A FUZZY REASONING APPROACH FOR DISTRIBUTION AUTOMATION M. Trovato, Member, IEEE G. Delvechio, nonmember
R. Bualoti, nonmember
[email protected]
[email protected] Politecnico di Bari, DEE Via E. Orabona 4, 70125 Bari-Italy Phone (39) 80-5460244 Fax (39) 80-5460410
Electrical Engineering Faculty Polytechnical University of Tirana Rr.”Qemal Stafa”, nr.476, Tirana, Albania Phone (355) 42-64150 Fax (355) 42-63854
Abstract - A new approach based in the fuzzy reasoning is proposed for the electricity service restoration in the distribution system followed a fault to minimised the out-ofservice time in out-of-service area with no overloaded components. After the location of the fault has been identified and the faulted zone has been isolated, a emergency heuristic restoration plan it was determined to restore the electricity service remote controlled for the high priority loads and manually for the ordinary loads. A proper short and long term restoration plan used the typical hourly load patterns and real-time metering of the loads on branching points is proposed in order to reach the electricity service for the ordinary loads with minimum of out-of-service time. A service restoration on the distribution system of ENEL Company is considered to illustrate the potentials of the suggested fuzzy reasoning approach. The procedure can be easily integrated in exist Distribution Dispatching Centre with a normal PC, so that a short and long term restoration plans can be reached with the available remote control very efficiently, suggesting to operators with imprecise linguistic terms the heuristic rules.
Keywords: Fuzzy reasoning approach, distribution system, electric power system, distribution automation, distribution system dispatching.
I. INTRODUCTION
In the last years, considerable attention has been placed on application of the fuzzy reasoning approach in solving the power system problems [1-13]. Several approaches for distribution system restoration have been proposed [1-10], based on heuristic search [1] or fuzzy reasoning [2,3,7]. Since the human experts play an important role in distribution system restoration, an approach based on fuzzy set theory [14] is proposed to take the heuristic rules and operators’experience into account in the process of service restoration plans. The service restoration is a problem with multiple objectives. A common approach is to select one of the objectives as the objective function and the others as the system constrains. The selection of the objective function depend from the structure of distribution system and the level of its remote control. So, in [1] as the objective function is selected “the minimal number of switching operations”, in [2] “a reasonably small number of switching operations” while in [3] “the minimum no interrupted customers”. Paper BPT99-082-23 accepted for presentation at the IEEE Power Tech’99 Conference, Budapest, Hungary, Aug 29-Sept 2, 1999.
Among the various restoration plans, we propose to select the restoration plan which satisfies the following conditions (1) Objective function The out-of service time must be minimised (2) Constraints No components will be overloaded The proposed approach is applied on the typical distribution system of ENEL in Italy. During the off-peak period, no overloads will be observed on the feeders. As a result, we will try to use the typical load patterns for implemented the restoration plan. Since the loads on SAT’s (Load Distribution Section) feeders and laterals are real-time metering and restoring at SCADA, the typical hourly (daily, monthly) load patterns and real-time system loads we can estimate. On the other hand since the SAT’s feeders and laterals are tie-switches remote controlled and the other tieswitches manually switched an alternative short and longterm restoration plan we can be reached. In the next section the proposed fuzzy reasoning approach is described. The effectiveness of the proposed fuzzy reasoning approach is demonstrated by the electricity service restoration on the future distribution system of Bari of ENEL Company. II. FORMULATION OF PROBLEM
Let’s consider a typical distribution system of ENEL in Italy (fig.1). It is noted from fig.1 that: • the distribution network is realised with tie-switches (TS) so that on can moves the open tie-switch to implement the optimal distribution switching on normal conditions and the electricity service restoration on faulted conditions; • the substation supplies the load not only directly via distribution lines (DL), but also through the SAT which is supplied via one/more primary lines (PL); • the SAT has also one/more secondary lines connected with others substations (or SAT) via a normally-open tie-switch; • the SAT is realised with double buses, as in fig.2, connected through normally-close tie-switch. At the first bus, the primary lines and ordinary loads (OL) are connected, while at the second, the secondary lines and high priority loads (HPL) as one.
Cabina Primaria Cabina MT/BT
Linee di distribuzione
Linea di alimentazione della satellite costituita da 3 cavi in parallelo
Linee di distribuzione
III. THE PROPOSED FUZZY APPROACH
Satellite
Linea di alimentazione ausiliaria
Carico prioritario
Congiuntore
Carico ordinario
From the typical residential and/or commercial load pattern (fig.3) we can see that in some hours the load level is low enough, so that the unfaulted primary lines, or the secondary lines of SAT, or both contemporaneously can supply the ordinary loads. It is noted that the operators tend to use linguistic variables for the knowledge representation. For example, they describe the load level after 5 o’clock “to increase quickly”. The fuzzy reasoning approach is employed to deal with this kind of “imprecision” as well as to use the operators experience to estimate the loads.
The fuzzy reasoning approach involves following steps: 1.Compile the heuristic rules used by operators in service restoration plans. 2.Perform fuzzy reasoning to reach the desired electricity service restoration plans in form of: • Long term restoration plan or • Short term restoration plan 1) The heuristic rules
Fig.1 The typical distribution system of ENEL
This heuristic rules will be used for fuzzy reasoning. 1 0.9
Current [pu]
When a fault occurs at one of the primary line, the circuit breaker of primary lines are tripped following the fault. The emergency heuristic restoration plan it was determined to restore electricity service of the high priority loads with remote control and manually that of the ordinary loads. So the buses tie-switch have to open and immediately secondary line’s tie-switches have to close, so to restore the electricity service of high priority loads. The electricity service of ordinary loads will be restored manually through supporting tie-switches (STS), so the restoration of ordinary loads will take a long time. The objective of the proposed service restoration is to restore the electricity service in out-of-service area minimising the out-of-service time. Among the various restoration plans, we propose to employed the hourly (daily, monthly) load patterns to supply the ordinary loads for short term restoration (during the time needed for electricity service in out-of-service area) or for long term one (during the time needed for repair faulted lines).
The following heuristic rules have been established through discussion with operators’ of Distribution Dispatching Centre as: •The radial structure of network will be keep; •The installed line current is twice the maximum of negotiated one; •A transient overload of line of about 5% is admitted (the relaying set is for 10% of overload); •An overload of substation is also admitted; •It is not admitted the long time overload; •If it was possible don’t acted the supporting tie-switches; •It is possible to switch all tie-switches of SAT, while they are remote controlled; •The error of real-time metering depend on the derive of loads; •It is very certain that the fault in another line it is improbable; •It is very certain that the voltage drop during the line it is very small while the line are very short.
4 243 primary lines
1243 ordinary loads
1 4 243
{
High priority secondary line loads
0.8 0.7 0.6 0.5 0.4
0
5
10
15
20
hours
Fig.2 The SAT’s scheme
Fig.3 A typical residential and/or commercial load pattern
µ(I)
2) The fuzzy reasoning procedures
1
The primary lines of SAT can be more then one and in the different passing way, so the possibility of the fault at only one of the primary line can be considered. For each primary faulted line, a restoration plan X can be described by the vector 1− ∆I za
X = [ x1, x2, x3, . . . . ]
and the best of restoration plan X, as well
The main restoration plans will be: 1.faulted primary lines open, the other primary lines can supply the loads; 2.faulted primary lines open, the other primary lines can supply the ordinary loads, while the high priority loads will be supplied by secondary lines; 3.all primary lines open, both high priority loads and ordinary loads will be supplied by the secondary lines. The restoration plans will be control in three different times: to - time when fault occur; t2 - time when the load will arrive maximum value (long term restoration plan) ; t1 - time when the manually restoration will be performed (short term restoration plan). The process of derivation of the electricity service restoration through fuzzy reasoning is shown in fig.4 and is explained in the following subsections. 2.1) Restoration plan at time to In the present work, the membership function for current lines, as shown in fig.5 are used. The factors ∆Ιza, ∆Izb are modified according the operators’comments. For each xi of restoration plan X, the lines current and their membership are calculated. The overall membership will be as follow ( xi )
1+ ∆I zb I= Jb / I z
Fig. 5 The membership function
Where xi is the faulted configuration to describe the states of the tie-switches with binary values 0 or 1.
[ ( xi)
1
( xi)
]
µ xi = min µJb1 , µ Jb2 , µJb3, KK
µx.to = max (µX,to) where
µX,to = [µx1 ,µx2 ,µx3 , . . .]
Two cases will be distinguish 1. µx.to = 0 no short or long term restoration plan at time to exist and the emergency restoration plan must proceed. 2. µx.to > 0 at least, exist a restoration plan at time to, xto (can be more then one), but must be analysed if it is the long term, the short term restoration plan or the very short one. 2.2) Long term restoration plan, time t2 In the present subsection, the restoration plan at time to, xto (can be more then one), will be analysed if it is a long term restoration plan. For each xto of restoration plan at time to, the line currents for the maximum negotiated loads and their membership are calculated. The factors ∆Ιza, ∆Izb of the membership function for current line are modified for this conditions, always according the operators’comments. The overall membership will be calculated in the same manner as at time to , and the maximum value µx.t2 of the best restoration plan xt2 will be established. At the other hand it will be calculated the overall membership of the emergency restoration plan y, depreciated by 0.8 (decided according the operators’ experience) µy = min[max (µy,t2), 0.8]
No, µx,to = 0 (the emergency restoration plan!) Exist No, xt2 is the short a restoration planxto at termrestoration the time to ? Yes, µ > 0 at least, No, J > Iz? plan x to , c exist a restoration Yes, the emergency planxto at time to. restoration plan (µx,t2 ≥ µy ?) Yes, xt2 is the long termrestoration plan.
Fig.4 Fuzzy reasoning approach for electricity service restoration
Also in this time two cases will be distinguish 1. µx.t2 ≥ µy then xt2 is the long term restoration plan to be reached very efficiently, suggesting to operators with imprecise linguistic terms the heuristic rules that can proceed. 2. µx.to < µy no long term restoration exist, but must be analysed if there is a short term restoration plan. 2.3. Short term restoration plan, time t1 In the present subsection, even when the long term restoration plan don’t exist we will analyse if at least, a short term restoration plan can be proposed so that the
electricity service of ordinary loads can be assured without out-of-service time. The typical hourly load patterns and real-time metering of the loads on branching points are used in order to reach the electricity service for the ordinary loads. The first step is the calculation of the line currents at time t1. The line current membership function [2] is
µ Jc (I ) =
1 I − m Jc 1+ α Jc
2
Where m is the mean value of the function (the most possible value) and α the spread of the function. We can see that µ(m ±α)=0.5 [2]. These parameters are calculated through SCADA date as follow:
TABLE 1 THE CORRESPONDENCE BETWEEN THE TYPICAL DERIVE OF CURRENT LINE AND LINGUISTIC VARIABLES
[0, 0.5[
[0.5, 0.10[
[0.10, 0.15[
[0.15, ∞ [
S
M
L
VL
On the other hand, a correspondence between the linguistic variables and numerical variable α according the operators’experience is shown in Table 2. TABLE 2 THE LINGUISTIC VARIABLES AND VARIABLE α
α
•Calculation of the parameter m From real-time metering we have the current line Jc(to) in the time to when the fault occur and from the typical hourly load patterns the current line Jo in the time to and the current line J1 in the time t1. Then the parameter m will be calculated
S
M
L
VL
0.05
0.10
0.15
0.20
And then α is calculated as
α = α ⋅m As the fuzzy value of line current is assumed the following:
J m = J c (t o ) ⋅ 1 J o
J1 J c = m + α = ( 1 + α ) ⋅m = ( 1 + α ) Jo
•Calculation of the parameter α From the typical hourly load patterns the derive of current line at the time t1 will be calculated
dJ c J c ( t 1 + ∆t c ) − J c ( t 1 − ∆t c ) ≅ dt 2∆t c where ∆tc is the sampling time of SCADA.
Derive of hourly load patterns [pu]
In fig.6 the typical derive of current line calculated from the typical hourly load patterns is shown. The derive of the current line is divided into four levels, i.e., small (S), medium (M), large (L) and very large (VL). The correspondence between their is shown in Table 1. 0.3 0.25 0.2 MG
J c ( t o ) = k ⋅J c ( t o )
or more exactly
k ⋅J c ( t o ) Jc = J c,max
if
k ⋅J c ( t o ) < J c,max
in the other case
As the fuzzy value of installed line current Iz, is assumed the same numerical value of current (α=0). The compare of the fuzzy values Jc and Iz (the compare between two fuzzy value is given in the Appendix) gives two distinguish cases: 1. Jc ≤ Iz then xt2 is the short term restoration plan, suggested to proceed so that the electricity service of ordinary loads can be assured during the time needed to act manually to supporting tie-switches. In this case also no out-of-time service will be for ordinary loads. 2. Jc > Iz no short term restoration plan exist and the emergency restoration plan must proceed.
0.15 G 0.1
IV. APPLICATIONS OF THE FUZZY REASONING APPROACH
M 0.05 P 0 0
5
10
15
20
Hours
Fig. 6 The typical derive of hourly load patterns
To examine the effectiveness of the proposed fuzzy reasoning approach, an electricity service restoration is performed on the future distribution system of Bari, Italy (ENEL Company) depicts in fig.7.
4.4 5 Mungivacca
4.4 5
Japigia
CP Bari Sud (100 MVA) 4.3
CP Bari Circonvallazione (80 MVA)
Aux
6.7
A fuzzy reasoning approach for restoration of the electricity service, minimising the out-of-service time, is proposed. A proper short and long term restoration plan used the typical hourly load patterns and real-time metering of the loads is established. A service restoration on the distribution system of ENEL Company is considered to illustrate the potentials of the suggested fuzzy reasoning approach. The procedure can be easily integrated in exist Distribution Dispatching Centre with a normal PC using the existing SCADA system.
5
Peroni Bitritto Bari sud Berera
4.5
4.4 Aux
Fiera
CP I. T. B. (70 MVA)
5.5
4.4
Aux
4
Colals
3
2
Crispi
3.7
3.7
8 Poggiofranco
Aux 6.1
2.5
2.2
Aux
6
4.8 1.8
4.8 1.8
1
All faulted primary line are open, both high priority loads and ordinary loads will be supplied by the secondary lines (long term restoration plan).
Aux
Carrassi
2
2
9.9
Arroccamento Capruzzi
7 3.8 3.8
Capruzzi
5.9
5.9 1.8
2.4
5
1.8
2.4
Arroccamento dogana
Simulation no 3 L =1 noLg = 3 to = 9
V. CONCLUSIONS
3.8
4.3 Aux Petruzzelli
Aux Massari
8.1
CP Garibaldi (80 MVA)
The faulted primary lines are open, the buses tie-switch is open, the high priority loads will be supplied by secondary lines while the unfaulted primary line can supply the ordinary loads (long term restoration plan) .
Fig.7. The future distribution system of Bari (ENEL Company) VI. REFERENCES
Through discussion with operators’the following value for the membership functions are established: at time to
at time t2
∆Iza = 0
∆Iza = 0.01
∆Ιzb = 0.05
∆Iza = 0
For two characteristic hours of load pattern: • 9 o’clock with maximum load and • 1 o’clock with minimum load, there are simulated the fault at one, two and three of primary lines. o
If we will call Lg the indication of primary lines, n Lg number of faulted lines, the result of simulation will be as follow: o
Simulation n 1 L =1 noLg = 1 to = 9 The faulted primary line is open, the other primary lines can supply the loads (long term restoration plan). o
Simulation n 2 L =1 noLg = 2 to = 9
[1] Y.Y.Hsu, H.M.Huang, H.C.Kuo, S.K.Peng, C.W.Chang, K.J.Chang, H.S.Yu, C.E.Chow and R.T.Kuo, “Distribution system service restoration using a heuristic search approach”, IEEE Trans. on Power Delivery, vol.7, pp. 734-740, 1992. [2] H.C.Kuo, Y.Y.Hsu, “Distribution system load estimation and service restoration using a fuzzy set approach”, IEEE Trans. on Power Delivery, vol.8, pp. 1950-1957, 1993. [3] Y.Y.Hsu, H.C.Kuo, “A heuristic based fuzzy reasoning approach for distribution system service restoration”, IEEE Trans. on Power Delivery, vol.9, pp. 948-953, 1994. [4] J. T. Saraiva, V. Miranda, L. M. V. G. Pinto, “Impact on some planning decisions from a fuzzy modelling of power systems”, IEEE Trans. on Power Systems, vol. 9, n° 2, pp.819-825, 1994 [5] A.Ferrero, S.Sangiovanni, E.Zappitelli, “A fuzzy-set approach to fault-type identification in digital relaying”, IEEE Trans. on Power Delivery, Vol.10, n° 1, pp.169-175, 1995. [6] S. F. Noor, J. R. McDonald, “Using fuzzy numbers in generation expansion planning”, Intelligent System Application to Power Systems, Proc. vol.1, pp. 145-151, 1994. [7] Y. Imamura, M. Kanoi, C. Fukui, H. Inoue, J. Kawakami, “Fuzzy inference application to planning of distribution network switching”, Intelligent System Application to Power Systems, Proc. vol.2, pp. 725-730, 1994.
[8] H. Ogi, Y. Takeshima, “Fuzzy user interface: its application to power system operation”, Electrical Engineering in Japan, vol. 111, n° 4, pp. 20-29,1991 [9] N. Kagan, R. N. Adams, “Electrical power distribution systems planning using fuzzy mathematical programming” Electrical Power & Energy Systems, vol. 16, n° 3, pp. 191196, 1994, [10]Y.-Y. Hsu, K.-L. Ho, “Fuzzy expert systems: an application to short-term load forecasting”, IEE Proceedings, vol. 139, n° 6, pp. 471-477, 1992.
and
[13]J. T. Saraiva, V. Miranda, L. M. V. G. Pinto, “Impact on some planning decisions from a fuzzy modelling of power systems”, IEEE Transactions on Power Systems, vol. 9, n° 2 pp. 819-825, 1994. [14]D. Dubois, H. Prade, “Fuzzy sets and systems: theory and application”, Academic Press inc., 1980 [15]T. Gönen, “Electric power distribution system engineering”, McGraw-Hill Book Company, 1987.
VII. APPENDIX Let X and Y be two fuzzy sets with membership functions respectively: µ x ( I) =
1 I − m x 2 1+ αx
I − m y 1+ αy
2
Definition 1 The union of two fuzzy sets The membership function of Z=X+Y is defined by
[11]J. Bezdek, “Fuzzy models - what are they, and why?”, IEEE Transactions on Fuzzy Systems, vol.1, n° 1, pp. 1-5, 1993. [12]A. K. David, Z. Rongda, “An expert system with fuzzy sets for optimal planning”, IEEE Transactions on Power Systems, vol. 6, n° 1, pp.59-65, 1991
1
µ y ( I) =
µ z ( I) =
where:
the variable fuzzy
1 I − m z 2 1+ αz
m z = m x + m y α = α + α x y z
Definition 2 The compare of two fuzzy sets The relation X>Y of the two variables fuzzy X and Y is possible if
m x > m y µ x ( Int ) = µ y ( Int) ≤ ε Where Int is the intersection abscise of the membership function and ε is the degree of separation (in general ε = 0.5). We can express more simply with the following relation:
mx − αx ≥ my + αy
