COMPONENT CONTRIBUTION TO THE TOTAL RELIABILITY OF THE WAMS NETWORK Текст научной статьи по специальности «Компьютерные и информационные науки»

Component Contribution to the Total Reliability

of the WAMS Network

M. I. Uspensky*

Institute for Social, Economic and Energy Problems of the North, Federal Research Center of the Komi Science Center of the Ural Branch of the Russian Academy of Sciences, Syktyvkar, Russia.

Abstract — Nowadays, the control of power systems relies on wide-area monitoring and control system (WAMS), which continuously measures and registers state vector values and is synchronized by signals from the uniform time system. A significant part of this system is the local information network, whose reliability largely determines the proper functioning of WAMS. One can assess the said reliability by dividing it into components. These are hardware or technical reliability associated with failure (destruction) of transmission channel elements or the integrity of communication lines, traffic reliability determined by time loss or data distortion without failure of a transmission channel element, software reliability related to errors in the development of exchange execution programs, and resilience against an external deliberate impact on the transmitted information. This paper addresses the assessment of the first three reliability components of the information network, shows its total value, and estimates the contribution of each component. The last component (resistance to an external deliberate action) is described in a huge number of works, which is why it is not considered in this paper.

Index Terms. Wide-area monitoring and control system, local infor-mation network, hardware and software reliability and availability, traffic availability.

I. Introduction The need for a correct estimation of power system state has led to the creation of a hierarchical system for monitoring transient conditions, i.e., a wide-area monitoring and control system (WAMS). It is based on the technology for measuring phasors (phase vectors) to collect vector information with the aid of phasor measurement

* Corresponding author.

E-mail: [email protected]

http://dx.doi.org/10.38028/esr.2021.01.0004 Received April 13, 2021. Revised April 17, 2021. Accepted April 25, 2021. Available online May 26, 2021.

This is an open access article under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2021 ESI SB RAS and authors. All rights reserved.

units (PMUs) using the signals from the global navigation systems that provide simultaneous measurement of phasors [1]. WAMS includes measuring transformers (PMUs), phasor data concentrators (PDCs), and equipment of the local information network (LIN). It allows us to control power system behavior by continuously observing system events. The WAMS reliability is determined by the reliability of every monitoring system component.

The network failure is determined by the loss of terminal communication, which implies not only the absence of such communication but also the distortion of the transmitted information. Then the network reliability includes four components. These are 1) hardware or technical reliability associated with a failure of transmission channel components or destruction of the integrity of communication lines, 2) traffic reliability determined by the time loss or distortion of data without a failure of the transmission channel component, 3) software reliability related to errors in the development of exchange execution programs, and 4) resistance to external actions targeted on the transmitted information.

The paper presents an approach to assessing three first components. An algorithm and implementation of this approach are considered on the example of a 10-node power system. Some features of the information network model are noted.

II. Hardware reliability of WAMS network

The hardware of WAMS network comprises network connections, electronics of PMUs and PDCs. Since the operation of PDC central processor and communication interface during duplication is similar to the operation of these components in PMU, we will use the reliability assessment of these blocks in [2] obtained from the system of Markov equations of state probabilities, given different lengths of the main and redundant communication channels. Then the availability of communication link of a network consisting of a duplicated information source (PMU, PDC, or, if necessary, an intermediate amplifier) and communication channel lines can be defined as

Ach = APDC 'Acom, (1)

where

A

2

M PDC

(m

PDC + ^ PDC

)2

(2)

Table 1. C37.118-2011 frame structure.

Field Size

Sync byte (SYNC) 2 bytes

Byte number of frame (FRAMESIZE) 2 bytes

PMU Identifier (IDCODE) 2 bytes

Seconds of counting (SOC) 4 bytes

Second fraction/quality flag (FRACSEC) 4 bytes

Status flag (STAT) 2 bytes

Vectors (PHASORS) 8n bytes (floating point)

Frequency (FREQ) 4 bytes (floating point)

Frequency change rate (DFREQ) 4 bytes (floating point)

Analog data (ANALOG) 8m bytes (floating point)

Digital data (DIGITAL) 2-l bytes (discrete values)

Cyclic Redundancy Check (CHK) 2 bytes

l is the number of discrete information sources; m is the number of analog information sources; n is synchronized vectors (magnitude and phase).

Table 2. Required channel bandwidth, Kbit/s.

Samples per second Number of PMUs

2 10 40 100

25 50 249 997 2392

50 100 499 1994 4984

100 200 997 3988 9969

since PDCs are of the same type, and

= -

Mml ' M-bl

(3)

(Mml + Kml )(Mrl + hi )

Here Apdc is the availability of the redundant information source; 1PDC and ^PDC are failure and recovery rates of the source, respectively. The physical availability of each element of the information carriers (twisted pair, optical fiber, high-frequency channel) is characterized by length l,, specific failure rate lml for the main line and Xrl for the redundant line, and the average recovery time rml for the main and rrl for the redundant line , per unit length. Since reliability indices of communication lines \ and rl approximately linearly depend on their length, and ^ = 1/ rl, it is easy to evaluate the working state probability of an information carrier element (,-th line availability) as

1/(rlnJ • I, ) 1

Aln,i =

r (4)

+K, ■ h) • h 1 + ■ r,nj ■ ¡2

It is worth noting that rln i includes two components: the distance-dependent failure search variable, and the recovery-related constant. Since the second component has small values, we neglect it. Consequently, the availability of the communication line is inversely proportional to its squared length. In contrast to duplication in electronics, where the backup device usually repeats the basic one, the storage media are most often duplicated by the elements of various reliability indices. This is because under normal conditions, communication is provided via the shortest line in the communication network, and in the case of redundancy, the information goes through the line remaining in the communication network, which can be significantly longer than the main one. Moreover, the approach to solving such a problem is the same as in the case of duplicating electronic units (2) but considers different values of lj and ^ for the j-th communication line (3).

III. Traffic reliability

The traffic reliability lies in timely information transmission, without loss and distortion associated with the exchange channel loading. Traffic-related losses are associated with an unacceptable delay or loss of some information due to the information channel overload but are not associated with the failure of channel device elements, which is taken into account in hardware reliability. Therefore, the traffic reliability is determined by the choice of channel capacity, given a delay in the transmitted information.

The information frame from the generation unit or power line, formed by each PMU, combines 9 vector measurements (3 currents and 3 voltages (magnitude and phase), 3 active and reactive power components); 2 analog values (generator current and voltage); the state of PMU, and the state of switching components. The transmission packet also includes the frequency and speed of its change, the time stamp, and the binding for interaction with the information network in the standard C.37.118-2011. The data frame structure is given in Table 1. The amount of information from one PMU takes bin = 89 + 28 + 2 + 2 = 92 (bytes). The amount of information per frame of one node (the first six points in Table 1) is bp = 6 + 8 + 8 + 2 = 24 (bytes). Depending on the number of PMUs (information sources of measurement), and transmitted measurements per second, the packet volume often varies from 100 to 400 bytes. The approximate channel bandwidth in Kbit/s, depending on the number of source devices and sampling rate, given a margin of 10 percent, is indicated in Table 2 [3]. In this case, 1 Kbit = 1024 bit.

Information delay is associated with both the type of the exchange channel and the time of unloading its receiving buffer. Packet delivery to a receiver requires time Td, which, in the general case, is determined by the signal propagation time T , the time of packet transmission over the communication line Tpt and the packet waiting time Twp in the queue in the communication unit

Td = Tsp + Tpt + Twp. (5)

The signal propagation time, Tsp in most communication systems is determined by the propagation time of the electric or optical signal (electromagnetic field). The pulse

1. Set power system scheme ana initial conditions

1

2 . Select the main and backup routes

1

3 . Determine links of every route

1

4 .Calculate infor mation

loads of route links under normal and

emergency conditions +

5 . Calculate route availability under normal and emergency

conditions

I

6 . Calculat e route availability taking into account redundancy

I

7 . Assess reliability

component for software

delay in the optical fiber is (3.5-5)-/ (ns) [4] and in the copper wire 5 / (^s) [5], where / is the channel length in km.

The packet transmission time, Tpt, depends on the rate of data transfer via the communication line vr (Kbit/s) and the packet volume or length Lp (Kbit)

Tpt = LJVtr (6)

The propagation speed depends only on the channel material. Therefore, the propagation time along the channel is constant. Transmission time depends only on the packet length.

The main idea behind the design of a data transmission network is to ensure the balance between traffic (the flow of requests X, in our case, the measurement frequency), the number of network resources (bandwidth) and the service quality (service flow parameter of request processing). Solving this problem involves considering two levels of the open system interaction model (OSI). network and channel.

Network level. Traffic routes over the network are considered at the network level. To this end, it is convenient to describe the communication network as a graph model [6] (in this case, non-oriented), in which the network nodes (routers) correspond to the graph vertices and the communication lines correspond to the graph arcs. The transmission time to the receiving node is the time spent by the packet in the network line. This time is random to a certain extent.

The intensity of load on the arcs of the network graph p j is determined by the ratio of the intensity of request flow from the information source node i to the intensity of the service flow from the destination node j (X,/j and depends on the number of devices and the amount of information from each device. In our case, the request flow intensity is determined by the frequency of parameter measurements at the nodes of the power system X = fmsr = l/Tmsr, service flow intensity is determined by the reciprocals of the packet delivery time ^ = 1/Td = 1/(Lp/vtr+Tpc), and since this time is shorter than the request period, Twp = 0. On the other hand, the receiver electronics creates an additional delay, Tre, of about 5 ^s on average. Then

Pij =

LP /

+ Tp + Tre

(7)

8 . Assess resist ance to external Impacts on information

9 . Conclude o n acceptability _of the option_

Fig. 1. Algorithm to research the information network reliability.

Channe/ /eve/. This level requires the evaluation of the necessary bandwidth of communication lines between network nodes. In the general case, an approximate formula can be used to estimate the probability of losses [7]

1 - P,,

_ "H Ni qij _~1 Nj+T pij '

1i\

- Pj

(8)

where Nj is the number of sections in the receiver storage j; Pj is the load intensity of line ij.

The absence of loss is determined as

Pj = 1 - q, (9)

Such an assessment corresponds to one information line connecting two nodes. Taking into account the sequence of

switching the communication lines of two nodes passing through the intermediate nodes, the overall assessment of the information loss probability is determined as

Q = 1-П jPj=1-П j (1-

4

(10)

IV Failure of the software The failure of the software (SW) is associated with its inconsistency with the objectives set. There are many definitions of software reliability. The most acceptable definition seems to be as follows Software reliability is the probability that the program will work without failures for a certain time, given the degree of their influence on the output results [8].

The frequency of statistical data errors reduced to 100 percent is given in Table 3 with a detailed description of "Incomplete or erroneous task."

The software is not subject to wear and tear and its reliability is determined only by the development errors. Thus, over time, this index should increase if the correction of detected errors does not introduce new errors.

Table 3. Frequency of some types of errors [9].

Cause of error Frequency, %

Deviation from the task 12

Neglect of programming rules 10

Incorrect data sampling 10

Erroneous logic or sequence of operations 12

Erroneous arithmetic operations 9

Lack of time to resolve 4

Incorrect interrupt handling 4

Invalid constants or source data 3

Inaccurate recording 8

Incomplete or erroneous task 28

ß

Errors in numeric values 12

Insufficient accuracy requirements 4

Erroneous characters or signs 2

Registration errors 15

Incorrect hardware description 2

Incomplete or inaccurate development basics 52

Ambiguity of requirements 13

Table 4. Routes for the main and redundant information exchange channels.

Source node Main channel Redundant channel

1 1-7-4 1-9-8-6-4

2 2-7-4 2-9-7-4

3 3-4 3-5-4

5 5-4 5-6-4

6 6-4 6-5-4

7 7-4 7-6-4

8 8-6-4 8-9-7-4

9 9-7-4 9-8-6-4

10 10-2-7-4 -

For critical applications, which should include the WAMS software, by the time the system is delivered to the client, it may contain from 4 to 15 errors per 100 000 lines of program code [10]. For clarity, we note that the number of code lines of WINDOWS XP is above 45 million, NASA has 40 million code lines, and Linux 4.11 kernel has more than 18 million code lines [11].

When evaluating the WAMS program of 10 million lines of code, the number of errors at the beginning of program operation is E = (V/100 000)4 = 400 (errors). Then, using the formula for the mean time between the software failures, we get

X SW = p - = 0.01400 = 4 -10-7

sir V 107

or

¡SW

1

10'

XSW ■ 8760

:285

4•8760

where E is the number of errors per program accepted for operation, V is the program volume in lines of code, p is the program complexity coefficient, usually in the range of 0.001 to 0.01, XSW is the failure rate and tSW is the mean time between the software failures (years), 8760 is the number of hours per year. With a value of one error per 1 000 code lines, accepted for applied software after testing with the same number of code lines, E = 10 000 errors:

. = p * = 0.0110000 = 10-5

Sir Yy 107

or

¡SW

1

105

8760

or about one failure in 12 years.

XSW ■ 8760

■ 11.4

v procedure for assessing the LIN reliability

Since the reliability of the local information network (LIN) is investigated for a given scheme, the research algorithm is as follows (Fig. 1).

1. Set a scheme of information exchange in the form of links between nodes, the length of links, and the type of links (wired, fiber-optic, high-frequency, etc.). Set also the initial conditions. These are the failure and recovery rates of information sources (PMUs) Xis and

respectively; specific failure rates of the main and redundant lines (Xml and Xrl); the average recovery time of the main and redundant lines (rml and rrl) per unit of length; propagation delay Tsp; delay in electronic devices Tre; transmission rate vr; transmission frequency or measurement period Tmsr, and the number of information sources at each node. A link means a connection between the adjacent nodes in the network.

2. Select the main and backup routes for the information exchange between the sources and the dispatching point. The main route is usually determined by the shortest path from the information source to the dispatching point, the backup one depends on the failed communication link.

3. Determine a route by its set of links.

4. Calculate information loads of links of every route under normal and emergency conditions in terms of link failure.

5. Based on the prepared information, calculate the hardware availability and traffic reliability of the routes under normal and emergency conditions.

6. Calculate the availability of routes taking into account redundancy.

Table 5. Availability of links of fiber-optic information exchange channel.

Link l, km Xcon, fail./yr. rcon, hr./recov. Aunt Link l, km Xcon, fail./yr. rcon, hr./recov. Aiint

1-7 150.0 2.628 31.32 0.990433883 4-6 30.0 0.5256 6.264 0.999364399

1-9 75.0 1.314 15.66 0.997397114 4-7 50.0 0.876 10.44 0.99869736

2-7 150.0 2.628 31.32 0.990433883 5-6 50.0 0.876 10.44 0.99869736

2-9 75.0 1.314 15.66 0.997397114 6-7 47.0 0.82344 9.8136 0.998818611

2-10 70.0 1.2264 14.616 0.997698469 6-8 145.0 2.5404 30.276 0.991038641

3-4 70.0 1.2264 14.616 0.997698469 7-9 130.0 2.2776 27.144 0.99273384

3-5 50.0 0.876 10.44 0.99869736 8-9 40.0 0.7008 8.352 0.99907246

4-5 40.0 0.7008 8.352 0.99907246

Table 6. Availability of the fiber-optic information exchange channel.

Node Amain channel Are^ndani channel Achannel with redundancy Node Amain channel Are^ndani channel Achannel wüh redundancy

1 0.989400945 0.987684744 0.99986947 7 0.990433883 0.998443352 0.999985109

2 0.989400945 0.989374459 0.999887379 8 0.990666305 0.991036328 0.999916336

3 0.997698469 0.998030512 0.999995467 9 0.991698503 0.99000482 0.999917025

5 0.99907246 0.998322147 0.999998444 10 0.987380523 0 0.987380523

6 0.999364399 0.998030512 0.999998748

Table 7. Availability of links of the power line information exchange channel.

Link l, km Xcon, fail./yr. rcon, hr./recov. Aunt Link l, km Xcon, fail./yr. rcon, hr./recov. Alint

1-7 150.0 2.94 28.5 0.990268019 4-6 30.0 0.588 5.7 0.999357643

1-9 75.0 1.47 14.25 0.997355058 4-7 50.0 0.98 9.5 0.998678619

2-7 150.0 2.94 28.5 0.990268019 5-6 50.0 0.98 9.5 0.998678619

2-9 75.0 1.47 14.25 0.997355058 6-7 47.0 0.9212 8.93 0.998802048

2-10 70.0 1.372 13.3 0.997661811 6-8 145.0 2.842 27.55 0.990883459

3-4 70.0 1.372 13.3 0.997661811 7-9 130.0 2.548 24.7 0.992608673

3-5 50.0 0.98 9.5 0.998678619 8-9 40.0 0.784 7.6 0.999060456

4-5 40.0 0.784 7.6 0.999060456

Table 8. Availability of the power line information exchange channel.

Node Amain channel Aredundant channel Achannel with redundancy Node Amain channel A redundant channel A channel with redundancy

1 0.98921669 0.987469907 0.999864884 7 0.99026802 0.998420046 0.999984624

2 0.98921669 0.989189439 0.999883426 8 0.99050449 0.990880875 0.999913409

3 0.99766181 0.997999793 0.999995323 9 0.99155486 0.989831215 0.999914123

5 0.99906046 0.998296664 0.9999984 10 0.98716037 0 0.98716037

6 0.99935764 0.997999793 0.999998715

Table 9. Resulting XZ and ^Z values of communication channels.

Source - node Fiber-optic channels Power line channels

Aï ßi Aï ßi

1 0.09589628 734.572164 0.109127394 807.5486398

2 0.083695895 743.08248 0.095243883 816.9324165

3 0.006031754 1330.67373 0.006854215 1465.551612

5 0.002472612 1588.79738 0.00280486 1752.642178

6 0.00203475 1625.44545 0.002306221 1794.935514

7 0.016936974 1137.37422 0.019264457 1252.864972

8 0.062884682 751.569245 0.071559069 826.33357

9 0.062221822 749.824533 0.070804518 824.418488

10 0.077536602 642.210362 0.088232547 706.0262268

7. Estimate the software component, in terms of software development reliability.

8. Assess the resistance to external impact on the information. Mentioning this point, we do not dwell in detail on such an assessment but refer the reader to the literary sources, for example, [12, 13].

9. Make a conclusion on the acceptability of the option under study and, if necessary, its weak points.

Table 10. Input data on the information network.

Link l, km bin bfr S bn z Z b"

1-7 150 2 1 2 1 5 3

2-9 75 2 1 3 2 5 3

10-2 70 1 1 1 1 1 1

3-4 70 6 2 6 2 6 2

3-5 50 0 0 0 0 6 2

9-7 130 1 1 4 3 6 4

9-8 40 0 0 0 0 6 4

8-6 145 1 1 1 1 7 5

7-4 50 1 1 7 5 7 5

6-5 50 1 1 0 0 7 3

6-4 30 6 2 7 3 13 7

5-4 40 1 1 1 1 8 4

7-6 50 6 2 0 0 7 5

2-7 150 0 0 0 0 5 3

1-9 75 0 0 0 0 5 3

Table 11. Loads p.. and probabilities q. of information loss of an individual link.

Link P"/ % %

1-7 0.01593 1.008E-09 0.04065 1.0643E-07

2-9 0.02477 9.099E-09 0.04064 1.0638E-07

10-2 0.00890 5.545E-11 0.00890 5.5455E-11

3-4 0.04583 1.929E-07 0.04580 1.9296E-07

3-5 - - 0.04583 1.9289E-07

9-7 0.03363 4.154E-08 0.04949 2.8233E-07

9-8 - - 0,04949 2.8221E-07

8-6 0.00891 5.557E-11 0.05835 6.3671E-07

7-4 0.05834 6.364E-07 0.05834 6.3645E-07

6-5 - - 0.05468 4.6204E-07

6-4 0.05468 4.619E-07 0.10412 1.0961E-05

5-4 0.00890 5.541E-11 0.06353 9.6904E-07

7-6 - - 0.05834 6.3644E-07

2-7 - - 0.04065 1.0649E-07

1-9 - - 0.04064 1.0638E-07

vI. power system model with wams

Let us consider the described approach on the example of a 10-node system considered in [14], Fig. 2. Without dwelling on the optimal composition of PMUs, we will assign PMU to each node of the network and select sites for PDCs at nodes 4 and 9. We determine the main and redundant channels of information exchange from the PMU of each node (Table 4 and Fig. 3). Fig. 4a indicates such links without redundancy, and Fig. 4b presents them with redundancy. For fiber-optic communication lines, the specific indices according to Table 12.4 from [15] and data from [16, 17] are = 0.01752 failure/(km/yr.); r, = 0.2088 hr./(km/recovery). Reliability indices of electronic devices with their duplication are 1PMU = 1.539 10-3 failure/yr., Vpmu = 5.922 recovery/yr., APMU = 0.999740 [2], lPDC = 2.673 10-6 failure/yr. and ^PDC = 740 recovery/yr., APDC = 0.999999996 [15].

vil. Technical availability of local information network

Table 5 presents the determined link availabilities of the information exchange channel, each including an information source (PMU or PDC) and the actual

fiber-optic connection, given that ^con = 8760/rcon recovery/ yr. Then the availability of individual information channel is determined as the product of availabilities of sequential links, which corresponds to a channel without redundancy, and the availability of the z-th channel with redundancy is calculated as

AcKl = 1 - (1 - Am_ckH1 - Ar ch,,), (11)

where Am chJ is the z-th main channel connection availability, and Ar chJ is the z-th redundant channel connection availability. The channel availabilities are given in Table 6 according to the connections (Table 4) and to the availabilities of the links (Table 5).

Let the line from the source to the dispatching node be a "channel" consisting of links between neighboring nodes. Table 6 shows that with a single set of links of communication channel, its availability varies in the range of one to three nines after the decimal point. The availability of communication with redundancy is maintained at the level of three nines after the decimal point, even if a source is located sufficiently far from the dispatching node, such as nodes 1 and 2. The availability of channel 10 is the value of the main channel availability since this channel has no redundancy, i.e., redundant communication lines.

Table 12. Probabilities of the route information loss.

Route Route QZ

1-7-4 6.37E-07 1-9-8-6-4 1.199E-05

2-9-7-4 6.87E-07 2-7-4 7.429E-07

3-4 1.93E-07 3-5-4 1.162E-06

5-4 5.54E-11 5-6-4 1.142E-05

6-4 4.62E-07 6-5-4 1.431E-06

7-4 6.36E-07 7-6-4 1.16E-05

8-6-4 4.62E-07 8-9-7-4 1.201E-06

9-7-4 6.78E-07 9-8-6-4 1.188E-05

10-2-7-4 6.37E-07

Table 13. Influence of load intensity p and the number of sections N on the probability of information loss q and error-free operation p for link 7-4.

# P N p q # P N p q

1 0 0 1 5 7 0.9998469 0.0001531

2 1 0.99009901 0.00990099 6 0.3 10 0.999995867 4.13344E-06

3 3 0.99999901 9.9E-07 7 100 1 0

4 0.01 5 1 9.9E-11 1 0 0 1

5 7 1 9.88098E-15 2 1 0.666666667 0.333333333

6 10 1 0 3 3 0.933333333 0.066666667

7 100 1 0 4 0.5 5 0.984126984 0.015873016

1 0 0 1 5 7 0.996078431 0.003921569

2 1 0.944874979 0.055125021 6 10 0.99951148 0.00048852

3 3 0.999813008 0.000186992 7 100 1 0

4 0.058341 5 0.999999364 6.36452E-07 1 0 0 1

5 7 0.999999998 2.16628E-09 2 1 0.588235294 0.411764706

6 10 1 4.30211E-13 3 3 0.864587446 0.135412554

7 100 1 0 4 0.7 5 0.942856074 0.057143926

1 0 0.000000000 1.000000000 5 7 0.973782312 0.026217688

2 1 0.909090909 0.090909090 6 10 0.991354799 0.008645201

3 3 0.999099909 0.000900090 7 100 1 1.11022E-16

4 0.1 5 0.999990999 0.000009000 1 0 0 1

5 7 0.999999909 0.000000090 2 1 0.500000025 0.499999975

6 10 0.999999999 9.000007E-11 3 3 0.750000038 0.249999962

7 100 1.000000000 0.000000000 4 0.9999999 5 0.833333375 0.166666625

1 0 0 1 5 7 0.875000044 0.124999956

2 0.3 1 0.769230769 0.230769231 6 10 0.909090955 0.090909045

3 3 0.98094566 0.01905434 7 100 0.990099059 0.009900941

4 5 0.998297759 0.001702241

The specific indices for communication lines using a high-frequency signal on power lines (Table 12.3 [4]) are X/ = 0.0196 failure/(km/yr.); r1 = 0.19 hr./(km/recovery). The rest of the data are the same. The availabilities of channel link and information exchange channels are given in Tables 7 and Table 8, respectively.

A comparison of Tables 5, 6 and 7, and 8 shows that the difference in availability between fiber-optic and high-frequency transmission is negligible. Table 8 shows that for optical fiber only the main channel determines the availability of node 10.

Based on the sequential connection of links of the main or redundant information channel and parallel operation of these channels on the server, we determine the failure rate Xs and the recovery rate for fiber-optic information

exchange channels. Then, Xi E = j, where i is the

j

main or redundant information channel, j is the link of

this channel. Further, we determine E =

1 - A

and

from the relation A = —— and find ve = TV

^ + X ; '

_ -ck^. The resulting XZ and for fiber-optic

E A

nch,i

and power lines are summarized in Table 9.

With a complex network of information connections, we can find a redundant connection from the server node to the node with failed connection, excluding the latter one. To do this, we use the depth-first and breadth-first search algorithm as proposed in [17]. It allows finding a backup path with failed connections, if one exists, or warning about its absence. When searching, the column "Redundant channel" is built in Table 4, and then the hardware reliability is evaluated for the found path. These backup routes are stored in Table 1 in the order of

G5 G6 G1 G2 G3 G4

300 ! J186 100 îJ62 200 ±J124 100±J62 200 ±J124 4 ±J3

G8 G9 G10

Fig. 2. Model diagram of the test power system. The black switch is on, the white one is off.

Fig. 3. The geographical location of the test power system (scale: 1cm = 20 km). Rectangle nodes contain generation. Circular nodes have only load.

Dispatching node

70 km

50 km

The first group PMUs

a)

145km^^ 40km The second group PMUs

b)

Fig. 4. Communication channels: a) without redundancy, b) with redundancy.

Table 14. An example of the difference between the values of two schemes by contribution of reliability components.

Ri R2 R3 R4 Qa Qb Mb Ma 100% Qa

0.9 0.9 0.9 0.9 0.0199 0.0361 44.87534626

0.9 0.8 0.8 0.9 0.0396 0.0784 49.48979592

0.8 0.9 0.8 0.9 0.0396 0.0684 42.10526316

0.8 0.8 0.8 0.8 0.0784 0.1296 39.50617284

Table 15. The difference in the reliability component contributions for two equivalent circuits.

■Amain A redundant Pnr Pern Qparal. Q.sequen. Qsequen. Qparal. ^QQO/ Qpa.ra.l.

0.989400945 0.987684744 0.999999363 0.99998801 0.00013053 0.000130663 0.102001899

0.989400945 0.989374459 0.999999313 0.9999992571 0.000112621 0.000112636 0.013328578

0.997698469 0.998030512 0.999999807 0.999998838 4.53284E-06 4.53589E-06 0.067205108

0.99907246 0.998322147 0.9999999999 0.99998569 1.55628E-06 1.56953E-06 0.844266885

0.999364399 0.998030512 0.999999538 0.999998569 1.25181E-06 1.25363E-06 0.144945673

0.990433883 0.998443352 0.999999364 0.9999884 1.48911E-05 1.50029E-05 0.745022642

0.990666305 0.991036328 0.999999538 0.999998799 8.36642E-05 8.36794E-05 0.018178718

0.991698503 0.99000482 0.999999322 0.99998812 8.2975E-05 8.30793E-05 0.125610524

0.987380523 0 0.999999363 0 0.012620106 0.012620106 0

Table 16. Data for calculating the contribution of components.

Source node

A channel with redundancy

Ql

10

0.99986947

1.199E-05

2 0.999887379 7.429E-07

3 0.999995467 1.162E-06

5 0.999998444 1.142E-05

6 0.999998748 1.431E-06

7 0.990433883 1.16E-05

8 0.990666305 1.201E-06

9 0.991698503 1.188E-05

1/285/10 = 3.5087719E-04

0.987380523

6.37E-07

1

1

Table 17. Calculation results of the contribution by component.

Source -node ConAi, 100% ConQi, 100% Conswt, 100% Corn,, 100% Az,t

1 73.49342727 6.750832704 19.75574003 0.01776077 0.999822399

2 75.86377335 0.500432399 23.63579425 0.01484516 0.999851552

3 11.11500184 2.849246004 86.03575216 0.00407827 0.999959217

5 3.237369106 23.76012545 73.00250545 0.00480637 0.999951937

6 3.31473698 3.788649056 92.89661396 0.00377707 0.999962229

7 24.18205538 18.83767661 56.98026802 0.00615787 0.999938422

8 69.74748092 1.001227823 29.25129126 0.01199527 0.99988005

9 63.85505894 9.14248991 27.00245115 0.01299427 0.999870062

10 99.71770723 0.005033503 0.277259265 1.26552017 0.987345249

decreasing availability. A similar operation is performed in the process of network building. In actuality, a redundant channel with operational connections and the highest availability is used, if necessary.

vIII. Traffic reliability

Let us consider the WAMS information channels for the power system, Fig. 2. The scheme of information connections with the distance scale is shown above in Fig. 3. Let us define the network conditions and characteristics. All data connections are made using fiber optics with a propagation delay Tsp = 5 ns. Electronic delay is Tre = 5 ^s. The transmission speed is vtr = 1 Mbit/s = 1048576 bit/s [17]. Measurement transmission frequency is 10 Hz or Tmsr = 0.1 s. Control center is located at node 4 of the power system (Fig. 4), information routes of each information transmission channel under normal and emergency conditions are shown in Table 4, and its last column shows the connection of the source node to node 4 via bypass routes in the case of failure of the main route component. Note that failure of link 10-2 results in a complete loss of communication with node 10. The initial data for the calculations are summarized in Table 10. Here, bin and bfr in the third and fourth columns are the values of bytes associated directly with the corresponding link of the line; £bnr and £bem are byte groups, including intermediate communication packets under both normal and emergency conditions caused by a failure of one of the links. N is determined by the maximum frame under normal operating conditions and equals 5.

The simulation results are shown in Tables 11 and 12, which indicate that the probability of information loss in the case of the calculated loads is very low. Let us consider the relationship between the information loss probability q and the load intensity p using the example of connection 7-4 with the rest of the same conditions. Using the same example, consider the effect of the number of storage sections N, Table 13.

It is clear that for N = 0, the probability of losing information is 1 since there is simply nowhere to receive it. With an increase in N, the value of q drops rather steeply, turning almost to zero already at N = 10. It is also obvious that the greater the load intensity p the greater the probability of information loss q. The rise is quick, which requires an increase in the number N of receiver storage sections.

IX. The component contribution to the total reliability of local information network

In the above sections, we determined the components of the WAMS information network reliability. In this section, we seek to determine the total reliability and the contribution of each component to this value. Initially, the question arose, what should be the contribution model of the component reliability should have? Let Ru be hardware reliability of the main /-th route, R/2 be hardware reliability of the backup /-th route, R/3 be the traffic reliability of the main /-th route, R/4 be the traffic reliability of the backup /-th route. The contribution model can have one of the following schemes (Fig. 5). In scheme (a), the hardware and the traffic component are combined first, and then

the main and backup routes are combined. In scheme (b), firstly, the hardware components of the main and backup routes are combined, then the traffic components of the same routes are combined, after which the obtained equivalents are connected sequentially. Equivalent values are determined as

Ra = 1 - (1 - RRX1 - R2R4), (12)

Rb = [1 - (1 - R,)(1 - R3)] [1 - (1 - R2)(1 - R4)], (13) With a large difference in the values of Rz, the relative difference between the equivalent values Q{ = 1 - Ri can reach ten percent. Thus, for example, if the difference between Rf is 0.1, this difference lies between 39 and 49 percent (Table 14).

Let us consider such a relationship (Table 15) between the availability values of the route of fiber-optic information

exchange channel (Amain and An

C0nA,i = ■

1 - A

'channel with redun.,i

Con

Q

a

■'LmJ

ConQt =

' Con.,i

100%; ConSWi =-

100%;

1

100%;

a)

b)

Fig. 5. Models of the route reliability component contribution to the total reliability.

software, n is the number of the information source nodes. Here we rely on the assumption that the software is divided equally among the node devices, i.e., in our case n = 10. Conx f is the sum of the shares of component unavailabilities. The total availability of a LIN route can be determined as

( 1

A = A

Z,i channel with redun.,i

■ (1 - QL,i ) •

1—

1

t

(15)

. from Table 6) and

the probabilities of the absence of information loss over a route due to the traffic load (Qnr and Qem from Table 12). Table 15 indicates that for the test scheme such a difference lies in the range of 0.01 to 0.85 percent, i.e., less than 1 percent. Therefore, when evaluating the components, any of the considered equivalent circuits can be used.

Further, we will estimate the contribution of reliability components to the local information network operation. It is more convenient to do that based on the component unavailability, i.e.,

tsw ■n 'Conz,i Cons,z = (ConA, z + ConQz z + ConSW z)-100%, (14) where ConA, is a share of technical unavailability, ConQ, is a share of unavailability due to traffic. Here Q^ t is used for an adverse event. ConSWz z is a share of unavailability for

For the considered scheme, the initial data on the fiberoptic network are summarized in Table 16. The calculation results are shown in Table 17.

Table 17 shows that the farther the source node from the dispatching node, the greater the weight of the hardware reliability component. On the other hand, the closer the source to the dispatching node, the heavier the traffic, which levels the total route availability out.

X. conclusions

The proper functioning of the WAMS information network is ensured by four components of its reliability. These are hardware or technical reliability associated with the failure of transmission channel elements or destruction of the integrity of information transmission lines; software reliability related to errors in the development of exchange execution programs; traffic reliability determined by the time loss or distortion of data without a failure of the transmission channel elements; and resistance to external deliberate impact on the transmitted information. The influence of the latter component is discussed in many works, for example, [12, 13], which is why it is not considered in the paper.

Convenient algorithmization of the assessment of the components of the local information network reliability simplifies the implementation of computer applications of the assessment.

The reliability of hardware (PMUs, PDCs) of such a network largely depends on the reliability of information carriers (optical fiber, radio waves, and others) and devices that ensure its operation. The paper deals with an approach designed to determine the parameters of such reliability on the example of a 10-node power system. Thus, with the appropriate redundancy, the hardware availability of the network, including information sources (PMUs), exceeds three nines after the decimal point for fiber optics and is slightly less when information exchange occurs over power lines. The ways of increasing the hardware reliability of the information network are considered.

The traffic reliability component is determined by the load intensity of each link and the information receiving capabilities associated with the receiver storage capacity. It is worth noting that there is a strong dependence of the probability of information loss on the number of sections in the receiver storage device, whose increase makes it possible to compensate within some range for the growth of this probability with an increase in the load intensity. The test network traffic availability also exceeded three nines after the decimal point.

R

R

R

R

1

2

1

2

R

R

R

R

3

4

3

4

In terms of software, the impact of the number of code lines on the value of this parameter is noted and its assessment is shown depending on the number of commands. A significant property of this index is its improvement with an increase in operating time. However, it can be incorrect due to new errors appearing when correction is made under operation. For the example of a WAMS program of 10 million code lines, the mean time between failures should be 285 years.

The study has revealed that despite different results obtained for various equivalent circuits, the error in their calculations for the range of requirements for their values lies within acceptable limits.

The contribution of the considered components to the total reliability has been assessed for the test scheme. The findings have shown that the greater the distance between the source node and the dispatching node, the greater the weight of the hardware reliability component. On the other hand, the closer the source to the dispatch center, the heavier the traffic, which equalizes the total availability of different routes.

References

[1] A. G. Phadke and J. S. Thorp, "Synchronized Phasor Measurements and Their Applications," New York, NY, USA: Springer, 2008, 260 p.

[2] M. I. Uspensky, "Estimation of the functioning reliability for the device of synchronized vector measurements," Relay protection and automation, no. 3, pp. 39-44, 2017. (In Russian).

[3] Real-Time Application of Synchrophasors for Improving Reliability, NERC, Princeton, NJ, USA, 10/18/2010, 77 p. Available at: http://www.naspi.org (accessed 09.02.2020)

[4] V. N. Tsukanov, M. Ya. Yakovlev, "Fiber-optic technology. Practical Guide," Moscow, M., Russia: Infra-Engineering, 2014, 304 p. (In Russian).

[5] A. E. Davydov, P. I. Smirnov, A. I. Paramonov, "Design of telecommunication systems and networks. Calculation of communication network parameters and traffic analysis," St. Petersburg, Russia: ITMO University, 2016, 47 p. (In Russian).

[6] M. O. Asanov, V. A. Baransky, V. V. Rasin, "Discrete mathematics: graphs, matroids, algorithms," Moscow, M., Russia: RHD, 2001, 288 p. (In Russian).

[7] N. B. Zeliger, O. S. Chugreev, G. G. Yanovsky, "Designing networks and transmission systems for discrete messages," Moscow, M., Russia: Radio and communications, 1984, 177 p. (In Russian)

[8] Yu. M. Morozov, "Reliability of hardware and software systems," St. Petersburg, Russia: State Polytechnic University, 2011, 136 p. (In Russian)

[9] V. N. Shklyar, "Reliability of control systems," Tomsk, Russia: Publishing house of Tomsk Polytechnic University, 2009, 126 p. (In Russian)

[10] V. O. Chukanov, V. V. Gurov, E.V. Prokopyeva, "Methods of ensuring software and hardware reliability for computing

systems," Russia, Presentation of the report at the seminar, .1-44 p. Available at: http://www.mcst.ru/files/5357 ec/ dd0cd8/50af39/000000/seminar_metody_obespecheniya _apparatno-programmnoy_nadezhnosti_vychislitelnyh_ sistem.pdf (In Russian). (accessed 12.03.2019)

[11] S. M. Borovikov, S. S. Dik, N. K. Fomenko, "A method for predicting applied software tools at the early stages of their development," Reports of the Belarusian State University of Informatics and Radioelectronics. 2019, no.5, pp. 45-51.

[12] Y. Zhang et al., "Cyber-Physical Security Analytics for Transactive Energy Systems," IEEE Trans. on Smart Grid, vol. 11, no. 2, pp. 931-941, March 2020.

[13] E. Martel, R. Kariger, P.-A. Graf, "Cyber Resilience in the Electricity Ecosystem: Principles and Guidance for Boards," Geneva, Switzerland, Centre for Cybersecurity and Electricity Industry Community, January 2019, 29 p. Available at: www3.weforum.org. (accessed 19.03.2020)

[14] M. I. Uspensky, S. O. Smirnov, "The Occurrence Reasons and Countermeasures to Power System Blackouts," The International Journal of Energy Engineering, no. 1, pp.1-8, 2014.

[15] W. Li, "Risk Assessment of Power Systems: Models, Methods, and Applications," New York, NY, USA: Wiley-IEEE Press, 2005, 325 p.

[16] "Reliability evaluation of the designed FOCL," Available at: http://www.icete.ru/pegibs-567-1.html. (In Russian). (accessed 23.11.2020)

[17] V. N. Gordienko et al., "Optical telecommunication systems. Textbook for high schools," Moscow, M., Russia: Hotline - Telecom, 2011, 368 p. (In Russian)

[18] M. I. Uspensky, I. V. Kyzrodev, "Power supply restoration in distributive networks," Reliability: Theory & Applications, vol.2, no. 2, June, pp. 72-84. 2011.

Michael Igorevich Uspensky graduated from Leningrad (St. Petersburg) Polytechnic Institute in 1971. He received his Ph.D. degree in engineering from Leningrad Polytechnic Institute in 1985. At present, he is a leading scientist at the Laboratory of Power Systems. M.I. Uspensky works for the Institute for Social, Economic and Energy Problems of the North at the Komi Science Center of the Ural Branch of the Russian Academy of Sciences in Syktyvkar, Russia.

His research interests include operating control and reliability of power system facilities.