Abstract-- This paper pren ts an application of fuzzy logic technique to quantify the equipment voltage sag immunity level. It describes the fuzzy ts and IF-THEN inference rules involved in a process of providing an equipment immunity factor bad on equipmen t voltage toleran ce test data. Typical voltage toleran ce en velopes, such as IEEE Std. 446 an d CBEMA curves, are
exploited i
n defi
n
i
n
g the fuzzy membership fu
n
ctio
n
s
correspon din g to various class of voltage sags verity an d duration s. Usin g the equipmen t voltage sag toleran ce test data, the propod fuzzy reasoning process provides a single factor that repren ts the relative immun ity level of the tested equipmen t. Previous voltage tolerance data of personal computers are ud to test the propod method and the immunity factors distributions of the tested equipment using various fuzzy rules are prented.
Index Terms—fuzzy t, immun ity factor, toleran ce curve, voltage sag.
I. I NTRODUCTION
O extend the rvice life of their equipment and to reduce the possibilities of interference with their products’ functions, manufactures of electrical equipment recommend that rvice disturbance levels in the distribution system be limited. The International Electrotechnical Commission (IEC) and I EEE have introduced the concept of electromagnetic compatibility and according to which electrical equipment should be compatible with the quality levels of the power system [1], [2]. On the other han
d, the power rvice company has to design its power system in such a way that the voltage at the point of delivery maintains an appropriate quality so that equipment can work properly.
Many uful indices have been propod to asss power quality and power acceptability. One of the indices ud to describe the system rvice voltage quality is the system average rms (variation) frequency index (SARFI), usually written as SARFI%V. This is the number of specified short-duration rms variations per system customer. The notation “%V” refers to the bus voltage percent deviation that is counted as an event. Other power quality indices have been propod bad on calculated energy (or lack of energy) delivered during voltage sag events [3]-[6].
C. N. Lu is with Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan (e-mail: cnl@ee.nsysu.edu.tw).
C. C. Shen is with the Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan (e-mail: d8931811@student.nsysu.edu.tw).
Process control equipment is extremely nsitive to voltage disturbances. By performing voltage sag tolerance test for each piece of equipment, it is possible to determine how long it will continue to operate after the supply becomes interrupted. The same test can be done for a sag of 10% (of nomi
nal), and for 20%, etc. I f the voltage becomes high enough, the equipment will be able to operate on it indefinitely. Connecting the points from the tests results in the so-called voltage-tolerance curve. The voltage-tolerance curve is an important part of I EEE standard 1346 [2]. This standard recommends a method of comparing equipment performance with the supply power quality. The voltage-tolerance curve is recommended for prenting the equipment performance.
Electrical equipment operates best when the rms voltage is constant and equal to the nominal value. I n power system, interference inevitably occurs on some occasions and therefore there is an overlap between the distributions of disturbance and equipment immunity levels (e Fig. 1 [1]). Planning levels of the system distribution level are generally equal to or lower than the compatibility level and are specified by the owner of the distribution network. Equipment immunity levels can be specified by relevant standards or agreed upon between manufactures and urs. At most locations where most equipment operate satisfactory, there is no overlap or only a small overlap of disturbance and immunity level (e Fig. 2 [1]). Currently, there is no clear definition for the system disturbance and equipment immunity levels shown in Fig 2.
Fig. 1. Illustration of basic voltage quality concepts with time/location statistics covering the whole system [1].
V oltage Sag Immunity Factor Considering
Severity and Duration
C. N. Lu, Senior Member, IEEE and C. C. Shen, Student Member, IEEE
T
Fig. 2. Illustration of basic voltage quality concepts with time statistics relevant to one site within the whole system [1].
Fig. 3 shows the well-known Computer Business Equipment Manufacturers Association (CBEMA) curve that was recommended by CBEMA to its members. The curve is a kind of reference for equip
ment voltage tolerance as well as for verity of voltage sags. The “revid CBEMA curve” adopted by the nformation Technology ndustry Council (ITIC), the successor of CBEMA, is shown as a dashed line in Fig. 3 [3].
Fig. 3. Voltage tolerance requirements for computing equipment [3].
A standard that currently describes how to obtain voltage tolerance of equipment is I EC 61000-4-11 [7]. I t defines a number of preferred magnitudes and durations of sags for which the equipment has to be tested. The equipment does not need to be tested for all the values, but one or more of the magnitudes and durations may be chon. The preferred combinations of magnitude and duration are shown in Table 1.
TABLE I
P REFERRED M AGNITUDES AND D URATIONS FOR E QUIPMENT I MMUNITY
T ESTING A CCORDING TO IEC-61000-4-11 [7]
Duration in Cycles of 50 Hz
Magnitude 0.5 1 5 10 25 50
家长感谢老师的朴实话
70
%
40
%
0 %
While describing equipment behavior through the voltage-tolerance curve, a number of assumptions are made. The basic assumption is that sag can be uniquely characterized through its magnitude and duration. As we have en in the previous literature, the definitions of magnitude and duration of a voltage sag currently in u for tolerance tests are far from unique. So far there is no generally accepted standard for quantifying equipment voltage sag immunity level. The two-dimensional voltage-tolerance curve clearly has its limitation. An approach that extends the voltage tolerance curve idea for reprenting the relative voltage sag immunity level is propod in this paper.
II. Q UANTIFYING E QUIPMENT V OLTAGE S AG I MMUNITY L EVEL Voltage nsitivity varies depending on the manufacture, differences in equipment or applications, years-of-u, and operating
conditions, etc. I n this paper, the uncertainty of nsitive load in dealing with voltage sag events is formulated by fuzzy logic theory through membership functions that do not u strict boundaries.
I n fuzzy logic reasoning, membership function describes the degree of a certain variable belonging to a fuzzy t. This degree of membership, expresd with a number in the interval of [0,1], is a measure of proximity to that t. A membership value of 1 means that the variable is fully satisfactory for that fuzzy t, whereas a value of 0 means that it is completely unacceptable in that fuzzy t. Any deviation is acceptable with an intermediate degree of satisfaction between 0 and 1. Such feature is suitable for modeling the vagueness associated with the power quality and many engineering problems [8], [9].
To simulate the human reasoning process, IF-THEN logic rules are ud to combine membership values of fuzzy variables. All the conquences for each defined rule are aggregated to give a final value indicating the clost to the real knowledge being modeled. The following steps are generally ud to solve the practical problems [8], [9]:
1): Describe of the problem in a linguistic form.
2): Define the input and output variables for the fuzzy inference system, who range and thresholds
are bad on empirical knowledge.
3): Define the number and shape of membership functions for each input and output variables.
4): Define the IF-THEN inference rules that reprent the system practical behavior being modeled.
5): Select the fuzzy operators for the defuzzification process.
6): Tuning the fuzzy inference system.
In our application, the two input variables are the voltage sag magnitudes expresd in percentage, and duration of the event expresd in logarithm of conds. The voltage sag immunity factor that reprents the relative capability of equipment in dealing with the voltage sag problems is chon as the output variable of the fuzzy system.
In this study, the input variable membership functions are
感恩的心手抄报bad on IEC 61000-4-11 and ITIC curves. Fig. 4 and Fig. 5
show the fuzzy ts of voltage sag magnitude (verity) and duration using numbers suggested by I EC for voltage sag tolerance tests. Fig. 6 and Fig. 7 are the membership functions defined according to I TI C curve. I n order to have an even distribution of the fuzzy ts for both input variables, a combination of Fig. 4 and Fig. 7 is also tested to determine the immunity factor of the equipment under study, The fuzzy membership function of the output variable, i.e., the voltage sag immunity factor, is shown in Fig. 8.
Fig. 4. Sag duration membership function bad on IEC data.
Fig. 5. Sag magnitude membership function bad on IEC data.
软件测试自我介绍
Fig. 6. Sag duration membership function bad on ITIC curve.
Fig. 7. Sag magnitude membership function bad on ITIC curve.
安全管理计划
Fig. 8. Membership function of voltage sag immunity factor.
To reprent the behavior of the studied phenomena, agreed I F-THEN rules bad on actual operating knowledge can be ud to form the fuzzy inference mechanism. One possible t of rules t
hat can be ud in the reasoning process is shown in Table I I. Table I I shows 30 (6x5) rules. For instance, if an equipment can sustain a “ Medium” voltage sag with a “Very Long” duration then its voltage sag immunity level is “Medium”. In this study, all IF-THEN rules have the same weight, and the implication method is implemented by “product”, which scales the output fuzzy t. For each combination of the fuzzy t values corresponding to the crisp input variable data, through the reasoning process, a fuzzy t output is generated from each rule. The outputs are then aggregated. The aggregation method is “sum”, which is simply the sum of each rule’s output t. The defuzzification method is the centroid calculation, which returns the center of area under the curve. After the defuzzification, a voltage sag immunity factor corresponding to the input sag test event is obtained. Refer to [8] for a detail description of the inference operations.
TABLE II V OLTAGE S AG I MMUNITY L EVEL IF-THEN R ULES
Voltage Sag Duration Voltage Sag
Magnitude Extremely Short Very Short Short Medium Long Very Long
Very Small Low Low Low Low Medium Medium
Small Low Low Low Medium Medium Medium Medium Low Low Medium Medium Medium High Large Low Medium Medium Medium High High Very Large Medium Medium Medium High High High
As mentioned above, the voltage tolerance curve was recommended in IEEE Std. 1346 for reprenting the voltage nsitivity of equipment, therefore, it is ud in this study to determine the equipment voltage sag immunity factor. Previous test results indicate that different types of equipment have different shape of tolerance curve. Fig. 9 shows three different tolerance curves of equipment. Equipment #3 is intuitively more nsitive than the others. To asss the
equipment voltage tolerance capability, the immunity factors of the “start” (A or B) and “knee” (C or D) point(s) calculated by the propod fuzzy inference operation are averaged. As shown in Fig. 9, each point has a combination of voltage sag verity and duration, and is ud as input for fuzzy logic operations. Using the membership functions shown in Fig. 4 and Fig. 5, Fig. 6 and Fig. 7, Fig. 4 and Fig. 7 as parate groups test cas, the immunity factors corresponding to the three equipments shown in Fig. 9 are prented in Table III. From Table I I I
, it can be en that using membership functions shown in Fig. 4 and Fig. 7, it provides better results than the other two choices. It has better differentiation.
Fig. 9. Equipment tolerance curves
TABLE III乐园计划
V OLTAGE S AG I MMUNITY F ACTORS U SING D IFFERENT M EMBERSHIP F UNCTION
D EFINITIONS
Immunity Factors Equipment No. Tolerance Curve “Start” Point “Knee” Point(s) Fig. 4 & 5 Fig. 6 & 7
Fig 4 & 7 1 B- C- F B C 0.7994 0.7783 0.7994 2 A- C- F A C 0.6000 0.7783 0.6000 3 A- C- D- E A C, D 0.6000 0.6531 0.5713
III. T EST R ESULTS ON P ERSONAL C OMPUTERS
Fig. 10 shows voltage tolerance curves of 17 personal computers obtained from Japane and U.S. studies [3]. Voltage sag immunity factors of the tested PCs can be obtained from the propod the fuzzy inference system. The distribution of the immunity factors and its accumulated density function are shown in Fig. 11. It can be en that using the membership functions shown in Figures 4 and 7, and the inference rules shown in Table II, the immunity factors have a distribution similar to a normal distribution.
f a normal distribution curve is plotted usin
g the mean (0.617) and the standard deviation (0.138) of the data shown in Fig. 11, then an estimate of the immunity capability of the tested PCs can be obtained and is shown in Fig. 12. This curve can be ud to determine the average number of equipment failures due to voltage problems per year if a similar curve reprenting the power rvice quality is available.
Fig. 10. Voltage tolerance curves of the 17 tested PCs.糯米排骨
Fig. 11. The distribution of immunity factors of the tested PCs
101010
怀念姥姥Duration in cond (s)
M a g n i t u d e i n p e r c e n t
Fig. 12. Immunity factor distribution estimated for tested PCs
Different inference rules are also tested, if the rules are changed to tho shown in Table I V, then the immunity factors distribution of the PCs becomes to that shown in Fig.
13. I t can be en that the distribution skews to the right. Thus, the distribution of the immunity factors depends strongly on the design of the I F-THEN rules ud in the inference system. As long as a t of general rules are agreed, then the propod method can be ud to determine relative voltage sag immunity levels of same products from different manufacturers.
TABLE IV
D IFFERENT V OLTAG
E S AG I MMUNITY L EVEL IF-THEN R ULES
Voltage Sag Duration
Voltage Sag Magnitude Extremely
Short
Very
Short
Short Medium Long
Very
曾厝垵好玩吗Long
Very Small Low Low Low Medium Medium Medium Small Low Low Medium Medium Medium High Medium Low Medium
Medium
Medium
High High Large Medium
Medium
Medium High High High Very
Large Medium Medium High High High High Fig. 13. Immunity factors distribution of the tested PCs bad on Table IV
IV. C ONCLUSION
I n the past, equipment urs had very few help in the
determination of the appropriate voltage quality of the supply for their equipment, manufacturers’ recommendations were not so well defined and were mostly limited to long duration events. This paper propos a method of building up a single factor that reprents the relative voltage sag immunity level of an equipment. Using the IEC and IEEE recommend voltage sag verity and duration for voltage tolerance tests, the input variables membership functions are defined and veral inference rules are tested. Test results have shown that the propod factor provides a convenient way for comparing voltage sag immunity level of nsitive equipment. If a similar procedure is ud to determine the disturbance level of a power rvice environment, an average number of equipment failures due to voltage sag incidents in a period of time can then be properly assd.
V. R EFERENCES
[1] Asssment of emission limit of fluctuating load in MV and HV Power
System, IEC 61000-3-7, 1996.
[2] IEEE Recommended Practice for Evaluating Electric Power System
Comp atibility with Electronic Process, I EEE Standard 1346-1998, May 1998.
[3] Math H. J. Bollen, Understanding Power Quality Problems- Voltage Sags
and Interruptions, IEEE Press, 2000.
[4] G. T. Heydt, R. Ayyanar, R. Thallam, “Power Acceptability,” IEEE
Power Engineering Review, pp. 12-15, Sept. 2002.
[5] R. S. Thallam, and G. T. Heydt, “Power acceptability and voltage sag
indices in the three pha n,” paper prented at the Panel Session on “Power Quality: Voltage Sag I ndices in the Three Pha Sen,” I EEE PES Summer meeting, Seattle, WA, July 2000.
[6] R. S. Thallam, “Power quality indices bad on voltage sag energy
values,” Proceedings of Power Quality 2001 Conference and Exposition, Chicago, IL, Sept. 2001.
[7] Testing and measurement techniques-Voltage dip s, short interrup tions
and voltage variations immunity tests, IEC 61000-4-11, 2001-03.
[8] Tutorial on Fuzzy Logic Ap p lication in Power Systems, EEE PES
Publication No, TP140-0. Jan. 2000.
[9] B. D. Bonatto, T. Niimura, H. W. Dommel, “A Fuzzy Logic Application to
Reprent Load nsitivity to Voltage Sag,” Proceedings of 8th International Conference on Harmonics And Quality of Power, vol. 1, pp.
60-64, 1998.
VI. B IOGRAPHIES
Chan-Nan Lu received Ph.D. degree from Purdue University. He was with General Electric Co. Pittsfield, Mass., and Harris Corp. Control Division, Melbourne Fl. His current interests are in power
system operations and power quality.
Cheng-Chieh Shen received his M.S. degree from the National Sun Yat-n University. He is now pursuing his Ph.D. degree at the National Sun Yat-n University.
