WO2020130810A1

WO2020130810A1 - Method and monitoring system for generator slow-coherency online identification and dynamic tracking

Info

Publication number: WO2020130810A1
Application number: PCT/NL2019/050841
Authority: WO
Inventors: Matija NAGLIC; Marjan POPOV; Martinus Arnoldus Matheus Maria VAN DER MEIJDEN
Original assignee: Technische Universiteit Delft
Priority date: 2018-12-17
Filing date: 2019-12-16
Publication date: 2020-06-25
Also published as: NL2022217B1

Abstract

A method and a monitoring system (8) being used as a part of a Wide Area Monitoring, Protection, and Control (WAMPAC) application for determining groups of generators operating synchronously in an electric power system (1). The method comprises collection of PMU (4) data, such as frequency measurements, from each of the plurality of the generators. The method may further comprise filtering with a low-pass filter, determining a generator dissimilarity parameter based on direction and strength of generator electromechanical coupling between pairs of the plurality of generators, dynamically determining the observation window length based on a predetermined threshold, discarding interfering coherency indices within the given observation window, a first-order exponential low-pass filter adaptive tracking for robust coherency estimation, and finally determining the number of groups of generators based on the generator dissimilarity parameter below a predetermined threshold.

Description

Method and monitoring system for generator slow-coherency online identification and dynamic tracking

Field of the invention

The present invention relates to a method and a monitoring system being used as a part of a Wide Area Monitoring, Protection, and Control (WAMPAC) application for (online) determining groups of generators operating synchronously in an electric power system, i.e. generator slow- coherency identification, wherein a plurality of generators are present in the electric power system. The method comprises collecting phasor measurement unit (PMU) data (e.g. frequency measurements) obtained from a PMU associated with each of the plurality of generators. The PMU is arranged to perform measurements on a terminal bus of an associated generator.

Background art

US patent publication US2018/0062390 discloses a system and method for primary power grid frequency response characterization using phasor measurement unit (PMU) data. Preprocessing of localized PMU based frequency measurements is applied combined with system identification techniques. The determined characteristics are applied in a supervisory control and data acquisition (SCADA) component. Pre-processing of PMU data includes filtering PMU frequency data to remove frequency content above a threshold (e.g. 1 Hz).

Summary of the invention

The present invention seeks to provide an improved method and a monitoring system being used for identifying groups of coherent generators in an electric power system.

According to the present invention, a method as defined above is provided, wherein the method further comprises filtering the collected PMU data with a low-pass filter, determining a generator dissimilarity parameter based on direction and strength of generator electromechanical coupling between pairs of the plurality of generators, determining groups of generators having a generator dissimilarity parameter below a predetermined threshold.

In an electric power system, generator coherency defines groups of generators operating synchronously. This serves as an important prerequisite-step of several emergency control schemes to identify power system control areas and improve transient stability. Using the present invention embodiments it is possible to (online) consolidate slow-coherent generators into groups and dynamically track the generator grouping changes following a contingency. The present invention embodiments may be advantageously applied in WAMPAC, e.g. as a pre-step of intentional controlled islanding, dynamic equivalencing to reduce the power system model size and complexity, and identification of system-wide control areas for applications such as the inter-area oscillation damping.

Short description of drawings

The present invention will be discussed in more detail below, with reference to the attached drawings, in which Fig. 1 shows a schematic diagram of an electric power system wherein the present invention embodiment is implemented;

Fig. 2 shows an exemplary graph showing angular deviations of generator distance vectors in a dynamic observation window, as calculated using one of the present invention embodiments;

Fig. 3 shows an exemplary graph showing angular deviations of generator distance vectors in a dynamic observation window, including a large disturbance in the electric power system; and

Fig. 4 shows a graph representing transitions between permanent and transient slow- coherency tracking in accordance with a further embodiments of the present invention.

Description of embodiments

The present invention embodiments can be applied in electric power systems as a standalone Wide Area Monitoring, Protection, and Control (WAMPAC) application, where the output of it can be further used for above mentioned use-cases. A simplified schematic diagram of an electric power system wherein the present invention embodiment implementation is shown in Fig. 1 . A plurality of generators 2 is connected to the electric power system 1 , which may be (partially) controlled by an individual generator control system (for online power system stabilizer (PSS) tuning of generators) which optionally is getting information from the monitoring system 8 in accordance with the present invention embodiments, e.g. by communicating generator control data 6 as indicated in the exemplary embodiment shown in Fig. 1 . Furthermore, a number of loads 3 are connected to the electric power system 1 . Each of the generators 2 is associated with a phasor measurement unit (PMU) 4, e.g. via the generator terminal bus (see further below for further details). Each PMU 4 sends its measurements to the monitoring system 8, e.g. via a PMU data receiver 7, using a supporting telecommunication network (wired or wireless).

Emerging renewable energy sources, decreased system inertia, and economic reasons have forced electric power systems to be operated closer to their stability limits. Unexpected disturbances, component failures, or human errors may cause large-scale power system emergencies, leading to a catastrophic system-wide blackout. To prevent such extreme events and improve system reliability, Synchronized Measurement Technology (SMT) supported

WAMS applications have been developed. Typically, supported by a global navigation satellite system, the SMT makes use of Phasor Measurement Units (PMUs) 4 to deliver time-synchronized measurements (synchro-measurements) from remote locations in near real-time. In order to increase the effectiveness of WAMPAC emergency corrective control applications on system stability, especially in case of intentional controlled islanding (ICI) and wide-area oscillation damping, the generator slow-coherency is often a required constraint.

In an electric power system 1 , generators 2 are said to be coherent if their rotor angles undergo similar time-domain response. Slow-coherent generator groups 5 (indicated as examples by dashed lines in Fig. 1 ), i.e. generators 2 swinging together at oscillatory frequencies of slow interarea modes, have a relatively strong electromechanical coupling. This observation serves as a basis for the identification of strongly connected coherent areas in the electric power system 1 , where the generators 2 have a high tendency to operate synchronously, even after exposure to a severe network perturbation, e.g. following a contingency. A prior art approach to identify slow-coherent generator groups 5 belongs to model-based methods. These methods perform the eigen-subspace analysis of the linearized power system model. The resulting analysis is valid only for a particular equilibrium point and suffers from the modelling inaccuracies and parametric uncertainties. While being able to provide important information about the general dynamic structure of the network, the slow-coherency theory does not take into account the transient dynamics of the electric power system 1 . However, during severe network operating conditions, the swings of generators 2 with respect to each other are influenced not only by the structure of the network but also by the type and location of the disturbance, generator internal electrical dynamics and controllers response. Any significant change in the power system operating condition, such as topology changes or large load steps, might cause the weakly slow-coherent generators 2 to change their grouping association, making the model-based methods not suitable for online use in actual power systems. Therefore, the ability to track the slow-coherent behaviour of generators 2 in a heavily disturbed power network in real-time is a relevant problem that cannot be directly solved by the model-based methods.

In order to overcome the abovementioned deficiencies, measurement-based methods have been developed as well. Their main advantage is an inherent ability to online identify generator coherency imposed by present power system operating conditions, as well as in independence from the system parameter data. Those methods can be coarsely sub-classified into mode estimation analysis, and time series similarity-based techniques. The methods, belonging to the first sub-class estimate the system parameters of interest (modes, frequency spectrum), and partition the coherent generators 2 into groups by using e.g. k-means, fuzzy, and agglomerative hierarchical clustering algorithm. While being able to extract the information about the inter-area oscillations, these techniques often suffer from the mode estimation related inaccuracies, and high processing power required to process the relatively long observation window. On the other hand, the time-series similarity-based methods identify generator coherency based on the similarities of the extracted features (indices), typically with less processing power required. Generally, those methods are most suitable for online operation but suffer from the inability to operate only on the frequency content of interest (inter-area oscillations). Recently, data mining technique has been presented to identify unstable system operation and identify coherent generators based on the supervised offline training of the binary classifiers. Despite the high accuracy of estimates, this method suffers from an inherent requirement to perform a substantial number of model-based supervised training simulations making this method suitable only for a limited set of disturbances. Others have presented a dynamic coherency identification method, capable of online tracking of coherency changes based on frequency deviations measurements. The method was applied to partition nongenerator buses to the related coherent generator grouping. However, this method has several limitations including (i) the used cosine dissimilarity measure takes into account only the orientation of electromechanical coupling, (ii) it fails to pre-process the measurements to retain only the frequency content of interest, and (iii) fail to detail the measurement window length and generator coherency tracking method. Generally, the available measurement based generator slow-coherency identification methods {i} do not pre-process the measurements to retain only inter-area oscillation frequencies of interest, {ii} require relatively long and non-adaptive observation window, {iii} do not perform observation window data selectivity for vigorous coherency identification in case of interfering pre- and post-event coherency indices, {iv} are validated upon conventional software simulated bus measurements rather than actual PMU synchro-measurements.

The present invention embodiments address the abovementioned deficiencies and present a novel SMT supported method for online generator slow-coherency identification, suitable for near real-time tracking of generator slow-coherency grouping. For this, in a first aspect of the present invention, a method is provided for determining groups of generators operating synchronously in an electric power system 1 (i.e. generator slow-coherency identification) wherein a plurality of generators 2 are present in the electric power system 1 . The method comprises collecting phasor measurement unit (PMU) data obtained (such as generator terminal bus frequency measurements) from a PMU 4 associated with each of the plurality of generators 2, filtering the collected PMU data with a low-pass filter, determining a generator dissimilarity parameter based on (both) direction and strength of generator electromechanical coupling between pairs of the plurality of generators 2, and determining groups 5 of generators 2 having a generator dissimilarity parameter below a predetermined threshold.

In a further aspect of the present invention, a monitoring system 8 is provided for implementing a Wide Area Monitoring, Protection and Control (WAMPAC) application for an electric power system 1 having a plurality of generators 2 with associated phasor measurement units (PMU) 4, the monitoring system 8 being arranged to receive PMU data from the plurality of phasor measurement units 4, and to execute the method according to any one of the embodiments described herein.

It is assumed that in an electric power system 1 consisting of N generators 2, each generator terminal bus is equipped with a PMU 4, reporting frequency measurements with 50/60 frame per second reporting rate (further referred as fps). With M being a total number of most recent past samples (measurements of interest) within an observation time interval (window), the samples x_{i t} to be examined are represented as X_t =

· , ;, _M] ^e H¾^lxiV of bus i, where i e {1,2, is associated with the PMU 4 location. The dataset containing M most recent samples of voltage frequency from N generator buses is presented by the following ensembled matrix, also called the observation window 14/:

In generator coherency identification a distance matrix DM e W,^NxN is used to define relations between pairs of generators, where DM_mn denotes the dissimilarity between mth and nth generator 2. For this, a wide variety of distance measures can be used to assess the coherency indices and evaluate the dissimilarity between the generators.

According to the present invention embodiments, a new generator dissimilarity measure technique is provided to thoroughly assess generator coherency indices as a direction and strength of generator electromechanical coupling. This is realized as a weighted combination of normalized distance matrixes, determined by using cosine and Minkowski p-metric shape-based distance measures. Generally, the cosine distance measure computes an angular displacement, whereas the Minkowski distance measure computes a modified Euclidean norm between a set of sample vectors X, embedded in M-dimensional vector d-space. The cosine dissimilarity distance measure dcos_mn (X) between two sample vectors X with M-dimensional points of generator m and n is defined as

and ranges from 0 to 2, where 0 indicates perfect angular alignment.

Thus, in a further embodiment, direction of generator electromechanical coupling is calculated using a cosine angular displacement calculation on the PMU data of pairs (m, n) of the plurality of generators 2.

Similarly, the Minkowski dissimilarity distance measure dmik_mn(X ) of order b = 1/2 between two sample vectors X with M-dimensional points of generator m and n is defined as

and ranges from 0 to , where 0 indicates perfect magnitude match.

In a further embodiment, strength of generator electromechanical coupling is calculated using an Euclidian distance calculation on the PMU data of pairs (m, n) of the plurality of generators 2.

The proposed distance matrix method represents a weighted combination of the normalized cosine distance matrixes dcosl/fC/)] e R^NxN and Minkowski distance matrixes dmik[X f )] E R^NxN of voltage frequency measurements, to assess the orientation and strength of generators electromechanical coupling, respectively.

To reduce the required memory and computational power, both cosine and Minkowsky symmetric distance matrixes, named as DM e E^WxW are converted into a row distance vectors DV e E^lxi of length 01 where the between generator distances are arranged in the order of

DV = [DM₁₂.DM₁₃. DM_1N, DM₂₃. DM_2>N . DM_{n-1 N}] E ^lxi (4)

So, in a further embodiment, the distance matrix is converted into a row of distance vectors.

In order to ensemble both distance matrixes into a single distance matrix, L2 vector normalization is performed beforehand by the following equation to obtain a normalized distance vector DVN\

Finally, the generator distance vector DVG e E^lxL to be used resembles the Euclidean norm of the weighted individual dissimilarities, where the elements of both normalized distance vectors DVN are represented as scalars in 2-dimensional Euclidean d-space by

DVG = 'w₁ · { DVNcos[X(f )]}² + w₂ · {DVNmik[X(f)]}² E M^lxL (6) where wi = 1, w_å = 0.5, represent the heuristically determined weighting factors of individual measures. In other words, in a further embodiment, the generator dissimilarity parameter comprises a distance matrix with a weighted combination of normalized cosine angular displacement calculation results and Euclidean distance calculation results (i.e. between sets of generator pairs).

Generator slow-coherency is typically defined upon frequency modes between 0.1 to 0.8 Hz, which are associated with the rotor oscillations between a group 5 of generators 2 or electric power plants. For the purpose of generator slow-coherency identification, it is prudent to pre- process the PMU measurements to retain only the slow inter-area frequency modes of interest. In a further exemplary embodiment of the present invention, the low-pass filter is a finite impulse response (FIR) low-pass filter with a pass-band between 0 and 0.8 Hz. In a further exemplary embodiment, the FIR filter is implemented as a digital filter.

To further enhance the quality of the present invention solution, in a further embodiment, the method further comprises applying a dynamic observation window length adjustment on the collected PMU data, wherein an (for each coherency identification instance)observation window length M is adjusted (e.g. increased)) until a predetermined condition is met.

In online generator coherency identification, a measurement observation window (see formula (1) above) is used to define the generator distance matrix (see formula (6) above), and is further used for partitioning of coherent generators 2 into groups 5 (see embodiment description below). Generally, the stronger the electric power system (1 ) perturbation is, the more conspicuous is the present generator coherency configuration. In other words, one could dynamically adjust the observation window length, driven by present electric power system 1 operating conditions. This increases the resolution of coherency identification and enables as close to real-time as possible operation. Moreover, with the decreasing window length M the sensitivity to coherency changes increases. Also, the decrease in the window length is proportionally related to the decrease in processing latency and computational power required, which are further important factors to consider. However, a too short an observation window may lead to erroneous results due to the lack of observability.

In this embodiment, the observation window length M is dynamically adjusted for each generator coherency identification process and solely depends on the present electric power system 1 operating conditions. The following exemplary procedure dynamically determines the minimum number of samples to be processed for rigorous coherency identification, enabling near real-time operation. This observation window length algorithm is based on a stability criterion, driven by the most recent two generator distance vectors (formula (6)) angular deviations in L-dimensional vector d-space, as illustrated in Fig. 2. The observation window length adjustment algorithm can be summarized as follows:

a. Initialization: set the window length to M = fps/2 (fps being the frame per second reporting rate of the PMU data), start online collecting the PMU measurements, fix the observation window starting position (remains fixed till Exit) to the first incoming sample being low pass FIR filtered, populate the observation window with M consecutive samples, determine the normalized generator distance vector DVG(t) by using equations (3) - (6), and save DVG(t) for later use.

b. Increase the window length as M = M + 1 and populate the window (formula (1)) with the next measurement interval samples, determine the DVG(t) and save it for later use.

c. Determine the cosine angle deviation ADVG(t) between the two most recent DVG vectors in L-dimensional vector d-space by using equations (2), and (7) and save it for later use.

ADVG(t) := cos ^®{dcos_{t® t} (DVG)} (7) d. Exit condition: if the median of the four most recent angular deviations ADVG(t) (7) drops below the heuristically determined threshold stab_tresh = 0.05°, as (see Fig. 2)

median{ DVG(t— 3) ... ADVG(t)} < stabjresh (8)

Then current widow length adjustment procedure finishes and continues with the data selectivity condition procedure (see below) and afterward with the step a. Otherwise, the procedure continues with the step b., and so forth.

During the transient period following a large contingency, such as a line trip, the generator coherency may change resulting in the change of coherency indices present in the measurements. In this case, the measurement observation window containing interfering pre- and post-event coherency indices may result in erroneous coherency identification. Especially during critical postevent conditions, it is prudent to perform data selectivity on the given observation window to retain only the observation window samples containing the coherency indices belonging to the most recent coherency configuration (post-event). This prevents erroneous coherency identification. The following steps are then added:

e. Initialization: flip the order of elements in the observation window (as determined according to the method embodiment described above), named as Whipped. In this way, we enable processing of samples in reverse direction to isolate only the samples belonging to the most recent coherency configuration.

f. Repeat a, b, c steps by using the Whipped.

g. Exit condition: a severe change in coherency indices is detected if the following condition is satisfied (see Fig. 3):

ADVG(t) > fps (9)

Afterward, a local minima search is performed on the ADVG, determined using Whipped, to identify the moment when the ADVG starts to deviate indicating coherency configuration change. This step tends to find the last dip ADVG_{)ocal min} in the ADVG before the exit condition in step g. is satisfied. In other words, this step finds the moment in window samples when the coherency indices start to change. The DVG to be used in tracking technique presented further is equal to the DVG(t) being used for the calculation of ADVG_{local min}. In this way, only the measurements containing coherency indices belonging to the most recent coherency configuration are used further for tracking as presented below. h. In case the condition in g step is not satisfied indicating no coherency change within the given observation window, then the DVG to be used in dynamic tracking (see below) is identical to the last determined DVG(t) in step b.

In generic wording, in a further embodiment, the method comprises setting the observation window start position using a local minima search in a reverse order sample set of collected PMU data being processed.

In a further group of embodiments, an adaptive coherency tracking algorithm is applied. The method further comprises operating in a permanent slow-coherency tracking mode or in a transient slow coherency tracking mode, wherein in the permanent slow-coherency tracking mode a lower weight (a) is given to the current normalized generator distance vector DVG(t) than in the transient slow-coherency tracking mode.

Generator coherency is a quasi-permanent system property under constant system operation conditions. During a severe contingency, such as the topology change, the generator coherency may change as a response of the generators 2 on the new operating state. To enable adaptive tracking of grouping changes of slow-coherent generators, two operation modes are proposed, named as permanent and transient tracking, being activated during quasi-steady-state and transient operation conditions, respectively. In both cases the first-order exponential low-pass filter is adopted to enable robust coherency identification, being prone to temporally changes in system operation conditions, caused by transients due to small load changes for example.

Permanent slow-coherency tracking is e.g. applied during steady-state conditions, the generator 2 coherency does not change significantly, but it may happen that due to small system perturbation the weakly-coherent generators 2 separate and form new groups 5. To enable robust generator coherency identification meanwhile being still able to adapt to grouping changes, the DVGA(t) vectorto be used as an input for the AP clustering (see below), resembles the proportional contribution of the most recent DVG(t) (see formula (6)) and the DVGA(t-1), being defined in the previous coherency estimation period, as

DVGA(t) := a DVG(t) + {(1 - a) DVGA(t - 1)} (10) where heuristically determined a = 0.25.

Transient slow-coherency tracking, on the other hand, is applied to enable responsive tracking (faster response) of the coherency identification algorithm on the generator grouping changes during transient conditions, the DVGA(t) to be used is defined as formula (10), though heuristically determined a = 0.5.

The transition between the operation modes is based on a cosine angular difference of the two most recent DVGA vectors (see Fig. 4), defined as

ADVGA(t) := cos ^{dcos^ DVGA)} (1 1 )

A significant increase in ADVGA(t) indicates a significant change in the generator coherency, while small changes indicate sustained conditions. To switch from permanent to transient mode or vice versa the following criterion applies:

where heuristically determined tran_tresh=20 and perm_tresh=10. To enable a smooth transition from transient to permanent mode (formula 12) at least four most recent ADVGA need to be determined during transient mode operation.

So, in one further embodiment of the present invention, a transition is made from permanent slow-coherency tracking mode to transient slow coherency mode if the most recent DVGA(t) (determined normalized generator distance angle vector) is higherthan or equal to a predetermined transient threshold value, e.g. 20.

In a further, related embodiment, a transition is made from transient slow-coherency tracking mode to permanent slow coherency mode if the median difference between a predetermined number (e.g. four) of consecutively determined normalized generator distance angle vectors DVGA(t) is lower or equal than a predetermined permanent threshold value, e.g. 10.

It is relevant to note that during the algorithm initialization period (transient mode by default) and when the transition from permanent to transient mode occurs (formula 12) the first DVGA(t) (formula 10) to be used further in the partitioning is equal to most recent DVG(t). In this way, the partitioning algorithm considers only the most recent coherency indices (formula 6) and neglects any past contributions (formula 10).

In an even further group of embodiments of the present invention, determining groups 5 of generators 2 having a generator dissimilarity parameter below a predetermined threshold comprises applying an unsupervised affinity propagation (AP) clustering algorithm, wherein outlier generators 2 are identified as independent groups 5 (or clusters) and a finite number of groups 5 of generators 2 are determined.

In generator coherency identification, a clustering technique is used to partition set of N generators 2 as nodes k e {l, 2, ... , N} into C = {c₁, c₂, ... , %} clusters (K total number of groups), typically based on a distance matrix, so that G =uf₌₁ c_t and c_t n c_j = 0,for i ¹ j. The main challenge is to partition the generators 2 into robust (over time) and an optimal number of groups 5 (or clusters). In this group of embodiments, the unsupervised affinity propagation (AP) clustering technique is adopted for the purpose of partitioning coherent generators 2 into groups 5.

The AP clustering is an exemplar-based technique, which based on the similarity matrix adopts the max-product algorithm on a factor graph to identify set of nodes as clusters’ center (exemplars), and partition the remaining nodes into the corresponding clusters. The AP clustering is based on the message passing approach between nodes, which in iterative steps maximizes the following unconstrained optimization problem: maxF

where S(i, c_t ) denotes the negative dissimilarity matrix between node i and its potential exemplar , and Sj (C) is a coherence constraint to guarantee the exemplar-consistency and eliminate incorrect results, defined as

if Cj ¹ j , but 3 C; = j

W = { _a (14) otherwise

To identify K exemplars as cluster centers and partition the remaining nodes into corresponding C clusters, the AP takes the negative distance matrix as an input ( S = -DM e E^iVxiV) and recursively updates the responsibility matrix R(i, k) = S(i, k) - max{A(i,j) + S(i,j)} e l^M , where j e {1,2, ... , n} but j ¹ k, representing the accumulated evidence of node k\o be the exemplar for node /^', and the availability matrix A(i, k) = rnm [o, R(fc, k) + sum{max(0, R(j , k))} , where j e

{1,2, but j ¹ i and j ¹ k, representing the accumulated evidence of node k to be the exemplar for node /. Finally, the resulting clusters C can be obtained by

argmax{A(i, k) + R(i, k)} ,_{1 5,}

The initialization of the AP preference parameter p = {p_fc}, in S(k, k) = p_k plays an important role in AP to facilitate node p_k to be chosen as an exemplar, control the number of clusters, and avoid trivial solution as every node chooses itself as its exemplar.

According to the present invention embodiment, an AP preference adjustment algorithm is proposed for an a priori identification of exemplar nodes. The algorithm automatically identifies outlier generators 2 as independent clusters/groups 5 and determines a finite number of groups 5. Consequently, it reduces the number of iteration steps of the AP clustering afterwards.

The proposed AF preference adjustment algorithm is based on the similarity vector value distribution to locate the cluster exemplars and related sub-cluster nodes. In short, the algorithm first, presumes all nodes as being potential exemplars. Second, based on the similarity matrix searches for centrally oriented nodes as exemplars. Third, based on a median absolute deviation and mean of distance vector in multiple steps identify the cluster sub-nodes and rejects them for being exemplars. Finally, the algorithm returns the defined preference vector p with identified exemplar nodes as:

0, exemplar

Pk = [ (16) —oo, otherwise

The following pseudocode illustrates the proposed AP preference adjustment algorithm implementation procedure.

Pseudocode 1. Determination of AP preference p parameter

1 input: DVGA(t) , output : p

2 ex= { exv } =1 , ke { 1 , 2 , N} //nodes as exemplars

3pn=(sn;J =0, ke { 1 , 2 , N} //processed nodes

4 dc= (mean (DVGA) +mad (DVGA) ) · 0.21 //distance

5 to cut based on DVGA value distribution

6 ca=sort (DVGA) //sort in ascending order

7 DMGA=squareform (DVGA) //convert to N*N

8 matrix

9 for i=l to size(ca) //try each ca distance

{m, n }=find {DMGA==ca ( i) } //find gen indexes

if pn{n)==0 L ex(n)==l L

‘ median {DMGA( : , n) } <= edian {DMGA ( : ,mj }

ce=n //gen n as potential exemplar

cs=m //gen m as potential sub-node go=true //flag to continue

I elseif pn (m) ==0 L ex (m) ==1

ce=m //gen m as potential exemplar

: cs=n //gen n as potential sub-node

i go=true //flag to continue

else

go=false //flag, nothing identified

endif

if go //continue with procedure?

pn(ce)=l //exemplar identified & processed

s=find [ { DMGA ( : , oe) <=dc } O - n]

if s>0 //cluster sub-nodes identified

ex(s) =0 //reject sub-nodes as exemplars

; pn(s)=l //sub-nodes being processed

for x=l to size(s) //for each sub-node

: , s (x) ) <=dc } O -pn]

nodes of cluster sub-nodes

ject sub-nodes as exemplars

b-nodes being processed

endif

endfor

elseif

pn(cs)=0 //mark as being verified

endif

endfor

q(16)

Inf //eq (16)

In summary, the present invention embodiments address the important challenges related to online measurement based generator slow-coherency identification, using a combination of one or more of the following:

1 . PMU measurement data pre-processing to retain only the inter-area oscillation frequencies of interest.

2. A generator dissimilarity measure technique to thoroughly assess generator coherency indices as a direction and strength of electromechanical coupling.

3. A dynamic observation window length method to dynamically determine the number of samples being processed.

4. An observation window data selectivity method to prevent mixing of interfering pre- and post-event coherency indices.

5. An adaptive coherency tracking algorithm for robust generator coherency identification during quasi-steady-state and transient conditions, following a disturbance. 6. A preference adjustment method of the unsupervised affinity propagation clustering to identify outlier generators and automatically define a finite number of coherent groups.

The present invention has been described above with reference to a number of exemplary embodiments as shown in the drawings. Modifications and alternative implementations of some parts or elements are possible, and are included in the scope of protection as defined in the appended claims.

Claims

1. Method for determining groups (5) of generators (2) operating synchronously in an electric power system (1),

wherein a plurality of generators (2) are present in the electric power system (1), the method comprising

collecting phasor measurement unit (PMU) data obtained from a PMU (4) associated with each of the plurality of generators (2),

filtering the collected PMU data with a low-pass filter,

determining a generator dissimilarity parameter based on direction and strength of generator electromechanical coupling between pairs of the plurality of generators (2),

determining groups of generators (2) having a generator dissimilarity parameter below a predetermined threshold.

2. Method according to embodiment 1 , wherein direction of generator electromechanical coupling is calculated using a cosine angular displacement calculation on the PMU data of pairs (m, n) of the plurality of generators (2).

3. Method according to embodiment 2, wherein strength of generator electromechanical coupling is calculated using an Euclidian distance calculation on the PMU data of pairs (m, n) of the plurality of generators (2).

4. Method according to embodiment 3, wherein the generator dissimilarity parameter comprises a distance matrix with a weighted combination of normalized cosine angular displacement calculation results and Euclidean distance calculation results.

5. Method according to embodiment 4, wherein the distance matrix is converted into a row of distance vectors.

6. Method according to any one of embodiments 1-5, wherein the low-pass filter is a finite impulse response (FIR) low-pass filter with a pass-band between 0 and 0.8 Hz.

7. Method according to any one of embodiments 1-6, wherein the method further comprises

applying a dynamic observation window length adjustment on the collected PMU data, wherein an observation window length M is adjusted until a predetermined condition is met.

8. Method according to any one of embodiments 1-7, wherein the method further comprises setting a observation window start position using a local minima search in a reverse order sample set of collected PMU data being processed.

9. Method according to any one of embodiments 1 -8, wherein the method further comprises

operating in a permanent slow-coherency tracking mode or in a transient slow-coherency tracking mode, wherein in the permanent slow-coherency tracking mode a lower weight (a) is given to the current normalized generator distance vector (DVG(t)) than in the transient slow-coherency tracking mode.

10. Method according to embodiment 9, wherein a transition is made from permanent slow-coherency tracking mode to transient slow-coherency mode if the most recent determined normalized generator distance angle vector (DVGA(t)) is higher than or equal to a predetermined transient threshold value.

1 1 . Method according to embodiment 9 or 10, wherein a transition is made from transient slow-coherency tracking mode to permanent slow-coherency mode if the median difference between a predetermined number of consecutively determined normalized generator distance angle vectors DVGA(t) is lower than a predetermined permanent threshold value.

12. Method according to any one of embodiments 1 -1 1 , wherein determining groups (5) of generators (2) having a generator dissimilarity parameter below a predetermined threshold comprises

applying an unsupervised affinity propagation (AP) clustering algorithm, wherein outlier generators (2) are identified as independent groups (5) and a finite number of groups (5) of generators (2) are determined.

13. Monitoring system for implementing a Wide Area Monitoring, Protection and Control (WAMPAC) application for an electric power system (1) having a plurality of generators (2) with associated phasor measurement units (PMU) (4), the monitoring system (8) being arranged to receive PMU data from the plurality of phasor measurement units (4), and to execute the method according to any one of embodiments 1 -12.

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