PL231678B1 - Method for measuring effective value and initial phase of sinusoidal alternating voltage and the system for measuring the effective value and initial phase of sinusoidal alternating voltage - Google Patents

Abstract

In the method and system, four instantaneous values of sinusoidally alternating voltage are measured at equal time intervals smaller than 1/2 of the period T of the voltage, obtaining the results u1 = u(t1), u2 = u(t2), u3 = u(t3), u4 = u(t4), where t1, t2, t3, t4 are subsequent measurement times. Based on the results obtained from the measurements, the value of the auxiliary parameter θ is calculated, and then the effective value and the initial phase of the sinusoidally alternating voltage are calculated. The system contains an analog-to-digital converter measuring the value of a voltage signal with a value proportional to the voltage at the input terminals. The measurement result from the analog-to-digital converter is sent to a queue of four buffers of memory units connected in series, storing the results of the last four measurements, which are connected to the parameter calculation system, which calculates the value of the auxiliary parameter θ and then calculates the effective value and the initial phase of the sinusoidally alternating voltage, after measuring the first four instantaneous voltage values, and after measuring each subsequent instantaneous voltage value. The calculated values of the sinusoidally alternating voltage parameters are sent by the system to the interface of the measuring system.

Description

The present invention relates to a system for measuring the parameters of sinusoidal alternating voltage, applicable in testing the physical properties of electrical circuit elements and the electrical properties of sinusoidal alternating current circuits; also used in sensor and biosensor systems and networks (medicine) and energy systems.

Known systems for determining the complex amplitude and the initial phase of a sinusoidal variable signal sampled periodically (at equal time intervals), but not necessarily sampled synchronously with the tested signal, are based on the methods presented in Duda K. , AGH Publishing House, Krakow 2011.

The first group consists of solutions based on signal spectrum interpolation - IpDFT. They consist in determining the spectrum of the signal covering at least one period with the use of appropriate time windows. Then, on the basis of the obtained spectrum, the highest fringe is estimated, on the basis of which the value of the frequency and amplitude of the complex signal is estimated. These solutions are characterized by the necessity to collect samples from more than one full period, high computational complexity, errors related to "leakage" of the window due to the asynchronism of the sampling period and the period of the measured voltage, and the necessity to determine irrational trigonometric functions.

The second group consists of solutions that use parametric methods based, inter alia, on the Kalman filter, especially its special case, which is the RLS (Recursive Least Squares) adaptive filter, or based on the PLL (Phase Locked Loop) software. According to the text of the quoted monograph, solutions using parametric models have better frequency resolution than DFT methods, but are characterized by even greater computational complexity in relation to DFT methods and difficulty in selecting the model.

The known solutions are characterized, first of all, by the necessity to collect many samples from more than one full period and high computational complexity, which is their significant disadvantage, especially in the case of portable battery multimeters. In such multimeters, it is very important to use the smallest computing power that allows to reduce the microprocessor operating frequency, and thus the electricity used, which has a significant impact on the cost of work and battery life. In addition, collecting samples from at least one period also affects the time taken to obtain the analysis results.

The essence of the system for measuring the effective value and the initial phase of a sinusoidal alternating voltage according to the invention is that the circuit comprises a pair of input terminals to which a source of a sinusoidal alternating voltage is connected, in particular a generator of a sinusoidal alternating voltage. Connected to a pair of output terminals is a circuit converting the input voltage into a voltage signal with a voltage proportional to the input voltage, in particular a differential amplifier. The analog input of the analog-to-digital converter is connected to the output of the system converting the input voltage. The measurement in this converter is excited by the signal coming from the digital clock signal generator system at equal time intervals Ts, which is smaller than% of the period T of the tested voltage. The digital output of the analog-to-digital converter is connected to the memory unit buffer containing the value of the last measurement and constituting one of four buffers connected in series and containing the values of the last four measurements ui = u (ti), U2 = ufa), U3 = ufa), U4 = trust), where ti, t2, t3, t4 are consecutive measurement times. In contrast, the outputs of the memory unit buffers are connected to the input of the parameter calculator. This system is activated after collecting the measurements, i.e. after measuring the first four instantaneous voltage values and after measuring each successive instantaneous voltage value. The excitation of the parameter calculation system is performed by the reset buffer circuit with a length of 4, the input of which is connected to the digital signal output from four interconnected buffers of memory units connected to the analog-to-digital converter informing that the measurement value has been written in the buffer queue. The reset buffer circuit is reset when the measurement is started and counts the digital initiation signals on its input. When the first, second or third initiation signal arrives, the reset buffer circuit does not transmit the wake-up signal, but when the fourth and subsequent initiation signals arrive, the reset buffer circuit transmits the wake-up signal to the parameter calculator. After excitation, the parameter calculation system calculates the auxiliary parameter Θ according to the formula:

PL 231 678 Β1

θ = - ^ ~ 2m, For m; θ = ^ 4 in ₂ for u- Irf + 4m ₂ ( ₂ + ₄ ) for u. 4m ₂ u, +. Θ ^{1 λ} jif + 4h ₂ (m ₂ + w ₄ ) for u-

4in ₂ = 0

Ψ 0 Λ Μ ² + 4μ ₂ (μ ₂ + ιι _Α ) <0

Ψ Ο Λ Μ, ² + 4 « ₂ (μ ₂ + U _Ą )> Ο Λ U, + 2μ ₃ <Ο ψ Ο Λ Μ, ² + 4« ₂ (μ ₂ + η ₄ )> Ο Λ W, + 2μ ₃ > Ο where if the calculated value of the parameter Θ meets the condition | θ | > 1- ε where ε e (0; ΙΟ ¹ ], then this value is changed to the value determined according to the formula:

θ = -ί + ε θ = 1-ε for <9 <0 for Θ> 0

Then, based on the calculated value of the auxiliary parameter Θ and the four instantaneous values of voltage, the system calculates the following parameters:

• effective voltage U _S k according to the formula:

_yy iu) —2u, u ₃ 6 + ul

U - a .-—- 2-2Θ ¹ initial phase for ti = 0 according to the formula:

arctg i ——— y / l-θ ¹ -180 ° d fa w ₂ - uf) <0 λ w, <0 arctg

- -90 ”0 °

90 ° u _{2 —} u _} e

Vl-æ? ² + 180 ° for «, -«, # <Ολ «,> 0 for w ₂ -uf) - Ολη, <0 for w ₂ - = Ολμ, = 0 for w ₂ —uf) - ΟλWj> 0 for w ₂ -uf)> 0 for the voltage versus time function expressed by the formula:

V2 «Μ = ^ - 1 ^ 1 ^ (^ + ^) initial phase for t4 = 0 according to the formula:

arctg arctg

-90 °

0 * arctg uf) - u ₃ - I -180 for uf) -u, <0 λ w ₄ <0 + 180 ° for uf) - ti ₃ <0 λ w ₄ > 0 for uf) —u ₃ = 0λμ ₄ <0 for uf) - « ₃ = 0λη ₄ = 0 for uf) - w ₃ = 0λη ₄ > 0 uf) -u ₃ for m ₄ # -w ₃ > 0

PL 231 678 Β1 for the function of voltage versus time expressed by the formula:

^u W = ^ - hl ^sin (^ ⁺ ^ 4)

The coefficient a appearing in the formula for effective voltage is a constant characteristic for a given measuring system, which is the ratio of the ratio between the voltage value at the input terminals of the system and the value at the output of the analog-digital converter. The unit of the coefficient a is volt [V]. This coefficient is used to transform the result at the output of the analog-digital converter, which is an integer, into a result which is the physical quantity of the voltage at the input of the measuring system. The calculated values of the sinusoidal alternating voltage parameters are transferred directly or indirectly by the parameter calculation system to the measurement system interface.

The advantage of the system for measuring the effective value and the initial phase of sinusoidal alternating voltage is the minimum number of measurement samples, a short measurement time that can be shorter than one period of the measured voltage, the possibility of asynchronous sampling, reduction of the energy cost and time of determining parameters. Additionally, when determining the effective voltage value, trigonometric functions are not used, but only the basic operations: addition, subtraction, multiplication, division and square root; while in determining the initial phase, only the arctg function is additionally used. A special advantage of the system, which distinguishes it from other solutions, is that, assuming no measurement and numerical error, the determined parameters do not have an error resulting from the measurement method, i.e. the obtained result is accurate.

The invention will be illustrated in an embodiment in Fig. 1, which shows a general measurement system, in which the generator G, connected to the input terminals of the measurement line, symbolically represents a system generating a sinusoidal alternating voltage.

The measuring system is adapted to be operated by the user via the INT interface. Through the INT interface, the user can set the operating parameters of the measuring system, start a measurement or read the measurement results. The INT interface is connected by a bi-directional digital bus with the KI interface controller.

The KI interface controller is adapted to work in two modes: in the measurement parameter setting mode and in the measurement mode. In the measurement parameter setting mode, the KI controller supports the INT interface - it downloads the sampling period setting parameter and gets the command to start the measurement. In addition, the KI controller writes the system operation parameter - the clock timing period Tclk via the digital bus in the memory unit TC, where the Tclk period is equal to the sampling period T _s .

When the command to initiate the measurement is received from the INT interface, the KI interface controller sends to the INT interface the information about the start of the measurement and sends a digital signal to the CLK clock and to the reset buffer system with a length of 4 in order to start the measurements. Then the KI controller suspends its operation in the communication mode, entering the standby mode until the appearance of a digital signal informing about the determination of the power parameters value from the UOP parameter calculator.

At the moment of the appearance of the parameter determination signal from the UOP system, the KI interface controller reads the determined sinusoidal alternating voltage parameters via digital buses: RMS voltage Usk stored in the USK memory unit, the initial phase φι for the time ti = 0 stored in the memory unit φ1 and the initial phase for the time T = 0 stored in the memory unit φ4 and sends them to the INT interface. The interface controller then checks via the digital bus if there is no message on the interface on the measurement completion. If there is no message about the completion of the measurements, the KI interface controller remains in the measurement mode, waiting for the next signal from the UOP circuit, informing about the next determination of the sinusoidal alternating voltage parameters, and repeats the entire procedure of the measurement mode. If the interface controller reads the measurement completion message from the INT interface, the KI controller sends a digital signal to the KTP controller about the completion of the measurements and then returns to the measurement parameter setting mode.

When a digital initiation signal comes from the KI controller, the UBR4 and CLK are reset. The CLK clock then reads the clock period value via the digital bus

PL 231 678 Β1

Tclk from the TC memory unit and sets its working period based on it. The task of the clock is to trigger the measurement in the ADC converter, whose input of external excitation of the measurement is connected with the clock output. The analog input of the ADC converter is connected to the output of the W amplifier, the differential input of which is connected to the terminals of the G generator. The task of the W amplifier is to condition the voltage of the G generator to the range of the ADC converter. This means that the voltage at the output of the amplifier W in relation to the mass is directly proportional to the voltage at the terminals of the generator G and the gain of the amplifier is selected so that at a given measuring range, the voltage at its output does not exceed the operating range of the ADC converter.

After completing the measurement of the instantaneous voltage value, the ADC converter sends a digital signal about the completion of processing to the buffer of the U1 memory unit. Additionally, the ADC converter sends the measurement result to the buffer of the U4 memory unit via the digital bus. The U1-U4 memory unit buffers have one digital input, which initiates writing of the value at the input of the buffer connected to the digital bus. After writing the value to the buffer, its value is fed to the output connected to the digital bus and the digital initiation signal is sent to another digital circuit. These buffers are connected such that the value from the ADC is supplied first to the buffer of the memory unit U4, then from the buffer U4 to U3, from U3 to U2 from U2 to U1; while the digital initiation signal, after the measurement is completed by the ADC converter, is fed to the U1 buffer, then from the U1 to U2 buffer, from U2 to U3 and from U3 to U4. Finally, the digital wake-up signal from the memory unit buffer U4 is fed to the reset buffer chip UBR4. Such a connection scheme means that at the outputs of the U1-U4 buffers there are successively the values of the last four measurements, with the value of the last measurement in the U4 buffer. The values at the outputs of all U1-U4 buffers are given by digital buses to the UOP parameter calculation system.

The 4 UBR4 reset buffer chip counts the digital initiation signals on its input. When the first, second or third trigger signal arrives, the buffer does not output an excitation signal, but when the fourth and subsequent trigger signals arrive, the UBR4 sends a trigger signal to its output, which is connected to the digital input of the external excitation of the UOP parameter calculator. That is, a trigger signal will be applied to the UOP after the first four instantaneous voltage values have been measured and after each successive instantaneous voltage value has been measured by the ADC.

The UOP parameter calculation system is used to calculate the values of sinusoidal alternating voltage on the basis of the measurement data collected in the U1-U4 buffers. The UOP waits for a digital wake-up signal from the UBR4 reset buffer circuit. At the moment of receiving the initiation signal, the UOP system reads, via digital buses, the values of samples ui from the U1 buffer, U2 from the U2 buffer, U3 from the U3 buffer and U4 buffer from the U4 buffer and on their basis calculates the value of the auxiliary parameter Θ according to the formula:

Θ

Θ

Θ

Θ __

2 «,

4m ₂ + 4m ₂ (m ₂ + m ₄ ) 4 « ₂ w, + + 4m ₂ (m ₂ + i / ₄ )

4w ₂ for u ₂ = 0 for u ₂ ^ 0λ «, '· + 4w ₂ (u ₂ + w ₄ ) <0 for w ₂ aO λ w ² + 4u, (w ₂ + m ₄ )> 0 λ Wj + 2m ₃ <0 for "0 λ ₂ ψ ² + 4H ₂ (m ₂ + _4)> 0, λ ', 2w + _3> 0, wherein if the calculated value of the parameter Θ satisfies the condition | θ | > 0.9999, this value is changed into the value determined according to the formula:

f6> = -0.9999 for? <0 1.9 = 0.9999 for <9> 0

PL 231 678 Β1

The calculated value of the parameter Θ the UOP system uses the digital bus to save it in the memory unit Θ. Then, the UOP system, using additionally stored in the memory unit Θ value of the auxiliary parameter Θ, which is read by means of digital buses, calculates and saves the following values of sinusoidal alternating voltage parameters:

• initial phase for ti = 0 according to the formula: f '

arctg 7T ^ -180 ° for u ₂ -ufl <0au, <0 arctg ^u '7ι θ ² + 180 'for u ₂ - ufl <Oam,> 0 -90 ° for u ₂ -u _} 6 = 0a u, <0 0 ° for u ₂ - ufl = 0 Au, = 0 90 ° for u ₂ -ufl = 0Au,> 0 arctg ⁱⁿ '7ΓΊ? ⁷ for u ₂ -u, 0> 0

for the voltage versus time function given by the formula:

V2 ^u 7) = ^ - 1 ^ 1 ^ (^ + ^) which saves via the digital bus in the memory unit φ1 the initial phase for L = 0 according to the formula:

= and arctg | arctg j

-90 °

0 °

90 ° arctg ufl-u ₃

-7l-0 ²

-7i-0 ²

7i-0 ²

180 ° for u-u _± 6 ₃ <0AU ₄ <0 + 180 'for U _A-0 u ₃ <0AU _4> U _A 0 of 0 - ₃ with au = 0 _A <0 of uft- u ₃ = 0 au ₄ = 0 for u ₃ 0 - u ₃ = Oaw,> 0 dia u ₃ Ou ₃ > 0 for voltage versus time function expressed as:

^u 7) = ^ - W ^sin (^ +%) which is saved by the digital bus in the memory unit q> 4, effective voltage U _S k according to the formula:

_T. u? -2u, u, 6 + u?

C. _t = aJ—- ^L ^ -— V 2-2Θ ² which it saves via the digital bus in the USK memory unit.

PL 231 678 Β1

The coefficient a appearing in the formula for the apparent voltage is a constant characteristic for a given measuring system, which is the ratio factor of the voltage at the two-terminal of the input of the system (generator voltage G) and the value at the output of the ADC. The unit of the factor a is the volt [V]. This factor is used to convert the result of the ADC output as an integer into a physical result of the voltage at the input of the system. For the system from Fig. 1, this coefficient is determined by the formula:

LSB where w is the gain of the amplifier W, while LSB is the voltage value corresponding to 1 bit of the ADC converter expressed in volts [V],

After saving the calculated values to the memory units, the UOP system sends a digital signal to the KI interface controller informing about the determination of the sinusoidal alternating voltage parameters.

The measurement arrangement of the invention outlined above is to be considered as an exemplary arrangement. The individual elements of the circuit may be in the form of digital or analog circuits. It will be obvious to a skilled person how to implement the individual blocks in order to fulfill their functionality. In one of the possible implementations, the measurement system may be implemented in the form of a processor controlled by appropriate software. In another embodiment, the measurement circuitry may be implemented as an FPGA programmable logic circuit.

Patent claims

Claims (6)

1. A system for measuring the effective value and the initial phase of a sinusoidal alternating voltage, containing: • a pair of input terminals, to which the source of sinusoidal alternating voltage (G) is connected, • a system connected to a pair of input terminals, converting the voltage on the input terminals into a voltage signal with a voltage proportional to the voltage on the input terminals, which is connected to the analog input of the analog-digital converter (ADC), the measurement of which is excited by a signal from a clock signal generator (CLK) in such a way that the converter (ADC) measures the voltage at equal intervals of time T _s which is less than% of the period 7 of the voltage under test, characterized in that • the output of the converter (ADC) is connected to the memory unit buffer (U4) being the last of the four buffers (U1-U4) connected in series and containing the values of the last four measurements ui = u (ti), u ₂ = u (t ₂ ) , U3 = u (tg, uą = u (tg, where ti, t2, fe, t4 are successive measurement times, • while the outputs of the buffers (U1-U4) are connected to the input of the circuit calculating parameters (UOP), which is excited after collecting the measurements and which calculates the auxiliary parameter Θ according to the formula: θ = «, 4 « ₂ for w ₂ = 0 for« 2 / Oam, ² + 4 «2 (« 2 + ^u i} for «2 * 0 aux + 4« ₂ («2 + ^u 4) ^> θ ^Λu ] + <0 u, + for «2 fΟλη, ² + 4« ₂ (m ₂ + w ₄ )> 0a «, + 2m ₃ > 0 PL 231 678 Β1 • by means of which it calculates the following parameters, which it transfers directly or indirectly to the system interface (INT): o rms voltage U _s x, according to the formula: uf -2u _l u ₁ 9 + uf 2-29 ² where a is the ratio between the voltage at the input terminals of the circuit and the value at the output of the converter (ADC); o the initial phase φ \, stored in the memory unit (φ1), for ti = 0 according to the formula: <P \ = arctg arctg -90 ° 0 ° 90 ° arct -180 ° for m ₂ -w ₁ 6 '<0aw _] <0 w _s u ₂ - u _x d 7l-0 ² + 180 ° for w ₂ -ufl <Oaw,> 0 for u ₂ -u _} 6 = 0 a <0 for w ₂ -u _} 9 = 0aWj = 0 for w ₂ -w, ^ = 0aw ₁ > 0 _v in ₂ w, æ? for u ₂ -u ₁ 9> Q for the voltage function with respect to time expressed by the formula: V2 «W = ^ - 1 ^ 1 ^ (^ + ^) o the initial phase q> & saved in the memory unit (cp4) for / 4 = 0 according to the formula: arctg arctg \ u, 9-u ₂ J in _3} -180 ° for ufl-fa <0aw ₄ <0 + 180 ° for <0aw ₄ > 0 -90 ° 0 ° 90 ° for ufi - fa = 0am ₄ <0 for w ₄ 0-u ₃ = 0aw ₄ = 0 for ufl - = 0 aw ₄ > 0 arctg ——— 7l-0 ^{2 *} \ ufl-u ₂ for w ₄ ć ? -m ₃ > 0 for the voltage versus time function expressed by the formula: ^M (0 = ^ - 1 ^ 1 ^ (^ + ^) 2. The measurement system according to claim 1, The method of claim 1, characterized in that if the arithmetic logic unit in the parameter computation system 6 * (UO ©) calculates the value of the parameter Θ satisfying the condition | > 1 - where e (0; 10 ¹ ], where preferably e [10 ⁵ ; 10 ² ], then this value is changed to the value determined according to the formula: PL 231 678 Β1 0 = -1 + £ for 0 <O 0 = 1- £ for?> 0 3. The measurement system according to claim 1, The method of claim 1, wherein the source of the sinusoidal voltage is a sinusoidal voltage generator (G). 4. The measurement system according to claim 1, A circuit according to claim 1, characterized in that the voltage processing circuit at the input terminals is a differential amplifier (W). 5. The measurement system according to claim 1, The method of claim 1, wherein the parameter computation circuit (UOP) is activated after measuring the first four instantaneous voltage values, and after measuring each successive instantaneous voltage value. 6. The measurement system according to claim 1 3. The parameter calculator (UOP) is excited by a reset buffer of length 4 (UBR4), which is reset at the moment of starting the measurements, which counts the digital excitation signals at its input connected to the digital signal output from four series connected memory unit buffers (U1-U4) connected to the converter (ADC) informing that the measurement value has been stored in the buffer queue, but when the first, second or third initialization signal is received, the reset buffer system (UBR4) does not transmit the wake-up signal, but when the fourth and subsequent initiation signals arrive, the reset buffer circuit (UBR4) passes a wake-up signal to its output connected to the digital wake-up signal input of the parameter computation circuit (UOP).