GB2567460A

GB2567460A - Method and apparatus for obtaining Thévenin equivalent parameters of a power network

Info

Publication number: GB2567460A
Application number: GB1716723.0A
Authority: GB
Inventors: Malengret Michel; Trevor Gaunt Charles; Robert Adams Stanley
Original assignee: University of Cape Town
Current assignee: University of Cape Town
Priority date: 2017-10-12
Filing date: 2017-10-12
Publication date: 2019-04-17
Anticipated expiration: 2037-10-12
Also published as: WO2019073430A1; GB201716723D0; GB2567460B

Abstract

A method and apparatus for obtaining the Thévenin equivalent parameters of a power network A method and apparatus for obtaining the Thévenin equivalent parameters of a power network. The method is performed at a point of common coupling 154 on the network wherein the point has a plurality m of wires 156, 158, 160, 162 and includes: injecting or drawing test modulated currents 190, 192, 194 into or from each of m-1 of the plurality of wires, wherein each of the test modulated currents simultaneously include at least two frequency components, a carrier frequency and a lower modulating frequency and no additional current is provided in the mth wire which provides a reference; obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling; calculating a magnitude of a Thévenin equivalent impedance at the two frequency components of each of the m-1 wires using the known injected or drawn test current and the obtained voltage for each frequency component; and obtaining the Thévenin equivalent parameter values of each of the m-1 wires using the calculated Thévenin equivalent impedance. The method can be repeated using a different set of the wires to determine the parameters for the mth wire.

Description

METHOD AND APPARATUS FOR OBTAINING THEVENIN EQUIVALENT PARAMETERS OF A POWER NETWORK

FIELD OF THE INVENTION

The invention disclosed herein relates to the determining of electrical variables within an electric circuit or power network. More specifically, it relates to obtaining Thevenin equivalent parameters.

BACKGROUND TO THE INVENTION

An electric network, also known as a power distribution network or a power transmission system, is a complex electric circuit for the delivery of generated electric power to the end user thereof. These power networks may extend kilometres and even span across entire countries and continents. These power networks generally have a number of power generators for the generation of electrical power; transmission and distribution networks for the transmission of the generated electrical power to loads at numerous end users; and loads which dissipate the electrical energy through the conversion thereof into thermal or mechanical energy, for example.

For various applications, it may be required to obtain the electrical parameters of a power distribution network. Due to the complexity of such networks and the unpredictable nature of power usage by end users, determining the electrical parameters of the entire network is problematic. It may therefore be more practical to determine the instantaneous electrical parameters of a power distribution network periodically as electrically perceived at a certain coupling point on the network.

One method for obtaining the electrical parameters of a power distribution network as electrically perceived at a certain coupling point on the network, is utilising Thevenin’s theorem and obtaining the so-called Thevenin equivalent voltage and Thevenin equivalent impedance of the network at that coupling point. These Thevenin equivalent parameters may then be utilised to model the power distribution network in relation to the coupling point. This information can be used for a several purposes such as improving transmission losses, voltage regulation, stability of network, protection, determining tariffs costs and for metering purposes to name but a few exemplary uses.

Obtaining these Thevenin equivalent electrical parameters requires obtaining the open circuit voltage at the coupling point and the current injected into or drawn from the coupling point, as the case may be. With these values known, the circuit as electrically perceived from the coupling point may be modelled as a voltage source with a series impedance.

The preceding discussion of the background to the invention is intended only to facilitate an understanding of the present invention. It should be appreciated that the discussion is not an acknowledgment or admission that any of the material referred to was part of the common general knowledge in the art as at the priority date of the application.

SUMMARY OF THE INVENTION

In accordance with this disclosure there is provided a method for obtaining the Thevenin equivalent parameters of a power network, the method performed at a point of common coupling on the network wherein the point of common coupling has a plurality m of wires and comprising: injecting or drawing test modulated currents into or from each of m-1 of the plurality of wires, wherein each of the test modulated currents simultaneously include at least two frequency components, a carrier frequency and a lower modulating frequency and no additional current is provided in the m^th wire which provides a reference;

obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling;

calculating a magnitude of a Thevenin equivalent impedance at the two frequency components of each of the m-1 wires using the known injected or drawn test current and the obtained voltage for each frequency component; and obtaining the Thevenin equivalent parameter values of each of the m-1 wires using the calculated Thevenin equivalent impedance of each of the m-1 wires.

A further features provides for the method to include obtaining Thevenin equivalent parameter values of the m^th wire using a calculated Thevenin equivalent impedance of the m^th wire by repeating the method for a different set of wires including at least one wire with known Thevenin equivalent parameter values.

In one embodiment, the method to include generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency and the lower modulating frequency; generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency by the lower modulating frequency, wherein the carrier frequency for each of the m-1 wires is displaced by 360/(m-1) degrees, and the lower modulating frequencies of the m-1 wires are all of equal amplitude and in phase, wherein no additional current is provided in the m^th wire which provides a reference by the sum of the test modulated currents being zero.

Still further features provide for the method to include deriving a magnitude of a Thevenin equivalent impedance of the m^thwire by:

injecting or drawing a test modulated current simultaneously including two frequency components into one of the plurality of m wires and a second wire of known Thevenin parameters;

obtaining an amplitude of the resultant voltage of the two frequency components at the m^th wire at the point of common coupling;

calculating a magnitude of a Thevenin equivalent impedance at the two frequency components of the m^,h wire using the known injected or drawn test current and the obtained voltage for each frequency component; and obtaining Thevenin equivalent parameter values of the m^th wire using the calculated Thevenin equivalent impedance of the m^th wire.

A further feature provides for the method to repeat for a different set of m-1 wires of the plurality of m wires thereby obtaining the Thevenin equivalent parameter values of the m^th wire.

In an alternative embodiment, the method includes generating test modulated currents for the m1 wires by pulse width modulating the carrier frequency and the lower modulating frequency.

Further features provide for the method to include drawing test modulated currents using pulse width modulation on m-1 wires by using switches in the wires with one switch open to result in a zero return current in the m^th wire which provides a reference; for the drawing of test modulated current to be repeated m-1 times with a different one of the m-1 wires having its switch open in order to obtain the amplitudes of the resultant voltage of the two frequency components for each of the wires; and for a plurality of each Thevenin equivalent parameter value for each of the m wires to be obtained after the drawing of test modules current has been repeated m-1 times and wherein the Thevenin equivalent parameter values for each wire is obtained by calculating an average each of the plurality of Thevenin equivalent parameters.

Further features provide for the method to include filtering the resultant voltage with a low pass filter before obtaining an amplitude of the two frequency components; for the frequency of the carrier frequency to follow a fundamental frequency of the power network and the lower modulating frequency to differ from the frequency components already present in the power network.

Further features provide for calculating a magnitude of a Thevenin equivalent impedance at the two frequency components to be by means of Tellegen’s theorem or an equivalent theorem; and for a feedback to be provided to measure injecting or drawing test modulated currents, for use as 3 the known injected or drawn test current for calculating the magnitude of the Thevenin equivalent impedance.

In one embodiment, obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling comprises a demodulation technique performed on measured voltage signals in the time-domain. In an alternative embodiment, obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling comprises Fourier analysis performed on measured voltage signals.

Further features provide for the step of injecting or drawing test modulated currents to be preceded by selecting the two frequency components from a group of preconfigured values to be simultaneously included in each respective injected or drawn current; and for the step of injecting or drawing test modulated currents to be preceded by measuring a voltage and/or current signal from at least one of the wires and automatically determining at least two usable frequency components that are not present in the measured signals to be simultaneously included in each respective injected or drawn current.

A still further feature provides for the method to include using the obtained Thevenin equivalent parameter values in deriving network measurements of one or more of the group of: true apparent power, non-active power, and power factor.

In a further aspect of this disclosure there is provided an apparatus for obtaining the Thevenin equivalent parameters of a power network comprising:

a coupling component for physically coupling to a point of common coupling on the network wherein the point of common coupling has a plurality m of wires;

a current component for injecting or drawing test modulated currents into or from each of m-1 of the plurality of wires, wherein each of the test modulated currents simultaneously include two frequency components, a carrier frequency and a lower modulating frequency and no additional current is provided in the m^th wire which provides a reference;

a voltage obtaining component for obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling;

an impedance calculating component for calculating a magnitude of a Thevenin equivalent impedance at the two frequency components of each of the m-1 wires using the known injected or drawn test current and the obtained voltage for each frequency component; and a Thevenin parameter obtaining component for obtaining Thevenin equivalent parameter values of each of the m-1 wires using the calculated Thevenin equivalent impedance of each of the m-1 wires.

A further feature of this aspect provides for the Thevenin parameter obtaining component to obtain Thevenin equivalent parameter values of the m^th wire using a calculated Thevenin equivalent impedance of the m^th wire by using the component with a different set of wires including at least one wire with known Thevenin equivalent parameter values.

In one embodiment, the current component includes a modulation component for generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency and the lower modulating frequency; and the current component to includes a modulation component for generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency by the lower modulating frequency, wherein the carrier frequency for each of the m-1 wires is displaced by 360/(m-1) degrees, and the lower modulating frequencies of the m-1 wires are all of equal amplitude and in phase.

Further features of this aspect provide for the current component to be for separately injecting or drawing a test modulated current simultaneously including two frequency components into one of the plurality of m wires; the voltage obtaining component to be for obtaining an amplitude of the resultant voltage of the two frequency components at the m^th wire at the point of common coupling; the impedance calculating component to be for calculating a magnitude of a Thevenin equivalent impedance at the two frequency components of the m^,h wire using the known injected or drawn test current and the obtained voltage for each frequency component; and the Thevenin parameter obtaining component to be for obtaining the Thevenin equivalent parameter values of the m^th wire using the calculated Thevenin equivalent impedance of the m^th wire.

Further features of this aspect provide for the apparatus to include a wire selection component for selecting a set of m-1 wires into which the current component injects or draws test modulated currents at a given time; and for the current component to comprise an inverter.

In in alternative embodiment, the current component includes a modulation component for generating test modulated currents for the m-1 wires by pulse width modulating the carrier frequency and the lower modulating frequency; the current component is for drawing test modulated currents using pulse width modulation on m-1 wires by using switches in the wires with one switch open to result in a zero return current in the m^th wire which provides a reference.

Further features of this aspect provide for the switches to be semiconductor switches that are operable to switch a load resistance to draw the test modulated currents; for each semiconductor switch to include a field effect transistor and a diode bridge rectifier to rectify the current switched by the field effect transistor; and for the drawing of test modulated current to be repeated m-1 5 times with a different one of the wires having its switch open in order to obtain the amplitudes of the resultant voltage of the two frequency components for each of the wires.

Still further features provide for the apparatus to include a current obtaining component for providing a feedback to measure injecting or drawing test modulated currents, for use as the known injected or drawn test current for calculating the magnitude of the Thevenin equivalent impedance; for the apparatus to include a frequency obtaining component for obtaining frequency components in voltage signals obtained by the voltage obtaining component; and for the frequency obtaining component to be for obtaining frequency components in current signals obtained by the current obtaining component.

In one embodiment, the frequency obtaining component includes a time domain component for obtaining the frequency components by carrying out a demodulation technique performed on the obtained signals in the time-domain; in another embodiment, the frequency obtaining component includes a frequency domain component for obtaining the frequency components by performing Fourier analysis on the obtained signals.

A further feature provides for the frequency selection component to select the two frequency components to make detection and measurement less susceptible to other sources of system noise or resonance thereby increasing the reliability of signal recognition.

An embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

Figure 1A is a block diagram of an apparatus for obtaining the Thevenin equivalent parameters of a power network;

Figure 1B is a schematic representation of a system in which the apparatus of Figure 1A connected to a point of common coupling on a power network is modelled by its Thevenin equivalent circuit;

Figure 2 is a flow diagram of an exemplary method for obtaining the Thevenin equivalent parameters of a power network;

Figure 3

is a flow diagram of an exemplary method for obtaining the Thevenin equivalent parameters of a power network;

Figures 4 to 6 are time domain graphs of modulated signals containing two frequency components;

Figure 7	is a combined graph of the signals of Figures 4 to 6;
Figure 8	is an alternative schematic representation of the system of Figure 1B in which current is drawn by the apparatus of Figure 1 A;
Figure 9	is a flow diagram of an alternative exemplary method for obtaining the Thevenin equivalent parameters of a power network;
Figure 10	is a further alternative schematic representation of the system of Figure 1B in which the apparatus of Figure 1A is implemented in an inverter; and
Figure 11	is a further alternative schematic representation of the system of Figure 1B in which the apparatus of Figure 1A is implemented in concert by two inverters and a computing device;
Figure 12	is a schematic representation of a further alternative apparatus for obtaining the Thevenin equivalent parameters of a power network; and
Figure 13	is a schematic representation of a system in showing a simplified schematic representation of the apparatus of Figure 12 coupled to a power network.

DETAILED DESCRIPTION WITH REFERENCE TO THE DRAWINGS

Exemplary methods of obtaining the Thevenin equivalent parameters of a power network are disclosed as well as apparatus in which these methods may be implemented. A system wherein the apparatus is coupled to a power network and configured to perform the methods is furthermore disclosed. The methods are performed at a point of common coupling on the power network such as coupling onto the bus bars within a switchboard or substation, a power outlet, or a power injection point, to name a few exemplary common coupling points that may be available on a power network. The methods obtain the Thevenin equivalent parameters at a coupling point on a power distribution network providing an in situ determining of these parameters.

In practice, the power network may, for example, be a four-wire three phase power network operating at a 50Hz or 60Hz fundamental frequency and the Thevenin equivalent parameters of each wire may be obtained by these methods. An exemplary application wherein obtaining these parameters may be desirable is to allow current, that is injected into or drawn from the network, to be configured for minimal power losses. Further applications may include the determining of quality of supply (QOS) parameters such as true apparent power and non-active power of a load, harmonic distortion, unbalance, analysing network stability and determining faults, to name a few examples. Consequently, the viability of power factor correction installations may be evaluated, for example.

GB 2,524,414B discloses a method for injecting power into or extracting power out of a power network at a point of common coupling to the power network wherein the point of common coupling has one or more wires. The method includes obtaining dynamically changing Thevenin parameters in the form of a Thevenin voltage and a Thevenin resistance of an equivalent Thevenin circuit with respect to each wire of the point of common coupling (PCC).

The described systems, methods and apparatus provide a means of obtaining the Thevenin equivalent parameters of a power network using techniques of modulation. A practical network can be replaced with m equivalent Thevenin circuits, each comprising a Thevenin equivalent voltage (V_th), Thevenin equivalent resistance (R_th), and a Thevenin equivalent reactance (X_th) in series, referred to a common weighted null voltage reference point. These Thevenin equivalent parameters vary as the loads, generators and topology of the physical network change. Active measurement of the Thevenin equivalent impedances of the network from the PCC requires the system to be perturbed, such as by varying the line current in a wire, and measuring the consequent change in the voltage, referring it to the chosen reference.

Two example embodiments are described: a first embodiment using amplitude modulation (AM) and a second embodiment using pulse width modulation (PWM). The two embodiments are implemented by different arrangements as described and can inject into or extract from the wires the currents in phase or quadrature with the original voltages, and even at various frequencies. The corresponding changes in voltage magnitude and phase shift are measured.

The described method of obtaining the Thevenin equivalent parameters of a power network is performed at a point of common coupling on the network. The method involves injecting or drawing a known modulated electric current into or from each of a plurality of wires. The injecting 8 or drawing of current is carried out at each of the m-1 wires simultaneously and includes at least two frequency components. The two frequency components of the known electric current are provided simultaneously by being included in a modulated signal using a modulating signal and a carrier signal described in more detail below.

In an m-wire system, there may be one wire being the neutral wire or ground (earth) wire of a system with a neutral. Alternatively, the system might not have a neutral wire and comprise m phase wires, such as in a delta-connected 3-phase three wire system or its equivalent with any other number of phases and without a neutral.

The described method obtains an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling. A magnitude of a Thevenin equivalent impedance at the two frequency components of each of the m-1 wires is calculated using the known injected or drawn test current and the obtained voltage for each frequency component. The Thevenin equivalent parameter values of each of the m-1 wires are then obtained using the calculated Thevenin equivalent impedance of each of the m-1 wires.

The modulation of the injected or drawn known modulated electric current may be in the form of amplitude modulation (AM), or pulse width modulation (PWM).

Amplitude modulation is a method normally used in communication technology in which a constant amplitude carrier frequency is multiplied by the signal of at least half of the carrier frequency (Nyquist Theorem). The signal at the receiving end is then demodulated to extract the original signal. In this application, a chosen current amplitude at the grid frequency is modulated (effectively multiplied). Since the current signal is then equivalent to the sum of two new frequencies, called side bands. The resultant grid voltages response are then extracted and used to calculate the Thevenin impedance.

Pulse width modulation methods used in communication introduces pulses of current with an amplitude of the carrier frequency but of a width that is modulated at a lower frequency. This results of a multitude of side bands around the carrier frequency. The principle current and corresponding voltage response side band are chosen.

In one embodiment, amplitude modulation is used and test modulating currents are injected at the point of common coupling of m wires. Currents may be injected into m-1 wires so that the sum of the test modulated currents of the m-1 wires is zero and provides no additional current in the m^th wire which provides a reference.

This embodiment of the described method uses m-1 modulated currents simultaneously corresponding to m-1 wires. The modulated frequency is chosen so that the modulated currents are equivalent to two frequencies in each wire and are equal in magnitude and at equal phase angles (360/m-1) with respect to adjacent wires. This overcomes the problem of previously known methods of shifting null point that makes the maths difficult to solve.

The method uses simultaneous injection of modulated signals into m-1 wires that sets up directly the reliable, sensitive measurement and simple, fast calculation of the Thevenin parameters. This is complemented by the measurement in the m^,h wire, or in a different set of m-1 wires.

In a first step m-1 modulated currents to be injected/drawn in m-1 wires are obtained by modulating a carrier frequency, the power frequency, by a lower frequency in such a way that the m^th wire injected/drawn current is zero. The carrier frequency signal utilised for each of the respective modulated wires are all displaced in time so as to obtain zero additional current in the m^thwire, whilst the lower frequency modulation are all in phase. This carrier signal displacement allows measurement in all m-1 wires simultaneously and acquiring measurements that are easy to solve.

The modulated currents are then injected by an apparatus so that these modulated currents also flow in each of the m-1 lines. The m^,hwire current will remain the same as it was before the injection of m-1 modulated currents. Each of the modulated currents in the m-1 wires can also be viewed as being equivalent to two equal currents where: the first is at a frequency equal to the difference between the carrier frequency and the modulated frequency, whilst the second current is at a frequency equal to the sum of the carrier and modulated frequency.

The magnitude of Thevenin corresponding frequency impedance for each of the m-1 wires can then be derived from the measured and/or derived value of the current and voltage components at the two above mentioned (equivalent) frequencies, using the Tellegen difference theorem.

In a further step separate step, the Thevenin impedance of the m^thwire may be derived. This may be derived by injecting a modulated current into the m^,hwire and the return current from any chosen wire or, alternatively, the method may be repeated for a different set of m-1 wires of the plurality of m wires thereby obtaining the Thevenin equivalent parameter values of the m^th wire. Having already determined the m-1 wires’ impedances, the m^thwire Thevenin impedance can be derived easily.

In an exemplary network with 4 wires, therefore with m = 4, the amplitude of each carrier signal of the three (m-1) wires’ modulated currents of the injected wire currents are chosen to be equal in magnitude but 120° out of phase with one another. The modulating signals are configured to be in phase with one another. This results in the three (m-1) injected currents summate to zero at any time. The sum of the (m-1) wires is always zero since the m-1 carrier currents add to zero and the modulation is the same for all of them and can be factored.

Applying the same modulating signal to all m-1 wires concurrently, and therefore that the modulated m-1 currents summate to zero at any time, has the result that no additional current results in the m^thwire and therefore no voltage drop across the m^th wire Thevenin impedance. This in turn implies that the voltage at the PCC can be used as the Thevenin side reference point which makes the derivations of the voltage drop across the other m-1 wires Thevenin, easy to determine.

The equal amplitude carrier frequency, displaced in time in each wire, is evenly spaced about the origin and therefore has a zero current sum at all times. This makes it much more straightforward to calculate the Thevenin parameter values of the wires, as one does not need to solve simultaneous equations due to the drop of voltage across the m^thwire Thevenin impedance when the current does not add to zero ( as described in paper All wires are treated equally, including the neutral if it exists. The total injected currents summation is zero (including the neutral) and are balanced at both frequencies current components. The product of the sum of carriers by a common factor is zero because the sum of carriers is zero.

In a second embodiment, pulse width modulation is used. In this embodiment, test modulating currents are drawn from the point of common coupling of m wires. Modulated currents may be drawn on m-1 wires by using switches in the wires with one switch open to result in a zero return current in the m^,h wire which provides a reference. The drawn currents may summate into a nonzero current that may cause a return current to flow in one of the m-1 wires which is equivalent to drawing a negative current. However, the open switch in the m^th wire ensures that no return current can flow therein and that the PCC of the m^thcan therefore be used as a reference.

The method is repeated with different wires having their switches open in order to obtain the amplitudes of the resultant voltage of the two frequency components for each of the wires. With each iteration, the wire having an open switch will be alternated between those equipped with switches such that a wire that had previously been used as a reference, and thus drew zero current, would in at least one iteration draw current and thus enable the determination of its Thevenin parameters. Multiple iterations may be performed which may enable more than one determination of one or more of the Thevenin parameters of the m wires. Averaging of the parameter values determined in more than one iteration for a particular wire may be performed to determine the Thevenin parameter values of the relevant wire.

Both methods include measuring the amplitude of the wire voltages and currents before and after modulation of the two frequency components of each wire at the point of common coupling on the network. The step of measuring the frequency components of the current and voltage may use a demodulation technique performed on the measured signals in which the amplitude of the each frequency component contained in the modulated signal may be obtained in the time-domain. As an alternative method, the frequency components may be obtained by means of Fourier analysis performed on the modulated measured signals.

The methods include using Tellegen’s theorem to calculate the absolute value of the impedance of each wire at each of the frequency components using the injected or drawn current component and measured voltage component. The Thevenin parameter values of each wire may then be obtained using the above calculated impedance magnitudes of each wire. The step of calculating the absolute value of the impedance of each wire at each of the frequency components may comprise using configured amplitude values of the injected or drawn current and voltage changes for the calculation. Alternatively, it may use measurements of the injected or drawn current for the calculation.

A block diagram is shown in Figure 1A that models the functional components of an apparatus (100) for obtaining the Thevenin equivalent parameters of a power network as seen from a point of common coupling thereon. These functional components may be hardware components, software components, or a combination thereof, that in concert perform a predetermined function. These functional blocks may furthermore be in communication with one another such as to provide for performing of a predetermined function through a concerted effort.

The apparatus (100) includes a coupling component (102) for establishing electrical communication between the apparatus (100) and each wire of a power network at a point of common coupling on the network.

The apparatus (100) furthermore includes a current component (104) for injecting or drawing a known electric current into or from each wire. The current component (104) is configured to inject or draw, as the case may be, a current into or from each wire that simultaneously includes at least two frequency components at known frequencies. In addition to having at least two frequency components, the phase and amplitude of each injected or drawn current are chosen such as to summate to zero at any time as will be discussed in more detail below.

The apparatus (100) also includes a voltage obtaining component (112) for measuring the voltage of each wire at the point of common coupling on the network. The voltage obtaining component 12 (112) may work in concert with one or more other functional blocks to obtain the amplitude of each frequency component in the measured voltage of each wire.

An impedance calculating component (114) of the apparatus (100) may be configured to calculate the absolute value of the impedance of each wire from the measured wire voltages and currents. This may be calculated at each frequency component using the injected or drawn current and measured voltage of each wire. The implementation of this functionality will be discussed in more detail below.

The apparatus (100) furthermore includes a Thevenin parameter obtaining component (116) for obtaining the Thevenin parameter values of each wire using the absolute value of the impedance of the relevant wire as determined by the impedance calculating component (114).

The current component (104) may include a modulation component (106) for generating an electric current for each wire having two known frequency components by means of a modulation technique. The modulation component (106) may generate these currents using a modulating signal and a carrier signal with the carrier signal having a greater frequency that that of the modulating signal.

The current component (104) may include a fundamental frequency follower component (108) for determining the nominal fundamental frequency of the power network. This fundamental frequency value may be communicated to the modulation component (108) in order to determine the required frequency for one or more of the modulating signal and carrier signal. This may further allow the modulation component (108) to exclude any integer multiple of the fundamental frequency or harmonic thereof.

The current component (104) may further include a current obtaining component (110) for obtaining measurements of the injected or drawn current as a feedback mechanism to determine whether the actual currents correspond with the configured current values. The current component (104) may be configured to communicate these measured current values to the impedance calculating component (114) for use in calculating the impedance values of each wire instead of the configured current values.

The apparatus may furthermore include a frequency obtaining component (118) in communication with one or both of the current component (104) and the voltage obtaining component (112) to assist in determining the frequency components present in a measured signals. The frequency obtaining component (118) may further include a time domain component (120) for determining such frequency components present in a measured signal by means of a time domain 13 demodulation technique. Alternatively or additionally, the frequency obtaining component (118) may include a frequency domain component (122) for determining the frequency components in a measured signal by means of Fourier analysis or other known methods performed on the measured signal in the frequency domain.

The apparatus (100) may include a frequency selection component (124) for selecting the frequency of each of the frequency components required to be present in the injected or drawn current into or from each wire. These frequencies may be selected from a group of preconfigured values. Alternatively, the frequency selection component (124) may be configured to obtain voltage and/or current signals from at least one of the wires through communication with the voltage obtaining component (112) and/or the current component (104) and using these measurements to automatically determine at least two usable frequencies that were not present in the originally measured signals before injecting a modulated current.

The apparatus (100) may further include a wire selection component (126) for selecting a set of m-1 wires into which the test current component injects or draws test modulated currents at a given time.

Figure 1B is an example schematic representation of a system (150) in which the apparatus (100) is coupled to a power network (152) at a point of common coupling (154) on the power network (152). In this exemplary system (150), the power network is a three-phase four-wire power network, having three phase wires (156,158,160) and a neutral wire (162) at the point of common coupling (154), that has been modelled by its Thevenin equivalent circuit (164). The Thevenin equivalent circuit (164) has a Thevenin equivalent impedance (166, 168, 170) in each respective phase wire (156, 158, 160) in series with a Thevenin equivalent voltage source (174, 176, 178) which are in turn connected to a common reference or neutral node (180). The Thevenin equivalent circuit (164) furthermore includes a Thevenin equivalent impedance (172) in the neutral wire (162).

The apparatus (100) is connected to the three phase wires (156,158,160) at coupling nodes (182, 184, 186) such that it is able to inject a current (190, 192, 194) into each respective phase wire and such that it may measure the phase voltages at the respective coupling nodes (182, 184, 186). A connection is also provided between the apparatus (100) and the neutral wire (162) at a reference node (188). In other embodiments as describe, the apparatus (100) may draw currents.

Referring to Figure 2, a flow diagram of an exemplary method (200) for obtaining the Thevenin equivalent parameters performed by the apparatus (100) connected to a power network. As an initial step, the apparatus (100) is coupled (202) to the point of common coupling (154) having mwires.

The method may inject or draw (204) test modulated currents into or from each of m-1 of the plurality of wires, wherein each of the test modulated currents simultaneously include at least two frequency components, a carrier frequency and a lower modulating frequency. The modulation may be carried out by amplitude modulation or by pulse width modulation techniques. M-1 wires are used so that the m^th wire may be used as a reference with no additional current provided in the m^,h wire. This may be carried out in a number of ways as described further below.

In one embodiment, the carrier frequency of the test modulated currents in the m-1 wires may be displaced by 360/(m-1) degrees and the modulating frequencies may all be of equal amplitude and in phase resulting in the sum of the test modulating currents being zero and providing no additional current in the m^th wire that therefore provides a reference. This embodiment is described below as the first embodiment using amplitude modulation.

In another embodiment, the modulated currents may be drawn on m-1 wires by providing switches in the wires with one switch open to result in a zero return current in the m^th wire which provides a reference. This embodiment is described below as the second embodiment using pulse width modulation.

The method may obtain (206) an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling (154).

The method may then calculate (208) a magnitude of a Thevenin equivalent impedance at the two frequency components of each of the m-1 wires using the known injected or drawn test current and the obtained voltage for each frequency component.

The method may obtain (210) the Thevenin equivalent parameter values of each of the m-1 wires using the calculated Thevenin equivalent impedance of each of the m-1 wires.

The method may then obtain (212) the parameters for the mth wire. This may be done in a number of different ways.

For the embodiment in which the test modulating currents sum to zero in m-1 wires, the method may be repeated for a different set of m-1 wires to obtain the m^th wire parameters; alternatively, a test modulating current may be applied to the m^th wire to repeat the method and obtain the parameters of the m^th wire.

For the embodiment using switches in the wires, the method may be repeated m-1 times with a different m^th wire having an open switch and averaging the results from the iterations.

Figure 3 is a flow diagram of an exemplary method (300) for obtaining the Thevenin equivalent parameters performed by the apparatus (100) connected to a power network in accordance with the first embodiment using amplitude modulation. As an initial step, the apparatus (100) is coupled (302) to the point of common coupling (154) having a four-wire bus as shown in the system (150) of Figure 1B. In this exemplary method, the power network (164) has a 50Hz nominal fundamental frequency corresponding to the power system’s rated frequency.

The apparatus (100) subsequently selects (304) the frequency of each frequency component that is required to be present in each current to be injected at a later stage of the method. In this embodiment, the apparatus (100) is preconfigured with the required frequency components being for example 40Hz and 60Hz. The apparatus (100) may be preconfigured with an assumed power network fundamental frequency of 50Hz. Alternatively, this step (304) may include determining the fundamental frequency of the power network.

Thereafter, the apparatus (100) performs (306) a modulation technique for example to generate a signal that simultaneously contains both a 40Hz and a 60Hz component of which the amplitudes are known. In this exemplary embodiment, the modulation technique is amplitude modulation (AM). A modulated signal having a 40Hz and 60Hz component is obtained by amplitude modulating a sinusoidal carrier signal with a frequency equal to the fundamental frequency, i.e. 50Hz, with a 10Hz sinusoidal modulating signal as is described below.

Amplitude modulation (AM) approach

Three 50Hz equal magnitude sinusoidal carrier signals are selected as carrier signals, which are 120° out of phase, for the amplitude modulated signals. The three carrier signals can therefore be expressed by the following three equations:

C-l = sin(2rt50t)

Equation 1: Carrier signal 1

2π

C₂ = A_r sin(2rt50t + —)

Equation 2: Carrier signal 2

2π

C₃ = A_r sin(2rt50t--—)

Equation 3: Carrier signal 3 where Ci, C₂ and C₃, are the first, second and third carrier signals respectively and Ai is a preconfigured amplitude. The modulating signal for the three signals are selected as 10Hz sinusoidal signals that are in phase with each other. The modulating signal for all three modulated signals may therefore be expressed as:

M = A₂ sin(2rcl0t)

Equation 4: Modulating signal where A₂ is a preconfigured modulation signal amplitude such that a desired modulation index may be obtained in the resulting modulated signals.

The three modulated signals may therefore be expressed as:

S_± = A_± A₂ sin(2rc50t) sin(2rcl0t)

Equation 5: Modulated signal 1

2π

5₂ = A_rA₂ sin(2rc50t + — )sin(2rcl0t)

Equation 6: Modulated signal 2

2π

5₃ = A_rA₂ sin(2rc50t--—) sin(2rcl0t)

Equation 7: Modulated signal 3 sample waveforms of which are shown in Figure 4, Figure 5 and Figure 6 respectively.

The three modulated signals Si, S₂ and S₃are shown together in the waveform of Figure 7. It will be appreciated that at any time, the sum of the values of the three signals at that time will be zero. Furthermore, it will be appreciated that each signal simultaneously contains a frequency component at 40Hz as well as 60Hz. This may be shown mathematically with the mathematical identity:

sin(a) sin(b) = - [cos(a + b) - cos(a - b)]

Equation 8: Trigonometric identity

The modulated signal in equation 5 can accordingly be rewritten as follows:

S-l = A_xA₂ sin(2rc50t) sin(2rcl0t)

ΑλΑ₂ .·. S_r = —-—[cos(27r40t) — cos(2rc60t)]

Equation 9: Modulated signal 1 alternate form and therefore simultaneously includes both a 40Hz and 60Hz frequency component. The same identity of Equation 8 may be used to show that S₂ and S₃also each include a 40Hz and a 60Hz component.

Subsequently, the three modulated signals (Si, S₂, S₃) are injected (308) into each phase wire (156, 158,160) as currents (190, 192,194) and summate at the neutral node (180). As shown above, the signals (Si, S₂, S₃) and therefore the currents (190, 192,194) are selected to summate to zero at any time. Therefore, no current will flow in the neutral wire (162) and the neutral wire impedance (172) will have no effect. The potential at the neutral node (180) is therefore the same as at the reference node (188) at this stage of the method (300).

Thereafter, the frequency components of the injected currents are obtained (310). In this embodiment, the frequency components as calculated for the injected currents are assumed to be the actual injected frequency components. It will be appreciated that a feedback mechanism could be utilised to confirm that the frequency component amplitudes are indeed as calculated. If not, corrective measures may be effected.

The frequency components of the voltages as measured (312) at the coupling nodes (182, 184,186) are also obtained. It will be appreciated that, since the Thevenin voltage sources (174, 176,178) are 50Hz sources, they are modelled as short circuits for the injected 40Hz and 60Hz components. Therefore, the 40Hz and 60Hz voltage components measured at the coupling nodes (182, 184,186) are in fact the voltage drops across the respective Thevenin phase wire impedances (166, 168,170) caused by the injected 40Hz and 60Hz current components flowing there through.

At this stage in the method the amplitudes of both the current through and the voltage across each phase wire Thevenin impedance (166, 168,170) are therefore known at two different frequencies. Accordingly, the absolute value of the phase wire Thevenin impedances (166, 168,170) can therefore be calculated (314) using these amplitude values.

For each phase wire Thevenin impedance (166, 168,170), its absolute value may be calculated

by Tellegen Difference Theorem.:

1₇ I \&^VZ_THf I l^zwl - 1., I Ι^Δ/ζ™/1

Equation 10: Absolute value of impedance where |Z_THf | is the absolute value of the Thevenin impedance at frequency f, i.e. |Rth + ]2πίLth| at a particular frequency and AVzTHt and ΔΙζτη which are equal to V_ZTHf and ΔΙζτηκ as the original 18 voltage and current components at these two chosen frequency did not exist prior to injecting or drawing the modulating currents’ equivalent frequencies (given that the Thevenin voltage at those frequency is zero is equivalent to a short circuit). The impedance value will be different at the two injected frequency components, in this embodiment 40Hz and 60Hz (which is equivalent to a 50Hz carrier modulated by a 10 Hz signal).

For each phase wire, there are therefore two unknowns, being the resistive and reactive components of the impedance. However, these two unknowns may be solved using algebra by means of the following two equations:

|Z₄ohzI = |R + j2rc40L|

Equation 11: Absolute value of impedance at 40Hz |ΖβοΗζΙ = |R + ,/2π60£|

Equation 12: Absolute value of impedance at 60Hz

Therefore, the inductance L of the reactive component of the impedance may be calculated (316) and, similarly, the resistive component of the impedance may be calculated (318) for the Thevenin equivalent impedance (166, 168, 170) of each phase wire (156, 158, 160).

Thereafter, the injection of two of the three modulated currents (182, 184, 186) are stopped such that only one of the modulated currents is injected (320) in only one of the three wires (156, 158, 160). The injected current will therefore not summate to zero at the fourth (neutral) current (180), will return through the neutral wire (162) and therefore also the neutral wire Thevenin impedance (172). As mentioned above, the relevant Thevenin voltage source is considered a short circuit for the 40Hz and 60Hz components of the injected modulated current (182, 184, 186). Therefore, the relevant phase wire impedance (166, 168,170) and the neutral wire impedance (172) will be in series and may be summated.

Therefore:

\Z_PH + z

Equation 13: Sum of phase wire and neutral wire impedances where Z_PH and Z_Nare the relevant phase wire impedance (166, 168, 170) and the neutral wire impedance (172) respectively; Vzph+zn is the voltage across the sum of these impedances and Izph+zn is the injected current flowing through these impedances.

Therefore, the same mathematical procedure as above may be used to solve the absolute value of the sum of the relevant phase wire impedance (166, 168, 170) the neutral wire impedance (172). With the relevant phase wire impedance (166,168,170) known, the neutral wire impedance (172) may be determined (322) by simple subtraction.

It will be appreciated that this method (300) may be performed periodically to compensate for changes in the dynamically changing power network arising from changes in network configuration, power supply and loading. It will furthermore be appreciated that, since the currents summate to zero at the neutral point when determining the phase wire Thevenin impedances, the potential of the neutral point will remain constant.

In subsequent periodic applications of this method (300) the frequency of the AM input signal may be changed to different values, for example by changing 10Hz to 5Hz (without limitation, requiring more complicated measurement, or with the limitation that the carrier frequency is an integer multiple of the modulating frequency, allowing the measurement to be kept simple).

Figure 8 is a schematic representation of a system (800) in which like reference numerals represent like features to the system (150) of Figure 1B. In this system (800) the apparatus (100) is connected to the three phase wires (183,184,185) at coupling nodes (182,184,186) such that it is able to draw a current (866, 868, 870) from each respective phase wire and such that it may measure the phase voltages at the respective coupling nodes (182, 184, 186). In this system (800), the apparatus (100) is therefore configured to modulate a load and thereby in turn modulate the drawn current (866, 868, 870).

The method (900) shown in the flow diagram of Figure 9 may be utilised using the system (800) of Figure 8 wherein like reference numerals represent like steps to the method (300) of Figure 3. In this exemplary method (900) the initial steps (302, 304, 306) are similar to that of the method (300) in Figure 3. Then, the method (900) includes the step drawing (908) a modulated current from each wire that each simultaneously includes at least two frequency components. Thereafter, the frequency components that are contained in the drawn currents may be obtained (910). The steps (312, 314, 318) of the method (300) in Figure 3 may then be used to obtain the absolute value of the impedance of each wire and, subsequently, their respective resistive and reactive components.

The impedance of the neutral wire may be obtained by drawing (920) a modulated current from a single phase wire and subsequently determining (322) its impedance.

An alternative amplitude modulation based technique the apparatus may be configured to modulate the power frequency (e.g. 50Hz) with a chosen low frequency (e.g. 10 Hz), low magnitude current. Applying the same modulating signal to all three phase wires, the vector magnitudes of the currents are the same and the neutral current is zero. The apparatus measures the injected current and the grid voltage and extracts the 10 Hz component from both by one of several practical methods of demodulation, e.g. Inphase and Quadrature (IQ) demodulation.

The rms values V_LF(rms) and li_F(rms) of the 10 Hz components are then calculated. The 10 Hz power is calculated as Plf = V_Lf x Ilf and is averaged over one cycle to get PLF(avg). The grid resistance is:ff = ^PLFj-^av9j

I_LF(rms)² while the impedance is:

Equation 14: Grid resistance ₌ V_LF(rms) I_LF(rms)

Equation 15: Grid impedance

The inductive reactance is therefore:

Xt = /z² - R²

Equation 16: Grid reactance and XLmay therefore be calculated by solving these equations from the obtained quantities.

Figure 10 is a schematic representation of a system (1000) in which like reference numerals represent like features to the system (150) of Figure 1B. In this exemplary system (1000), an inverter (1010) is coupled to the power network (202) at the point of common coupling (154) on the power network (202). The inverter (1010) in this exemplary system (1000) is configured to implement the functional components of the apparatus (100) of Figure 1 A.

The hardware configuration of an inverter provides a convenient platform on which to implement the functionality of the apparatus (100) of Figure 1A. It may include Field Programmable Gate Arrays (FPGAs), Digital Signal Processors (DSPs), microcontrollers and the like, which may be configured to implement one or more of the functional blocks in software. It furthermore provides the power electronics required to generate the currents required and the sensing devices required for voltage and/or current measurements to implement the exemplary methods above such as the method (300) of Figure 3.

Figure 11 is a further schematic representation of a system (1100) in which like reference numerals represent like features to the system (150) of Figure 1B. In this exemplary system (1100), two inverters (1011,1012) are coupled to the power network (202) at the point of common coupling (154). A first and a second inverter (1011, 1012) are both in communication with a computing device (1110) through a communication channel (1115).

The first and second inverters (1011,1012) and the computing device (1110) form, in concert, the apparatus (100) of Figure 1A. The required functional blocks of Figure 1A may be implemented by either of the inverters (1011, 1012) and/or the computing device (1110) by hardware and/or software. Furthermore, any step of the exemplary methods above may be executed at either of the inverters (1011, 1012) and/or the computing device (1110). Therefore, for example, the first inverter (1011) in this exemplary system (1100) may be configured to generate and inject the required currents (190, 192, 194) and the second inverter (1012) may be configured to measure the voltages at the coupling nodes (182, 184, 186) of the point of common coupling (154). The computing device (1110) may furthermore be configured to request measurements from the second inverter (1012) and to instruct the first inverter (1011) to generate and inject currents as required for implementation of the above exemplary methods.

A test working compensator may be implemented with two banks of three single-phase inverters: one bank used for measurement of Thevenin equivalent parameters of the source network by injecting an AM signal, phase distributed to sum to zero at the Thevenin point; and a second inverter providing the non-active power compensation. A third inverter bank with batteries may allow power to be exported into the grid without disturbing the experimental results. In a practical installation all three functions may be combined in one inverter.

Pulse Width Modulation (PWM) Approach

It will be appreciated that the apparatus may be configured to draw modulated currents by connecting a load impedance to the coupling nodes. These currents may be modulated by using semiconductor switches configured so as to obtain the desired modulated currents. A controller may be in communication with the respective semiconductor switches and may facilitate the controlling thereof. It will be further appreciated by those skilled in the art that the controller may be configured to switch the impedances hard into and out of circuit by using a pulse width modulated technique so as to increase the efficiency of such an apparatus and to limit the power dissipated within the semiconductor switches themselves.

An exemplary embodiment of part of the apparatus (1200) for obtaining the Thevenin equivalent parameters is shown in Figure 12 and is an adaptation of the apparatus (100) of Figure 1. As such, like reference numerals indicates like features to that of the latter apparatus (100). Figure 12 shows the power electronics of the apparatus (1200) and may form part of the current component (104). The apparatus (1200) is configured for use with a three-phase, four-wire power network and includes three connectors (1202,1204,1206) for connection of the apparatus (1200) to the three phase conductors of the power network and a fourth connector (1208) for connection of the apparatus (1200) to the neutral conductor of the power network.

The apparatus (1200) includes three load circuits (1210, 1212, 1214) that are in use connected to the phase conductors of the power network for drawing modulated currents from the respective phase conductors with the neutral conductor as common reference for the three load circuits. Each load circuit (1210,1212,1214) includes a load resistor (1216,1218,1220) and in the present embodiment each comprises two 1kilo-Watt (kW) heater elements connected in parallel. Each load circuit (1210, 1212, 1214) further includes a semiconductor switch that, when activated, causes the relevant load circuit to draw current from the phase conductor it is connected to.

In the present embodiment, the semiconductor switches are field effect transistors (FETs) (1222, 1224, 1226), which are unidirectional semiconductor switches. For this reason, each load circuit (1210, 1212, 1214) includes a full-bridge diode rectifier (1228, 1230, 1232) for rectifying the alternating current drawn from the phase conductors. In the present embodiment, the modulation component (122) may generate a pulse width modulation (PWM) switching signal that may be applied to the gate terminal of the relevant FET (1222, 1224, 1226) to activate the relevant FET. Thus, when the FET (1222, 1224, 1226) is in a deactivated state (such that the switch is “open”), its gate voltage will be substantially zero volts and the resulting current drawn by the apparatus from the relevant phase conductor also zero. When the relevant FET (1222, 1224, 1226) is in an activated state (such that the logical switch is “closed” and therefore drawing current), its gate voltage will be pulse width modulated so that a pulse width modulated current is drawn from the phase conductor through the load resistor (1216, 1218, 1220) to which it is connected. As will be shown below, the PWM currents drawn from the phase conductors include at least two frequency components.

Each load circuit further includes a passive first order low pass filter in the form of an “LC” filter (1234, 1236, 1238), each comprising a series inductor (1240, 1242, 1244) and a shunt capacitor (1246, 1248, 1250), for smoothing the currents drawn from each of the phase conductors of the grid by attenuating the high order harmonics.

The FETs (1222, 1224, 1226) are switched with a PWM switching signal having a high switching frequency (f_s) (in the present embodiment chosen from the group consisting of 10 kHz, 15 kHz or

Hz) and a duty cycle that is sinusoidally weighted at a modulation frequency (fmod). The ontime duration (t_on) of the PWM signal may be expressed by the equation:

A_mton ~ ~p~ * cos(27r/_motjt)

F_s

Equation 17: On-time duration of the PWM switching signal duty cycle where A is smaller than 1 and chosen such as to allow a comparatively small current to flow through the load resistors (1216, 1218, 1220). The fundamental frequency (fgrid) of the power system, in the present embodiment 50 Hz, is used as the carrier frequency of the modulated current and the FETs (1222, 1224, 1226) are switched at the modulation frequency fmod- This results in a spectrum of current frequency being drawn from the supply including at least two frequency components. This spectrum includes the carrier frequency (fgrid) as well as multiple side bands at f_grid+fmod_and f_grid-fmod_as well as integer multiples thereof.

This may be derived as shown below, where c(t) is the carrier signal and m(t) is the modulating signal:

c(t) = A_c x sin 2nf_gridt

Equation 18: Carrier signal m(t) = A_m x cos(2nf_modt)

Equation 19: Modulating signal where A_m is the modulation index and must always be smaller than 1. The result of the modulation is then:

y(O ^— A_c sin 2nf_gridt + - [5ίη(27τ(^_Γ;^ + f_mod)t) + sin(27r(fg_rt_d

Equation 20: Modulated signal

Figure 13 shows the apparatus (1200) of Figure 12 connected to a three-phase, four wire power system. The apparatus (1200) is shown in a simplified schematic form where the LC filters (1234, 1236, 1238) and rectifiers (1228, 1230, 1232) have been omitted and in which the FETs (1222, 1224, 1226) are shown as ideal switches and will thus in the context of this Figure be referred to as “switches”. The apparatus (1200) may be used to determine the Thevenin equivalent parameters (166, 168, 170, 172) of the four-wire power system as follows.

In the present embodiment, f_grid is 50Hz and f_mOd is 30Hz. Therefore, the frequency components (fgrid + f mo d) and (fgrid - fmod) will be 80Hz and 20Hz respectively and will be collectively referred to below as “the sidebands”. It is again emphasised that since the power system frequency is 50Hz, the Thevenin sources (174, 176, 178) are modelled as a short circuit for frequencies other than 50Hz. When considering the influence of the sideband currents, this short-circuit model will therefore apply.

In an initial set of (m-1) steps, thus three steps in the present embodiment, each of the switches (1222, 1224, 1226) are sequentially left open with the relevant load resistor (1210, 1212, 1214) thus not drawing any current while the remaining two switches are closed and therefore drawing a PWM current through the other two load resistors. Figure 13 shows a first step in which a first switch (1222) is left open such that there is no current (866) drawn through its corresponding load resistor (1210) while the remaining two switches (1224,1226) are closed with their corresponding load resistors (1212, 1214) thus drawing a current (868, 870). In this first step shown in Figure 13, the first phase conductor (156) is therefore the m^th wire and the two remaining phase conductors (158, 160) and the neutral conductor (162) are therefore the (m-1) wires.

Since the first switch (1222) is open, it is ensured that the current drawn by the first load resistor (1210) and thus through the first Thevenin impedance (1666) at each of the sideband frequencies is zero. Therefore, there is no voltage drop across the first Thevenin impedance (166) at the sideband frequencies and the potential at the first connector (1202) as well as the first PCC (182) are the same as that of the neutral node (180). The voltages measured at the sideband frequencies across the Thevenin impedances of the (m-1) conductors (158, 160, 162) may therefore be measured at their respective PCC’s (184,186,188) with reference to the PCC of the m^th wire (182).

It will be appreciated that test modulated currents are therefore simultaneously drawn from two of the (m-1) wires, i.e. the second and third phase conductors (158, 160) while a test modulated current is injected into the neutral conductor (162) through the summation (1310) of the drawn currents as shown in Figure 13. However, this return current is the equivalent of drawing a negative current and will therefore also be considered to be a drawn current in the context of this embodiment.

The resultant voltages at the sideband frequencies may therefore be obtained for each of the (m1) wires (158, 160, 162) at their PCC’s (184, 186, 188). The magnitudes of the drawn currents (868, 870, 1310) may be known through measurement and in the present embodiment is measured using current transformers (CT’s). Therefore, the magnitude of a Thevenin equivalent impedance (168, 170, 172) at the sideband frequencies may be obtained for each of the (m-1) 25 wires using the known drawn test currents (868, 870, 1310) and the obtained voltage for each sideband frequency. Thevenin equivalent parameter values of each of the (m-1) wires may thus be obtained by using the calculated Thevenin equivalent impedance of each of the (m-1) wires.

By following the same procedure two further times and each time selecting another switch (1224, 1226) as the m^th wire, the Thevenin equivalent impedances (166, 168, 170, 172) of all four wires (156, 158, 160, 162) may be obtained. It will be appreciated that by performing the steps described above three times, two sets of Thevenin equivalent impedances will be obtained for each of the phase conductors (156, 158, 160) whilst three sets of Thevenin equivalent impedances will be obtained for the neutral conductor (162). These values may be averaged if there are small discrepancies between the Thevenin equivalent impedances obtained during each iteration of the procedure above.

In order to obtain the Thevenin parameters, i.e. the resistive and reactive components of each Thevenin impedance, fast Fourier transforms (FFT’s) are performed on both the voltage and current measurements. The magnitudes of the sideband frequency components are taken from the FFT results for the currents and voltages. The magnitude of the relevant Thevenin impedance at each sideband frequency, hereunder referred to as Z₂o and Z₈o respectively, may be obtained by dividing the voltage component at each sideband (V₂o and V₈o) by the current component at each sideband (l₂₀ and l₈₀):

|z₂₀1 — |ζ₂ρ|

1^20 I

Equation 21: Absolute value of Thevenin impedance at20Hz |Z₈₀| —

1^80 I

Equation 22: Absolute value of Thevenin impedance at 80Hz

Having obtained these impedance magnitudes, it may be inserted into the following two equations to solve the two unknowns Rth and Lth, wherein Rth and Lth are the resistive and inductive components of the Thevenin equivalent impedance respectively, and j is the unit imaginary number with j²= -1.

|Z₂ol = \Rth + j2rt20L_ra|

Equation 23: Thevenin parameters at 20Hz and

1^801 ^— l^ff™ + j27r80L_TH|

Equation 24: Thevenin parameters at 80Hz

It will be appreciated that the apparatus (1200) could be adapted to have a switch in each of the m wires in which case in each iteration one switch would be closed and one switch would be open. However, in a practical implementation it may be desirable to minimise the number of semiconductor switches to reduce overall size of the apparatus and to reduce thermal management required to cool the semiconductor switches.

Known methods inject signals of two different frequencies close to the power system frequency in successive pairs of wires and implement a difficult calculation to make the measurement of the Thevenin equivalent parameters.

The descried method and apparatus provide for fast determination of the Thevenin parameters by injecting or drawing currents into all the phase wires but one having two simultaneous frequency components, allowing the phase wire impedances to be immediately solved by algebra.

The described method modulates the power frequency at a chosen frequency which is lower than the rated frequency and injects a signal into each of m-1 wires, such that it is straightforward from the response to calculate the parameters for each wire. The modulation frequency may be changed for successive measurements to improve sensitivity in the presence of noise and other similar devices and to reduce the potentially misleading effects of resonances at some frequencies.

The apparatus may include a wire current measurement component for determining the current frequency spectrum of the network over the possible range of modulation (that is between 0 and 2 times the carrier or power frequency) to measure frequency components that would constitute noise interference with the side-band frequencies generated by the AM or PWM approaches. High levels of a frequency component in this range may be communicated to the modulation component (122 in Figure 1 A) in order to exclude modulation at a frequency with high ‘noise’.

The applicant proposes a method of obtaining the Thevenin equivalent parameters at a coupling point on a power distribution network that provides an in situ determining of these parameters and without requiring the open circuit of the power network.

An apparatus is described that generates a modulated signal that is easily and reliably recognized by the measurement component reduces the risk of misinterpreting noise. The modulated signal may be varied to make detection and measurement less susceptible to other sources of system noise or resonance thereby increasing the reliability of signal recognition.

This information can be used for a several purposes, such as improving: transmission losses, voltage regulation, stability of network, protection, determining tariffs reflecting transmission costs and metering. Moreover. The information is particularly useful in that it is needed to determine the true power factor, non-active currents and power components and optimal compensating current 10 require to correct the power factor or minimise transmission losses.

Throughout the specification and claims unless the contents requires otherwise the word ‘comprise’ or variations such as ‘comprises’ or ‘comprising’ will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group 15 of integers.

Claims

CLAIMS:

1. A method for obtaining the Thevenin equivalent parameters of a power network, the method performed at a point of common coupling on the network wherein the point of common coupling has a plurality m of wires and comprising:

injecting or drawing test modulated currents into or from each of m-1 of the plurality of wires, wherein each of the test modulated currents simultaneously include at least two frequency components, a carrier frequency and a lower modulating frequency and no additional current is provided in the mth wire which provides a reference;

2. The method as claimed in claim 1, including obtaining Thevenin equivalent parameter values of the mth wire using a calculated Thevenin equivalent impedance of the mth wire by repeating the method for a different set of wires including at least one wire with known Thevenin equivalent parameter values.

3. The method as claimed in claim 1 or claim 2, including:

generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency and the lower modulating frequency.

4. The method as claimed in claim 3, including:

generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency by the lower modulating frequency, wherein the carrier frequency for each of the m-1 wires is displaced by 360/(m-1) degrees, and the lower modulating frequencies of the m-1 wires are all of equal amplitude and in phase, wherein no additional current is provided in the mth wire which provides a reference by the sum of the test modulated currents being zero.

5. The method as claimed in claim 4, wherein the method includes:

deriving a magnitude of a Thevenin equivalent impedance of the mthwire by:

obtaining an amplitude of the resultant voltage of the two frequency components at the mth wire at the point of common coupling;

calculating a magnitude of a Thevenin equivalent impedance at the two frequency components of the mth wire using the known injected or drawn test current and the obtained voltage for each frequency component; and obtaining Thevenin equivalent parameter values of the mth wire using the calculated Thevenin equivalent impedance of the mth wire.

6. The method as claimed in claim 4, wherein the method repeats for a different set of m-1 wires of the plurality of m wires thereby obtaining the Thevenin equivalent parameter values of the mth wire.

7. The method as claimed in claim 1 or claim 2, including:

generating test modulated currents for the m-1 wires by pulse width modulating the carrier frequency and the lower modulating frequency.

8. The method as claimed in claim 7, including:

drawing test modulated currents using pulse width modulation on m-1 wires by using switches in the wires with one switch open to result in a zero return current in the mth wire which provides a reference.

9. The method as claimed in claim 8, wherein the drawing of test modulated current is repeated m-1 times with a different one of the m-1 wires having its switch open in order to obtain the amplitudes of the resultant voltage of the two frequency components for each of the wires.

10. The method as claimed in claim 9 wherein a plurality of each Thevenin equivalent parameter value for each of the m wires is obtained after the drawing of test modules current has been repeated m-1 times and wherein the Thevenin equivalent parameter values for each wire is obtained by calculating an average each of the plurality of Thevenin equivalent parameters.

11. The method as claimed in any one of claims 1 to 10 including filtering the resultant voltage with a low pass filter before obtaining an amplitude of the two frequency components.

12. The method as claimed in any one of the preceding claims, wherein the frequency of the carrier frequency follows a fundamental frequency of the power network and the lower modulating frequency is different from the frequency components already present in the power network.

13. The method as claimed in any one of the preceding claims, wherein calculating a magnitude of a Thevenin equivalent impedance at the two frequency components is by means of Tellegen’s theorem or an equivalent theorem.

14. The method as claimed in any one of the preceding claims, including:

providing a feedback to measure injecting or drawing test modulated currents, for use as the known injected or drawn test current for calculating the magnitude of the Thevenin equivalent impedance.

15. The method as claimed in any one of the preceding claims, wherein obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling comprises a demodulation technique performed on measured voltage signals in the time-domain.

16. The method as claimed in any one of the preceding claims, wherein obtaining an amplitude of the resultant voltage of the two frequency components at each of the m-1 wires at the point of common coupling comprises Fourier analysis performed on measured voltage signals.

17. The method as claimed in any one of the preceding claims, wherein the step of injecting or drawing test modulated currents is preceded by selecting the two frequency components from a group of preconfigured values to be simultaneously included in each respective injected or drawn current.

18. The method as claimed in any one of the preceding claims, wherein the step of injecting or drawing test modulated currents is preceded by measuring a voltage and/or current signal from at least one of the wires and automatically determining at least two usable frequency components that are not present in the measured signals to be simultaneously included in each respective injected or drawn current.

19. The method as claimed in any one of the preceding claims, including using the obtained Thevenin equivalent parameter values in deriving network measurements of one or more of the group of: true apparent power, non-active power, and power factor.

20. An apparatus for obtaining the Thevenin equivalent parameters of a power network comprising:

a current component for injecting or drawing test modulated currents into or from each of m-1 of the plurality of wires, wherein each of the test modulated currents simultaneously include two frequency components, a carrier frequency and a lower modulating frequency and no additional current is provided in the mth wire which provides a reference;

21. The apparatus as claimed in claim 20, wherein the Thevenin parameter obtaining component obtains Thevenin equivalent parameter values of the mth wire using a calculated Thevenin equivalent impedance of the mth wire by using the component with a different set of wires including at least one wire with known Thevenin equivalent parameter values.

22. The apparatus as claimed in claim 20 or claim 21, wherein the current component includes:

a modulation component for generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency and the lower modulating frequency.

23. The apparatus as claimed in claim 22, wherein the current component includes:

a modulation component for generating test modulated currents for the m-1 wires by amplitude modulating the carrier frequency by the lower modulating frequency, wherein the carrier frequency for each of the m-1 wires is displaced by 360/(m-1) degrees, and the lower modulating frequencies of the m-1 wires are all of equal amplitude and in phase.

24. The apparatus as claimed in claim 23, wherein:

the current component is for separately injecting or drawing a test modulated current simultaneously including two frequency components into one of the plurality of m wires;

the voltage obtaining component is for obtaining an amplitude of the resultant voltage of the two frequency components at the mth wire at the point of common coupling;

the impedance calculating component is for calculating a magnitude of a Thevenin equivalent impedance at the two frequency components of the mth wire using the known injected or drawn test current and the obtained voltage for each frequency component; and the Thevenin parameter obtaining component is for obtaining the Thevenin equivalent parameter values of the mth wire using the calculated Thevenin equivalent impedance of the mth wire.

25. The apparatus as claimed in claim 23, including:

a wire selection component for selecting a set of m-1 wires into which the current component injects or draws test modulated currents at a given time.

26. The apparatus as claimed in any one of claims 20 to 25 wherein the current component comprises an inverter.

27. The apparatus as claimed in claim 20 or claim 21, wherein the current component includes:

a modulation component for generating test modulated currents for the m-1 wires by pulse width modulating the carrier frequency and the lower modulating frequency.

28. The apparatus as claimed in claim 27, wherein the current component is for drawing test modulated currents using pulse width modulation on m-1 wires by using switches in the wires with one switch open to result in a zero return current in the mth wire which provides a reference.

29. The apparatus as claimed in claim 28 wherein the switches are semiconductor switches that are operable to switch a load resistance to draw the test modulated currents.

30. The apparatus as claimed in claim 29 wherein the semiconductor switch includes a field effect transistor and a diode bridge rectifier to rectify the current switched by the field effect transistor.

31. The apparatus as claimed in any one of claims 28 to 30, wherein the drawing of test modulated current is repeated m-1 times with a different one of the wires having its switch open in order to obtain the amplitudes of the resultant voltage of the two frequency components for each of the wires.

32. The apparatus as claimed in any one of claims 20 to 31, including:

a current obtaining component for providing a feedback to measure injecting or drawing test modulated currents, for use as the known injected or drawn test current for calculating the magnitude of the Thevenin equivalent impedance.

33. The apparatus as claimed in any one of claims 20 to 32 further including a frequency obtaining component for obtaining frequency components in voltage signals obtained by the voltage obtaining component.

34. The apparatus as claimed in claim 33, wherein the frequency obtaining component is for obtaining frequency components in current signals obtained by the current obtaining component.

35. The apparatus as claimed in either claim 33 or claim 34 wherein the frequency obtaining component includes a time domain component for obtaining the frequency components by carrying out a demodulation technique performed on the obtained signals in the time-domain.

36. The apparatus as claimed in either claim 33 or claim 34, wherein the frequency obtaining component includes a frequency domain component for obtaining the frequency components by performing Fourier analysis on the obtained signals.

37. The apparatus as claimed in any one of claims 20 to 36, including a frequency selection component for selecting the two frequency components to make detection and measurement less susceptible to other sources of system noise or resonance thereby increasing the reliability of signal recognition.