determining the channel capacity in scada systems using polling ...

DETERMINING THE CHANNEL CAPACITY IN SCADA SYSTEMS USING POLLING PROTOCOLS. Joaquín Luque, Isabel Gómez, José I. Escudero Department of Electronic Technology University of Seville

Abstract. This article presents a method for calculating the capacity of a multi-point communications channel when a polling protocol is used. Both an exact solution and an approximate but easier-to-use solution are obtained. With the results derived here, the number of remote stations that can communicate with the control center over a single channel can be determined. The analytical results are compared to the traffic results measured experimentally.

I. INTRODUCTION The use of SCADA (Supervisory Control And Data Acquisition) systems is a well-established reality in the operation of electrical power networks. Frequently these systems have a distributed structure with a star topology in which some remote stations (RTU: Remote Terminal Units) comunicate with a control center, which sends them the network status and receives the pertinent commands [1]. To reduce the connection costs for the communications required for this type of architecture, communications between the control center and each RTU is not point-to-point, but rather the control center splits several communications lines so that several remotes communicate over each one. Thus, the connection is multi-point [2]. Obviously, the greater the number of remotes that share the same communications link, the fewer total number of connections that will be required and, therefore, the lower the cost of the communications infrastructure that will be required for SCADA functions. On the other hand, however, by increasing the number of remote stations sharing a link, the time assigned to each one will be less, and thus the time required to communicate all the RTU's information will increase. The optimum number of remotes

that can share the same link thus will be that amount that gives the lowest cost (i.e. the maximum number of remotes) without violating the communication time requirementes. In practice, the calculation of this optimum number of remotes is carried out by informal, heuristic methods, often depending upon the experience of the system's designer. In this paper we will try to demonstrate a formal method for responding to the following question: how many RTU's can share a link without degrading system performance? Obviously, the answer will depend upon various parameters such as link velocity, message length, the amount of information generated by each RTU, etc. But it will also depend significantly upon the communications protocol used to communicate between the control center and the remotes [3]. In many control centers, this protocol takes a question-answer form [4] [5]. The control center polls the first remote on the link; if the remote has information to send, it does so, and if not, it sends a null message. The control center goes on the poll the second remote and so on successively until it has contacted all the remotes on the link, at which time it starts over again with the first RTU. While keeping in mind the full extent of this procedure, we will concentrate our study on a protocol such as the one described. II. GENERATING THE INFORMATION For the purposes of our study, we wi ll consider that an RTU transmits three types of information to the control center [6], two of which are done cyclically, and the third, sporadically. The first type of cyclic information (typically information about analogical and digital network measurements) we shall call "measurements", and it contains a perishable image of the electrical network; which is to say that once a certain amount of time has passed, if it has not been able to transmit, it will become invalid and will be substituted for other equivalent, but more recent, information. This type of information is by far the most common. In contrast, the second type of cyclic information (for example, commands to the remotes, control information, etc.), which we shall call

"general" messages, does not lose its validity over time and is not substituted for more recent information. Finally, we will consider that the remote is capable of generating sporadic and spontaneous messages- which we shall call "incidents"- with urgent information (usually alarms and incidents that have occurred in the network) that should be sent on to the control center as quickly as possible. Let us also consider that each RTU generates measurement messages in accordance with an exponential distribution with average Tm, or in other words, each RTU generates, on average, one measurement message every Tm seconds. Similarly, we will consider that general messages are generated exponentially in each remote with an average of Tg seconds. Finally we will assume that incident messages are very rare and do not affect normal channel traffic. Keeping all this in mind, we will state that each RTU generates messages exponentially with an average Tr, shown as

1 Tr

=

1 Tm

+

1

(1)

Tg

Fig. 1. Temporal diagram of the polling protocol.

which contains information. It is easy to deduce that the time elapsed in a response cycle with information is:

t pp =

2P Cp

+ 2 T c + 2 D p (3)

or

1 . (2) Tr= 1 1 + Tm T g III. PROTOCOL BEHAVIOR WITH LITTLE TRAFFIC The polling protocol under consideration alternates cycles of questions whose response will be a message with information, with other cycles whose response is a null message. In any case, in order to study the protocol's behavior, the following parameters must be considered: P: M:

Cp: Tc:

Dp:

Number of bits in the polling message and the null message. Number of bits in the messages with information (we will assume that they all have the same length). Capacity in bits per second (bps) of the physical link used. Switching time required to change from receiving or idle state to transmission state. Propagation delay caused by the physical medium.

In Fig. 1 these parameters can be seen in a typical example which has two cycles of null responses and one

while the null response cycle will have a duration of

t pm =

P+M Cp

+ 2 T c + 2 D p . (4)

If in a complete polling cycle to all (N) remotes on the link Np null responses and thus N-Np responses containing information are received , the total time elapsed will be

T p = N p t pp + (N - N p ) t pm . (5) Now let us see what the protocol's capacity is. We know that each remote generates on average one message with M bits every Tr seconds, meaning that the total traffic generated on a line with N remotes is N.M/Tr bps. If we initially assume that all the messages generated by the remote are finally transmitted by the protocol, which occurs when the channel has little traffic, the capacity of the protocol will obviously be

C* =

NM

(6)

Tr

and remembering that the capacity of the physical medium is CP , we can calculate the protocol's efficiency by

C * = N M . (7) * S = C p C pT r

IV. PROTOCOL BEHAVIOR: GENERAL SOLUTION k

 T p  -T   eT ∞  Tr  . (13) nc = ∑ (k - 1) k! k=2 p

The previous equation is only valid when the traffic over the channel is very low, and thus all the information generated by the RTU's can be effectively transported by the protocol. Nevertheless, when the traffic increases, the transmission of a particular message will require a longer wait, thereby forcing into action the mechanism which renews the perishable information. New measurement information is generated by an RTU before the previous data could be sent; hence this new information substitutes the old whose time limit has expired and will thus never be sent. We call this phenomenon message collision, and we will assume that it affects all the messages generated in the RTU. (This is a good approximation, since the majority of the messages generated are perishable, and only a few are general messages.) Let us now calculate the effect the collision process has on the behavior of the protocol. Each remote generates messages exponentially with an average time of Tr. This is a typically Poisson process for which we know [7] that the probability that it will generate k messages in time T is given by equation

r

This summation can be shown to equal Tp

nc = e- T + r

Tp - 1. (14) Tr

The number of messages generated by a remote and modified by the collision effect in the queue- i.e. the number of actual messages generated in interval Tp - is Tp

nre = n r - nc = 1 - e- T . (15) r

This is equivalent to saying that each remote generates an actual message every Tre seconds. This time can be related to Tr and Tp by the equation

k

 T  -T   eT ρ(k) =  T r  . (8) k! r

On average, the number of messages generated by a remote during a polling cycle to all the remotes will be ∞ k p

T =T  k ρ - (k) (9) nr = E[k] ∑   e T ∞ kr=0 T  (10) nr = ∑ k k! k =0

n re =

Substituting the Tr generation interval for the actual generation interval in the efficiency equation 1 we obtain

p

which can be shown to equal

nc = ∑ (k - 1)ρ(k) (12) k=2

S=

NM C p T re

=

NM C pT p

Tp

(1 - e- T ). (17) r

Substituting Tp for equation ¡Error!Marcador no definido. we obtain

Tp . (11) Tr

But not all the messages generated are transmitted since some of them are eliminated by collisions with others in the message queue. The average number of messages that collide and are therefore eliminated in a time period Tp is given by the following equation ∞

p r

r

nr =

Tp T Tp . _ T re = p = (16) T re n re 1 - e-TT

S=

N NM (1 - eC p [ N p t pp + (N - N p ) t pm ]

pt pp+(N - N p

Tr

)t pm

).

(18) Everything is known in this expression except Np. But if in a cycle with duration Tp, (N-Np) informational messages are transmitted, the capacity of the protocol will be

C=

(N - N p )M

approximate solution for medium traffic loads across the channel. The advantage of using the approximate solution lies in the possibility of obtaining results analytically.

(19)

Tp and the efficiency is

S=

(N - N p )M C = . (20) C p C p [ N p t pp + (N - N p ) t pm ]

The exact analytical solution for the protocol described is obtained from the solution of the system of equations formed by equations 1 and 1 which has two unknowns, S and Np. Unfortunately, this is a complex formula, which must be solved in each case by numerical methods. V. PROTOCOL SOLUTION

BEHAVIOR:

APPROXIMATE

Nevertheless, an approximation exists which is valid for a large number of applications. This approximation consists of assuming that a polling cycle to all the remotes always obtains a response containing information from all of them, i.e. that assuming that Np=0. Under these conditions 1 becomes

S′=

M C p t pm

(1 - e-

N t pm Tr

). (21)

This approximate equation of efficiency (S') will coincide with the exact solution (S) when the channel is saturated, or in other words, when it has a heavy traffic load. But, both expressions also coincide when the number of remotes is low, and thus the traffic is light. In effect, one only has to remember that for small x values, the following approximation can be made:

The protocol studied here was implemented, and different measurements of interest were taken of it. Figure 2 shows the dependence of the efficiency in relation to the number of remotes, for a set of typical parameter values (speed: 600 bps; switching time: 10 milliseconds; measurement message: 380 bits; polling message: 60 bits; propagation delay: 0.3 milliseconds; generation interval for measurement messages: 4 seconds). In this diagram the points obtained experimentally and the exact and approximate solutions can be seen, which confirm the results obtained above. VI. MEASUREMENT UPDATE CYCLE While efficiency is a valuable measurement for evaluating the capabilities of a protocol, from the user's point of view other measurements are more desirable. The first one of these tells us what the cycle is for updating the mesaurement messages. Though nominally each remote sends a measurement message every Tm seconds, due to the effect of the collisions, the actual cycle Tme could be different, especially in situations where the link is saturated. To calculate it, let us consider a time period T. The total number of messages that arrive at the control center within this interval from the N remotes, will be Nt =N.T/Tre, and the number of measurement messages Nme=N.T/Tme. Since the general messages are not affected by the collision process, the actual generation of this type of message matches the nominal amount, by which we can

1 - e-ax ≈ ax. (22) Applying this to 1 and 1, we verify that for small numbers of remotes, we can state the following :

S ≈ S′ ≈

NM

(23)

C pT r

which on the other hand matches the value of S in (7) for unsaturated channels. In summary, the approximate equation for the efficiency shown in 1 will coincide with the general solution both for low and heavy traffic situations, with some expected deviation in the

Fig. 2. Protocol efficiency.

occurs until transmission of it begins, and on the other hand, by the time used to transmit the incident from the remote to the control center. Since the incident can occur at any moment, we will assume that with a uniform distribution, the average wait time will be T1=Tp/2, where Tp was the duration of the polling question-and-answer cycle to all of the remotes. On the other hand, the time required for the transmission of an incident message from a remote to the control center will be given by

T 2 = T c + Dp +

M Cp

. (27)

Therefore, the delay in the transmission of an incident is given by

Fig. 3. Measurement refresh cycle.

state that the number of messages received by the control center in T seconds will be Ng=N.T/Tg. Obviously, Nt =Nme+Ng or expressed another way, Nme=Nt -Ng. Based on the above, the measurement refresh cycle is given by (24)

NT

NT NT 1 = = = . T me = N T N T 1 1 N me N t - N g T re T g T re T g

Di =

Tp+ + + M . (28) T c Dp 2 Cp

In the previous equation the only unknown value is Tp, which can be obtained by combining equations ¡Error!Marcador no definido. and 1. The resulting expression is (29),

(24)

Tp=

N M t pp . (29) M - S C p ( t pm - t pp )

Remembering 1 we obtain (25)

T re =

NM (25) S Cp

which, when substituted into (24) gives (26)

1

. (26) T me = S Cp - 1 N M Tg In (26) the value for efficiency (S) can be obtained from either the general or the approximate solution, according to whether greater precision or ease of calculation is preferred. Figure 3 shows the values for the measurement update cycle according to the theoretical results derived here, and are compared to the experimentally obtained results. VII. INCIDENT TRANSMISSION DELAY Let us now look at the delay in transmitting an incident. This delay is composed of, on the one hand, the average RTU wait time from the moment the incident

substituting this result, we find (30)

Di =

N M t pp M +T c + D p + . (30 2[M - S C p ( t pm - t pp )] Cp

) Here again, either the general or the approximate solution can be used for the value of efficiency (S), according to the desired objectives. Figure 4 shows both the theoretical and experimental values obtained for the incident transmission delay. VIII. CONCLUSIONS In this paper, equations have been obtained which relate the efficiency, the measurement update cycle and the incident transmission to the number of remotes on a link operated with a polling protocol. Using these results, the maximum number of remotes that can be placed on a multi-point link connected to a control center can be determined. In effect, this maximum value for the number of remotes will be that amount at which the efficiency, the

measurement update cycles and the incident transmission delays stay within the bounds of the permissible values necessary for proper network operation.

X. REFERENCES [1]

Dennis J. Gaushell and Henry T. Darlington, "Supervisory Control and Data Acquisition", Proceedings of the IEEE, vol. 75, no. 12, December 1987, pp. 1645-1658.

[2]

D.J. Gaushell and J.H. Noland, "Telecommunication Options", IEEE Tutorial Course, Fundamentals of Supervisory Systems, 1991, p.35.

[3]

Isabel Gómez, Joaquín Luque and José I. Escudero, "Medium Access Control Protocols for Electrical Power Network Control", Proceedings of the 1992 Bilkent International Conference on Lightwave Technology and Communications, Bilkent University, Ankara, Turkey, July 1992. pp. 23-29.

[4]

L.Krishnan and W. Zimmer (Editors), "Polling vs. Event Reporting. What are the Tradeoffs?", Integrated Network Management II, Elsevier Science Publishers B. V. (North-Holland), 1991, p. 339.

[5]

Prasad Raja , Guevara Noubir, Luis Ruiz, Jean Hernández and Jean-Dominique Decotigne, "Analysis of Polling Protocols for Fieldbus Networks", ACM SIGCOMM, Computer Communication Review, pp. 69-90.

[6]

H. Lee Smith and Wayne R. Block, "RTUs Slave for Supervisory Systems", IEEE Computer Applications in Power, January 1993.

[7]

Mischa Schwartz, Telecommunications Networks Protocols, Modeling and Analysis, AddisonWesley, 1988, p. 24.

Fig. 4. Incident transmission delay.

IX. BIOGRAPHIES Joaquín Luque received his degree in Industrial Engineering in 1980 and his Doctorate in Industrial Engineering in 1986 from the University of Seville (Spain). Since 1980, he has worked for several companies in the area of SCADA systems for electrical networks, participating in some of the primary EMS projects in Spain. He is currently a professor of electronic engineering at the University in Seville, and he is a member of the IEEE. Isabel Gómez received her Physics (Electronics) degree in 1989 from the University of Seville (Spain). She has been a professor of electronic engineering at the University in Seville since 1990, where she is doing research on problems in computer communications for the control of electrical power networks. José I. Escudero received his Physics degree in 1979 from the University of Seville (Spain). Since then, he has held several teaching positions. He has been a professor of electronic engineering at the University in Seville since 1989. Mr. Escudero has focused his research activity on the study of computer network performance.