component
Ideal active power is expressed as the product of the instantaneous voltages and currents averaged over one period of voltage or current. However when voltage, current, and power from distorted waves are included, the voltage, current, and active power are expressed as follows.
*n is the number of harmonic orders, U and I are the nth order component voltage and current
RMS values, and φn is the nth order component voltage and current phase difference.
RMS values, and φn is the nth order component voltage and current phase difference.
We know that the active power from the voltage and current of the distorted wave is the sum of the active powers obtained from the products of the voltages, currents, and power factors of the same harmonic component (frequency). The value of the products of voltages and currents from differing frequency components is 0, which tells us that this can not be the active power. When measuring the active power, it is enough to use a measuring instrument having lower-frequency bandwidth characteristics even if either the voltage or current has a high frequency component.
2.3. Three-Phase Power
Three-Phase Power Is the Sum of Each PhaseThree-phase power can be determined by summing the three phases of power as measured by a wattmeter (see figure 3). However, as shown in figure 4, a neutral wire is not always present in actual power systems. In such cases, Blondel’s Theorem allows one to find the power by summing the results from two wattmeters, as in figure 4.
Figure 3: Method of measuring three-phase power with three wattmeters
Figure 4: Three-phase, three-wire measurement using the two wattmeter method
Blondel’s TheoremIf energy be supplied to any system of conductors through N wires, the total power in the system is given by the algebraic sum of the readings of N wattmeters, so arranged that each of the N wires contains one current coil, the corresponding voltage coil being connected between that wire and some common point. If this common point is on one of the N wires, the measurement may be made by use of N-1 wattmeters.
Rather than using three wattmeters to measure power from each phase of voltage and current with reference to a neutral wire, the two wattmeter method involves measurement of power from two line voltage between the terminal and two phase current. In theory, the total three-phase power value will be the same with either method. This is explained in figure 5 below using vectors.
Figure 5: Vector diagram of three-phase voltage and current
3. Mechanisms of Power Measuring Instruments
3.1. Benchtop vs. Portable Powermeters
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| Picture 1: The CW240 |
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| Picture 2: The WT3000 benchtop type powermeter |
On the other hand, numerous types of benchtop models are available, ranging from 1-channel input models for single-phase measurements and 2- or 3-channel models for three-phase measurements, on up to 6-channel models that can measure two three-phase systems simultaneously. These types generally allow direct current input which affords higher measurement precision than the portables, perform measurement together with other types of measuring instruments, and are frequently rack-mounted into systems for product evaluation and testing (see Picture 2).
Powermeter Architecture
Figure 6 illustrates the structure of a typical digital powermeter. The unit consists of a voltage input section, current input section, DSP, CPU, display, and interface.
Input voltage is normalized in the voltage input circuit by a voltage divider and OP amp, then sent to the A/D converter. In the current input circuit, a flow divider forms a closed circuit, and the voltages on either side of the flow divider are amplified and normalized in the OP amp before being routed to the A/D converter. With this system, the current input circuit will not open even if the current range is switched, enabling safe range switching even when electrified as well as remote control via communications. The output from the A/D converters in the voltage and current circuits (the digital data) is insulated with an isolator and sent to the DSP. In the DSP, sampled digital values that have been converted to the second power or instantaneous power are summedadded for measuring the data update rate, and those summed values are divided by the number of samples to determine the measured values of voltage, current, and active power.
There are other methods in addition to the resistive potential voltage input method shown in figure 6, such as the VT (voltage transformer) method. One must select a measuring instrument that has the input format best suited to the circuit under test. For current input, there are the shunt input and CT (current transformer) methods. And especially with portable types, there is the clamp-on probe current input method. With the VT, CT, and clamp-on probe methods, the powermeter itself has no isolators because the input section is insulated from the primary circuit.
Figure 6: Powermeter architecture
3.2. High Voltage Measurement: Be Watchful of Heat Emissions from Input Circuits and the Voltage Coefficient
This section consists of a primary input circuit for dividing the input voltage into easily-processed low voltages, and a range switching circuit for normalization. The input accuracy of the powermeter is greatly influenced by the characteristics of the primary input amp. Also, when the voltage circuit is connected to the measurement circuit, the voltage input resistance acts as a load with respect to the power supply. Therefore, it can be favorable to have as large of a resistance value as possible.3.3. Current Input Circuit: Shunt Resistance
The current input circuit converts current input into easily-processed signals. The shunt resistor can be used depending on the measured current values and objectives.Shunt Resistor
Voltage is detected on both sides of the shunt resistor when current is passed through it. Measurement with resistors is more technically established than other methods, and highly accurate measurements can be taken because there is wide array of resistors to choose from. However, resistors present the problem of drift resulting from heat released when current flows through them. To suppress heat emissions, the resistance value must be reduced. However, when the resistance is low, it becomes difficult to maintain flatness-of-field in the frequency characteristics because the inductance component inside the resistor becomes relatively large. Also, since the voltage on the output side becomes miniscule, attention must be given to the thermal electromotive force inside the resistor. The thermal electromotive force arises due to the junction inside a resistor of one type of metal with a conductor of another type of metal. To obtain highly accurate measurements, selection of the material for the resistor and conductor is critical.
3.4. Calculation Section
Active power is calculated by averaging the products of the instantaneous voltages and currents. Conventional analog power measuring instruments measured power by multiplying voltage and current with an analog multiplier and taking averages using an LPF. The mainstream present-day powermeters use digital sampling and digital averaging. The advantages of the digital modality are as follows.- Since there are few analog circuits, measurements of high accuracy and reliability from instrument to instrument are more easily obtained.
- The digital format eliminates the divergence in temporal correlation of the measured values that occurs due to differences in the response characteristics of LPFs and other devices. For example, since the power factor is calculated from the measured values of voltage, current, and power, the simultaneity of the measured values is important. Measurement and calculation can occur simultaneously.
- Good accuracy (linearity) is achieved with extremely small inputs. and the power factor error is small.
- Sampled data can be processed digitally, enabling waveform display, analysis, and other functions.
Digital sampling method powermeters have the following means available for finding power values with averaging.
FIR (finite impulse response) digital filtering
IIR (infinite impulse response) digital filtering
FIR Type Digital Filtering Provides Rapid Response
With this method, in principle, rapid response can be achieved since active power can be calculated by averaging results from a single period.
IIR Type Digital Filtering Provides Easily-Obtained Stable Measured Values
With IIR type digital filters, active power is determined by smoothing the calculated instantaneous power. There is no need to detect the period, and theoretically there are no periods of paused measurement. Therefore, these filters have the advantage of being able to obtain stable measurements.
3.5. Harmonic Measurement Function: PLL Circuits and FFT Calculation for Power Measurement and Evaluation of Power Quality
The measurement principle here is the same as that of FFT analyzers. However, in contrast to analysis of frequency criteria by an FFT analyzer, the powermeter’s harmonic analysis function analyzes the frequency orders in the integer multiples of the fundamental wave. Therefore it is necessary to obtain samples that are synchronized to the fundamental frequency. This synchronized sampling is achieved by the PLL circuit. Figure 7 shows an overview of the PLL circuit.
Figure 7: Generation of a sample block synchronized to the input signal period by the PLL circuit
The phase comparator compares the phases of two input clocks and pulse-outputs a phase difference signal. When voltage is applied, the phase difference signal is converted to DC in a loop filter and sent to a voltage controlled oscillator (VCO) that can change the oscillation frequency. The output from the VCO feeds back to the phase comparator. Before arriving at the phase comparator, the frequency output from the VCO is converted to its reciprocal (1/N) to become N times the frequency of the input frequency.This process allows the samples to be synchronized to the input signal, and facilitates accurate measurement of the input signal’s fundamental wave and its integer multiple components. The equations for the fundamental wave components are shown below.
A distinctive feature of these expressions is that they can determine reactive power Q directly. Apparent and reactive power of distorted waves are not accurately defined, but the basic definition of the relationship between active, reactive, and apparent power in each frequency component given in item 2.1 is upheld.
4. Actual Measurement Example: Inverter Power Consumption
An inverter is a type of power transformer that can be simply described as a DC to AC converter. When converting DC signals to AC signals, a switching circuit is used to change the pulse width, and a pseudo-AC signal output is created. This modulation method in which the pulse width is changed is called a pulse width modulation ?PWM?method. Figure 8 diagrams the modulation process.
Figure 8: Diagram of inverter modulation
Measurement Bandwidth Needed for Inverter Measurement
The most common use of inverters is for motors, and motors constitute loads with resistance and inductance connected in series. As an example, if a PWM voltage of fundamental frequency 30 Hz and carrier frequency 10 kHz is applied to an R-L load of R = 1 ? and L = 1 mH, figure 9 shows the R-L load frequency characteristics and the content ratio spectrum of PWM voltage signals and active power.
Even if a PWM voltage that has high-frequency components is applied to the R-L load, the load characteristics almost totally prevent harmonic current from flowing. As stated in section 2.2, it is enough to use a measuring instrument having low frequency bandwidth characteristics in terms of either voltage or current for measurement of active power. Therefore even if extremely high frequency components are included in the voltage PWM signal, high measurement bandwidth is not necessarily required as these components are not included in the current signal. Considering the example in figure 9, in the case of motor drive inverters, it is sufficient to have a measurement bandwidth of up to several times the carrier frequency to maintain a certain degree of high measurement accuracy.
Notes on Voltage Measurement with Recent Inverter Drive Motors
When testing inverter motors, the motor’s drive characteristics are thought to be influenced by the RMS fundamental wave of the inverter’s output voltage. Also, as the fundamental wave RMS value of sinewave modulated PWM is almost identical to the measured value obtained with the rectified mean value calibrated to the rms value (voltage MEAN), measurement by rectified mean value calibrated to the rms value seems to be sometimes used for inverter voltage measurements. However, with variable PWM control in recent years and other non-sinewave PWM modulation signals, there are cases in which the rectified mean value calibrated to the rms value yields measurements that are far removed from the fundamental wave. In such cases, as in section 3.4, the powermeter can accurately measure the fundamental wave if it employs a harmonic measurement function. Conventional powermeters required a changing of modes when measuring active power or RMS current with high-speed sampling, but more recent powermeters can measure voltage, current, power, and harmonics simultaneously. This not only makes measurement easier, but also allows simultaneous measurement of power and fundamental wave values. With inverter drive circuits, heat emissions that change with the passage of time have a substantial effect on instrument characteristics, so it can be very important to capture data at the same time.
A motor is an R-L load, so when frequency is high, impedance increases
As for the power spectrum, the carrier frequency is extremely small relative to the fundamental component. Figure 9: Example of PWM inverter voltage and power content ratio, and R-L load frequency characteristics
