Convolution integral for synchronized phasor

Systems, methods, and apparatus for providing a synchronized phasor in power system based on voltage and current measurements, sampling of the voltage and current measurements and convolving the samples with a function.

FIELD OF THE INVENTION

This invention generally relates to electrical power distribution networks, and in particular, to methods, apparatus, and systems for computing and reporting synchronized phasors at points along the network.

BACKGROUND OF THE INVENTION

Electrical distribution networks, such as the power grid conditions can be categorized by varying relationships between the current and voltage at various points of the network. Therefore, phasor measurement that provides information on both magnitude and phase of current and voltage at a point of measurement on the power grid has a significant importance for network operation. Such measurements can further be used for monitoring the performance of the power grid, monitoring and controlling power generation units, lines connecting stations and substations and used by protective relays or other devices distributed throughout the power grid. Power grids currently have a relatively significant amount of hardware supporting phasor measurement units (PMUs) on the power grid to provide phasor information based on voltage and current measurements at various points on the power grid.

There is a trend for future electrical power grids towards measuring and monitoring the phasors in a synchronized fashion based on the Institute of Electrical and Electronic Engineers (IEEE) C37.118 standard. Such synchronized phasors, also referred to as synchrophasors, typically need to be synchronized to about 1 micro-second (μs) or less across the power grid. To accomplish this by conventional methods, PMUs capable of synchronized measurements, are distributed throughout the power grid. Each PMU receives a common clock, reporting current, and voltage phasors at a sampling instance based on the received clock signal. The clock signal therefore must be delivered to each PMU with a relatively high level of Master Clock-to-PMU precision, such as for example, +/−500 nano-seconds (ns) across all PMUs on the grid. Typically clock signals from satellite systems are used for such purposes.

The use of synchronized phasor measurements can therefore require replacing legacy phasor measuring capable devices that use asynchronized sampling with phasor measuring capable devices that use synchronized sampling involving potentially significant investment.

BRIEF SUMMARY OF THE INVENTION

Certain embodiments of the invention can provide systems, methods, and apparatus for PMUs and determining synchronized phasors. Certain embodiments of the invention can further include asynchronous sampling of input signals using existing legacy hardware and timestamping asynchronously sampled signals and convolving the sampled data with a function to determine synchronized phasors. In one aspect, embodiments of the invention may allow the use of asynchronized sampling PMUs to generate synchronized phasor data. In another aspect, embodiments of the invention may allow the use of PMUs that do not sample in a synchronized manner with other PMUs to generate synchronized phasors with only software upgrades to the PMUs.

In one embodiment, a method can include receiving an input signal, repeatedly sampling the input signal with an asynchronous sampling period, and receiving a clock signal. The method can further include providing a timestamp from the clock signal to each sample of the input signal, and then convolving the samples of the input signal with a function using corresponding timestamps to determine a synchronized phasor of the input signal.

In another embodiment, a PMU can include an input port for receiving at least one input signal, at least one analog-to-digital converter for sampling each of the at least one input signals at an asynchronous sampling period, and a receiver for receiving a clock signal to timestamp each of the samples of the at least one input signals. The PMU can further include at least one circuit to perform a convolution on the samples of each of the at least one input signals with a function using corresponding timestamps to determine a synchronized phasor of each of the input signals.

In yet another embodiment, a power grid can include at least one voltage or current sensor for sensing at least one voltage or current signal and providing at least one input signal and at least one PMU. Each PMU can include an input port for receiving the at least one input signal, at least one analog-to-digital converter for sampling each of the at least one input signals at an asynchronous sampling period, a receiver for receiving a clock signal to timestamp each of the samples of the at least one input signals, and at least one circuit to perform a convolution on the samples of each of the at least one input signals with a function using corresponding timestamps to determine a synchronized phasor of each of the input signals.

Other embodiments, features, and aspects of the invention are described in detail herein and are considered a part of the claimed inventions. Other embodiments, features, and aspects can be understood with reference to the following detailed description, accompanying drawings, and claims.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention may provide apparatus, systems, and methods for improved measurements of synchronized phasors on a power grid. The improvements may entail providing synchronized phasors using preexisting hardware, such as existing protective relays, that sample input signals in an asynchronous manner. Additionally, the existing legacy protective relays that currently generate non-synchronized phasors may only require software updates that provide new algorithms for generating synchronized phasors. In one aspect, input signals, such as voltage and current measurements, can be sampled asynchronously and timestamped with a synchronized clock. The timestamped samples can further be convolved with a function to generate a synchronized phasor. In one embodiment, the asynchronous sampling frequency can be based partly on the frequency of the input signals.

Example embodiments of the invention will now be described with reference to the accompanying figures.

Referring now toFIG. 1, a simplified schematic diagram of an example power distribution system100that can be operated in accordance to an embodiment of the invention can include a power generation unit102, supplying electrical power via utility power lines104to a step-up transformer110that provides high voltage power to high voltage transmission lines112carried by high voltage line towers118. The power distribution system100can further include a step-down transformer120receiving high voltage power from the high voltage transmission lines112and providing electrical power to distribution lines122carried by distribution line poles128to an end user132. The high voltage transmission lines112and electrical power to distribution lines122can have points where currents and voltages on the lines can be measured using phasor measuring capable devices such as protective relays, meters, or other devices. Each of these devices can include a phase measurement unit (PMU)130,134,140, and146that can be integrated into phasor measuring capable devices or provide standalone phasor measurement capability. In other words, the PMUs130,134,140, and146can be integrated in, for example, a protective relay, or be a stand-alone device for determining a synchronized phasor. The PMUs130,134,140, and146may measure current or voltage measurement signals on the utility power lines104, high voltage transmission lines112, distribution lines122, or other components within the power distribution system100. The PMUs130,134,140, and146can calculate synchronized phasors based on the current and voltage measurements and may provide the determined synchronized phasor to a phasor data concentrator (PDC)156. The PDC156can determine the system conditions based on the measurement signals from one or more of the PMUs130,134,140, and146, and provide the synchronized phasor information to a higher level PDC or super PDC160or control center.

It should be noted thatFIG. 1is schematic in nature and although a single power generation unit102is depicted, the power distribution system100can have multiple utilities or power generation units, providing power from a variety of energy sources. The variety of energy sources may include, but are not limited to, coal, natural gas, hydroelectric, nuclear, solar-thermal, solar photovoltaic, wind, coastal tides, geothermal, hydrogen, or combinations thereof. The power generation unit102may provide power to the step-up transformer110at a variety of voltages in the range of about 50 volts to about 25000 volts, depending on the source of energy and operational parameters of the generation unit102. The step-up transformer110may provide electrical power and the high voltage transmission lines112may transmit electrical power in a voltage range of about 6 kilo-volts (kV) to 500 kV.

The step-down transformer120may receive relatively high voltage from the high voltage transmission lines112and provide a relatively lower voltage, such as, for example, 120 volts root mean square (Vrms) or 220 Vrms, to the distribution lines122. In one embodiment, the step-down transformer120may be a part of a distribution substation that may include other elements such as surge protectors and lightning arrestors. In another embodiment, the power distribution system100may include multiple step-down transformers geographically spaced from each other and receive power from the high voltage transmission lines112.

Although a single end user132is depicted for a simplified and conceptual view of the power distribution system100, the power distribution system100may have a plurality of end users. The end users132may be any variety of electrical power consumers, including residential consumers and business consumers.

Although the PDC156and the super PDC160are depicted as being co-located with the power generation unit102, in one embodiment, the PDC156and the super PDC160can be located in relatively close proximity of the PMUs130,134,140, and146, such as mounted on a high voltage line tower118or on a distribution line pole128. In other embodiments, the PDC156can be located in proximity of the step-up transformer110, the step-down transformer120, a control station, or any other location where the PDC156can receive synchronized phasor signals from the PMUs130,134,140, and146.

Still referring toFIG. 1, the PMUs130,134,140, and146can include any known type of current measurement device such as an ammeter or any known type of a voltage meter. The meters can provide a time series of voltage or current measurement signals to the PMUs130,134,140, and146. In certain embodiments, the PMUs130,134,140, and146may measure current or voltage from secondary devices such as transformers and relays located on the power distribution system100, rather than directly from power lines104,112, and122.

It should be noted that althoughFIG. 1only depicts four PMUs130,134,140, and146, there may be any number of PMUs in the power distribution system100. For example, there may be a single PMU corresponding with each geographic location on the power distribution system100. In other words, there may be a PMU associated with and receiving measurement signals from various elements of the power distribution system100so that synchronized phasors at these various elements and locations can be viewed concurrently.

Although inFIG. 1the PMUs130,134,140, and146are depicted as being on or near distribution lines122, high voltage lines112, and utility power lines104, or the poles128or towers118carrying the same, the PMUs130,134,140, and146can be located in any convenient location. For example, the PMUs130,134,140, and146can be integrated into, for example, relays or transformers that are electrically connected to and in proximity of the various conductive lines104,112, and122.

The PMUs130,134,140, and146may provide synchronized phasor information to the PDC156by any known methods including, but not limited to, direct wired link or wireless link. In one embodiment, the PDC156may receive synchronized phasor information from more than one PMU130,134,140, and146. Furthermore the PDC156may be communicatively coupled to client servers (not shown) to provide real time or delayed synchronized phasor information to end users for any variety of purposes, including, but not limited to, monitoring the power distribution system100, controlling the power generation unit102, or bringing online or taking offline additional power generation units. Although the PDC156is depicted as being co-located with the power generation unit, the PDC156can be located in any location where the PDC156can be provided with data from one or more PMUs130,134,140, and146and can be accessed by end users.

Referring now toFIG. 2, an example PMU140according to an embodiment of the invention is shown to be communicatively coupled via communication links162,164, and166to one or more meters168,170, and172, respectively, to receive measurement signals from the meters168,170, and172. The communication links162,164, and166can be any variety of known links including, but not limited to, direct wire coupling and wireless coupling. The communication links162,164, and166may be connected to input ports174,176and178for receiving at least one input signal, respectively. The PMU140can further include a receiver179for receiving a clock signal. The receiver179can include an antenna along with associate receiver electronics, such as, for example, a pre-amplifier and a demodulator, as is well known in the art. The clock signal can be received by the receiver179from various known sources, such as from a global positioning satellite (GPS) clock signal, a National Institute of Standards and Technology (NIST) clock signal, a Global Navigation Satellite System (GLONASS) clock signal, a Compass Navigation system clock signal, a Galileo positioning system clock signal, an Indian Regional Navigational Satellite System clock signal, a Regional Navigational Satellite System clock signal, or combinations thereof. The clock signal from the receiver179and the measurement signals from the meters134,136, and138can be provided to PMU hardware and software180.

In certain embodiments the receiver179can receive a clock signal via a wired or wireless connection from non-global navigation satellite systems (GNSS). Furthermore, in certain other embodiments of the invention, the reference clock receiver block179may be optional. In such embodiments, a reference clock signal may be provided to PMU140over one or more special ports, such as Irig-B or pulse per second (PPS) or over network connections, such as Network Time Protocol or Precision Time Protocol (IEEE 1588).

Referring now toFIG. 3, an analog PMU hardware and software180is described as constituent functional blocks. Input measurement signals182may be provided to the PMU140and passed through an anti-aliasing filter184, to an analog-to-digital converter (A/D converter)186. The output of the A/D converter186is a sampled input measurement signal xi, that can be provided to a system frequency estimation block188that can estimate the frequency of the input signals182. A sampling period block190can receive the frequency estimation of the measurement signals182and provide a sampling frequency based at least partly on the frequency estimation that is provided to the A/D converter186for the purposes of sampling the input measurement signals182. The A/D converter186sampled measurement signal xi, can also be provided to a filter192and the output of the filter192can be provided to a phasor calculations block194which can determine a non-synchronous phasor and provide power distribution system protection algorithms196. The protection algorithms196may be, for example, to control protection relays (not shown) on the power distribution system100.

The sampled input measurement signal xiof the A/D converter186can further be provided to a convolution synchro-phasors calculation block200. The convolution synchro-phasors calculation block200can also receive a clock signal from a clock202via the receiver179. The convolution synchro-phasors calculation block200can pair each sampled input measurement signal xiwith a corresponding timestamp tiand then use the timestamped sampled measurement xiand perform a convolution with a function. The output of the convolution synchro-phasors calculation block200can optionally be post filtered in a synchro-phasors post filter block204to provide a synchronized phasor output220.

The anti-aliasing filter184can provide a mechanism for preventing sampling errors by filtering out high frequency noise and signals from the input measurement signals182. The input measurement signals182may have spurious and transient signals, as well as induced noise from meters168,170, and172that can inject relatively high frequency components that when sampled at a frequency equal to or less than twice the frequency of the high frequency components may lead to aliasing errors during sampling at the A/D converter186. As a result, the anti-aliasing filter184can be used to remove high frequency components from the input measurement signals182, so that the input measurement signals182can significantly comply with the Nyquist-Shannon criterion in order for the sampling frequency to be used for sampling the input measurement signals182at the A/D converter186.

The system frequency estimation block188may be implemented to estimate the frequency of the input measurement signals182by any known methods in either the time or frequency domains. Such techniques may include, but are not limited to, the use of triggered integrators and comparators, such as zero-crossing triggers, in the time domain or the use of digital Fourier transform (DFT) analysis in the frequency domain.

The sampling period block190may provide a sampling period and thereby sampling frequency to the A/D converter186based on the estimated system frequency determined by the system frequency estimation block188. Therefore, the sampling frequency of the A/D converter186may be asynchronous. In other words, the sampling frequency of the A/D converter186may be determined based upon real time factors and not be predetermined.

In one embodiment, the sampling frequency may be determined as an integer multiple of the system frequency estimation. As a non-limiting example, consider that the estimated system frequency is 60 Hz as determined at the system frequency estimation block188and the integer multiple is 64, then the A/D converter184sampling frequency may be determined to be 3.84 kHz at the sampling period block190. If the system frequency is found to drift over time, so that at a subsequent time the system frequency is found to be, for example, 61 Hz, then the A/D converter186sampling frequency may be determined as 3.904 kHz, at the sampling period block190. As such, it is apparent that the sampling frequency of the A/D converter186in this example is not predetermined, but rather asynchronous and determined based upon one or more other parameters.

It should be noted that in certain embodiments of the invention, the system frequency estimation block188may be optional. In such embodiments, at block190a sampling period is provided to the A/D converter186that is asynchronous. In other words, the sampling frequency provided to the A/D converter186may not be linked to either the clock202or the system frequency. Therefore the sampled data from the A/D converter186must be timestamped at the convolution synchro-phasors calculation block200to be able to conduct the required calculations.

The A/D converter186can be any known type of A/D converter including, but not limited to, a ramp-compare A/D converter, an integrating A/D converter, a sigma-delta A/D converter, or the like.

The synchro-phasors post filter block204can filter out low frequency and high frequency noise from the output of the convolution synchro-phasors calculation block200to provide the synchronized phasor output220with reduced noise or different reporting rate. The synchro-phasors post filter block204may include, for example, a band pass filter. In other embodiments the synchro-phasors post filter block204may include a high-pass filter or a low-pass filter or reporting rate converter.

It should be noted that the PMU input measurement signals182may be any number of independent time series signals and the PMU140may process each of the input measurement signals182concurrently or relatively nearly concurrently. As a non-limiting example, the PMU140may receive eight independent or pseudo-independent input measurement signals and process all eight signals as eight channels of the PMU140. The eight independent channel may be, for example, a current and voltage measurement at a particular location on the power distribution system100for a first phase, a second phase, a third phase, and a neutral connection of a three-phase power distribution system. In such a three-phase power distribution system, each of the three phases may have a relative phase of approximately 120° with each other.

In other embodiments, the input signals may be derived from current and voltage measurements on the power distribution system100, such as, for example, at least one of the following: (i) a voltage of a power element; (ii) a current of a power element; (iii) a resistance of a power element; (iv) real power of a power element; (v) reactive power of a power element; (vi) power factor of a power element; (vii) frequency of a power element; or (viii) a rate of frequency of a power element.

The synchronized phasor output220of the PMU140may be synchronized to the clock202. Therefore, if the power distribution system100has more than one PMU, then the phasors outputted by each of the PMUs may be synchronized to the clock202and therefore to each other.

Some legacy PMU equipment that do not generate synchronous phasors, but only non-synchronous phasors, may use asynchronous sampling of input signals. The legacy PMUs may also have the ability to receive a clock signal or can be modified to receive a clock signal. In one embodiment, the convolution synchro-phasors calculation block200may be implemented using existing hardware on legacy PMUs with a software upgrade to legacy PMUs. Therefore, in one embodiment, the apparatus for determining a synchronized phasor as disclosed herein may be implemented on legacy PMUs with relatively minor modifications to such systems. The relatively minor modifications required on legacy PMUs to be able to generate synchronized phasors in accordance to embodiments of the invention may be relatively less expensive than replacing legacy PMUs on the power distribution system with new PMU hardware.

It should be noted that the topology of the PMU140may be modified in various ways in accordance with certain embodiments of the invention. For example, in certain embodiments, one or more functional blocks may be placed and executed at a different location relative to the other functional blocks of the PMU140. Additionally, in other embodiments, other functional blocks may be added or removed from the PMU140.

Referring now toFIG. 4, the structure of the example convolution synchro-phasor calculation block200is shown to include a quadrature signal (e−iω0tk)210and the timestamped sampled input signals (xi, ti) provided to a multiplier block212that multiplies the two signals and then can provide the output of the multiplier212to a filter, such as a low pass filter214to generate a synchronized phasor output. ωo, is the nominal fundamental frequency of the power distribution system100. For example, ωo, can be 60 Hz or 50 Hz.

The operation of the convolution synchro-phasor calculation block200will now be described by way of an example. Assume input signal is sinusoidal waveform:
x(t)=M·cos(ωt+φ)  (1)

Where M is the magnitude in volts (V), ω is the frequency in radians per second (rad/s), and φ is radians.

By applying Euler's identity, the input signal can be shown as:
x(t)=M·(ei(ωt+φ)+e−i(ωt+φ))/2  (2)

At the multiplier block212, the input signal is multiplied by the quadrature signal210to yeild:
x(t)·e−ω0t=M·(ei(ωt+φ)+e−i(ωt+φ))·e−ω0t/2  (3)

Low pass filter214can remove the sum frequency component (+) to yield the synchronized phasor value:
Y(t)=M·ei((ω−ω0)t+φ)/2·√{square root over (2)}  (5)

If the input signal frequency is equal to system fundamental frequency (w=wo), then the magnitude and phase become time independent:

For a symmetrical function, F(t), as is the case with the low pass filter214, with length T the synchronized phasor calculation can be the convolution integral as implemented by the convolution synchro-phasors calculation block200:

Numerical integration algorithms may be used to determine the value of the synchro-phasor, Y(t). Any known numerical integration algorithm may be used including, but not limited to, interpolation algorithms, adaptive algorithms, or combinations thereof.

Referring now toFIG. 5, an example method300for determining a synchronized phasor of an input signal is disclosed. At block302, an input signal may be received. The PMU140may receive this input signal182as discussed with reference toFIG. 3. At block304, the input signal can be repeatedly sampled based on an asynchronous sampling frequency. As discussed above, the asynchronous sampling frequency may be determined by a combination of system frequency estimation block188and sampling period block190. Furthermore, repeatedly sampling the input signal can be implemented with the A/D converter186. At block306, a clock signal is received, such as from clock202. At block308, a timestamp is provided to each sample of the input signal based on the clock signal. At block310, the samples of the input signal are convolved with a function using the corresponding timestamps to determine a synchronized phasor of the input signal.

It should be noted that the method300may be modified in various ways in accordance with certain embodiments of the invention. For example, one or more operations of method300may be eliminated or executed out of order in other embodiments of the invention. Additionally, other operations may be added to method300in accordance with other embodiments of the invention.

While certain embodiments of the invention have been described in connection with what is presently considered to be the most practical and various embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.