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DYNA http://dyna.medellin.unal.edu.co/ Voltage Sags Assessment by an Extended Fault Positions Method and Monte Carlo simulation Evaluación de Hundimientos de Tensión mediante un Método Extendido de Posiciones de Falla y Simulación de Monte Carlo Jorge W. Sagrea, John E. Candelob & Johny H. Montañac b a Grupo de Investigación en Sistemas Eléctricos de Potencia, Universidad del Norte, Barranquilla, Colombia. [email protected] Departamento de Energía Eléctrica y Automática, Facultad de Minas Universidad Nacional de Colombia, Medellín, Colombia. [email protected] c Departamento de Ingeniería Eléctrica, Universidad Técnica Federico Santa María, Chile. [email protected] Received: January 15th, 2015. Received in revised form: January 15th, 2015. Accepted: January 15th, 2015. Abstract To evaluate the voltage sags at specific points of the electrical power system, this article proposes an extended method of fault position combined with Monte Carlo simulation. The proposed method allows to build the distribution function of indicator SARFI at bus bars of interest, considering the randomness of: i) location of faults in lines; (ii) generation dispatch, and (iii) variation of the pre-fault voltage in the bus bar at the time that the fault was produced. Voltage profiles were obtained by means of a power flow, considering changes in generation dispatch, the load on bus bars, and the topological configuration of the system in the area of vulnerability (AOV). The method was applied to the Atlantic Coast area of the National Interconnected Power System of Colombia. The distribution of the number of voltage sags per year, depending on their magnitude in bus bars of the electrical system and the impact of generation on the voltage sags, was determined. With a higher number of plants dispatched, voltage sags caused by faults were less severe, due to the robustness of the power system and the voltage support. Keywords: voltage sags; power quality; Monte Carlo; fault position method; electromagnetic compatibility. Resumen Para evaluar los hundimientos de tensión en puntos específicos del sistema eléctrico de potencia, este artículo propone un método de posiciones de falla extendido combinado con simulación de Monte Carlo. El método propuesto permite construir la función de distribución del indicador SARFI en las barras de interés, considerando la aleatoriedad de: i) los puntos de falla en líneas; ii) el despacho de generación; iii) variación del perfil de tensión pre-falla en las barras al momento de ocurrir la falla que lo produce. Los perfiles de tensión se obtuvieron por medio de un flujo de carga, considerando cambios en los despachos de generación, la carga en barras y la configuración topológica del sistema en el área de vulnerabilidad. El método fue aplicado al área de la costa atlántica del Sistema de Potencia Interconectado Nacional de Colombia. Se determinó la distribución del número de hundimientos de tensión al año en función de su magnitud en las barras del sistema eléctrico y el impacto de la generación sobre los hundimientos de tensión. A mayor número de plantas despachadas, los hundimientos de tensión ocasionados por fallas fueron menos severos, debido a la robustez del sistema y el soporte de tensión. Palabras clave: hundimientos de tensión; calidad de potencia, Monte Carlo; método de posición de falla; compatibilidad electromagnética. 1 Introduction The requirements of users of electricity service for better power quality have grown increasingly since the last three decades. The reason is the economic impact of power quality, especially voltage sags, caused in electrical companies, customers and manufacturers of end use equipment [1]. Several factors affect the power quality [1–3]: devices powered by electronic converters, speed drivers and CFL, are a source of harmonics. Distributed generation and renewable sources can create voltage variations, flicker and harmonic distortion. Furthermore, energy efficiency equipment are also an important source of disturbance of power quality. In addition to the above, all these devices are very sensitive to © The authors; licensee Universidad Nacional de Colombia. DYNA 81 (184), pp. 1-2. April, 2014. Medellín. ISSN 0012-7353 Printed, ISSN 2346-2183 Online Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. voltage sags because they are manufactured with narrow ranges of operation for competitive reasons. Many power quality studies have been conducted and reported previously, for example: i) measurement techniques, ii) evaluation of voltage sags and, iii) economic impacts of equipment damage and losses in industrial processes. In [4] two stochastic methods for voltage sags prediction are compared: method of critical distance and fault positions method. The results were presented by means of maps showing the variation of the voltage sags (duration and magnitude) into the network. In [5] the application of probabilistic methods are presented to predict and characterize the events frequency in the power system to assess their impact, allowing to know how often an user can be affected. In [6] is shown an analytic method to determine the probability density function of voltage sags caused by threephase faults. This method considers the impact of fault positions in the transmission lines and generation dispatch. In [7], the Monte Carlo method is used to evaluate the voltage sags magnitude and unbalance, considering stochastic factors. In [8], an extended fault positions method was used to calculate the distribution of voltage sags experienced by the users in the Finland Electric System during one year. In [9], an extending monitoring of bus bar unmeasured by means of voltage sags estimation was presented. The estimation is performed by a simulation method that combines fault stochastic data with residual voltages during the fault, calculated deterministically. In [10], the impact of fault probability distribution model of transmission lines in assessing the number of voltage sags and their characteristic are analyzed. In [11], the behavior of voltage sags using fault positions and Monte Carlo method is evaluated. The results shows that Monte Carlo method provided a better statistical description of voltage sags, due to the fault positions method only gives long-terms average values, whereas Monte Carlo shows the total distribution function. In [12], the fault positions method and Monte Carlo simulation were compared in order to evaluate stochastically the voltage sags behavior in a large transmission system. This work shows that fault positions method cannot be used to predict the behavior of a particular year, unless correction factors are used to adjust the behavior. Whereas fault positions method gives average values, Monte Carlo method describe totally the frequency distribution function of voltage sags index (SARFIX: System Average RMS Frequency Index; average number of voltage sags per year with magnitude < X%). In [13], a method of Monte Carlo simulation that takes into account the fault positions method to evaluate voltage sags index was applied. This method considers the randomness of the pre-fault conditions and uncertainty in failure rates. In [14], a method for stochastic prediction of voltage sags generated by faults in the power system was presented. Furthermore, in this research article a method for determining the AOV was proposed. In [15], the influence of generation dispatch and the failures rates changing in time on the stochastic prediction of voltage sags is discussed. In [16], the fault positions method to predict stochastically the frequency and characteristics of balanced and unbalanced voltage sags in distributions systems was presented. The fault positions and Monte Carlo methods have provided good results to evaluate the impact of generation in voltage sags and SARFI indexes. Unfortunately, they do not consider the random behavior of generation dispatch and flat voltage profiles in the faulted bus bar and the bus bar of interest when this behavior is studied. In this paper, an extended fault positions technique and Monte Carlo Method to evaluate the voltage sags is proposed. Random faults, changes in generation dispatch, and load variation are considered to evaluate different operating conditions. The voltage profiles in bus bar are updated continuously using the power flow. Topology changes of bus bars and transmission lines are also considered in the simulation. Although, voltage sags can be originated by lightning, disconnection of large loads, etc, this work focus only on faults in bus bars and overhead lines of the power system. 2 Voltage sags Voltage sag is “a decrease in r.m.s. voltage or current at the power frequency for durations of 0,5 cycle to 1 min. Typical values are 0,1 to 0,9 p.u.” (obtained from IEEE 1346). They are caused by events with large current flows flowing through the network impedances as a result of a fault in any point of the distribution or transmission system affecting customer connection point [2,4,11,12,17]. Events that can cause voltage sags are short-circuits in the power system, transformers energization, capacitors disconnection, circuit breaker operations, starting of large motors and large changes in load on the power system. Voltage sag is characterized mainly by means of magnitude and duration [1–3,18–21], this is shown in Figure 1. Additionally, voltage sag can be characterized by the frequency of occurrence, phase shifting, start point in the voltage waveform and shape and type of voltage sag. 2 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. Figure 1. Characteristics of voltage sags. Standard IEC 61000-4-30 [21], presents calculation of a sliding reference voltage using a first-order filter with a 1 minute time constant. The filter is given by the expression presented in (1). 𝑈𝑠𝑟(𝑛) = 0.9967 ∗ 𝑈𝑠𝑟(𝑛−1) + 0.0033 ∗ 𝑉(10/12)𝑟𝑚𝑠 Figure 2. Flow chart of the methodology (1) 4 Fault positions method Fault positions method is a stochastic method to predict the expected number of voltage sags in a specific node of the network. This method considers faults in different places of the network, as is shown in Figure 3. Electrical variables for each fault is stored: residual voltage and duration on the interest nodes, as is shown in Table 1. Where, Usr(n) is the present value of the sliding reference voltage, Usr(n-1) is the previous value of the sliding reference voltage, and V(10/12)rms is the most recent 10/12 cycle r.m.s. value. Vrms(1/2) is computed from the voltage samples in time domain, as shown in (2) [2,3,21]. 𝑁 𝑉𝑟𝑚𝑠 (1/2) 1 = √ ∑ 𝑣𝑖2 𝑁 (2) 𝑖=1 Where, i is each sample, N is the number of samples and vi are the voltage values in time domain. The value obtained from the N previous samples is updated every half-cycle. Most meters measure as voltage sag magnitude the lower value of the Vrms(1/2) computed each half-cycle in time domain [2]. The reason of this decision is the tolerance curve according to which the device trips instantaneously when the voltage drops below the threshold [2]. Figure 3. Fault points to estimate the voltage sags. 3 Methodology The failure rate is assigned to each fault position. The transmission lines are divided in a specific number of fixed positions. Each position has a failure rate, which is proportional to segment longitude. Thus, frequency, magnitude and duration is determined for each fault position, allowing to calculate the expected number of voltage sags per year [4,6,8,9,11,12,14,16,22,23]. This work was made using the fault positions method combined with Monte Carlo simulation method. Figure 2 shows the procedure to study the voltage sags in a power system. 3 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. Table 1. Failure report for many points into the network. Item Fault Failure rate Sags position magnitude 1 Bus bar 1 x faults/year 0 2 … y faults/year 30% . Bus bar n … … . Line 1 … … . … … … n Line n m faults/year 75% 7. If the accumulated time is less than simulation time selected in step 2, go to step 3. Otherwise go to step 8. 8. Analyze the results statistically. Duration (ms) 120 70 … … … 240 5.1 Statistical analysis of results The great volume of data obtained by Monte Carlo analysis has to be summarized by means of statistical tools. The most important results from Monte Carlo are the longterm mean values and the frequency distribution of mean values [2,11,12,25]. Computation of the mean values and standard deviation of the voltage sags lower than the defined magnitudes must be carried out. Commonly, the magnitudes are form 0.1 to 0.9 in steps of 0.1. It is also important to calculated, minimum, maximum, median and quartiles 1, 2 and 3. Once the deviation, mean value 𝑋̅ and standard deviation s are known, the confidence intervals for the expected value can be obtained, as expressed in (3) [11,12,25]. 𝑠 𝑠 (3) 𝑆𝐴𝑅𝐹𝐼𝑋 ∈ [𝑋̅ − 2.05. ; 𝑋̅ + 2.05. ] 𝑛 𝑛 √ √ Where, 𝑋̅ is the mean value of voltage sags per year computed from the simulation of n years, s is the standard deviation of results from the simulation of n years, n is the number of years of simulation, and the constant 2.05 is the critic value of t-student distribution for 95% of confidence. Unlike the conventional fault positions method, where the fault positions are fixed, in the proposed method on this work, the positions are randomly assigned anywhere in the transmission line for each type of electrical fault. 5 Monte Carlo Method To obtain the distribution function of the expected values of voltage sags (SARFIx), is used the Monte Carlo simulation, which generates values of stochastic variables associated with the study, as is summarized in Figure 4 [11,12,24]. 5.2 Area of vulnerability The elements of the AOV are identified by means of power system analysis software that takes into account fault analysis. Faults are simulated at each node of the network, taking into account the worst scenery, thus: Figure 4. General structure of Monte Carlo method applied to evaluation of voltage sags. Three-phase fault solidly-grounded (Rf=0) Minimum generation dispatch Time of maximum demand Faults are simulated sequentially by voltage level, recording for each fault the residual voltage in the node under study and the electrical distance between node and fault point. Thus, for each voltage level is obtained the maximum distance for which the residual voltage is lower than 0,9 p.u. (critical distance). The steps of the algorithm to implement the Monte Carlo method are [9,11,12]: 1. Select the observation node 2. Select the years of simulation 3. For elements in the AOV, generate a random number and convert it in fault time according to the probability distribution of failure rate of the element. Compute the accumulated time. 4. Generate a random number and convert it in a position over the transmission line according to the probability distribution of this parameter. 5. For each fault, generate a random number and convert it in one fault type (SLG, LL, LLG, LLL) according to the probability distribution function of fault type. 6. Compute the residual voltage as a result of the fault in the observation node, according to analytical calculations. 5.3 Simulation time According to records of meters installed in the node of interest, the number of voltage sags per year are between 250 and 340. Thus, considering 360 voltage sags per year and the expected error lower than 2% for a confidence of 95%, the minimum number of years to be considered in the simulation is 25. 5.4 Stochastic factors There are five stochastic factor considered in this work. a. Resistance at the fault point 4 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. b. c. d. e. Fault type Fault position (lines) Time period of the faults Generation dispatch (number of plants in AOV) under study (El Rio substation). Table 2 shows probabilities of different fault types at each voltage level of the network under study. Table 1. Probability of faults for each voltage level Voltage Probability by fault type (%) (kV) 1 2 3 13.8 31.5 46.2 22.3 34.5 25.3 49.0 25.7 110 79.0 15.6 5.4 Total 42.0 39.0 19.0 These five factors are considered in the simulations in order to evaluate their impact in the voltage sags into the network. 5.4 Resistance The resistance is modeled stochastically as a normal random variable with standard deviation equal to 1 [26]. The mean value of resistance is obtained from records of phaseground faults recorded by distance protection relays located in zone 2 close to neighbor substation. A statistical validation was conducted with at least 20 records obtained from the distance relays in the AOV. The mean value of the resistance at the fault point was calculated by means of this procedure: it was employed historical data (at least 20 events) of phase-ground faults that involves distance relay in zone 2 located near to substation B (see Figure 5). The voltage and current waveform from records stored in the relay are considered for the calculation. Based on these waveforms and neglecting the impedance in zone 2 after substation B in transmission line B-C (Zl2), is calculated the fault impedance. 𝐼𝑓 = 𝑉𝑓 𝑉𝑓 𝑉𝑓 = ≈ 𝑍𝑠𝑝 𝑍𝑙 + 𝑍𝑙2 + 𝑍𝑓 𝑍𝑙 + 𝑍𝑓 For each voltage level (bus bars), the total voltage sags is counted (1 phase, 2 phases and 3 phases). The probability of each one is calculated as a percentage from the total events for each voltage level. 5.6 Fault position in transmission lines Many methods in the literature consider a constant number of segments for dividing the transmission line; therefore each segment has a fixed failure rate. In this work the transmission line is not divided into segments but the fault position is computed by means of a random number generated from the probability distribution. This random number is multiplied for the length of the overhead line and the fault position is obtained. (4) 5.7 Time period of the faults Therefore, Zf can be obtained from the above equation, as expressed in (5) 𝑍𝑓 = where: Vf = If = Zsp = Zl = 𝑉𝑓 − 𝐼𝑓 ∗ 𝑍𝑙 𝐼𝑓 The time of occurrence of a fault is obtained by means of a random number generated between 0 and 23. 0 means the time from 00:00 to 01:00, 1 means the time from 01:00 to 02:00 and so on; 23 means the time from 23:00 to 24:00. From the time of occurrence generated randomly and the load profile at each bus bar is computed the demand of each node in the network and the pre-fault voltage by means of a power flow. (5) Fault voltage Fault current Impedance from source up to fault point Impedance of transmission line A – B 5.8 Generation dispatch The mean value of fault impedance is the average value of the fault impedances estimated by means of equation (4) based on the records of faults of the power system. As the previous parameters, the generation dispatch is also generated randomly from the probability distribution. In this work, the generation dispatch has two options: 1) all generation plants dispatched and, 2) operation without generation plants connected to 110 kV bus bars. The voltage sags analysis was developed in a real power system considering four generation scenarios: a. Baseline scenario: 30% of time are all generators dispatched. This is a typical behavior during the dry season in Colombia (4 months). b. Scenario 2: 40% of time are all generators dispatched. This occurs when the dry season is a little bit longer (5 months). c. Scenario 3: 60% of time are all generators dispatched. Dry season is even longer (7 months). Figure 5. Transmission line representation 5.5 Type of fault The type of fault was obtained randomly from the probability distribution of faults at each voltage level. The probability of each fault is computed from voltage sags data in bus bars at 13.8 kV, 34.5 kV and 110 kV of the substation 5 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. d. Scenario 4: 70% of time are all generators dispatched. This scenario is present during “El Niño” phenomenon, thus the dry season is even longer (8 months) The Atlantic Coast area of the National Interconnected Power System of Colombia was used to test the proposed method. General information about this power system is presented in Table 3. 5.9 Definition of dynamic variables Table 3. Number of elements of the power system. Voltage Bus bar Line (kV) 13.8 228 620 34.5 120 121 66 33 20 110 102 51 220 17 34 500 10 10 Total 510 856 The load profile at each bus bar of the network is simulated as dynamic variable. Additionally, the failure rate of transmission lines and substations of the AOV are considered dynamics. For the failure rate, it is assumed that the time between bus bar and substation faults and the power system substations follow an exponential distribution. Failure rate of elements in the AOV is calculated from the real statistics of the power quality obtained from the actual power system. 5.10 Figure 6 shows the single-line diagram of the Atlantic Coast area of the National Interconnected Power System of Colombia, which is used for power quality studies. Model validation The main purpose of this section was to compare the actual measures of three years with the expected average of voltage sags found with simulations during a long period (25 years) [25]. The first step of the statistical procedure is to determine the confidence intervals from the results of the simulation in the points of interest. The confidence intervals provide the estimated range of values which may include the true population parameter. If some independent samples of the population are measured repeatedly and the confidence interval is calculated, then a percentage (confidence level) of the obtained intervals will include the population parameter [11,12]. To estimate the confidence intervals, the method of percentiles is used, regardless of the probability distribution [25]. Then, with a significance level of α% [a confidence level of (1-α)%], the upper and lower limit of the confidence interval is calculated using the percentile α/2, denoted by Pα/2, and a percentile of 100-α/2, denoted by P respectively. The adopted confidence level is usually 95% (α=5%) and confidence interval limits are P [25]. 5.11 Figure 6. Single-line diagram of the power system test case. The aim of the simulation was to characterize the behavior of the power system using the number of voltage sags as a function of the magnitude and the duration in a point. The selected point was the bus bar 13.8 kV of the El Río substation with coupled and uncoupled bus bars, B1 and B2, as shown in Figure 6. Voltage sags duration 6.2 Bus bars of interest Theoretically, the best way to calculate the duration of each voltage sag is to know the clearance time of the fault. Therefore, a knowledge of the fault currents, protection relays settings and breakers time is needed. Obtaining all the information from distribution networks is sometime a difficult assignment, due to the amount of data required to update continuously the databases. Based on [27], in this research a random generation of voltage sags duration was implemented in simulation, considering the distribution probability of voltage sags durations, registered by meters at the bus bars. 6 Length (km) 29779 3100 290 1401 1870 1870 38310 This study analyzed stochastically the behavior of the voltage sags at a bus bar with a number of users connected to the point. Table 4 shows the information of the number of users connected to the bus bar. The simulation considered 8687 users connected to the bus bar B1, 3672 users connected to the bus bar B2, and 12359 users connected to the coupled bus bars. Table 4. Number of users in the El Rio substation. Type of users Bus bar Bus bar B1 B2 Commercial 1619 1209 Industrial 95 134 Government 38 31 Residential 6935 2298 Power system test case 6 Bus bars B1 and B2 2828 229 69 9233 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. Total 8687 3672 12359 7 Results and analysis 7.1 Area of vulnerability Figure 7 shows a diagram of the reduced power system to conduct the different studies. The AOV for the selected bus bars were calculated using three-phase faults at each bus bar to evaluate the voltage magnitudes. (a) Figure 7. Single-line diagram of El Río substation. A fault at each bus bar was applied with zero impedance and a minimum number of maximum demand generation plants. Table 5 presents a summary of the critical distances for different voltage levels defining the AOV. Table 5. Results of the AOV. Voltage Critical (kV) Distance (km) 13.8 20 34.5 15 110 20 220 280 500 700 (b) Figure 8. SARFI90% per year for the scenario 1, (a) bus bar B1 (b) bus bar B2. Substations 7.3 Distribution of voltage sags Barranquilla Barranquilla Barranquilla Atlantico, Bolivar and Magdalena Costa Atlántica, San Carlos, Primavera and Ocaña Figure 9 and Figure 10 show the frequency distribution of SARFI90% for the bus bars B1 and B2, respectively. 7.2 Power quality indices Figure 8 shows the behavior of Monte Carlo simulation for bus bars B1 and B2, respectively. Figures 8a and 8b show the SARFI90% for each year of simulation and the behavior of the voltage sags in the bus bar B1 and B2 of El Rio substation. The index SARFI90% changes for the first years, but after the 8th year becomes stable. Figure 9. Frequency distribution of SARFI90% for the bus bar B1. 7 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. Comparing the results of the Monte Carlo simulation for both scenarios, coupled and uncoupled bus bars and considering the same failure rate of the elements in the AOV, the results show that the coupled bus bars generate a high number of voltage sags than the uncoupled bus bars. If the number of generation plants increase, the problem becomes less detectable. With the exception of the bus bar, B2, for the year 2010, the values obtained through monitoring the bus bars, B1 and B2, are contained in the corresponding confidence intervals of the expected number of voltage sags considering at least two scenarios. 7.5 Voltage sags duration The probability distribution function used in this research to generate the duration of the voltage sags is shown in Figure 12 for 13.8 kV, in Figure 13 for 34.5 kV and in Figure 14 for 110 kV. These results were obtained combining the magnitude and duration of the voltage sags. Figure 10. Frequency distribution of SARFI90% for the bus bar B2. In this figure, the differences between the distribution of the bus bars, B1 and B2, for the scenarios simulated are presented. Most of the annual voltage sags for bus bar B2 are lower that bus bar B1, which helps identify best configurations from the electrical network. Figure 11 shows the expected number of sags per year and the SARFIx for ranges between 0% and 90% for the bus bars, B1 and B2, of El Rio substation. Figure 12. Accumulative distribution function of voltage sags duration in 13.8 kV Figure 11. Number of sags vs magnitude ranges and SARFIx. 7.4 Results of the model Table 6 shows the number of actual voltage sags versus the number of voltage sags simulated for the bus bars, B1 and B2. The measurements of the actual voltage sags were carried out for the years 2010, 2011 and 2012. The results of the Monte Carlo simulation were obtained according to the fourgeneration dispatch scenarios defined in the methodology. In the long term, the expected number of voltage sags with magnitude 90% (SARFI90%) is lower for the bus bar B2 than the bus bar B1, due the expected value for the SARFI90% in bus bar B2 is less than the corresponding percentile P2.5% for all scenarios. Figure 13. Accumulative distribution function of voltage sags duration in 34.5 kV. 8 Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. Figure 14. Accumulative distribution function of voltage sags duration in 110 kV. Table 7 shows the accumulated voltage sags for the coupled and uncoupled bus bars, B1 and B2. The voltage sags magnitudes with the coupled bus bars, B1 and B2, are similar to the voltage sags magnitudes obtained with the uncoupled bus bars, B1 and B2. The number of voltage sags is greater with the coupled bus bars. Table 6. Actual vs simulated voltage sags for bus bars B1 and B2. Monitoring Scenario 1 (Gmax 30%) Bus bar 2010 2011 2012 P2.5% P97.5% VE Confidential interval of 95% Scenario 2 (Gmax 40%) Scenario 3 (Gmax 60%) Scenario 4 (Gmax 70%) P2.5% P97.5% VE P2.5% P97.5% VE P2.5% P97.5% VE B1 326 313 293 321.6 353.2 336.0 306.2 342.4 323.5 282.2 314.0 298.0 272.0 302.4 286.8 B2 341 315 315 300.2 330.4 314.6 284.6 317.6 301.9 265.6 291.0 277.7 253.6 282.0 266.9 B1 B2 - - - 366.2 397.4 379.6 342.0 373.2 356.5 296.6 334.0 314.5 276.6 314.0 295.1 Table 7. Voltage sags density according to the magnitude and the duration. Magn. Bus (pu) bar 0 50 100 150 B1 336.04 305.92 231.96 65.12 0.9 B2 314.56 287.80 216.48 61.36 B1B2 379.56 339.44 254.80 69.80 B1 196.72 185.04 140.60 39.04 0.8 B2 184.12 175.00 131.80 36.76 B1B2 209.80 195.80 145.40 39.88 B1 130.80 124.68 94.28 26.72 0.7 B2 121.88 117.64 87.32 23.56 B1B2 143.00 135.92 100.36 26.72 B1 73.52 70.00 53.80 15.16 0.6 B2 67.52 65.04 47.60 13.12 B1B2 88.68 84.28 62.36 17.20 B1 37.84 35.88 26.84 7.36 0.5 B2 32.60 31.40 22.12 6.48 B1B2 43.64 40.96 31.48 8.32 B1 24.40 23.32 17.24 4.76 0.4 B2 22.04 21.24 14.80 4.28 B1B2 25.56 23.84 18.00 4.64 B1 15.92 15.28 11.08 3.20 0.3 B2 14.44 13.84 9.92 2.72 B1B2 19.48 18.36 13.76 3.28 B1 10.96 10.44 7.40 2.32 0.2 B2 9.60 9.20 6.64 1.84 B1B2 13.00 12.20 9.44 2.36 B1 4.16 3.84 2.52 0.96 0.1 B2 3.88 3.56 2.60 0.96 B1B2 5.84 5.40 4.28 0.92 200 40.16 38.44 44.08 23.76 22.36 24.56 16.44 14.32 16.72 9.08 7.84 10.92 4.00 3.76 5.00 2.68 2.44 2.68 1.80 1.72 1.80 1.28 1.16 1.28 0.60 0.56 0.60 Duration in miliseconds 250 300 350 28.64 20.64 12.36 27.04 19.88 11.24 30.56 21.72 12.80 16.16 11.44 6.36 15.00 11.08 5.16 16.60 11.60 5.88 11.44 8.20 4.60 9.36 6.88 2.96 10.84 7.56 3.52 6.36 4.28 2.44 5.08 3.84 1.76 7.20 5.04 2.04 2.96 2.28 1.32 2.44 1.76 1.04 3.44 2.24 1.08 2.04 1.64 1.08 1.72 1.28 0.76 1.96 1.28 0.60 1.24 1.00 0.64 1.28 0.96 0.60 1.32 0.92 0.40 0.92 0.72 0.44 0.80 0.64 0.40 1.04 0.84 0.36 0.44 0.32 0.16 0.48 0.48 0.36 0.52 0.44 0.16 9 400 6.36 6.28 7.32 2.24 2.20 2.72 1.44 0.92 1.28 0.68 0.52 0.76 0.44 0.40 0.44 0.36 0.36 0.24 0.28 0.36 0.20 0.24 0.32 0.20 0.12 0.28 0.08 500 4.44 4.52 5.40 1.48 1.44 2.00 1.04 0.60 0.92 0.48 0.36 0.52 0.32 0.28 0.36 0.24 0.28 0.20 0.20 0.28 0.16 0.20 0.24 0.16 0.12 0.24 0.08 600 2.72 3.12 3.28 0.88 0.92 1.48 0.64 0.40 0.68 0.32 0.24 0.36 0.24 0.20 0.24 0.20 0.20 0.12 0.16 0.20 0.08 0.16 0.16 0.08 0.08 0.16 0.04 700 1.68 1.76 1.80 0.48 0.40 0.84 0.28 0.20 0.48 0.12 0.04 0.24 0.12 0.04 0.16 0.08 0.04 0.08 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 800 0.80 0.80 1.00 0.20 0.28 0.48 0.12 0.08 0.28 0.04 0.04 0.16 0.04 0.04 0.08 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 900 0.40 0.36 0.48 0.08 0.12 0.36 0.04 0.04 0.24 0.04 0.04 0.16 0.04 0.04 0.08 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 DYNA http://dyna.medellin.unal.edu.co/ Table 8 shows the accumulated voltage sags for different percentages of SARFI. The information is presented for the coupled and uncoupled bus bars, B1 and B2. Table 8. Voltage sags evaluated for bus bars B1 and B2 with different SARFIx. SARFI Bus Scenarios bars 1 2 3 4 B1 336.04 323.52 298.00 286.76 90% B2 314.56 301.92 277.68 266.92 B1-B2 379.56 356.48 314.48 295.08 B1 196.72 190.80 179.20 173.48 80% B2 184.12 178.72 166.96 162.60 B1-B2 209.80 200.24 182.60 174.68 B1 130.80 124.96 112.84 107.12 70% B2 121.88 116.52 104.76 100.64 B1-B2 143.00 133.84 115.72 108.48 B1 73.52 69.60 60.64 56.32 60% B2 67.52 64.32 55.52 52.48 B1-B2 88.68 82.00 67.52 60.36 B1 37.84 36.00 32.24 30.76 50% B2 32.60 31.12 29.24 28.04 B1-B2 43.64 41.24 34.60 31.24 For all the SARFI studied, the number of accumulated voltage sags is greater for the bus bar B1 than the bus bar B2. Furthermore, the coupled bus bars present a greater number of voltage sags for all scenarios studied. 8 Conclusion References [1] [2] [3] [4] [5] [6] [7] [8] [9] In this research the extended fault positions and the Monte Carlo methods were used to evaluate the impact of voltage sags in a power system. Random faults in transmission lines, variation of generation dispatch, and variation of load were considered for the simulation. As the results show a high impact of the voltage sags into the power system operation, the parameters and the method consider in this research should be included in future power quality analysis. Statistical tests were conducted with the results that the greater number of generation plants dispatched in the AOV, the lower the magnitude of the voltage sags and the index SARFI. The proposed method allowed to evaluate the reconfiguration of bus bars to reduce the number of voltage sags, obtaining that the coupled bars brings a greater impact in voltage sags, compared to the results obtained with uncoupled bars. [10] [11] [12] [13] [14] Acknowledgements [15] This research was supported in part by the energy strategic area of the Universidad del Norte, Barranquilla, Colombia. The authors thank to the company ELECTRICARIBE for the valuable information provided for this research. [16] Dugan R.C., McGranaghan M.F., Santoso S. and Beaty H.W. Electrical Power Systems Quality. 3a ed., McGraw-Hill Education; 2012. Bollen M.H. Understanding Power Quality Problems: Voltage Sags and Interruptions, 1a ed., New Jersey: Wiley-IEEE Press, 1999. Bollen M.H. and Gu I. Signal processing of power quality disturbances, 1a ed., Wiley-IEEE Press, 2006. Qader M.R. and Bollen M.H. Stochastic prediction of voltage sags in a large transmission system. IEEE Trans Ind. Appl. 35, 1999, pp. 152–62. Sikes DL. Comparison between power quality monitoring results and predicted stochastic assessment of voltage sags“real” reliability for the customer. IEEE Trans Ind Appl. 36, 2000, pp. 677–82. Lim Y.S. and Strbac G. Analytical approach to probabilistic prediction of voltage sags on transmission networks, en IEE Proc. - Gener. Transm. Distrib., 149(1), 2002, pp. 7-14. Faried S.O., Billinton R., Aboreshaid S. and Fotuhi-Firuzabad M. Probabilistic evaluation of voltage sag in transmission systems, en IEEE Bol. PowerTech - Conf. Proc., 2003, p. 169– 74. Heine P. Voltage Sag in Power Distribution Networks, tesis (Doctorado de Ciencias en Tecnología), Finlandia, Helsinki University of Technology, 2005. Olguin G. Voltage Dip (Sag) Estimation in Power Systems based on Stochastic Assessment and Optimal Monitoring, tesis (Doctorado), Chalmers University of Technology, 2005. Milanović J.V., Aung M.T. and Gupta C.P. The influence of fault distribution on stochastic prediction of voltage sags. IEEE Trans. Power Deliv., 20(1), 2005, pp. 278–85. Olguin G., Aedo M., Arias M., and Ortiz A. A Monte Carlo simulation approach to the method of fault positions for stochastic assessment of voltage dips (sags), en Proc. IEEE Power Eng. Soc. Transm. Distrib. Conf., 2005, pp. 1–6. Olguin G., Karlsson D. and Leborgne R. Stochastic assessment of voltage dips (Sags): The method of fault positions versus a Monte Carlo simulation approach, en IEEE Russ. Power Tech, PowerTech, 2005. Caramia P., Carpinelli G., Di Perna C., Varilone P. and Verde P. Fast probabilistic assessment of voltage dips in power systems, en 9th Int. Conf. Probabilistic Methods Appl. to Power Syst. PMAPS, 2006. Park C.H. and Jang G. Stochastic estimation of voltage sags in a large meshed network. IEEE Trans Power Deliv., 22(3), 2007, pp.1655–1664. Park C.H., Jang G. and Thomas R.J. The influence of generator scheduling and time-varying fault rates on voltage sag prediction. IEEE Trans. Power Deliv. 23(2), 2008, pp. 1243–1250. Goswami A.K., Gupta C.P. and Singh G.K. The method of fault position for assessment of voltage sags in distribution © The authors; licensee Universidad Nacional de Colombia. DYNA 81 (184), pp. 1-2. April, 2014. Medellín. ISSN 0012-7353 Printed, ISSN 2346-2183 Online Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014. [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] systems, en IEEE Reg. 10 Colloq. 3rd Int. Conf. Ind. Inf. Syst. ICIIS, 2008. McGranaghan M.F., Mueller D.R. and Samotyj M.J. Voltage sags in industrial systems. IEEE Trans Ind Appl. 29(2), 1993, pp. 397-403. Quality I. IEEE recommended practice for monitoring electric power quality. IEEE Recomm Pract Monit Electr., 1995. Std I., Systems P., Subcommittee R., Committee E., Industry I., Society A., et al. IEEE Recommended Practice for the Design of Reliable Industrial and Commercial Power Systems. Analysis, 1997. IEC. IEC 61000-2-8 Voltage dips and short interruptions on public electric power supply systems with statistical measurement results, 2002. IEC. IEC standard 61000-4-30, Testing and measurement techniques—Power quality measurement methods, 2003. Quaia S. and Tosato F. A method for analytical voltage prediction, en IEEE Bol. PowerTech - Conf. Proc., 2003, p. 181–6. Park C.H., Hong J.H. and Jang G. Assessment of system voltage sag performance based on the concept of area of severity. IET Gener. Transm. Distrib. 4(6), 2010, pp. 683-693. Bollen M.H. Reliability analysis of industrial power systems taking into account voltage sags, en Conf Rec 1993 IEEE Ind Appl Conf Twenty-Eighth IAS Annu Meet, 1993. De Oliveira T., Carvalho Filho J.M., Abreu J.P. and Chouhy Leborgne R. Voltage Sags: Statistical Evaluation of Monitoring Results based on Predicted Stochastic Simulation, en 12th Int Conf Harmon Qual Power, 2006. Avendano-Mora M., Milanović J.V., Patel B., Zhang Y. The influence of model parameters and uncertainties on assessment of network wide costs of voltage sags, en 10th Int. Conf. Electr. Power Qual. Util. EPQU’09, 2009. Wämundsson M. Calculating voltage dips in power systems, using probability distributions of dip durations and implementation of the moving fault node method. Chalmers University of tecnology, 2007. Jorge W. Sagre received his Bs. degree in Electrical Engineering in 1978 from the Universidad Nacional de Colombia (Bogotá) and a M.Sc. in Electrical Engineering from Universidad del Norte, Barranquilla, Colombia. His employment experiences include: the Corporación Eléctrica de la Costa Atlántica, CORELCA TRANSELCA S.A. E.S.P. and ELECTRICARIBE S.A. E.S.P. His research interests include: planning, operation and control of power systems, power quality and regulation. John Edwin Candelo Becerra received his Bs. degree in Electrical Engineering in 2002 and his PhD in Engineering with emphasis in Electrical Engineering in 2009 from Universidad del Valle, Cali, Colombia. His employment experiences include the Empresa de Energía del Pacífico EPSA, Universidad del Norte, and Universidad Nacional de Colombia. He is now an Assistant Professor of the Universidad Nacional de Colombia, Medellín, Colombia. His research interests include: planning, operation and control of power systems, and smart grids. Johny Montaña is full time professor of the Department of Electrical Engineering at Universidad Federico Santa María in Valparaiso, Chile. He received his Electrical Engineer degree in 1999, M.Sc. in High Voltage in 2002 and Ph.D. in Electrical Engineering in 2006 from Universidad Nacional de Colombia. His employment experiences include Universidad Nacional de Colombia as Research Assistant (2000-2005), Siemens SA as Design Engineer Jr. (2006-2009) and full time professor at Universidad del Norte Colombia (2010-2013). His research and teaching interests include lightning protection systems, lightning location systems and grounding systems. 11