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Title:
BAND-LIMITED DIFFERENTIATOR FOR GRID APPLIANCE CONTROLLERS
Document Type and Number:
WIPO Patent Application WO/2015/112237
Kind Code:
A1
Abstract:
A method and device for measuring electrical grid data in the presence of noise is disclosed. Noisy frequency data is received from the grid. The noisy data is filtered above a predetermined frequency. The filtered data is differentiated using band-limited differentiator. The data may be filtered and differentiated simultaneously by the band-limited differentiator.

Inventors:
CHASSIN DAVID P (US)
Application Number:
PCT/US2014/065474
Publication Date:
July 30, 2015
Filing Date:
November 13, 2014
Export Citation:
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Assignee:
BATTTELLE MEMORIAL INST (US)
International Classes:
G01R19/00; H02J3/00; G01R23/02
Foreign References:
EP2660613A12013-11-06
Other References:
SARKAR A ET AL: "Second-degree digital differentiator-based power system frequency estimation under non-sinusoidal conditions", IET SCIENCE, MEASUREMENT AND TECHNOLOGY,, vol. 4, no. 3, 6 May 2010 (2010-05-06), pages 105 - 114, XP006035071, ISSN: 1751-8830, DOI: 10.1049/IET-SMT:20080138
MEDLIN W G ET AL: "Bandpass digital differentiator design using quadratic programming", SPEECH PROCESSING 1. TORONTO, MAY 14 - 17, 1991; [INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH & SIGNAL PROCESSING. ICASSP], NEW YORK, IEEE, US, vol. CONF. 16, 14 April 1991 (1991-04-14), pages 1977 - 1980, XP010043342, ISBN: 978-0-7803-0003-3, DOI: 10.1109/ICASSP.1991.150783
GOWAID I A ET AL: "Improved inertia and frequency support from grid-connected DFIG wind farms", POWER SYSTEMS CONFERENCE AND EXPOSITION (PSCE), 2011 IEEE/PES, IEEE, 20 March 2011 (2011-03-20), pages 1 - 9, XP031870626, ISBN: 978-1-61284-789-4, DOI: 10.1109/PSCE.2011.5772589
Attorney, Agent or Firm:
GOKCEK, A.J. (K1-53Richland, Washington, US)
Download PDF:
Claims:
CLAIMS

We claim:

1. A method of measuring electrical grid data in the presence of noise, comprising:

a. receiving noisy data from the grid;

b. filtering the noisy data above a predetermined frequency; and

c. differentiating the filtered data using a band-limited differentiator.

2. The method of Claim 1 wherein the data is filtered and differentiated simultaneously by the band-limited differentiator.

3. The method of Clam 1 wherein the differentiating comprises determining the derivative of the filtered data.

4. The method of Claim 1 wherein the predetermined frequency for cutting off noise from the noisy data is at least 0.5 Hz.

5. The method of Claim 1 wherein the filtered and differentiated data is used by a grid appliance controller.

6. The method of Claim 1 wherein the noisy data includes at least one of the following: frequency signals and voltage or current signals.

7. The method of Claim 1 further comprisin estimating inertia of the electrical grid as a function of load.

8. The method of Claim 1 further comprising measuring zero-crossing times of

approximately 60 Hz AC power in homes.

9. The method of C laim 1 wherein the receiving noisy data from the grid comprises

measuring instantaneous AC voltage or currents from the grid.

10. The method of Claim 1 wherein the band-limited differentiator is a band-limited digital differentiator.

1 1. A dev ice for measuring electrical grid data in the presence of noise comprising:

a. a band-limited differentiator for filtering noisy data from the grid above a

predetermined frequency and differentiating the filtered data; and

b. a grid appliance controller including the band-limited differentiator.

12. The device of Claim 1 1 wherein the differentiator is a digital differentiator.

13. The device of Claim 1 1 wherein the noisy data includes at least one of the following: frequency signals and voltage or current signals.

14. The dev ice of Claim 1 1 wherein the differentiator simultaneously filters and

differentiates the data.

15. A method of measuring electrical grid data in the presence of noise, comprising:

a. receiving noisy frequency data from the grid;

b. filtering the noisy frequency data above a frequency of at least 0.5 Hz; and c. differentiating the filtered data using a band-limited digital differentiator; wherein the data is filtered and differentiated simultaneously by the band-limited digital differentiator.

16. The method of Claim 15 wherein the differentiating comprises determining the

derivative of the filtered data.

1 7. The method of Claim 15 wherein the filtered and differentiated data is used by a grid appliance controller.

18. The method of Claim 1 further comprising estimating inertia of the electrical grid as a function of load.

1 . The method of Claim 15 further comprising measuring zero-crossing times of

approximately 60 Hz AC power in homes.

20. The method of Claim 15 wherein the receiving noisy frequency data fi-om the grid

comprises measuring instantaneous AC voltage or currents from the grid.

Description:
BAND-LIMITED DIFFERENTIATOR FOR GRID APPLIANCE CONTROLLERS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] T is application claims priority to U.S. Provisional Application Serial No.

61 /929,594, filed January 21 , 2014, titled "BAND-LIMITED DIFFERENTIATOR DESIGN FOR GRID FRIENDLY CONTROLLERS," and from U.S. Patent Application No.

14/539,436, filed November 12, 2014, titled "BAND-LIMITED DIFFERENTIATOR FOR GRID APPLIANCE C NTROLLERS".

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002 j This invention was made with Government support under Contract

DE-AC0576RLO 1 830 awarded by the LIS. Department of Energy. The Government has certain rights in the invention.

TECHNICAL FIELD

[0003] This invention relates to digital differentiators. More specifically, this invention relates to band-limited digital differentiators for control of grid friendly appliances.

BACKGROUND

[0004] Frequency control plays an important role in preserving the power balance of a multi-machine power system, such as an electrical grid. Power system frequency drops when supply from generators falls below demand. When the change in frequency is large, the reduction in supply can trigger protection systems that may result in system separation, loss of load, and customer outages. [0005] Grid friendly appliance controllers detect imderfrequency events in the home and turn off the appliance in response to a system event. However, local noise that may emanate from induction motors and switched power electronic equipment can mask the slower changes in grid frequency that the controller is designed to respond to.

[0006] What is needed is an improved device and/or method of determining frequency for grid friendly appliance controllers.

SUMMARY

[0007] The present invention is directed to methods and devices for measuring electrical grid data in the presence of noise. In one embodiment, the method includes receiving noisy data from the grid. The method also includes filtering the noisy data above a predetermined frequency. The method further includes differentiating the filtered data using a band-limited differentiator.

[0008] In one embodiment, the data is filtered and differentiated simultaneously by the band-limited differentiator.

[0009] The di fferentiator returns the derivative of the filtered data.

[0010] In one embodiment, the predetermined frequency for cutting off noise from the noisy data is at least 0.5 Hz.

[0011] In one embodiment, the filtered and differentiated data is used by a grid appliance controller.

[00121 The noisy data includes, but is not limited to. frequency signals, voltage signals, and/or current signals.

[0013] In one embodiment, the method further includes estimating inertia of the electrical grid as a function of load.

[0014] In one embodiment, the method further includes measuring zero-crossing times of approximately 60 Hz AC power in homes. 10015] In one embodiment, the method measures instantaneous AC voltage or currents from the grid.

[0016] The band-limited differentiator can be a band-limited digital differentiator.

[0017] In another embodiment of the present invention, a device for measuring electrical grid data in the presence of noise is disclosed. The device includes a band-limited differentiator for filtering noisy data from the grid above a predetermined frequency and differentiating the filtered data. The device also includes a grid friendly appliance controller including the band-limited differentiator. In one embodiment, the differentiator is a digital differentiator.

[0018] In another embodiment of the present invention, a method of measuring electrical grid data in the presence of noise is disclosed. The method includes receiving noisy frequency data from the grid; filtering the noisy frequency data above a frequency of at least 0.5 Hz; and differentiating the filtered data using a band-limited digital differentiator, wherein the data is filtered and differentiated simultaneously by the band-limited digital differentiator.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A is a graph of frequency with respect to time for a synthetic input signal of raw data.

[0020] Figure 1 B is a graph of acceleration with respect to time, which is the derivative of the input signal of Figure 1 A.

[0021 ] Figure 2 A is a graph showing a true input signal of Figure 1 A in the presence of noise - or measured signal - with respect to time.

[00221 Figure 2B is a graph showing the output of a conventional differentiator with respect to time of the noisy input signal shown in Figure 2 A. [0023 J Figure 3 is a graph showing the output of the band-limited differentiator of the present invention for the true and measured input signals.

[00241 Figure 4A shows the frequency changes for a real frequency measured at 60 Hz using the band-limited differentiator of the present invention with a conventional 0.5 Hz low- pass filter.

[0025] Figure 4B shows the derivative of the filtered signal of Figure 5 A using the band- limited differentiator of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] The following description includes the preferred best mode of embodiments of the present invention. It will be clear from this description of the invention that the invention is not limited to these illustrated embodiments but that the invention also includes a variety of modifications and embodiments thereto. Therefore the present description should be seen as illustrative and not limiting. While the invention is susceptible of various modifications and alternative constructions, it should be understood, that there is no intention to limit the invention to the specific form disclosed, but, on the contrary, the invention is to cover all modifications, alternative constructions, and equivalents falling within the spirit and scope of the invention as defined in the claims.

[0027 j The present invention includes methods and devices using a novel band-limited differentiator for applications that use, for example, grid appliance controllers to better regulate electrical power supply and demand.

[0028] In one embodiment, the band-limited digital differentiator has an odd length N and the transfer function is:

[0029] The coefficients are assumed anti-symmetric, i.e.:

h(N-i)/2 - 0 and i = ~h N _^ n for n = 0, 1, ... , (Λ' - l)/2 [0030] so that:

H(e> a> ) = e-' MM .j. x T s(io)

[0031] where:

[0032] M = — l)/2 is the number of design variables:

[0033] x = [λ'ι λ ' 2 · · - M] T are the design variables in vector form;

[0034] x m = 2h M - m for m = 1,2, ... M are the individual variables: and

[0035] s(a>) = [sin ω sin 2ω ■■· sin Μω] τ is the frequency band vector.

[0036] The design of the band-limited digital differentiator can then be described by the optimization problem:

ων π

minimize J(x) — j [x 7 s(cu)— ω/Τ ] 2 άω + j [χ τ 5{ω ] 2 άω

0 ω α

[0037] where ω ρ and ω α are the passband and stopband edges, respectively, and T s is the sampling interval in second of the signal to be differentiated. To solve this optimization problem using conventional methods }{x) is presented in the standard form:

y(x) = x T Qx— 2x T p + constant

[0038] The global minimizer is given by:

x * ~ Q _i p

[0039] from which an optimal band-limited differentiator is obtained.

[0040] The objective function can be transformed into the standard form by rearranging it as:

/(*) = x 1 I

x T Qx -2x T p ^constant

[0041] so that the following is found: I s{ )s{ ) T άω + I s(a))s(co) T da)

[0042] and p =— <i>s(co)da>

(0043] Integrating the member (m, n) of Q when m≠ n over the interval [a, b] gives: sin((m— n)b)— sin((m - n)a) sin((m + ri)b)— sin((m + n)a)

m— n m + n

(0044 j When m = n, this results in: d— a sin(2?n6)— sin(2m )

8m

Integrating the member (m) of p over the interval [a, b] gives:

sin m — mb cos ?nb— sin ma + ma cos ma

T s m 2

EXAMPLE

[0046] The follo ing serves to illustrate certain embodiments and aspects of the present invention and are not to be construed as limiting the scope thereof:

[0047] Figure 1 A is a graph of frequency deviation with respect to time for an input signal of raw data. In this example, the data is electrical grid data. The input signal of Figure 1A does not include noise.

[0048] The data represents frequency or. more specifically, the deviation of frequency relative to 60 Hz. As shown in Figure 1A, the frequency fluctuates up and down slowly because the grid has inertia. [0049] Figure I B is a graph of acceleration with respect to time, which is the derivative of the input signal of Figure i A. The acceleration, which represents frequency change over time, can be calculated by finding the derivative of frequency by time. The curve of Figure

1 B is a point by point differentiation of the frequency.

[0050] Figure 2 A is a graph showing a true input signal in the presence of noise - or measured signal - with respect to time.

[00511 Figure 2B is a graph showing the output of the conventional differentiator with respect to time of the measured input signal shown in Figure 2 A. Each noise point in Figure

2A is differentiated to yield the acceleration, which represents noise not the signal. The noise is much higher than the signal. In other words, the signal is hidden because of the noise after differentiation of each noise point.

[0052] Based on the desired frequency response, the original signal in this example is below 10 Hz, and the noise is above 175 Hz. At a sampling rate of 512 Hz, the passband ω ρ = 0.27Γ Hz and the stopband edge ω α = 0.5π Hz are suitable values to use for one embodiment of an optimal band-limited differentiator (BLD).

[0053] The BLD transfer function coefficients of one embodiment are shown in Table 1.

Table 1 : Optimal band-limited differentiator coefficients

h 0 = -h 22 = -0 . 799613

h " ~1 = -h " 21 = -0 . 680845

h ~? = -h " 20 = 2 . 37278

h ~ 3 = -h " 19 - 5 . 61932

h ~ 4 -h ~ 18 = 1 . 1806

h " ~ 5 = -h " l 7 = -12 . 4 947

h ~ ~ 6 = -h " 16 = - 19 . 8373

h " -rf " l5 = 0 . 616533

h " ~ 8 = -h " l 4 = 4 6 . 8053

h ~ 9 = -h " " 13 = 81 . 8494

h " 10 = -h " 12 = 65 . 5435

h ~ 11 = 0

[0054] Figure 3 is a graph showing the output of the band-limited differentiator present invention for the true and measured input signals. 1 055] The performance of the example optimal band-limited differentiator far exceeds that of the conventional differentiator, as shown in Table 2, which evaluates the signal-to- noise ratio of the test signals, excluding the first and last 0.04 seconds of the signals.

Table 2: Signal-to-noise ratios of differentiators

Conventional Band-limited

SNR = 20 \og\\s\\ 2 /\\n - s\\ 2 -25.7 dB 46.1 dB

[0056] The design of digital differentiators for measuring electrical grid data has been significantly improved using the methods and designs described herein. Many applications exist that may benefit from use of the present methods and designs. For example, so-called grid-friendl appliances sample zero-crossing times of the 60 Hz AC power in homes and use a sliding window average to compute electric grid interconnection frequency to decide whether to shed the appliances' loads following a generator outage. An advantage of the band-limited differentiator is that it would be immune to local noise that can emanate from induction motors and switched power electronic equipment which can mask the slower changes in grid frequency that the controller is designed to respond to.

[0057] Another application is in estimat ion of the grid interconnection inertia using local low-cost frequency measurements such as those used in grid-friendly appliance zero-crossing detectors. Significant dev iations in frequency occur when there is a large difference between generation and load. During the first few seconds after a major outage, the overall interconnection inertia can be estimated by using the relation: [0058] where df/dt is the rate of frequency change in Hz/s, ΔΡ is the power change per unit (pu) of system ioad base, and M is the inertial constant in pu.seconds. The inertial properly is largely determined by the mix of generators running at the time of the outage. In this example, a conventional 0.5 Hz low-pass filter was used to identify the rate of frequency change with acceptable results as shown in Figures 4 A and 4B.

[0059] Figure 4 A shows the frequency changes for a real frequency measured at 60 Hz using the band-limited differentiator of the present invention ith a conventional 0.5 Hz low- pass filter. In Figure 4 A. the data is filtered at approximately 25 seconds.

[0060] Figure 4B shows the derivative of the filtered signal of Figure 4 A using the band- limited differentiator of the present invention. The derivative of the filtered signal is calculated at approximately 25 seconds.

[0061] The calculations needed to estimate system inertia are very sensitive to the peak value of the rate of frequency change and thus ver sensitive to the quality of the filter used prior to differentiation. Using an optimally designed differentiator such as described herein can significantly improve the overall result of the inertial estimate, thus requiring fewer outages, to provide a reasonably accurate estimate of system inertia as a function of load. This in turn would allow power system engineers to more accurately estimate the evolution of inertia over time, particularly in response to changing generation mix as more wind and solar generation come online, and adjust the probability threshold for activating a grid friendly appliance controller.

[0062] While a number of embodiments of the present invention have been shown and described, it will be apparent to those skilled in the art that many changes and modifications may be made without departing from the invention in its broader aspects. The appended claims, therefore, are intended to cover all such changes and modifications as they fall within the true spirit and scope of the invention.