Analysis of disturbances in power systems5390106Abstract A method for extracting, after data collection (DC) of a sampled analog signal (x(k)), a logical description of the signal by identification of the state (A, .phi.) of the signal, that is, the amplitude and phase of the signal, as well as an event (.DELTA.A, .DELTA..phi., k=h) which causes a change of a state at a sample k=h, that the identification (SE) is performed with the aid of a truncated general Fourier series with an exponentially decreasing constant, and that the identified parameters are supplied as input data to an expert system (ES) for forming the basis of a superordinate fault analysis together with binary data originating from other signals, the result thereof then being readable on a user interface (UI) (FIG. 6). ). Claims We claim:
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Number of samples Coefficients of the model
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<20 a.sub.1, b.sub.1
20-30 a.sub.0, a.sub.1, b.sub.1, (b.sub.0 = 0)
30-40 a.sub.0, a.sub.1, b.sub.0, b.sub.1
>40 a.sub.0, a.sub.1, b.sub.0, b.sub.1, a.sub.2,
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b.sub.2.
4. A method for obtaining signal outputs signifying fault determination of an electrical signal according to claim 1, wherein the accuracy coefficient (.delta.) has a value: 0.05<.delta.<0.15. 5. A method for obtaining signal outputs signifying fault determination of an electrical signal according to claim 1, wherein the coefficient estimation parameter estimator in said step of detecting the state and raw event includes the step of minimizing the quadratic error. Description TECHNICAL FIELD
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State 1 State 2
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Amplitude: 1.0 2.0 (A)
Relative phase position:
0 90 (.phi.)
Start sample (time):
k = 1 k = h
End sample (time): k = h - 1 k = n
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The transition from one state to another creates an "event", which is described by the sample or the time at which the event occurs as well as an amplitude and/or phase change. Consequently, the event which brings about the above-mentioned change of state can be described as:
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Event 1
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Event sample: k = h
Amplitude change +1.0 (.DELTA.A)
Phase change: +90 (.DELTA..phi.)
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Under the detailed description of the invention given below, it will be proved that the combination of events and states makes it possible to analyze a process in a rule-based system. Although all times have been indicated here in discrete time, that is, by k=1, 2, . . . , this is quite equivalent to indicating x in continuous time, apart from x not being defined between the sample times. However, in the sampled system no event on the sampled signals can be indicated with better accuracy than what is allowed by the sampling interval. Generally, a signal x(k) which is defined by a number n of samples, that is, where k=1, 2, . . . , n, may have more than one event and more than two states. If it is assumed that events occur at samples k equal to h.sub.1, h.sub.2, . . . h.sub.p, the number of states within the scope of the n samples will be equal to p+1. Each state has a given/calculated start and end sample, k.sub.1 and k.sub.2, respectively. Thus, the following applies:
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State 1: k.sub.1 = 1 k.sub.2 = h.sub.1 - 1
State 2: k.sub.1 = h.sub.1
k.sub.2 = h.sub.2 - 1
State p + 1: k.sub.1 = h.sub.p
k.sub.2 = n
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The process of extracting events and states from a sampled analog signal may be divided into two steps. Step 1 is intended to be a fast identification of the events, later on in the description designated a "raw event identification", in the supervised signal. In step 2, the states and the events are filtered by identifying the state and event parameters of the signal in an interval given by the raw event registration in step 1. The event and state parameters obtained in this way may be used as input signals to a new type of expert system for forming, together with binary data, the basis for the superordinate analysis of electric power systems. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a partially sinusoidal stationary signal. FIG. 2 is a schematic view of the extraction process for obtaining, from a sampled analog signal, the event and state parameters. FIG. 3 shows how a raw event detection according to the invention may be performed. FIG. 4 illustrates a flow diagram for raw event detection. FIG. 5 shows a block diagram for step 2. FIG. 6 shows a block diagram for diagnosis. DETAILED DESCRIPTION OF THE INVENTION FIG. 1 shows a partially sinusoidal stationary signal which is characterized by two separate "states" and an "event" which separates the states, as described under the summary of the invention above, and the state parameters indicated there. It is clear from the figure that the event occurs at a sample with k=h, that the state 1 is defined as comprising the samples from k=1 to k=h-1 and that the event 2 is defined as comprising the samples k=h to k=n. As shown in FIG. 1, T.sub.s indicates the sampling interval or the sampling time. FIG. 2 shows the two steps in the extraction process, mentioned in the above description. Sampled values x(k) of the input signal are passed to step 1, S1, for raw event detection. The raw events which are detected are passed, together with x(k), to step 2, S2, where a state and event identification takes place. To be able to describe the contents of the two steps more closely, the following designations are also needed, in addition to the designations A, .DELTA.A, .phi., .DELTA..phi., x(k) and "k", namely:
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x (k) the estimated input signal ("x circumflex")
.sup..about.x (k)
the estimation error for the input signal ("x
tilde")
T.sub.S sampling time, time between each sample
.omega. basic angular frequency of the input signal
N number of terms in a truncated Fourier series
L number of samples in a window, window length in
discrete time
a, b coefficients in a mathematical model of the input
signal (see equation (1)).
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Generally, an estimated signal can be described with the aid of a truncated Fourier series and an exponentially decreasing constant part according to the following: ##EQU1## The raw event detection in step 1 must be sensitive to be able to detect fast consecutive events. For this reason, in one embodiment of the invention, a half-cycle Fourier filter will be used, as exemplified in FIG. 1, with a number of samples L=.pi./.omega.T.sub.s. Thus, a sliding window is used which, during the calculation, is successively moved one sample at a time. Otherwise, the filtering is performed as shown in FIG. 3. The sampled values x(k) of the signal are passed to the Fourier filter FF which in one embodiment utilizes a truncated Fourier series with only one fundamental component to estimate its coefficients a and b. Thus, the estimated signal x(k) is described as x(k)=a cos (k.omega.T.sub.s)+b sin (k.omega.T.sub.s) (2) To the decision logic DL which is included in step 1 to determine whether a raw event has taken place there is passed, besides the estimated values of a and b, also the difference between actual and estimated signal, which difference is formed in a summator SS. A flow diagram which describes the raw event detection in step 1 is shown in FIG. 4. For all the samples in the input data file, estimated values of a and b are computed according to a(k)=a(k-1)+2x(k)[cos{k.omega.T.sub.s }-cos {(L-k).omega.T.sub.s }]/L(3) b(k)=b(k-1)+2x(k)[sin{k.omega.T.sub.s }-sin {(L-k).omega.T.sub.s }]/L(4) Then the estimated signals x(k) and the difference x(k) between estimated and calculated values are calculated, that is, x(K)=a(k) cos {k.omega.Ts}+b(k) sin {k.omega.T.sub.s } (5) x(k)=x(k)-x(k) (6) With the aid of this difference signal (6), the decision logic is able to determine when a raw event occurs on the signal x(k), that is, according to FIG. 1 when k=h. The decision is made when .vertline.x(k=h).vertline.>.lambda. (7) where .lambda. is related to the amplitude of the signal according to .lambda.=.delta..sqroot.[a.sup.2 (h-1)+b.sup.2 (h-1)] (8) and where .delta. is the accuracy coefficient related to the desired accuracy. In one embodiment of the invention, the following applies: 0.05<.delta.<0.15 (9) It should be pointed out that the estimation error equation according to (6) and the difference (7) is valid in general and independently of how many terms in equation (1) that will be used for the estimation. By continuously monitoring when the absolute amount of the difference signal exceeds this limit value, the time or the k-value for an event can be determined. The objective of the identification in step 2 is to identify the states between the different events in the signal in a more accurate way. This identification is also generally based on the general description of the signal according to equation (1). It is then suitable that the number of terms in the Fourier series with associated coefficients that are to be determined depend on how many samples are available for the state in question. In one embodiment, the model implemented in step 2 is arranged according to the invention such that the number of terms and coefficients, respectively, which are to be used depending on the number of available samples in the state are as follows:
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Number of samples Coefficients of the model
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<20 a.sub.1, b.sub.1
20-30 a.sub.0, a.sub.1, b.sub.1 (b.sub.0 = 0)
30-40 a.sub.0, a.sub.1, b.sub.0, b.sub.1
>40 a.sub.0, a.sub.1, b.sub.0, b.sub.1, a.sub.2,
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b.sub.2
A block diagram for step 2 is shown in FIG. 5. The parameter estimator PE is supplied with identified raw events, that is, the values of k when k=h as well as the stored sampled values x(k) of the input data file. On the basis of estimated parameters, a state is defined by A, .phi., k=1, k=h-1 and an event as a change of A and .phi. as well as the event sample, that is, .DELTA.A, .DELTA..phi. and k=h. There are a plurality of different methods to use for the coefficient estimation. According to the invention and in the model, however, a method based on a minimization of the quadratic error, that is, a so-called LS method (Least Square) is used. The purpose of using a model which models more coefficients than those which directly describe the state is to achieve as good an estimation of the fundamental component as possible. The identification is carried out according to the invention as a complete calculation for the whole state, and no calculation with a sliding window is performed. The reason for this is that all the samples are available for the states. The procedure is then repeated for all states. By identifying the states of the raw events recorded in step 1 and then checking the difference between two adjacent states, possible false events may be suppressed and the two adjacent states be joined. Thereafter, a new identification is made, now with a larger number of available sample points. In this way the accuracy can be considerably increased. The amplitude and phase and the amplitude and phase difference, respectively, for each state are calculated as: ##EQU2## where index "m" indicates a sample in the middle of the state, that is, ##EQU3## This procedure is repeated until the difference between the states is sufficiently great for both amplitude and/or phase, for example when the differences are greater than 10% of the current amplitude and phase values, respectively. To sum up, the procedure comprises the following processing steps: 1. Estimate the states (A, .phi., k=1, k=h-1) between given event samples (points in time). 2. Determine the events (k=h, .DELTA.A, .DELTA..phi.), remove events with too small change. 3. If an event is removed, return to point 1. 4. When the event criteria are fulfilled, the event values are supplied as input data to the expert system for further evaluation. By representing the analog signals in the form shown, it will be possible, as mentioned before, to process these signals together with binary signals in an expert system. FIG. 6 shows a block diagram of a complete system for diagnosis with data collection, DC, state and event detection SE according to the invention and the subsequent expert system ES. The evaluation of the expert system is then clear from a suitable user interface UI, which may be a visual display unit and/or a printout from some connected printer. In the expert system, the signals and their sequence of states are checked against a number of rules which characterize, for example, different faults in a power system. An example of such a rule are the following criteria for detecting a single-phase ground fault: If an Event is identified in the current of one phase with the amplitude change .DELTA.A at the sample point k=h, and If an Event is identified in the zero sequence current with the amplitude change .DELTA.A.sub.0 at the same sample point, and If .DELTA.A.sub.0 and .DELTA.A>10% of the rated current, Then a phase-to-ground fault has occurred in that phase at the sample point k=h. An expert system comprises a great number of rules concerning faults in a power system as well as faults in circuit breakers or relay and control systems.
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