Method and device for detection of sub-synchronous oscillations in a power system

Abstract

A method for detection of a sub-synchronous oscillation in a power system includes measuring a three-phase measurement signal of an electric system value, analyzing the measurement signal to detect an oscillation component of the measurement signal having an oscillation frequency lower than a system frequency of the power system, deciding whether the detected oscillation component at the oscillation frequency qualifies as a sub-synchronous oscillation, and disconnecting a generator from the power system that might be affected by the sub-synchronous oscillation. To detect sub-synchronous oscillations with low computational effort and good accuracy, an amplitude of each phase of the oscillation component is calculated and compared against a threshold, a sub-synchronous oscillation is detected upon exceeding the threshold during a given time delay, and a fault signal is generated upon detecting a sub-synchronous oscillation. A device having a processing unit is also provided.

Claims

1. A method for detection of a sub-synchronous oscillation in a power system, the method comprising: measuring a three-phase measurement signal of an electric system value; analyzing the measurement signal to detect an oscillation component of the measurement signal having an oscillation frequency being lower than a system frequency of the power system; deciding whether the detected oscillation component at the oscillation frequency qualifies as a sub-synchronous oscillation; disconnecting a generator from the power system that might be affected by the sub-synchronous oscillation; calculating an amplitude of each phase of the oscillation component and comparing the amplitude of each phase against a respective threshold; detecting a sub-synchronous oscillation upon the amplitude of one or more phases of the oscillation component exceeding the threshold during a given time delay; and generating a fault signal upon detecting a sub-synchronous oscillation.

2. The method according to claim 1, which further comprises using an adaptive notch filter to calculate the amplitude of each phase of the oscillation component.

3. The method according to claim 1, which further comprises: checking each phase of the oscillation component for a transient state by calculating a rate of change of an amplitude of a fundamental component of the measurement signal; and blocking the generation of the fault signal upon detecting a transient state for at least one phase.

4. The method according to claim 1, which further comprises: checking the oscillation component for an asymmetry state by comparing a phase of the oscillation component having a maximum value with a phase of the oscillation component having a minimum value; and blocking the generation of the fault signal upon detecting an asymmetry state.

5. The method according to claim 1, which further comprises disconnecting the generator from the power system by opening a circuit breaker when a fault signal is present.

6. The method according to claim 1, which further comprises providing the electric system value as an electric current or an electric voltage present at a measurement location of the power system.

7. A device for detection of a sub-synchronous oscillation in a power system, the device comprising: a processor for measuring and analyzing a three-phase measurement signal of an electric system value to detect an oscillation component of the measurement signal having an oscillation frequency being lower than a system frequency of the power system and deciding whether the detected oscillation component at the oscillation frequency qualifies as a sub-synchronous oscillation, said processing unit being configured to perform the method according to claim 1; and a command interface for outputting a signal to disconnect a generator from the power system that might be affected by the sub-synchronous oscillation.

8. The device according to claim 7, wherein the device is part of an electric protection device for monitoring and protecting the electric power system.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

(1) FIG. 1 is a block diagram showing an overview of a part of a power system with a generator and a device for detection of sub-synchronous oscillations;

(2) FIG. 2 is a simplified block diagram of steps of a method for detection of sub-synchronous oscillations;

(3) FIG. 3 is a diagram showing an exemplary filtering characteristic of a pre-processing filter;

(4) FIG. 4 is a block diagram showing an exemplary structure of a digital adaptive notch filter;

(5) FIG. 5 is a diagram showing a detailed view of an exemplary decision logic for detecting sub-synchronous oscillations;

(6) FIG. 6 is a diagram showing a detailed view of an exemplary decision logic for detecting a transient system status;

(7) FIG. 7 is a diagram showing a detailed view of an exemplary decision logic for detecting an asymmetry status; and

(8) FIG. 8 is a diagram showing an exemplary decision logic respectively combining the detection of sub-synchronous oscillations with the detection of a transient system status and an asymmetry status.

DETAILED DESCRIPTION OF THE INVENTION

(9) Referring now in detail to the figures of the drawings, in which similar or identical elements may be provided with the same reference signs, and first, particularly, to FIG. 1 thereof, there is seen a schematic overview of a part of a three-phase power system 10. A generator 11 transforms rotational energy into electrical energy and applies a voltage to phases a, b, c of the power system 10. A power transformer 12 may be used to adapt the voltage to a required voltage level. A circuit breaker 13 is installed to connect the generator 11 to or disconnect it from the remainder of the power system 10. An electric system value (e.g. a three-phase voltage or a three-phase current) is measured at a measurement location 14 and a respective three-phase measurement signal is produced and fed to a protection device 15, which may be a stand-alone protection device for detecting sub-synchronous oscillations only, or may be a multi-purpose protection device that also performs several other protection functions for the power system (e.g. over-current protection, over-voltage protection, distance protection, etc.). The protection device 15 contains a measurement unit to receive and pre-process the measurement signal. The protection device further contains a processing unit to analyze the measurement signal and to detect a possible sub-synchronous oscillation, and a command interface to transmit a tripping signal to the circuit breaker 13 in order to disconnect the generator 11 from the remaining power system 10.

(10) Referring now to FIGS. 2 to 8, it will be explained in more detail, how the detection of a sub-synchronous oscillation (SSR) is performed.

(11) A general overview of the proposed SSR protection scheme is depicted in FIG. 2. The proposed SSR protection scheme is formed of three stages: a pre-processing stage 20, a filtering stage 21 and a decision logic 22. The decision may optionally be stabilized against unwanted errors during the SSR-detection by a transient status detection and an asymmetry status detection, both are only schematically depicted as a block 23 in FIG. 2 and will be explained in more detail below.

(12) In FIG. 2, a measurement signal x(n) is fed to the pre-processing stage 20 which is implemented as a digital filter. The pre-processing filter is a combination of a highpass filter (e.g. Butterworth 3rd order) and a lowpass filter (e.g. Chebyshev type II 12th order). An exemplary filter characteristic of the pre-processing filter is depicted in FIG. 3.

(13) In the second stage 21, the output xf(n) of the first stage 20 is fed into an adaptive notch (AN) filter. Typically, these filters are used for frequency tracking, amplitude estimation and noise cancellation. For the purpose of SSR detection, a digital AN filter has been adopted, and its general structure is depicted in FIG. 4.

(14) The input signal xf(n) goes through a bandpass filter 40 having a transfer function HBP(z) and three outputs are obtained: the error e(n), the isolated component y(n) having the dominant SSR frequency (“oscillation component”) and the sensitivity s(n) obtained through the transfer function HS(z) of a filter block 41. Detailed formulas are presented below:

(15) $\begin{array}{cc}{H}_{BP}\left(z\right)=\frac{k_2\left(1-z^{-2}\right)/2}{1-\left(1-k_2-k_1^2\right)z^{-1}+\left(1-k_2\right)z^{-2}}& \left(1\right)\\ H_S\left(z\right)=\frac{2k_1{z}^{-1}}{1-\left(1-k_2-k_1^2\right)z^{-1}+\left(1-k_2\right)z^{-2}}& \left(2\right)\\ s\left(n\right)=\frac{\partial y\left(n\right)}{\partial k_1}& \left(3\right)\end{array}$

(16) Parameter k.sub.1 is controlling the central frequency of the AN filter f.sub.0 and it can be adapted recursively using the following formulas:

(17) $\begin{array}{cc}{k}_1\left(n+1\right)=k_1\left(n\right)-\mu e\left(n\right)\frac{s\left(n\right)}{v\left(n\right)}& \left(4\right)\\ v\left(n\right)=v\left(n-1\right)\lambda +\left(1-\lambda \right)s^2\left(n\right)& \left(5\right)\end{array}$

(18) where μ and λ are tuning parameters.

(19) Now that the parameter k.sub.1 is updated at each step to track the dominant SSR frequency of the signal, that frequency can be calculated as follows:

(20) $\begin{array}{cc}f\left(n\right)=\frac{\theta \left(n\right)f_s}{2\pi }& \left(6\right)\\ \theta \left(n\right)=2{\sin }^{-1}\left\{\frac{k_1\left(n\right)}{2\sqrt{1-k_2/2}}\right\}& \left(7\right)\end{array}$

(21) where f.sub.s is the sampling frequency.

(22) The amplitude SSR_A(n) of the isolated component y(n) can be obtained directly from the signal y(n) using an RMS window. For increased accuracy, the value of the estimated frequency is used to adapt the window length:

(23) $\begin{array}{cc}\mathrm{SSR\_A}\left(n\right)=\sqrt{\frac{2}{N_{\mathrm{RMS}}\left(n\right)}\underset{m=0}{\overset{N_{\mathrm{RMS}}\left(n\right)-1}{.Math.}}{y}^2\left(n-m\right)}& \left(8\right)\\ N_{\mathrm{RMS}}\left(n\right)=\mathrm{round}\left(N_C{f}_S/f\left(n\right)\right)& \left(9\right)\end{array}$

(24) where N.sub.c is the number of full cycles used in the amplitude calculation (e.g. the value of 2 cycles can be used). The values of parameters k.sub.1 and k.sub.2 are initialized as follows:
k.sub.1=2√{square root over (1−k.sub.2/2)} sin(πf.sub.0/f.sub.s)  (10)
k.sub.2=1−r.sup.2  (11)

(25) where r is a parameter controlling the bandwidth of the AN filter. Stable filters require values below 1. The value of k.sub.1 is then adapted, but the value of k.sub.2 remains constant.

(26) Additionally, to improve the stability of filter adaptation, the range of adaptation is bounded. For example, a 10 Hz range can be chosen (with a central frequency f.sub.0 in the middle) and the corresponding values of minimum and maximum allowed values of parameter k.sub.1 are obtained. An additional check ensures that the adapted value k.sub.1 stays within this range. It should be noted that the input signals of the algorithm (“electric system value”), whether currents or voltages, are expected to be in per unit system.

(27) As mentioned with regard to FIG. 2, a stabilization of the decision making process can be achieved by i.a. checking whether there exists a transient system state. In order to determine a transient system state, the measurement signal x(n) has to be further processed to calculate a rate of change ROC_FC_A(n) of the amplitude of the fundamental frequency component (“fundamental component”) of the power system. The amplitude of the fundamental component can be obtained using a pair of sine and cosine windows:

(28) $\begin{array}{cc}{a}_s\left(k\right)=\sin \left[\left(\frac{{\mathrm{lN}}_1-1}{2}-k\right)\Omega \right]& \left(12\right)\\ a_c\left(k\right)=\cos \left[\left(\frac{{\mathrm{lN}}_1-1}{2}-k\right)\Omega \right]& \left(13\right)\\ N_1=\frac{f_S}{f_1}& \left(14\right)\\ \Omega =\frac{2\pi f_1}{f_S}& \left(15\right)\end{array}$

(29) where l is the window length in number of cycles of the fundamental component, f.sub.1 is the frequency of the fundamental component and 0≤k≤IN.sub.1−1. In order to achieve immunity to any possible sub-synchronous components it is recommended to use l=8. Additionally, the frequency response of the filter can be smoothened with a Hanning window:

(30) $\begin{array}{cc}w\left(k\right)=0.5\left[1-\cos \left(\frac{2\pi k}{{\mathrm{lN}}_1-1}\right)\right]& \left(16\right)\end{array}$

(31) where 0≤k≤IN.sub.1−1. For a given input signal x(n) the output of the filters can be calculated as follows:

(32) $\begin{array}{cc}{y}_s\left(n\right)=\frac{4}{{\mathrm{lN}}_1}\underset{k=0}{\overset{{\mathrm{lN}}_1-1}{.Math.}}x\left(n-k\right)a_s\left(k\right)w\left(k\right)& \left(17\right)\\ y_c\left(n\right)=\frac{4}{{\mathrm{lN}}_1}\underset{k=0}{\overset{{\mathrm{lN}}_1-1}{.Math.}}x\left(n-k\right)a_c\left(k\right)w\left(k\right)& \left(18\right)\end{array}$

(33) Then, the amplitude of the fundamental component can be calculated as follows:
FC_A(n)=√{square root over (y.sub.s.sup.2(n)+y.sub.n.sup.2(n))}  (19)

(34) Finally, the rate of change of the amplitude of the fundamental component can be obtained simply as:
ROC_FC_A(n)=FC_A(n)−FC_A(n−1))f.sub.s  (20)

(35) The third stage of the algorithm depicted in FIG. 2 is the decision logic 22. In one favorable embodiment, three parallel logical blocks are implemented within the decision logic: SSR pickup (see FIG. 5), transient system state blocking (see FIG. 6) and SSR asymmetry check (see FIG. 7). The outputs of these logical blocks are then combined to produce the final decision as depicted in FIG. 8.

(36) Two sets of three phase signals have been used for the logic input. The first one is the estimated amplitude of the SSR component in each phase calculated as in equation (8):
SSR_A_a,
SSR_A_b,
SSR_A_c,

(37) all of them in per unit. The second set is the estimated rate of change of amplitude of the fundamental component in each phase calculated as in equation (20):
ROC_FC_A_a,
ROC_FC_A_b,
ROC_FC_A_c,

(38) all of them in per unit. As can be seen in FIG. 5, the SSR pickup element is responsible for detecting abnormal SSR levels (SSR_pickup) and producing an appropriate output signal when the condition holds in all three phases for a predefined amount of time (SSR_delay).

(39) The SSR detection can be stabilized by the transient system state blocking scheme and the asymmetry state blocking scheme as depicted in FIGS. 6 and 7.

(40) As can be seen in FIG. 6, the transient blocking element is responsible for detecting a condition, in which the absolute value of the estimated rate of change of amplitude of the fundamental component is above a predefined threshold (ROC_pickup) in at least one phase. The output signal is held for a predefined amount of time (ROC_delay) using a dropout delay.

(41) As can be further seen in FIG. 7, the SSR asymmetry check element ensures that that the estimated amplitudes of the SSR component in all three phases have similar values. The ratio of minimum to maximum value at each time instant is compared with a predefined setting (SSR_asymmetry). A setting of 1 means that the estimated amplitudes need to be identical and any smaller setting will allow for some level of asymmetry (e.g. a setting of 0.95 means that 5 asymmetry is allowed).

(42) The output of all three elements is combined to produce the final decision, as can be seen in FIG. 8. The protection will operate only if SSR component is detected and at the same time no transient is detected and the SSR asymmetry is at an acceptable level (no major asymmetry).

(43) The proposed solution provides a good accuracy of the SSR estimation with relatively low computational requirements and the decision logic provides secure operation of the protection. A good accuracy of the proposed solution is achieved through the use of an AN filter, which further isolates the dominant SSR component by filtering out other components, possibly not related to any SSR event. The filter also allows for frequency estimation, which in turn can be used to adapt the RMS window length. The AN e.g filter is a 2nd order IIR filter, which means it has fixed computational requirements (window length does not change) and the computational burden is much lower when compared to a FIR filter of similar characteristic. The proposed decision logic optionally has two blocking conditions to ensure security from misoperation: a transient blocking and an asymmetry check. This ensures a high degree of safety during unrelated events, such as transients, power oscillations or energization of a nearby transformer.

(44) The proposed solution can be used both in stand-alone devices as well as in a multi-purpose protection device. In the latter case the decision logic can complement e.g. any existing generator protection.

(45) Although the present invention has been described in detail with reference to the preferred embodiment, it is to be understood that the present invention is not limited by the disclosed examples, and that numerous additional modifications and variations could be made thereto by a person skilled in the art without departing from the scope of the invention.

(46) It should be noted that the use of “a” or “an” throughout this application does not exclude a plurality, and “comprising” does not exclude other steps or elements. Also, elements described in association with different embodiments may be combined. It should also be noted that reference signs in the claims should not be construed as limiting the scope of the claims.