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Composite power system adequacy assessment in terms of well-being
Computers and Electrical Engineering 28 (2002) 501–512 www.elsevier.com/locate/compeleceng
Composite power system adequacy assessment in terms of well-being L. Goel *, L.S. Low School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore Received 16 June 2000; received in revised form 28 October 2000; accepted 8 November 2000
Abstract This paper presents a system well-being evaluation method that divides the composite power system operating condition into several states depending on the level to which the adequacy and security constraints are satisfied. Conventional composite system reliability indices typically do not reflect the ability of the system to withstand, without resulting in load curtailment or other violations, the abrupt loss of system components. The well-being evaluation method provides an extra index for system planners or designers to decide whether or not the power system is capable, based on the deterministic criteria, to withstand unplanned outages of system components without violation of specified constraints. The well-being indices, which are the probabilities of the system being in the healthy, marginal and at risk states, provide this important and intuitively interpretable information for system planning and operations. Studies on two test systems were done to examine the effect of load levels, system component removal and addition on the wellbeing indices. The bus well-being indices for selected buses of the two test systems were also calculated and compared with the system well-being indices. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Composite systems; Well-being analysis; Adequacy assessment; Health analysis; Deterministic criteria
1. Introduction It is almost indisputable that electrical energy is an essential ingredient in the daily life and development of a modern society. Electricity customers would like their power supply to be continuously available and with good quality. There is, however, a trade-off between continuity,
*
Corresponding author. Tel.: +65-790-4542; fax: +65-791-2687. E-mail address: [email protected] (L. Goel).
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reliability and economic considerations. In addition, it is technically impossible to eliminate totally the need to remove equipment for maintenance and the possibility of unplanned equipment outages. Hence, the aim of power systems is basically to supply customers, small or large, with reasonably reliable, good quality, and continuous electrical energy as economically as possible [1]. With this, the reliability assessment of power systems becomes an important part of power system planning, evaluation and operation. Power system reliability can be defined as the probability of a system performing its required function for the period of time intended under the operating conditions encountered [2]. The currently available reliability assessment techniques can be divided into two distinct categories of deterministic and probabilistic techniques [3,4]. In general, deterministic approaches recognize specific concerns regarding certain properties of the power system and use discrete measures of the network components, such as the number of generating units, transmission lines and transformers etc., that must fail before it is considered impossible for the system to supply the load demand [5]. However, for large power systems, there are many combinations of failures that could cause interruption of supply or violations of constraints and the deterministic criteria may not be able to include all of these possibilities into consideration. Due to this and the fact that it does not take into account the stochastic nature of power systems, deterministic approaches are considered unrealistic, although they serve as convenient rules of thumb. Probabilistic approaches recognize all the possible combinations of equipment outages that would cause a violation of system constraints (computation limitations not considered) and provide more realistic system indices. Deterministic approaches are widely used by many utility companies in planning [6] as they are easier to be understood and applied. A new approach was proposed that embeds deterministic criteria into probabilistic indices in generation capacity planning and composite power system health evaluation using a well-being framework [7–9]. This approach is probabilistic in nature and provides system designers and operators with intuitively interpretable system indices. System reliability can be subdivided into two basic aspects of system adequacy and security. System adequacy assessment is concerned with steady state post outage analysis of the bulk power supply while security is basically dynamic condition analysis [8]. Indices such as the loss of load probability and expectation [10] reside in the area of adequacy assessment, as they are concerned with steady state performance of power systems. A security constrained adequacy evaluation method has been developed that includes security constraints like voltage violations, transmission line load carrying capabilities, etc., in the analysis of system health [8]. The method, combined with the approach that embeds deterministic criteria in probabilistic evaluation, provides a comprehensive approach that produces system indices that are easily interpretable, with both adequacy and security constraints taken into account [11,12]. In this method, the power system operating conditions are classified into three different states of healthy, marginal and at risk.
2. Adequacy and security constraints applied The operating limits which have to be satisfied in an operating power system are termed as the security constraints [8]. The security constraints to be applied in a study depend on the purpose behind the study. Load curtailment lies in the adequacy domain and is considered a violation. In evaluating the system indices, load curtailment at any of the buses in the system is considered a
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violation. For bus well-being indices, only load curtailed at the bus considered is counted as a violation. Composite system reliability assessment includes not just the ability of the system to meet load demand but also its ability to transfer the associated electrical energy to various load points in an acceptable fashion. Hence, in addition to load curtailment, other security constraints have to be considered as well. These include line flows, voltage magnitudes, generating unit MVAR limits constraints and split and isolated networks. The occurrence of all the above is considered to be a violation of the system constraints.
3. Classification of system operating states by contingency enumeration In system well-being analysis, the system operating states are categorized into healthy, marginal and at risk states as shown in Fig. 1. The classification of the above states depends on the extent to which the deterministic criteria and system constraints are satisfied under the power system operating conditions. Given a basic power system with specified constant load demand, the operating conditions for different outages of various system components and the base case can be examined in a straightforward fashion by direct simulation via a computer program called C O M R E L . For composite power systems the components considered are generating units and transmission lines. The composite power system is said to be residing in the healthy state when all the system constraints are satisfied, and can meet the deterministic criterion that the loss of any component considered will not result in the system constraints being violated. If the system can operate within the constraints but is unable to meet the deterministic criterion, then it is operating in the marginal state. Lastly, in the at risk state, one or more of the system constraints is violated. The detailed definition of these states can be found in Ref. [9]. The probabilities associated with the different contingencies are evaluated and the various system well-being indices can be calculated from these probabilities. Hence, the healthy, marginal, and at risk state probabilities are the probability of the composite system to be operating in the healthy, marginal and at risk state respectively. The above contingency enumeration technique is theoretically sound but not always practically feasible especially for large composite power systems. It should be noted that the complete enumeration of different contingencies for large power systems requires a lot of computation memory and time. For example, for a large system with 70 enumerable components, there are 270
Fig. 1. Composite system operating states.
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different states, including the base case, to be considered. In our studies, the C O M R E L software is used and up to fourth level outages of generating units and third level outages of transmission lines and combined generating units and line outages are considered [13]. Due to the fact that the probabilities of the operating states are not evenly distributed across the levels (that higher level outages generally have less probabilities of occurrence), the higher-level outages may not contribute much to the well-being indices. This is, however, very subjective. On the other hand, whether a certain level of contingency selection is sufficient depends very much on the size of the system under consideration. In our studies using C O M R E L , the total probability considered was generally up to 0.99997 (for the modified Roy Billinton test system (MRBTS) [15]) and 0.986 (for the IEEE-reliability test system (IEEE-RTS) [16]). For the MRBTS, since the total probability considered is very close to unity, the higher order outages can be conveniently treated as being in at risk state, and the no problem contingencies can then be treated as being in marginal state. However, this is not the case for IEEE-RTS. In the test results for the IEEE-RTS, the higher order contingencies are totally excluded. The no problem state probability [14], which is the total probability of boundary states that are not at risk, has to be stated for every test case involving IEEE-RTS.
4. Description of test systems The various studies described in this paper to illustrate the development of composite power system well-being analysis were conducted on two test systems: the MRBTS [15] and the IEEERTS [16]. The MRBTS has five buses as shown in Fig. 2. The MRBTS is modified from the original RBTS with bus 6 and the line between bus 5 and bus 6 removed. This is because the single
Fig. 2. Single line diagram of the MRBTS.
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outage of the above-mentioned line will result in an isolated bus 6, which means zero healthy state probability. The IEEE-RTS is a relatively larger power system with 24 buses in which sufficient complexity has been included. The single line diagram of the RTS is shown in Ref. [16], and is therefore not repeated here. The peak loads for the MRBTS and IEEE-RTS are 185 and 2850 MW respectively. Common-mode failures are not considered in the studies. A more detailed description of the test systems can be found in Refs. [15,16] respectively.
5. Study results The concept of well being described in the previous section is applied to both test systems and the well-being indices for both test systems were calculated – selected results are presented in this section. In each study, AC load flow was used to detect violations like voltage magnitudes and reactive power limits that cannot be detected by DC load flow. Table 1 shows the well-being indices for MRBTS and IEEE-RTS when the system load demand is constant at their respective peak levels throughout the study duration. The reason for the zero healthy state probability is that one of the lines between bus 1 and bus 3 get overloaded for the first level outage of the other line. For small systems like the MRBTS, the healthy state probability is perhaps unable to provide much information regarding the margin for which the system is able to operate before running into a marginal state, unless the base case probability (the probability of the system operating without any outage throughout the study period) is also stated. The reason for this is that the smallest healthy state probability possible is the base case probability only, which requires the base case to be in healthy state and all first level outages to be in marginal state. In the case of the MRBTS, the base case probability is 0.8046. This means that the healthy state probability is either zero or at least 0.8046. When the base case probability is stated, the healthy state probability gives a better idea of the extent to which the specific deterministic criteria could be specified and how ‘‘far’’, in terms of the components on outage, is the system away from entering marginal state. Adding an extra transmission line, increasing the line rating of the line or by other possible means, could alleviate the zero healthy state probability due to the overloaded line. The choice of the method to be used depends on the effectiveness of the method on improving the indices and the economic considerations. The well-being indices for the MRBTS when extra lines are added, are shown in Table 4 (Section 5.2). The IEEE-RTS has a higher healthy state probability of 0.3871. The base case probability is lower at 0.2305 due to the relative largeness of the size of the system compared to the MRBTS. Tables 2 and 3 show the variation of the well-being indices with the changes in system load level as a percentage of the system peak load for the MRBTS and the IEEE-RTS. Table 1 Composite system well-being indices for MRBTS and IEEE-RTS Well-being indices for MRBTS and IEEE-RTS MRBTS IEEE-RTS
Healthy
Marginal
At risk
No probability
Total probability considered
0.0 0.387095
0.989333 0.478096
0.010511 0.102927
0.000138 0.017973
0.999982 0.986091
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Table 2 System indices with changes in load levels for the MRBTS Load level (%)
Well-being indices
100 95 90 85 80 75 70
Healthy
Marginal
At risk
0.0 0.0 0.918425 0.928518 0.988924 0.989193 0.995458
0.989333 0.997427 0.080047 0.070502 0.010925 0.010685 0.004519
0.010667 0.002573 0.001528 0.000980 0.000151 0.000122 0.000023
Table 3 System indices with changes in load levels for the IEEE-RTS Load level (%)
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
100 95 90 85 80 75 70
0.387095 0.462278 0.757853 0.858623 0.893026 0.907277 0.939555
0.478095 0.454489 0.178732 0.084295 0.051347 0.036902 0.005173
0.102927 0.041678 0.015029 0.004850 0.001212 0.001165 0.00037
0.017974 0.027646 0.034477 0.038323 0.040506 0.040747 0.041326
0.986091 0.986091 0.986091 0.986091 0.986091 0.986091 0.986091
It can be seen from Table 3 that as the load level decreases, the healthy state probability increases and the marginal and at risk state probabilities decreases for both the MRBTS and the IEEE-RTS. 5.1. Effect of load level on bus well-being indices The load at some buses may be more essential than at other buses. The individual load busÕ well-being indices give an idea of how selected individual busesÕ performance is. The bus wellbeing indices are generally more ‘‘healthy’’ than the overall system indices as in this case only load curtailed at the designated bus is considered as a violation whereas load curtailed at other buses does not affect the busÕ well-being indices. System violations like overloaded lines, MVAR violations, etc., are still included in the evaluation process. By comparing the system and the various busesÕ well-being indices, the more ‘‘risky’’ buses that deteriorate the system well-being indices can be determined and appropriate action (e.g. generation addition) can be taken. The bus well-being indices of bus 3 and bus 4 of the MRBTS at different load levels are shown in Fig. 3. An extra line between bus 1 and bus 3 is added to the MRBTS so that the healthy state probability for the buses will not be zero (see section above). It can be seen that the healthy state probability for bus 3 is generally higher than that of bus 4 across the load levels considered. At the same time, the at risk state probability of bus 3 is lower than that of bus 4 over the same load levels. This indicates that other system violations being the
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Fig. 3. Variation of bus and system well-being indices with load level for MRBTS.
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same, load is curtailed more often at bus 4 than at bus 3 at all load levels considered. Also, the system healthy state probability for the MRBTS with line [1,3] added is 0.8529, which is only slightly lower than the corresponding value for bus 4. This shows that bus 4 is a relatively more ‘‘risky’’ load point in the system and appropriate safety measures can be taken to improve the well-being indices, if required. Similar tests were performed on the IEEE-RTS and four selected bus (5, 9, 15, 20) well-being indices are as shown in Fig. 4. From Fig. 4, it can be seen that bus 15 is more ‘‘risky’’ than other buses across the specified load levels, and bus 20 is the least ‘‘risky’’ bus among the four buses considered here. Similar tests can be performed on the other remaining buses to analyze the indices so that appropriate actions can be taken.
5.2. Effect of selected line addition and removal on system well-being indices The strategy of adding lines to alleviate or improve well-being indices can be extremely costly especially when the line that has to be added stretches over a long distance. Also, adding lines can have different effects on power systems of different sizes. With regard to the well-being indices, the addition of lines that could alleviate risk caused by lower level outages will result in a relatively larger improvement in the well-being indices. However, adding extra lines in most cases for the MRBTS and the IEEE-RTS does not improve the system well-being indices in any significant manner, except in the case of adding line [1,3] to the MRBTS, which increases the healthy state probability from 0.0 to 0.854255. It should be noted that line addition is aimed primarily at alleviating overloading of lines. If there are fewer lower level contingencies that would result in overloaded lines, then the addition of lines will not be very effective in improving the well-being indices. The effect of removal of selected lines on the well-being indices of IEEE-RTS was also investigated and the results are shown in Table 4. The system indices were calculated at 80% peak load level. The original well-being indices at the designated load level of 80% peak level with no line removed are shown in Table 2. As can be seen, the removal of the selected lines generally results in a deterioration of the indices. The removal of some lines even results in zero healthy state probability. This is always the case when a bus is connected to only one line when a certain line is removed. If a bus were connected to only one line, the single outage of that line would result in the isolation of the bus. Load will have to be shed if the generation in that bus is not sufficient. The removal of lines also decreases the healthy state probability quite significantly. However, the largest deterioration of the indices comes from the increase of the at risk state probability. The original at risk state probability was increased from 0.000151 (from Table 2) to at least 0.001210 (from Table 4). The removal of line [14,16] even resulted in an at risk state probability of 0.007934. The total probability considered changes as lines are added to or removed from the original IEEE-RTS. The comparisons between the effects of removal and addition of different lines have to be made with the total probability considered as a parameter. As only one line is added in each case, the total probability considered does not change much and stays quite constant at the level 0.986 for each case, which made the comparison possible.
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Fig. 4. Variation of bus and system well-being indices with load level for IEEE-RTS.
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Table 4 Well-being indices for the IEEE-RTS with different lines removed Line removed from system
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
Line Line Line Line Line Line Line Line Line Line Line Line
0.901193 0.0 0.0 0.0 0.909654 0.895486 0.897454 0.830917 0.0 0.0 0.911623 0.888662
0.043338 0.944303 0.943874 0.943824 0.035353 0.049522 0.047549 0.113665 0.938600 0.943626 0.032858 0.055423
0.001212 0.001605 0.001641 0.002382 0.001210 0.001215 0.001298 0.001345 0.007934 0.002301 0.001390 0.001737
0.040414 0.040240 0.040204 0.039968 0.040138 0.040132 0.040049 0.040263 0.039629 0.040242 0.040286 0.040334
0.986157 0.986148 0.985719 0.986174 0.986355 0.986355 0.986350 0.986190 0.986163 0.986169 0.986157 0.986156
[1,2] [1,5] [2,4] [2,6] [9,11] [10,11] [10,12] [12,23] [14,16] [15,21] [17,22] [21,22]
5.3. Effect of selected generating unit removal and addition on system well-being indices Some amount of generation can be shut down for generating unit maintenance or can serve as spinning reserves when the system load demand is at off-peak level. The effects of removing various generating units for maintenance, assuming two-state models for the generators [10], during off-peak load level are considered in this section. The IEEE-RTS system is used for the tests and the load level is fixed at 70% of the system peak level. Table 5 shows the study results of system indices with selected single generator removals. The details of the units can be found in Ref. [16], and are summarized here in Table 6. The effect of generating unit addition/removal on the indices is unpredictable, although generally, the higher the rating of the generating unit removed, the more the system well-being indices are affected. Addition or starting up of generating units can be used to improve the system well-being indices during high load levels. The effect of adding different generators at various buses in the IEEE-RTS on the system well-being indices is examined here. Table 7 shows the selected study results. The tests were performed at the peak load level of 2850 MW. It can be seen that the addition of generator #211 increases the healthy state probability and reduces the at risk state probability most significantly, followed by generator #181 and generator Table 5 Well-being indices for the IEEE-RTS with different generating units removed Unit removed from system
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
Generator Generator Generator Generator Generator Generator Generator
0.782406 0.819608 0.755635 0.803074 0.793817 0.742703 0.785125
0.197902 0.127325 0.192976 0.146092 0.154916 0.204805 0.170038
0.002313 0.000895 0.003117 0.000344 0.000919 0.002518 0.002505
0.003876 0.039089 0.036244 0.038115 0.037933 0.037599 0.032384
0.986497 0.986917 0.987972 0.987625 0.987585 0.987625 0.990052
#221 #151 #131 #71 #231 #161 #211
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Table 6 Information of selected generating units in the IEEE-RTS Generating unit
Location (Bus)
Number
Rating (MW)
Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator
Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus
6 5 1 3 3 2 1 2 1 1 1
50 12 155 197 100 155 350 76 400 155 400
#221 #151 #156 #131 #71 #231 #233 #23 #181 #161 #211
22 15 15 13 7 23 23 2 18 16 21
Table 7 Well-being indices for IEEE-RTS with different generating units added Unit added to system
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
Generator Generator Generator Generator Generator Generator Generator Generator Generator
0.413614 0.584111 0.439098 0.408485 0.584610 0.434357 0.597536 0.585228 0.630290
0.470546 0.328716 0.472206 0.463465 0.339782 0.458129 0.327182 0.354601 0.293621
0.078997 0.041204 0.041512 0.090128 0.020512 0.068808 0.015572 0.014204 0.014469
0.021328 0.030445 0.031284 0.022399 0.038043 0.023979 0.041156 0.030444 0.042066
0.984485 0.984476 0.984100 0.984477 0.982947 0.985273 0.981446 0.984477 0.981446
#221 #156 #131 #71 #233 #23 #181 #161 #211
#161. Generators #181 and #211 have the highest rating of 400 MW. It is apparent again that the addition of a generator with higher rating will result in the most significant improvement in the well-being indices. If the topology of the system is not considered, this will always be the case. In composite systems, however, the ability of the system to transfer the required electrical energy to the appropriate load buses is taken into consideration as well, and the effect of adding generators should be considered together with the configuration of the components in the composite system. 6. Conclusions A method that incorporates the conventional deterministic criteria into the probabilistic approach to evaluate the reliability of composite generation and transmission systems is illustrated in this paper. The method divides the operating conditions of a composite power system into three domains of healthy, marginal and at risk. The various state probabilities can be quantified by a contingency enumeration technique. Based on the specified deterministic criterion, the approach allows more insight into the well being of the composite system in addition to the conventional system risk index. The concept is applied to two separate test systems, the MRBTS and the
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IEEE-RTS. Studies were performed to obtain the well-being indices for these systems and the relationships between system and bus well-being indices were briefly addressed. Tests were also performed to examine the effect of the removal and addition of various system components on the well-being indices, and study results show that component additions/removals can have a marked inconsistent impact on the system well-being. References [1] IEEE Task Force on Predictive Indices. Bulk system reliability – predictive indices. IEEE Trans Power Syst 1990;5(4):1204–13. [2] Billinton R, Allan RN. Power system reliability in perspective. IEE Electron Power, 1984, p. 231–6. [3] Eua-Arpon B, Cory BJ. The application of deterministic and probabilistic methodologies to spinning reserve policy in thermal generation scheduling. IFAC Control Power Plans Power Systems, Munich, Germany, 1992. [4] Wang L, Gallyas K, Tsai DT. Reliability assessment in operational planning for large hydro-thermal generation systems. IEEE Trans Power Appar Syst 1985;PAS-104(12):3382–7. [5] Billinton R, Aboreshaid S, Fotuhi-Firuzabad M. Well-being analysis for HVDC transmission systems. IEEE Trans Power Syst 1997;12(2):913–8. [6] Vojdani AF, Williams RD, et al. Experience with applications of reliability and value of service analysis in system planning. IEEE Trans Power Syst 1996;11(3):1489–96. [7] Billinton R, Fotuhi-Firuzabad M. A basic framework for generating system operating health analysis. IEEE Trans Power Syst 1994;9(3):1610–7. [8] Billinton R, Khan E. A security based approach to composite power system reliability evaluation. IEEE Trans Power Syst 1992;PWRS-7(1):65–71. [9] Billinton R, Lian G. Composite power system health analysis using a security constraint adequacy evaluation procedure. IEEE Trans Power Syst 1993;9(2):936–41. [10] Billinton R, Allan RN. Reliability assessment of large electric power systems. Boston: Kluwer Academic Publishers; 1988. [11] IEEE Task Force on Bulk Power System Reliability. Bulk power system reliability concepts and applications. IEEE Trans Power Syst 1988;3(1):109–17. [12] Leita De Silva AM, Endrenyi J, Wang L. Integrated treatment of adequacy and security in bulk power system reliability evaluations. IEEE Trans Appl Supercond 1993;3(1):275–85. [13] C O M R E L UserÕs Manual. Power Math Associates, Inc., August 1995. [14] Khan E. Bulk load points reliability evaluation using a security based model. IEEE Trans Power Syst 1997;13(2):456–61. [15] Billinton R, Kumar S, et al. A reliability test system for educational purposes – basic data. IEEE Trans Power Syst 1989;PWRS-3(4):1238–44. [16] IEEE Committee Report. IEEE reliability test system. IEEE Trans Power Appar Syst 1979;PAS-98(6):2047–54. Lalit Goel was born in New Delhi, India, in 1960. He obtained his B.Tech. degree in electrical engineering from the Regional Engineering College, Warangal, India in 1983. He obtained his M.Sc. and Ph.D. degrees in electrical engineering from the University of Saskatchewan, Canada, in 1988 and 1991 respectively. His main research interests are power system planning and reliability cost/ benefit evaluation of electric power systems. He joined the School of EEE at the Nanyang Technological University, Singapore in 1991 where he is presently an associate professor. Dr. Goel is a senior member of the IEEE. He received the 1997 Teacher of the Year Award for the School of EEE, Nanyang Technological University, Singapore. Dr. Goel was the Organizing Chairman of the 1998 IEEE EMPD Conference in Singapore. He was also the Vice-Chairman of the IEEE Power Engineering SocietyÕs Winter Meeting 2000 held in Singapore in January, 2000. Dr. Goel received the IEEE Power Engineering Society Power Chapter SingaporeÕs Outstanding Engineer Award, 2000. L.S. Low obtained his B. Eng. in Electrical Engineering from Nanyang Technological University (Singapore) in 1999. He is currently studying for his M. Eng. in Electrical Engineering at the Nanyang Technological University (Singapore).
Composite power system adequacy assessment in terms of well-being L. Goel *, L.S. Low School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore Received 16 June 2000; received in revised form 28 October 2000; accepted 8 November 2000
Abstract This paper presents a system well-being evaluation method that divides the composite power system operating condition into several states depending on the level to which the adequacy and security constraints are satisfied. Conventional composite system reliability indices typically do not reflect the ability of the system to withstand, without resulting in load curtailment or other violations, the abrupt loss of system components. The well-being evaluation method provides an extra index for system planners or designers to decide whether or not the power system is capable, based on the deterministic criteria, to withstand unplanned outages of system components without violation of specified constraints. The well-being indices, which are the probabilities of the system being in the healthy, marginal and at risk states, provide this important and intuitively interpretable information for system planning and operations. Studies on two test systems were done to examine the effect of load levels, system component removal and addition on the wellbeing indices. The bus well-being indices for selected buses of the two test systems were also calculated and compared with the system well-being indices. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Composite systems; Well-being analysis; Adequacy assessment; Health analysis; Deterministic criteria
1. Introduction It is almost indisputable that electrical energy is an essential ingredient in the daily life and development of a modern society. Electricity customers would like their power supply to be continuously available and with good quality. There is, however, a trade-off between continuity,
*
Corresponding author. Tel.: +65-790-4542; fax: +65-791-2687. E-mail address: [email protected] (L. Goel).
0045-7906/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 5 - 7 9 0 6 ( 0 1 ) 0 0 0 0 3 - 9
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reliability and economic considerations. In addition, it is technically impossible to eliminate totally the need to remove equipment for maintenance and the possibility of unplanned equipment outages. Hence, the aim of power systems is basically to supply customers, small or large, with reasonably reliable, good quality, and continuous electrical energy as economically as possible [1]. With this, the reliability assessment of power systems becomes an important part of power system planning, evaluation and operation. Power system reliability can be defined as the probability of a system performing its required function for the period of time intended under the operating conditions encountered [2]. The currently available reliability assessment techniques can be divided into two distinct categories of deterministic and probabilistic techniques [3,4]. In general, deterministic approaches recognize specific concerns regarding certain properties of the power system and use discrete measures of the network components, such as the number of generating units, transmission lines and transformers etc., that must fail before it is considered impossible for the system to supply the load demand [5]. However, for large power systems, there are many combinations of failures that could cause interruption of supply or violations of constraints and the deterministic criteria may not be able to include all of these possibilities into consideration. Due to this and the fact that it does not take into account the stochastic nature of power systems, deterministic approaches are considered unrealistic, although they serve as convenient rules of thumb. Probabilistic approaches recognize all the possible combinations of equipment outages that would cause a violation of system constraints (computation limitations not considered) and provide more realistic system indices. Deterministic approaches are widely used by many utility companies in planning [6] as they are easier to be understood and applied. A new approach was proposed that embeds deterministic criteria into probabilistic indices in generation capacity planning and composite power system health evaluation using a well-being framework [7–9]. This approach is probabilistic in nature and provides system designers and operators with intuitively interpretable system indices. System reliability can be subdivided into two basic aspects of system adequacy and security. System adequacy assessment is concerned with steady state post outage analysis of the bulk power supply while security is basically dynamic condition analysis [8]. Indices such as the loss of load probability and expectation [10] reside in the area of adequacy assessment, as they are concerned with steady state performance of power systems. A security constrained adequacy evaluation method has been developed that includes security constraints like voltage violations, transmission line load carrying capabilities, etc., in the analysis of system health [8]. The method, combined with the approach that embeds deterministic criteria in probabilistic evaluation, provides a comprehensive approach that produces system indices that are easily interpretable, with both adequacy and security constraints taken into account [11,12]. In this method, the power system operating conditions are classified into three different states of healthy, marginal and at risk.
2. Adequacy and security constraints applied The operating limits which have to be satisfied in an operating power system are termed as the security constraints [8]. The security constraints to be applied in a study depend on the purpose behind the study. Load curtailment lies in the adequacy domain and is considered a violation. In evaluating the system indices, load curtailment at any of the buses in the system is considered a
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violation. For bus well-being indices, only load curtailed at the bus considered is counted as a violation. Composite system reliability assessment includes not just the ability of the system to meet load demand but also its ability to transfer the associated electrical energy to various load points in an acceptable fashion. Hence, in addition to load curtailment, other security constraints have to be considered as well. These include line flows, voltage magnitudes, generating unit MVAR limits constraints and split and isolated networks. The occurrence of all the above is considered to be a violation of the system constraints.
3. Classification of system operating states by contingency enumeration In system well-being analysis, the system operating states are categorized into healthy, marginal and at risk states as shown in Fig. 1. The classification of the above states depends on the extent to which the deterministic criteria and system constraints are satisfied under the power system operating conditions. Given a basic power system with specified constant load demand, the operating conditions for different outages of various system components and the base case can be examined in a straightforward fashion by direct simulation via a computer program called C O M R E L . For composite power systems the components considered are generating units and transmission lines. The composite power system is said to be residing in the healthy state when all the system constraints are satisfied, and can meet the deterministic criterion that the loss of any component considered will not result in the system constraints being violated. If the system can operate within the constraints but is unable to meet the deterministic criterion, then it is operating in the marginal state. Lastly, in the at risk state, one or more of the system constraints is violated. The detailed definition of these states can be found in Ref. [9]. The probabilities associated with the different contingencies are evaluated and the various system well-being indices can be calculated from these probabilities. Hence, the healthy, marginal, and at risk state probabilities are the probability of the composite system to be operating in the healthy, marginal and at risk state respectively. The above contingency enumeration technique is theoretically sound but not always practically feasible especially for large composite power systems. It should be noted that the complete enumeration of different contingencies for large power systems requires a lot of computation memory and time. For example, for a large system with 70 enumerable components, there are 270
Fig. 1. Composite system operating states.
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different states, including the base case, to be considered. In our studies, the C O M R E L software is used and up to fourth level outages of generating units and third level outages of transmission lines and combined generating units and line outages are considered [13]. Due to the fact that the probabilities of the operating states are not evenly distributed across the levels (that higher level outages generally have less probabilities of occurrence), the higher-level outages may not contribute much to the well-being indices. This is, however, very subjective. On the other hand, whether a certain level of contingency selection is sufficient depends very much on the size of the system under consideration. In our studies using C O M R E L , the total probability considered was generally up to 0.99997 (for the modified Roy Billinton test system (MRBTS) [15]) and 0.986 (for the IEEE-reliability test system (IEEE-RTS) [16]). For the MRBTS, since the total probability considered is very close to unity, the higher order outages can be conveniently treated as being in at risk state, and the no problem contingencies can then be treated as being in marginal state. However, this is not the case for IEEE-RTS. In the test results for the IEEE-RTS, the higher order contingencies are totally excluded. The no problem state probability [14], which is the total probability of boundary states that are not at risk, has to be stated for every test case involving IEEE-RTS.
4. Description of test systems The various studies described in this paper to illustrate the development of composite power system well-being analysis were conducted on two test systems: the MRBTS [15] and the IEEERTS [16]. The MRBTS has five buses as shown in Fig. 2. The MRBTS is modified from the original RBTS with bus 6 and the line between bus 5 and bus 6 removed. This is because the single
Fig. 2. Single line diagram of the MRBTS.
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outage of the above-mentioned line will result in an isolated bus 6, which means zero healthy state probability. The IEEE-RTS is a relatively larger power system with 24 buses in which sufficient complexity has been included. The single line diagram of the RTS is shown in Ref. [16], and is therefore not repeated here. The peak loads for the MRBTS and IEEE-RTS are 185 and 2850 MW respectively. Common-mode failures are not considered in the studies. A more detailed description of the test systems can be found in Refs. [15,16] respectively.
5. Study results The concept of well being described in the previous section is applied to both test systems and the well-being indices for both test systems were calculated – selected results are presented in this section. In each study, AC load flow was used to detect violations like voltage magnitudes and reactive power limits that cannot be detected by DC load flow. Table 1 shows the well-being indices for MRBTS and IEEE-RTS when the system load demand is constant at their respective peak levels throughout the study duration. The reason for the zero healthy state probability is that one of the lines between bus 1 and bus 3 get overloaded for the first level outage of the other line. For small systems like the MRBTS, the healthy state probability is perhaps unable to provide much information regarding the margin for which the system is able to operate before running into a marginal state, unless the base case probability (the probability of the system operating without any outage throughout the study period) is also stated. The reason for this is that the smallest healthy state probability possible is the base case probability only, which requires the base case to be in healthy state and all first level outages to be in marginal state. In the case of the MRBTS, the base case probability is 0.8046. This means that the healthy state probability is either zero or at least 0.8046. When the base case probability is stated, the healthy state probability gives a better idea of the extent to which the specific deterministic criteria could be specified and how ‘‘far’’, in terms of the components on outage, is the system away from entering marginal state. Adding an extra transmission line, increasing the line rating of the line or by other possible means, could alleviate the zero healthy state probability due to the overloaded line. The choice of the method to be used depends on the effectiveness of the method on improving the indices and the economic considerations. The well-being indices for the MRBTS when extra lines are added, are shown in Table 4 (Section 5.2). The IEEE-RTS has a higher healthy state probability of 0.3871. The base case probability is lower at 0.2305 due to the relative largeness of the size of the system compared to the MRBTS. Tables 2 and 3 show the variation of the well-being indices with the changes in system load level as a percentage of the system peak load for the MRBTS and the IEEE-RTS. Table 1 Composite system well-being indices for MRBTS and IEEE-RTS Well-being indices for MRBTS and IEEE-RTS MRBTS IEEE-RTS
Healthy
Marginal
At risk
No probability
Total probability considered
0.0 0.387095
0.989333 0.478096
0.010511 0.102927
0.000138 0.017973
0.999982 0.986091
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Table 2 System indices with changes in load levels for the MRBTS Load level (%)
Well-being indices
100 95 90 85 80 75 70
Healthy
Marginal
At risk
0.0 0.0 0.918425 0.928518 0.988924 0.989193 0.995458
0.989333 0.997427 0.080047 0.070502 0.010925 0.010685 0.004519
0.010667 0.002573 0.001528 0.000980 0.000151 0.000122 0.000023
Table 3 System indices with changes in load levels for the IEEE-RTS Load level (%)
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
100 95 90 85 80 75 70
0.387095 0.462278 0.757853 0.858623 0.893026 0.907277 0.939555
0.478095 0.454489 0.178732 0.084295 0.051347 0.036902 0.005173
0.102927 0.041678 0.015029 0.004850 0.001212 0.001165 0.00037
0.017974 0.027646 0.034477 0.038323 0.040506 0.040747 0.041326
0.986091 0.986091 0.986091 0.986091 0.986091 0.986091 0.986091
It can be seen from Table 3 that as the load level decreases, the healthy state probability increases and the marginal and at risk state probabilities decreases for both the MRBTS and the IEEE-RTS. 5.1. Effect of load level on bus well-being indices The load at some buses may be more essential than at other buses. The individual load busÕ well-being indices give an idea of how selected individual busesÕ performance is. The bus wellbeing indices are generally more ‘‘healthy’’ than the overall system indices as in this case only load curtailed at the designated bus is considered as a violation whereas load curtailed at other buses does not affect the busÕ well-being indices. System violations like overloaded lines, MVAR violations, etc., are still included in the evaluation process. By comparing the system and the various busesÕ well-being indices, the more ‘‘risky’’ buses that deteriorate the system well-being indices can be determined and appropriate action (e.g. generation addition) can be taken. The bus well-being indices of bus 3 and bus 4 of the MRBTS at different load levels are shown in Fig. 3. An extra line between bus 1 and bus 3 is added to the MRBTS so that the healthy state probability for the buses will not be zero (see section above). It can be seen that the healthy state probability for bus 3 is generally higher than that of bus 4 across the load levels considered. At the same time, the at risk state probability of bus 3 is lower than that of bus 4 over the same load levels. This indicates that other system violations being the
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Fig. 3. Variation of bus and system well-being indices with load level for MRBTS.
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same, load is curtailed more often at bus 4 than at bus 3 at all load levels considered. Also, the system healthy state probability for the MRBTS with line [1,3] added is 0.8529, which is only slightly lower than the corresponding value for bus 4. This shows that bus 4 is a relatively more ‘‘risky’’ load point in the system and appropriate safety measures can be taken to improve the well-being indices, if required. Similar tests were performed on the IEEE-RTS and four selected bus (5, 9, 15, 20) well-being indices are as shown in Fig. 4. From Fig. 4, it can be seen that bus 15 is more ‘‘risky’’ than other buses across the specified load levels, and bus 20 is the least ‘‘risky’’ bus among the four buses considered here. Similar tests can be performed on the other remaining buses to analyze the indices so that appropriate actions can be taken.
5.2. Effect of selected line addition and removal on system well-being indices The strategy of adding lines to alleviate or improve well-being indices can be extremely costly especially when the line that has to be added stretches over a long distance. Also, adding lines can have different effects on power systems of different sizes. With regard to the well-being indices, the addition of lines that could alleviate risk caused by lower level outages will result in a relatively larger improvement in the well-being indices. However, adding extra lines in most cases for the MRBTS and the IEEE-RTS does not improve the system well-being indices in any significant manner, except in the case of adding line [1,3] to the MRBTS, which increases the healthy state probability from 0.0 to 0.854255. It should be noted that line addition is aimed primarily at alleviating overloading of lines. If there are fewer lower level contingencies that would result in overloaded lines, then the addition of lines will not be very effective in improving the well-being indices. The effect of removal of selected lines on the well-being indices of IEEE-RTS was also investigated and the results are shown in Table 4. The system indices were calculated at 80% peak load level. The original well-being indices at the designated load level of 80% peak level with no line removed are shown in Table 2. As can be seen, the removal of the selected lines generally results in a deterioration of the indices. The removal of some lines even results in zero healthy state probability. This is always the case when a bus is connected to only one line when a certain line is removed. If a bus were connected to only one line, the single outage of that line would result in the isolation of the bus. Load will have to be shed if the generation in that bus is not sufficient. The removal of lines also decreases the healthy state probability quite significantly. However, the largest deterioration of the indices comes from the increase of the at risk state probability. The original at risk state probability was increased from 0.000151 (from Table 2) to at least 0.001210 (from Table 4). The removal of line [14,16] even resulted in an at risk state probability of 0.007934. The total probability considered changes as lines are added to or removed from the original IEEE-RTS. The comparisons between the effects of removal and addition of different lines have to be made with the total probability considered as a parameter. As only one line is added in each case, the total probability considered does not change much and stays quite constant at the level 0.986 for each case, which made the comparison possible.
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Fig. 4. Variation of bus and system well-being indices with load level for IEEE-RTS.
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Table 4 Well-being indices for the IEEE-RTS with different lines removed Line removed from system
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
Line Line Line Line Line Line Line Line Line Line Line Line
0.901193 0.0 0.0 0.0 0.909654 0.895486 0.897454 0.830917 0.0 0.0 0.911623 0.888662
0.043338 0.944303 0.943874 0.943824 0.035353 0.049522 0.047549 0.113665 0.938600 0.943626 0.032858 0.055423
0.001212 0.001605 0.001641 0.002382 0.001210 0.001215 0.001298 0.001345 0.007934 0.002301 0.001390 0.001737
0.040414 0.040240 0.040204 0.039968 0.040138 0.040132 0.040049 0.040263 0.039629 0.040242 0.040286 0.040334
0.986157 0.986148 0.985719 0.986174 0.986355 0.986355 0.986350 0.986190 0.986163 0.986169 0.986157 0.986156
[1,2] [1,5] [2,4] [2,6] [9,11] [10,11] [10,12] [12,23] [14,16] [15,21] [17,22] [21,22]
5.3. Effect of selected generating unit removal and addition on system well-being indices Some amount of generation can be shut down for generating unit maintenance or can serve as spinning reserves when the system load demand is at off-peak level. The effects of removing various generating units for maintenance, assuming two-state models for the generators [10], during off-peak load level are considered in this section. The IEEE-RTS system is used for the tests and the load level is fixed at 70% of the system peak level. Table 5 shows the study results of system indices with selected single generator removals. The details of the units can be found in Ref. [16], and are summarized here in Table 6. The effect of generating unit addition/removal on the indices is unpredictable, although generally, the higher the rating of the generating unit removed, the more the system well-being indices are affected. Addition or starting up of generating units can be used to improve the system well-being indices during high load levels. The effect of adding different generators at various buses in the IEEE-RTS on the system well-being indices is examined here. Table 7 shows the selected study results. The tests were performed at the peak load level of 2850 MW. It can be seen that the addition of generator #211 increases the healthy state probability and reduces the at risk state probability most significantly, followed by generator #181 and generator Table 5 Well-being indices for the IEEE-RTS with different generating units removed Unit removed from system
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
Generator Generator Generator Generator Generator Generator Generator
0.782406 0.819608 0.755635 0.803074 0.793817 0.742703 0.785125
0.197902 0.127325 0.192976 0.146092 0.154916 0.204805 0.170038
0.002313 0.000895 0.003117 0.000344 0.000919 0.002518 0.002505
0.003876 0.039089 0.036244 0.038115 0.037933 0.037599 0.032384
0.986497 0.986917 0.987972 0.987625 0.987585 0.987625 0.990052
#221 #151 #131 #71 #231 #161 #211
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Table 6 Information of selected generating units in the IEEE-RTS Generating unit
Location (Bus)
Number
Rating (MW)
Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator
Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus
6 5 1 3 3 2 1 2 1 1 1
50 12 155 197 100 155 350 76 400 155 400
#221 #151 #156 #131 #71 #231 #233 #23 #181 #161 #211
22 15 15 13 7 23 23 2 18 16 21
Table 7 Well-being indices for IEEE-RTS with different generating units added Unit added to system
Well-being indices Healthy
Marginal
At risk
No probability
Total probability considered
Generator Generator Generator Generator Generator Generator Generator Generator Generator
0.413614 0.584111 0.439098 0.408485 0.584610 0.434357 0.597536 0.585228 0.630290
0.470546 0.328716 0.472206 0.463465 0.339782 0.458129 0.327182 0.354601 0.293621
0.078997 0.041204 0.041512 0.090128 0.020512 0.068808 0.015572 0.014204 0.014469
0.021328 0.030445 0.031284 0.022399 0.038043 0.023979 0.041156 0.030444 0.042066
0.984485 0.984476 0.984100 0.984477 0.982947 0.985273 0.981446 0.984477 0.981446
#221 #156 #131 #71 #233 #23 #181 #161 #211
#161. Generators #181 and #211 have the highest rating of 400 MW. It is apparent again that the addition of a generator with higher rating will result in the most significant improvement in the well-being indices. If the topology of the system is not considered, this will always be the case. In composite systems, however, the ability of the system to transfer the required electrical energy to the appropriate load buses is taken into consideration as well, and the effect of adding generators should be considered together with the configuration of the components in the composite system. 6. Conclusions A method that incorporates the conventional deterministic criteria into the probabilistic approach to evaluate the reliability of composite generation and transmission systems is illustrated in this paper. The method divides the operating conditions of a composite power system into three domains of healthy, marginal and at risk. The various state probabilities can be quantified by a contingency enumeration technique. Based on the specified deterministic criterion, the approach allows more insight into the well being of the composite system in addition to the conventional system risk index. The concept is applied to two separate test systems, the MRBTS and the
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IEEE-RTS. Studies were performed to obtain the well-being indices for these systems and the relationships between system and bus well-being indices were briefly addressed. Tests were also performed to examine the effect of the removal and addition of various system components on the well-being indices, and study results show that component additions/removals can have a marked inconsistent impact on the system well-being. References [1] IEEE Task Force on Predictive Indices. Bulk system reliability – predictive indices. IEEE Trans Power Syst 1990;5(4):1204–13. [2] Billinton R, Allan RN. Power system reliability in perspective. IEE Electron Power, 1984, p. 231–6. [3] Eua-Arpon B, Cory BJ. The application of deterministic and probabilistic methodologies to spinning reserve policy in thermal generation scheduling. IFAC Control Power Plans Power Systems, Munich, Germany, 1992. [4] Wang L, Gallyas K, Tsai DT. Reliability assessment in operational planning for large hydro-thermal generation systems. IEEE Trans Power Appar Syst 1985;PAS-104(12):3382–7. [5] Billinton R, Aboreshaid S, Fotuhi-Firuzabad M. Well-being analysis for HVDC transmission systems. IEEE Trans Power Syst 1997;12(2):913–8. [6] Vojdani AF, Williams RD, et al. Experience with applications of reliability and value of service analysis in system planning. IEEE Trans Power Syst 1996;11(3):1489–96. [7] Billinton R, Fotuhi-Firuzabad M. A basic framework for generating system operating health analysis. IEEE Trans Power Syst 1994;9(3):1610–7. [8] Billinton R, Khan E. A security based approach to composite power system reliability evaluation. IEEE Trans Power Syst 1992;PWRS-7(1):65–71. [9] Billinton R, Lian G. Composite power system health analysis using a security constraint adequacy evaluation procedure. IEEE Trans Power Syst 1993;9(2):936–41. [10] Billinton R, Allan RN. Reliability assessment of large electric power systems. Boston: Kluwer Academic Publishers; 1988. [11] IEEE Task Force on Bulk Power System Reliability. Bulk power system reliability concepts and applications. IEEE Trans Power Syst 1988;3(1):109–17. [12] Leita De Silva AM, Endrenyi J, Wang L. Integrated treatment of adequacy and security in bulk power system reliability evaluations. IEEE Trans Appl Supercond 1993;3(1):275–85. [13] C O M R E L UserÕs Manual. Power Math Associates, Inc., August 1995. [14] Khan E. Bulk load points reliability evaluation using a security based model. IEEE Trans Power Syst 1997;13(2):456–61. [15] Billinton R, Kumar S, et al. A reliability test system for educational purposes – basic data. IEEE Trans Power Syst 1989;PWRS-3(4):1238–44. [16] IEEE Committee Report. IEEE reliability test system. IEEE Trans Power Appar Syst 1979;PAS-98(6):2047–54. Lalit Goel was born in New Delhi, India, in 1960. He obtained his B.Tech. degree in electrical engineering from the Regional Engineering College, Warangal, India in 1983. He obtained his M.Sc. and Ph.D. degrees in electrical engineering from the University of Saskatchewan, Canada, in 1988 and 1991 respectively. His main research interests are power system planning and reliability cost/ benefit evaluation of electric power systems. He joined the School of EEE at the Nanyang Technological University, Singapore in 1991 where he is presently an associate professor. Dr. Goel is a senior member of the IEEE. He received the 1997 Teacher of the Year Award for the School of EEE, Nanyang Technological University, Singapore. Dr. Goel was the Organizing Chairman of the 1998 IEEE EMPD Conference in Singapore. He was also the Vice-Chairman of the IEEE Power Engineering SocietyÕs Winter Meeting 2000 held in Singapore in January, 2000. Dr. Goel received the IEEE Power Engineering Society Power Chapter SingaporeÕs Outstanding Engineer Award, 2000. L.S. Low obtained his B. Eng. in Electrical Engineering from Nanyang Technological University (Singapore) in 1999. He is currently studying for his M. Eng. in Electrical Engineering at the Nanyang Technological University (Singapore).