III CHAPTER Analysis Methodology CHAPTER 3 ANALYSIS METHODOLOGY: Provides information on preliminary design aspects regarding data sampling, benchmarking indices and overall program layouts. 3.1 INTRODUCTION Chapter two provided background information on harmonic distortion and especially BI. This chapter focuses on the methodology and techniques that were used and implemented in the analysis programs. Network selection, data sampling and program layouts are discussed. 3.2 NETWORK AND SEGMENT SELECTION The benchmarking methodology made use of a network in the North-West province supplying various mining, farming, residential and industrial loads. The principles of the BI as discussed in chapter 2, requires weighing the VTHD data as recorded, to account for the size of the connected load at the PCC. The network was divided into segments as explained in section 2.7. It was attempted to keep segments as small as possible to enhance accuracy of the indices. To calculate BI requires a constant voltage rating across the segment area. It must be noted that the impact of voltage distortion on a nearby consumer does not have the same impact on a consumer far away [3]. Thus, the segment weight value is used to normalise the harmonic distortion for the whole circuit segment, which increases the accuracy of the BI. Parameters taken into account when dividing a network into different circuit segments are the voltage, segment size, monitoring points and segment weight. The segments were chosen in accordance with the distribution voltage. Each segment must contain at least one monitoring point. The selected monitoring point has a PQ monitor at 88 kv substations. Figure 3.1 shows a transmission layout for the North-West province. The blue lines represent the 88 kv distribution networks, while the black dots are the substations of interest. In order to determine the segments and the weight of the segments, a map of the North-West province municipalities was masked over the transmission map, to visually establish which transmission line feeds which municipality. Figure 3.2 illustrates this concept. A benchmarking model for harmonic distortion in a power system 51
The circuit segments were chosen based feed from the transmission lines supplied from the main substation. For example, the Watershed substation is located in municipality number 12. From Figure 3.2 it can be seen that the substation feeds multiple municipalities (Number 3, 8, 9, 10, 12 and 13) from an 88 kv distribution network. All of these municipalities were then grouped together to create a circuit segment. This technique was applied to the whole distribution network, which resulted in seven circuit segments (Figure 3.3). Municipality 1, 2 and 4 are exceptions, which were fed from a substation outside the North-West province and did not contain any large distribution substations within the municipality boundary. It was decided not to include these municipalities into this study. The distribution voltage of municipalities 14, 15 and 19 (segment 4) are rated at 66 kv. It was decided to include this segment into the study, as VTHD values are normalised in principle and these areas did have a large distribution substation within them (Carmel). The final distribution network with all the segments are displayed in Figure 3.4 and segment information summarised in Table 3.1. The municipalities were used to create a circuit segment by determining the population served by each substation. Municipality s populations were used to estimate the number of electrical power consumers in such a segment. The exact consumer load or connected apparent power (kva) data per municipality was not available. However, the weight can be related to other weighing factors such as the sensitivity of consumer loads and not just connected apparent power load (kva) [29]. The BI used, requires the connected apparent power load (kva) value and reasonable estimations were made [29]. The number of people that have access to electrical energy was obtained from the 2001 census [39]. The number of households per municipality that have access to electrical energy was used to estimate the connected apparent power (kva). It is estimated that for every 100 households the total power usage will be 500 kva [3]. Industrial, commercial and farming usage will not be part of the weighting factor. However, electrified households will still provide a good normalisation factor. Appendix A provides transmission maps of the North-West province with much more detail, which was used to determine the segments. Appendix E provides an example of how the 2001 census data were obtained, in order to estimate connected apparent power [37], [38]. Table 3.2 displays the connected apparent power (kva) values for each segment used in this project [37], [38]. Table 3.1: Segment descriptions. Segment Segment Color PQ Monitor Name Municipality Number Segment 1 Watershed (88 kv) 3,8,9,10,12,13 Segment 2 Lomond (88 kv) 20,21 Segment 3 Ararat (88 kv) 18 Segment 4 Carmel (66 kv) 14,15,16 Segment 5 Hermes (88 kv) 5,6,7,11 Segment 6 Spitskop (88 kv) 17 Segment 7 Trident (88 kv) 16 A benchmarking model for harmonic distortion in a power system 52
Figure 3.1: Distribution network of the North-West province, Appendix A provides detailed maps. A benchmarking model for harmonic distortion in a power system 53
Figure 3.2: Distribution map masked by municipality map. Appendix A provides detailed maps. A benchmarking model for harmonic distortion in a power system 54
Figure 3.3: Circuit segmentation of the North-West province. Figure 3.4: Network area used for benchmarking project. A benchmarking model for harmonic distortion in a power system 55
Table 3.2: Summary of municipalities and connected kva [37], [38]. Segment No Map number Name Total Population Electrified Households Connected Apparent Power Load (kva) 1 12 Ditsobotla Municipality 147600 23854 119,270 1 10 Mafikeng Municipality 259478 46550 232,750 1 3 Naledi Municipality 58104 9747 48,735 1 9 Ratlou Municipality 104324 17238 86,190 1 8 Tswaing Municipality 114155 17471 87,355 1 13 Zeerust Municipality 137443 22356 111,780 2 20 Madibeng Municipality 405352 67091 335,455 2 21 Moretele Municipality 177905 30583 152,915 3 18 Rustenburg Municipality 395540 81844 409,220 4 19 Merafong Municipality 210481 36649 183,245 4 14 Potchefstroom Municipality 128352 24959 124,795 4 15 Ventersdorp Municipality 43079 6801 34,005 5 11 Klerksdorp Municipality 434858 75656 378,280 5 6 Lekwa Teemane Municipality 50507 7540 37,700 5 5 Mamusa Municipality 48365 7506 37,530 5 7 Maquassi Hills Municipality 69038 10732 53,660 6 17 Moses Kotane Municipality 236845 56275 281,375 7 16 Kgetlengriver Municipality 36477 6457 32,285 N/A 4 Greater Taung Municipality 182164 20421 102,105 N/A 2 Kagisano Municipality 96385 15461 77,305 N/A 1 Molopo Municipality 11689 1760 8,800 A benchmarking model for harmonic distortion in a power system 56
3.3 DATA SAMPLING One objective of this dissertation is to apply analytical methods to process a vast amount of VTHD readings. This is done using BI as presented in chapter 2. Calculating these BI is complex, due to the different types of loads in the networks. The load profile is of dynamic nature as determined by the loading at each consumer. As proven by the DPQ Project the majority of loads in the networks are non-linear and regularly switched [13]. For Example a company that uses arc-welders will by assumption, cause more voltage waveform distortion during daytime, when they are more active than at night. Taking measurements of steady state phenomena such as harmonics is not the same as recording a transient PQ phenomenon. Certain PQ phenomena including dips or surges, exceed predefined thresholds values, which activates the PQ monitor and records the event. This means the PQ recorder operates only when there is an event. Harmonics can affect every fundamental waveform cycle differently. To record every cycle will yield an abundance of data. The South African PQ standard, NRS 048 is based on the IEC 61000 standard. It specifies that PQ monitors make use of 10-minute aggregated values for THD in voltage. VTHD is calculated per fundamental cycle for each phase, aggregated to 3-second values and then to 10-minute values. Such a 10-minute value is therefore a reflection of average VTHD of the past 10-minutes [17]. The data used in this study was obtained by this method. The representation of three-phase harmonic distortion data is another aspect that needs to be addressed. Some distribution loads are served by a single-phase supply, which could cause higher harmonic distortion in one phase than the other. This results in a type of phase unbalance with regards to harmonic distortion. One method to characterise distortion, is to treat each phase separately and calculate a VTHD value for each phase. The problem is that the harmonic distortion can exceed threshold limits by three times the value [4]. Option two, is to calculate an average VTHD value for the three phases. The disadvantage of this method is the possibility of concealing high harmonic distortions, which could exist in one phase. The NRS 048 [17] and IEEE 519 [6] approves of averaging the phases. Single-phase harmonic assessments are more applicable at the PCC with lower voltages. Calculation of BI in this study makes use of the total load in kva, connected to the PCC where the PQ instrument records the VTHD values. PQ data was provided by Eskom s Performance, Audits and Compliance division [39]. PQ recorders are installed at various substations and recorded PQ data is used to populate Eskom s database. To calculate BI, voltage harmonic distortion data was collected for a 24-month period. Data used in this study is from April 2007 to April 2009. This time frame is compliant according to section 4.2.5.2.4 of the NRS 048 part 2 [17]. Section 4.2.5.2.1 of the same A benchmarking model for harmonic distortion in a power system 57
standard also states that the data must contain up to the 40 th harmonic component [6], [17]. Harmonics beyond the 50 th component do not contribute much to VTHD of the system. Eskom s PQ monitors sample at 128 samples per cycle, which is sufficient to gain adequate data that contain the necessary harmonic components. This is in accordance with the Nyquist theory, which states that the sampling frequency must be twice that of the highest frequency embedded in the original signal [30]. Appendix D shows the main windows from Eskom s trend viewer [39]. This program was used to extract the data from the QoS database into Excel format. 3.4 METHODOLOGY The benchmarking methodology requires processing of a vast amount of VTHD data in preparation for the BI as discussed above. Two software programs were designed to meet this objective. The functional flow diagram for the analysis is shown in Figure 3.5. Program 1 can be applied to any VTHD data from any substation and is used to calculate histograms, cumulative percentage, preliminary index vales, CP95% values, CP99% values and mean VTHD values. Program 1 will execute 168 times, which represents measurements for seven segments over 24 months. The results from this program are used to calculate BI. The input and output files are in Excel format. Program 2 imports all the output files from program 1 and is configured to process data from all seven segments at the same time. The analysis program is not universal, as it is specifically designed to accommodate seven segments from the network discussed above. It calculates BI such as SATHD, SATHD_CP95%, SATHD_CP99% and SATHDi by using the connected apparent power load (kva) data and output data from program 1. The BI is calculated for each phase and the average value between the three phases. Figure 3.5 illustrates the interaction between program 1 and 2 to calculate BI. Figure 3.5: Functional flow diagram of benchmarking analysis. A benchmarking model for harmonic distortion in a power system 58
3.5 PROGRAM 1 Preliminary calculations per month for each segment are done by program 1. The final results are imported into program 2. Program 1 is a generic model and can process measured VTHD recordings. This characteristic reduces the length of the program code. It consists of various programmable functions, which are used to calculate necessary parameters. The functionality of each section of program code will be discussed in conjunction with the functional flow diagram of program 1 (Figure 3.6). The full code of program 1 is shown in Appendix B. Figure 3.6: Functional flow diagram of the programs. A benchmarking model for harmonic distortion in a power system 59
DATA INPUT Data is obtained from the QoS database, in Excel format for each segment and month. The data is imported into MathCAD via the import function. Each phase VTHD measurement is moved into its own phase array, because BI calculations are done per phase. DATA CONDITIONING It was noted by reviewing the obtained data that some VTHD measurements were not taken per 10- minute intervals. At these timeous measurements the entries were void. When the data is imported into MathCAD, the program makes this void entry a zero. For example, when a histogram is constructed there will be a zero bin with a very high number of occurrences (frequency). However, this is not a true reflection of phase VTHD. An algorithm was created to eliminate zero entries with the condition that all phase s entries have to be zero. The reasons for these void/zero entries can be related to events such as transmission faults, load shedding etc. Figure 3.7 and 3.8 shows histograms obtained with and without zero entry elimination. Figure 3.7: Histogram obtained from VTHD data, without zero entry elimination. Figure 3.8: Histogram obtained from VTHD data, with zero entry elimination. A sample count algorithm counts the number of entries that is above zero. This is done to evaluate the data obtained from the QoS database. This information is exported and used in program 2 to calculate average measurements recordings for all months per segments. A benchmarking model for harmonic distortion in a power system 60
This algorithm uses the zero entry data and calculates the average value between the three phases. This is done per timeous measurement and stored in an average phase array. HISTOGRAM FUNCTION MathCAD function creates histogram output data. The number of bins and input data array are specified. This function is applied to all three phases for each month and segments. CUMULATIVE PROBABILITY ALGORITHM The output data from the histogram function is used to calculate CP values at 95% and 99%. This can only be done after the CP curve values have been determined. Table 3.3 shows an example of how the cumulative values are calculated. An algorithm was developed to determine the highest and lowest threshold CP values. The functionality of the algorithm is displayed in Figure 3.9. By means of interpolation, the CP values at 95% or 99% can be obtained. These results will be used to calculate BI. Table 3.3: Example of calculating cumulative probability curve values. Bin Frequency Cumulative Description 1 10 10 10+0 2 20 30 20+10 3 30 60 30+30 4 40 100 40+60 5 50 150 50+100 Figure 3.9: Functional flow diagram for cumulative probability algorithm. A benchmarking model for harmonic distortion in a power system 61
INDEX ALGORITHM, 1% TO 4% This algorithm is designed to count the number of VTHD recordings that exceeds a predetermined threshold limit. The threshold limits are set from 1 to 4. This data is then divided by the total amount of measurements to calculate the percentage value. The code is displayed in Appendix B, page 12 to 16. AVERAGE DATA AND MEAN VTHD ALGORITHM The average data algorithm, calculates the average between the red, white and blue phase for a timeous measurement. For example, in Table 3.4 the value 2.23, in the average (10 min) column is the average of all phases for that measurement taken at the specified time. The mean VTHD algorithm calculates the average VTHD value per phase and also for the average (10 min) column. Table 3.4: Example of calculating cumulative probability curve values. Table=VT_HARMONIC Meter point=watershed 275/132kV SLOT_DT THD_BLUE THD_RED THD_WHITE AVERAGE (10 min) 2008/07/01 00:05 2.3 2.1 2.3 2.23 2008/07/01 00:15 2.1 2 2.2 2.10 2008/07/01 00:25 2 2 2 2.00 : : : : : Mean 2.13 2.03 2.17 2.11 OUTPUT PARAMETERS When all the above mentioned parameters are calculated, the results are exported into an Excel file, which represents one month s coefficients for a certain segment. Program 2 will import all Excel files simultaneously and use the information to calculate BI. 3.6 PROGRAM 2 Program 2 is specifically designed for only those data obtained from all seven segments over a period of 24 months. The objective of this program is to calculate BI as described in chapter 2. The 168 Excel data files from program 1 are imported and coefficients used to do the calculation. The complete code of program 2 is displayed in Appendix C. Figure 3.10 illustrates the functional flow diagram of program 2 A benchmarking model for harmonic distortion in a power system 62
Figure 3.10: Functional flow diagram for program 2. A benchmarking model for harmonic distortion in a power system 63
DATA INPUT AND ARRAY FUNCTION The data input block form Figure 3.10, implements a MathCAD function that imports all Excel files from program 1 and assigns a specific name to the data array. Data is extracted and placed into specific arrays like: MTHD, CP95%, CP99% and index arrays (table 3.5). The rows (0 to 24) of the arrays represents the months (April 2007 to 2009), while the columns (0 to 6) represent the seven segments. Table 3.5: Data arrays created from input data. X represents an array. DATA ARRAYS Mean CP 95% CP 99% Index 1 Index 2 Index 3 Index 4 RED X X X X X X X PHASE DATA WHITE X X X X X X X BLUE X X X X X X X AVERAGE X X X N/A N/A N/A N/A Figure 3.11 illustrates a typical example of a data array. Figure 3.11: Example of data array for MTHD_ Blue phase. A benchmarking model for harmonic distortion in a power system 64
SEGMENT DATA Segment data as described in Table 3.1 and 3.2 is assigned to a segment array. This data will be used as a weighing factor to calculate BI. BI: SATHD, SATHD CP95%, SATHD CP99% AND SATHDI These specified algorithms use the data arrays and segment data array to calculate BI (SATHD, SATHD CP95%, SATHD CP99% and SATHDi) as described in chapter 2. The BI is calculated per month across all segments. OUTPUT AND GRAPH FUNCTION All calculated indices are displayed in graphical format and exported to Excel to have a final output file. 3.7 SUMMARY This chapter provides the methodology, which was used to calculate harmonic distortion indices. The selected distribution network was a section of the national grid, located in the North-West province. The network was divided into segments with a PQ recorder based inside each segment. Data was collected from the Eskom QoS database for each segment. The data was then imported into MathCAD where mathematical analysis was done by program 1 and 2. Program 2 delivered the harmonic BI, which is discussed in detail in chapter 4. A benchmarking model for harmonic distortion in a power system 65