Effect of Embedded Induction Generators on Short-Circuit Detection Pieter Vermeyen, Student Member, IEEE, Johan Driesen, Member, IEEE, Ronnie Belmans, Fellow, IEEE, Daniel Van Dommelen, Senior Member, IEEE
Index Terms--Dispersed generation, induction generator, power distribution protection, power system modeling, power system simulation, short-circuit current.
for the parameters of this system. By changing the values of the parameters, a wide range of configurations is investigated. Within this system, short circuits are simulated. This model is used to investigate how the detection of a short circuit in a feeder is influenced by a generator located between the circuit breaker and the fault, and for which system configurations the influence is strongest. Because of the generator’s contribution to the short-circuit current, the voltage drop over the feeder section between the generator and the fault increases. This can result in an increased voltage at the point of interconnection with the main grid, which results in a lower fault current from the grid. In order to limit the scope of the exploration of this method, the generator used in the system is limited to one type: the induction generator, which is used often in practice, e.g. in CHP units. In order to study the effect of this generator, disconnection of the generator when a fault occurs is assumed not to happen, although present practice usually requires disconnection of local generators. The simulations are conducted using SimPowerSystems (Matlab).
I. INTRODUCTION
II. GENERAL MODEL OF A DISTRIBUTION SYSTEM
NTRODUCING embedded generators in radial distribution grids may cause protection problems [1]-[13] . The need for an adaptation of the protection scheme when a significant amount of generation capacity is installed locally, is an impediment to the use of dispersed generation. Case studies concerning these problems are discussed in [1]-[3], [5], [7], [8], [12] and [13]. A flexible protection system, applicable to every distribution grid and capable of dealing with changing configurations, would be the ideal solution. When only specific cases or examples of situations are investigated, the design of protection systems for distribution grids containing local generation units remains an ad-hoc process. Conclusions regarding protection problems in a specific grid contribute little to the development of a general approach to problems related to the use of local generators. In order to develop a general protection system, a systematic approach in protection research is the appropriate way. In this discussion, a proposal for a more general methodology is presented. It consists of modeling a simple distribution system and calculating a series of possible values
To study the effect of a local generator on the detection of short-circuit currents, a distribution feeder is modeled in a general way. The model is shown in Fig. 1. It consists of a voltage source with internal impedance, representing the main grid (15 kV, 50 Hz, R/X=0.1 [14], [15]); a distribution transformer T1; a distribution feeder (400 V) consisting of a three-phase cable with a neutral conductor; a passive load (configuration: grounded wye) at the end of the feeder; a generator somewhere along the feeder and a transformer T2 connecting the generator to the feeder.
Abstract--The application of embedded generators in distribution grids has consequences for the protection systems. A general approach is described for assessing the impact of induction generators on the detected short-circuit current in a distribution feeder. A simple system is simulated for a large number of parameter variations. The goal is to find those system configurations for which the negative impact on short-circuit detection is strongest. First, the simulated system is described and the calculation and choice of the parameters of this system are discussed. The parameters of concern are: short-circuit power of the grid, cross-sectional area of the cable conductors, location of the generator, power of the generator and minimum short-circuit current. Next, the simulation results are discussed. It is found that an induction generator does not pose a problem for detection of three-phase and double line-to-ground faults when one feeder is considered. With line-to-line faults and single line-to-ground faults, problems may occur. The significance of an additional parameter is discussed: the number of generators.
I
P. Vermeyen, J. Driesen, R. Belmans and D. Van Dommelen are with the Department of Electrical Engineering, Katholieke Universiteit Leuven, Belgium. (
[email protected], http://www.esat.kuleuven.be/electa)
142440178X/06/$20.00 ©2006 IEEE
15 kV/400 V
1
2
4
5
T2
T1 grid
3
A
induction generator
Fig. 1. Outline of the system that is simulated.
Five nodes are defined along the feeder, at equal distances. Nodes 1 to 4 are the possible locations of the generator. Faults are applied at node 5 (the location of the load). Current is measured between the distribution transformer and node 1. In the following paragraphs, the different aspects of the model
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PSCE 2006
are discussed. A similar system is used in [13] to study the effect of a local generator, connected by means of an inverter, on detection of overcurrent, caused by faults with medium impedance. In the work presented here, however, faults with low impedance (short circuits) are considered. A. Short-Circuit Protection For the protective relay of the low-voltage feeder, relay type 50/51 is assumed. Its characteristic consists of an inverse-time section for overcurrent and a definite-time section for shortcircuit current (high overcurrent). When the current reaches a certain value in the definite-time section, the circuit breaker is activated immediately or with a fixed time delay. The latter is considered in this discussion. In order to assess the effect of the local generator on short-circuit detection, the fault currents resulting from the simulations are analyzed. Interruption of the current is not simulated. B. Grid Configurations The system is characterized by five parameters that are independent of each other. These are the short-circuit power of the grid (SSC), the cross-sectional area of the conductors (AC), the location of the generator, the relative power of the generator and the minimum short-circuit current (IMSC). 1) Short-Circuit Power of the Grid: The grid’s maximum contribution to the short-circuit current is determined by SSC on the HV side of transformer T1. In order to cover a wide range, five possible values are assigned to this parameter: 50, 100, 200, 500 and 1000 MVA. 2) Cross-Sectional Area of the Conductors: The rated current (IR) of the feeder is determined by AC of the cable. For this parameter, the following 12 standard values are used: 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240 and 300 mm2. 3) Location of the Generator: This parameter determines the fraction of total feeder impedance between the distribution transformer and the generator and between the generator and the fault. The possible locations are nodes 1 to 4. The feeder sections between the nodes are of equal length. 4) Relative Power of the Generator: The possibilities for the power of the generator are relative to the rated power of the feeder. The chosen values are 50, 100 and 200 % of the rated power. In the case of 100 %, the power consumed locally is supplied by the generator. At 200 %, power is exported. For the discussion of simulation results, mainly 50 % and 200 % are used. The generator is referred to as a half-sized or a double-sized generator respectively. 5) Minimum Short-Circuit Current: A required minimum short-circuit current (IMSC) is assumed. In [16] values for IMSC are given, corresponding to a series of values for the rated current of protective devices. For the rated currents from 80 A to 500 A, IMSC is 5.5 to 7.8 times higher than the rated current. For simplicity, one factor is used (six) for all cable crosssections. In order to show the effect of a higher IMSC, an alternative factor (twelve) is used as well. This means two groups of configurations are created: one with IMSC equal to 6•IR and one with IMSC equal to 12•IR. The threshold current of the definite-time section of the relay characteristic has to be lower than IMSC, in order to detect short-circuit currents with the definite-time section.
Each combination of parameter values is referred to as a configuration. 1440 configurations can be described with these five parameters. C. Rated Power of the System Components The values of the parameters of the main grid, the distribution transformer and the cable are determined without taking into account the local generator. Rated power of all elements is derived from AC of the cables. For each cross section, the manufacturer provides a value for the permissible current. A rated current (IR) equal to 90 % of the permissible current is assigned to each cross section. With IR, the rated apparent power SR is calculated. Next, a distribution transformer is selected for each cable section. As mentioned in the previous paragraph, the power of the local generator is chosen relatively to SR of the cable. D. Cable Impedance The impedances of the cable are calculated using the specifications of a cable series produced by Nexans [17]. This cable consists of four copper conductors: three phase conductors and one neutral (Fig. 2). The four conductors are of equal size. The arrangement of the conductors results in unbalanced cable impedance. Usually balanced conditions are assumed in textbooks. For this series of cables, conductors with AC equal to 50 mm2 or higher are sector-shaped. For simplicity, it is assumed all cables have round conductors.
A
B *
N
r
**
* DAC = DBN ** DAN = DBC = DAB = DCN
C
Fig. 2. Arrangement of the three phase conductors (A, B and C) and the neutral conductor (N) of the cable.
1) Resistance: The AC resistance of the phase conductors of the cables is calculated taking into account the skin effect and the proximity effect [18], as well as the stranding of the conductors and the cable [19]. 2) Self-Reactance: The self-reactance XS of the conductors [18] is used for calculating the voltage drop over the feeder under normal conditions: balanced load, no fault. 3) Indeterminate Inductance: In order to simulate a threephase model for unbalanced situations using Matlab, the flux linkages of each phase and the neutral conductor have to be considered [20], [21]. With the flux linkages, the indeterminate self-inductances and the indeterminate mutual inductances of the phases are calculated. For the corresponding mutual reactances, the following identities apply: XAB = XBC = XCN = XAN and XAC = XBN. 4) Capacitance: Because the capacitive current in the cables is very low compared to the fault current, the capacitances of the cable are not taken into account. E. Length of the Feeder Feeder lengths have to be selected. Because the goal is to determine for which configurations the influence of the local generator on current detection is strongest, maximum feeder
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AC SSC
10 16 25 35 50 70 95 120 150 185 240 300
lengths are used. In this way, the main grid’s contribution to the fault current is minimal. The generator’s influence will be strongest. In determining suitable feeder lengths, the local generator is not taken into account. Maximum length is derived from two criteria. First, a maximum allowed voltage drop of 10 % is assumed [22]. The lengths are calculated by assuming rated current, a resistive load at the end of the cable and the afore-mentioned voltage drop over the total length. These calculations result in a specific length for each value of AC. Secondly, the short-circuit current is considered. The cable has to be short enough so as to obtain a sufficiently high current when a short circuit arises at the end of the feeder (node 5), in order to have quick disconnection. The two possibilities for the minimum short-circuit current IMSC mentioned before are used. The feeder has to be sufficiently short for each combination of SSC and AC and for each of the four fault types mentioned in the next paragraph. This adds dependence on SSC to the cable length. Based on these criteria, a feeder length is calculated for each combination of values for SSC, AC and IMSC. Each combination of SSC and AC is an element of a matrix in which the rows correspond to SSC and the columns to AC. This is shown in Fig. 3. The markings in this figure are referred to further on. In Table I calculated minimum and maximum values for feeder length (LF) and series impedance of the feeder (RF, XF and ZF) are given.
50 100 200 500 1000
Fig. 3. Matrix of combinations of SSC (MVA) and AC (mm2). X: used for additional simulations with two and four generators.
F. Short Circuits The following faults are simulated: three-phase fault, lineto-line fault, double line-to-ground fault and single line-toground fault. For the fault resistance and the ground resistance, a value of 1 mȍ is used. For the configurations with IMSC equal to 6•IR, this value is 2.9 % of the minimum value and 0.4 % of the maximum value of the impedance ZF of the feeder, given in table I. For 12•IR, this value is 7.7 % of the minimum and 0.6 % of the maximum value of ZF. G. Transformer Parameters The system contains two three-phase transformers. A distribution transformer connecting the feeder to the main grid (T1, configuration: HV: delta, LV: grounded wye) and another through which the generator is connected to the feeder (T2, both sides: grounded wye). The p.u. parameters of these transformers are calculated on the basis of technical data for cast-resin transformers from the manufacturer Pauwels. Where the transformer ratings in the manufacturer’s data do not correspond to the desired ratings, the parameters are calculated by means of interpolation.
Distribution transformers usually supply multiple parallel feeders. Therefore, the choice is made to dimension the distribution transformer for three times the rated power of the feeder. The rated power of the second transformer is equal to that of the generator. Because the ratio of this transformer is 1:1, its parameters are derived from the low-voltage parameters of the distribution transformer. TABLE I MINIMUM AND MAXIMUM VALUES OF FEEDER CHARACTERISTICS, AND CORRESPONDING CONFIGURATIONS
IMSC LF (m) RF (mW) XF (mW) ZF (m W)
6 12 6 12 6 12 6 12
IR IR IR IR IR IR IR IR
Min. value 140 86 24 9.2 12 7.5 35 13
Configuration MVA ; mm2 50-1000 ; 10 50; 10 50; 300 50-200; 300 50-1000; 10 50;10 50; 300 50-200;300
Max. Value 368 152 285 178 29 12 285 179
Configuration MVA ; mm2 200-1000; 150 200-1000; 120 50-1000; 10 100-200; 10 200-1000; 150 200-500; 120 50-1000; 10 100-200; 10
H. Generator Model and Parameters The generator is a four-pole induction generator (400 V, 50 Hz, stator: ungrounded wye). It is modeled using the equations given in [23]. These equations are given in the appendix. The electrical parameters of the induction generator are derived from data given in [24]. The inertia constant and the rated torque are taken from technical data [25]. The generator consists of an induction machine and a mechanical power source. The total moment of inertia is estimated by multiplying the inertia of the induction machine by two. The power of the generator is an important variable. An obvious maximum value is twice the power that is consumed in the local grid. In this case, current in the distribution transformer is at the rated value and power is transferred from the local grid to the supplying grid. Local power generation can be limited to lower levels by other factors, such as voltage profile and thermal capacity of system components. These considerations are not taken into account here. The torque applied to the generator is a constant value. In Table III in the appendix the apparent power and the inertia constant of twelve generators are given. III. DISCUSSION OF SIMULATION RESULTS During a short circuit, transient behavior is displayed by the induction generator. For example, for a double-sized generator (at node 1, SSC = 500 MVA, AC = 120 mm2, IMSC = 6•IR) the times after the start of the short circuit, on which the generator current reaches 95 % of the steady-state fault current for a three-phase, line-to-line, double line-to-ground and single line-to-ground fault, are 0.15, 0.11, 0.11 and 0.07 seconds, respectively. In order to take into account these transients, the system is simulated in the time domain. By checking the pre-fault results, the steady state of the generator is verified. One simulation is carried out for each combination of SSC, AC, IMSC, location of the generator, generator size and fault type. This results in a large number of
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simulations. In order to assess the impact of the generator on the detection of faults, the detected current in the system with a local generator is compared to the current detected originally in the system without generator. Because of the way the cable lengths are calculated, the current for each of the four fault types is equal to or higher than 6•IR or 12•IR, respectively, when the generator is not used. Each simulation results in a time sequence of values. These are converted to RMS values. Because the direct-current component is negligible, this conversion is done by dividing the peak values of the sine waves by ¥2 [26]. Next, in order to limit the amount of data to be analyzed, the values at two moments are selected: at 0.1 s and 0.2 s after the start of the fault. Time delays of circuit breakers are situated around these values. In Fig. 4 the result of a simulation of a line-to-line fault is shown. For the different fault types, without the contribution of a local generator, the currents in the different phases are not equal. For the line-to-line fault (Fig. 4), for instance, this is caused by the current through the load at node 5. Due to the short circuit, the voltages of the two lines concerned are in phase. Consequently the currents through the phases of the load that correspond to the shorted lines are identical and in phase. The fault currents are identical but opposite. The detected current is the sum of the load current and the fault current. As a result, the amplitudes of the detected currents are different, as is shown in Fig. 4 (dashed lines). When a generator is used and a line-to-line fault or a double line-to-ground fault occurs, the difference between the detected currents is larger, as is shown in Fig. 4 (solid lines). This is caused by the asymmetry of the three-phase voltage at the generator terminals, which results in different phase currents. Because of this, the effect of the generator on the detected current is different for each phase. 2500
Current (A)
2000 1500 1000 500 0 −0.1
0
0.1
0.2
0.3
0.4
Time (s)
Fig. 4. Detected fault current during a line-to-line fault. System configuration: SSC = 500 MVA, AC: 120 mm2, double-sized generator at node 2. Solid lines: currents in the two shorted phases. Dashed lines: current without a generator. Dotted line: IMSC = 6•IR .
It is assumed a three-phase relay and circuit breaker are used. A three-phase disconnection is initiated as soon as the current in one of the phases is sufficiently high. Because of this, configurations for which at least one of the phase currents is high enough, do not pose a fault-detection problem. Configurations that are potentially problematic are those where all phase currents are significantly lower than the current originally detected. In this case, the detected current
could be situated in the inverse-time section of the relay’s characteristic, instead of the definite-time section, resulting in an unwanted increase in interruption delay. When the phases are protected independently, all phase currents have to be taken into account. In this paragraph, the system configurations are identified for which the fault current in each phase is lower than 90 % of the minimum current originally detected, i.e. without the presence of a generator. These configurations are labeled “low current”. This provides a general view of the influence of the generator. Currents will be expressed as a per unit (p.u.) value, with 1 p.u. being the original fault current. Afterwards, currents are compared to IMSC. This provides the subset of configurations which are problematic, as in these cases it is possible the circuit breaker does not trip at the desired moment. For this comparison, currents will be expressed as a percentage of IMSC, so as to distinguish these values form the p.u. values. In order to outline the sets of configurations with low currents, reference is made to the matrix in Fig. 3. This matrix is repeated four times in Fig. 5, once for each fault type. In the following discussion, sets of configurations with the same value for SSC are referred to as rows of the matrix in Fig. 3. Sets with the same value for AC are referred to as columns. Rows and columns are indicated with the value of the corresponding variable, e.g. row “500” or column “25”. For the following discussion of detected current, distinction between the instants at 0.1 s and 0.2 s after the start of the fault is made only when there is a considerable difference. A. Three-Phase Fault 1) Comparison with the Original Fault Current: For the three-phase fault, no low-current situations are found when a half-sized generator is used: for all configurations the three phase currents are higher than 0.9 p.u. For configurations with larger generators, currents are lower. For a double-sized generator, simultaneously low currents do occur. In Fig. 5a the region of low current is indicated for a double-sized generator at node 1 at 0.1 s, for IMSC equal to 6•IR, i.e. columns “10” to “50” (striped area). At 0.2 s this region is extended with column “70”. When the power of the generator is decreased or the location of the generator is shifted towards node 5, the low-current region is reduced towards the smaller cable sizes. At node 2, it consists of columns “10” to “35”. For a generator at node 3 or 4, there is no low-current region. The low-current region is largest for a double-sized generator at node 1. The overall minimum is found for columns “10” and “16”, at 0.2 s. For these cases, the phase currents range from 0.79 to 0.81 p.u. For the systems with IMSC equal to 12•IR and the generator at node 1, the low-current region at 0.1 s is indicated in Fig. 5a by means of dots. At 0.2 s this region is extended to column “25”. Decreasing the power of the generator or placing the generator at the next node reduces this region. Again, the overall minimum is found for columns “10” and “16” at 0.2 s. Here the phase currents range from 0.85 to 0.87 p.u. 2) Comparison with IMSC: In Table II the minimum detected current is given for each fault type, for both designs (IMSC = 6•IR or 12•IR) and for the half-sized and double-sized
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50 100 200 500 1000
10 16 25 35 50 70 95 120 150 185 240 300
AC SSC 50 100 200 500 1000
10 16 25 35 50 70 95 120 150 185 240 300
generator. The values for the three-phase fault show that for IMSC equal to 6•IR the detected current does not drop below the tripping current: the minimum value is 110 %. For the designs with IMSC equal to 12•IR, the minimum value is 97 %. This means an induction generator does not interfere with shortcircuit detection when a three-phase fault occurs.
a b c d
Fig. 5. Low-current combinations (< 0.9 p.u.) for a) three-phase, b) line-toline and d) single line-to-ground fault. Combinations with currents < 0.95 p.u. for c) double line-to-ground fault. Double-sized generator at node 1 at 0.1 s. Striped area: IMSC = 6•IR, dotted area IMSC = 12•IR .
B. Line-to-Line Fault 1) Comparison with the Original Fault Current: For the line-to-line fault, no low-current situations are found when a half-sized generator is used. For larger generators, low-current situations are found. For a double-sized generator at node 1, the low-current region at 0.1 and 0.2 s consists of columns “10” to “70” (and combination 50 MVA / 95 mm2 at 0.1 s) (Fig. 5b). For the other nodes, no low-current region is found. The two phase currents are lowest for a double-sized generator at node 1, at 0.2 s. The lowest currents are found for the configurations with AC equal to 10 and 16 mm2 and the combination 50 MVA / 25 mm2. For these cases, the current in one phase is 0.67 p.u. and in the other phase 0.84 to 0.85 p.u. For the systems with IMSC equal to 12•IR, the low-current region at 0.1 s consists of columns “10” to “25” and the combination 50 MVA / 35 mm2 (Fig. 5b). The overall minimum is found for the combination 500 MVA / 10 mm2, at 0.2 s: the phase currents are 0.76 and 0.87 p.u. 2) Comparison with IMSC: For a double-sized generator in a system with IMSC equal to 6•IR, the detected currents of one phase are lower than IMSC, except for several configurations situated in columns “120” to “300”. The minimum current is 80 % (Table II). The current in the other phase is 108 %, resulting in adequate fault detection. There are no configurations for which both currents are lower than 100 %. For the systems with IMSC equal to 12•IR, the minimum current is 76 %. The current in the other phase is 103 %. For the configurations in columns “10” and those with SSC from 50 to 200 MVA in column “16”, with a double-sized generator at node 1, are both currents lower than 90 %. For these cases, the maximum of both phase currents is lowest at 50 MVA / 10 mm2. The currents are 77 and 88 %. Here the transition from the inverse-time section to the definite-time section of the relay’s characteristic should be below 88 % of 12•IR, in order to keep the fault current during a short circuit in the definitetime section. C. Double Line-to-Ground Fault 1) Comparison with the Original Fault Current: For the
double line-to-line fault, no currents lower than 0.9 p.u. are found when a half-sized generator is used. For the doublesized generator, a small number of low-current combinations are found. In order to provide more information in Fig. 5c, the combinations indicated are those with both currents lower than 0.95 p.u. instead of 0.9 p.u. With IMSC equal to 6•IR, the configuration for which the maximum of both phase currents is lowest, is 50 MVA / 150 mm2 / node 1. The currents are 0.78 p.u. and 0.9 p.u. With IMSC equal to 12•IR, the configuration for which the maximum of both phase currents is lowest, is 100 MVA / 120 mm2 / node 1. The currents are 0.85 p.u. and 0.93 p.u. 2) Comparison with IMSC: For nodes 1 to 3 there are configurations for which the current in one phase is lower than 100 %. For the configurations with a double-sized generator and IMSC equal to 6•IR, the minimum current is 88 % (Table II). The current in the other phase is 115 %. For the configurations with IMSC equal to 12•IR, the minimum current is 81 %. The current in the other phase is 103 %. There are no cases for which both currents are lower than 6•IR or 12•IR, respectively. These findings lead to the conclusion that there is no detection problem when a double line-to-ground fault occurs. TABLE II LOWEST CURRENTS, IN % OF IMSC. TIME = 0.2 S. *: H ALF -SIZED GENERATOR, **: D OUBLE -SIZED GENERATOR
Fault
Three-phase
Line-to-line Double lineto-ground Single lineto-ground
IMSC
Generator at node
Half-sized Generator
Double-sized generator
Current [%]
Current [%]
6 IR
1
128
110
12 IR
1
109
97 80
6 IR
3 * / 2 **
113
12 IR
4 * / 3 **
96
76
6 IR
2 * / 1 **
113
88
12 IR
1
95
81
6 IR
1
94
81
12 IR
1
94
86
D. Single Line-to-Ground Fault 1) Comparison with the Original Fault Current: When a single line-to-ground fault occurs, the detected current for all configurations is lower than the current without the presence of a generator. For configurations with IMSC equal to 6•IR and a half-sized generator, the currents lie between 0.94 and 0.99 p.u. For a double-sized generator, currents lie between 0.79 and 0.95 p.u. For configurations with the generator at node 1, the low-current region consists of columns “10” to “240”, as is shown in Fig. 5d. When the generator is moved away from node 1, the low-current region becomes smaller. At node 3 it consists of columns “10” to “185”. At node 4 it consists of columns “50” to “185”. For configurations with IMSC equal to 12•IR and a half-sized generator, the currents lie between 0.96 and 1 p.u. For a double-sized generator, currents lie between 0.84 and 0.96 p.u. The lowest currents are found for the configurations with a double-sized generator at node 1, at 0.2 s, AC equal to 10 and 16 mm2. For the configurations with IMSC equal to 6•IR, the
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current is 0.79 to 0.8 p.u. For the configurations with IMSC equal to 12•IR, the current is 0.84 to 0.86 p.u. 2) Comparison with IMSC: For configurations with IMSC equal to 6•IR and with a half-sized generator, the detected current is lower than 100 % for cable sections of 70 mm2 and higher. For nodes 3 and 4 some configurations in columns “240” and “300” result in currents that are higher than IMSC. For both possible values of IMSC the minimum current is 94 %. For a double-sized generator the detected current is lower than 100 % for cable sections of 35 mm2 and larger for nodes 1 and 2. For the other two nodes, this region starts at column “50”. Currents that are lower than 90 % are found in columns “50” to “185” for nodes 1 and 2. This region becomes smaller if the generator is moved further away from the transformer. For node 4, these currents are found in columns “70” to “150”. The minimum current is 81 % (node 1, 50 MVA, 70 mm2) (Table II). For the configurations with IMSC equal to 12•IR, the minimum current is 86 % (node 1, 100 MVA, 25 mm2). 3) Ground Current: Because detected current is lower than 90 % of IMSC for half of the configurations with a generator at node 1 or 2, the ground current IG is considered as well (IG = IA + IB + IC + IN). When IG is compared to its value without the contribution of the generator, it is found that for configurations with IMSC equal to 6•IR there are configurations for which IG is affected negatively. For a generator at node 1 all configurations result in lower current. For a half-sized generator the minimum current is 97 % of the original IG (50 MVA / 185 mm2). For a double-sized generator, the minimum current is 90 % (50 MVA / 300 mm2). For configurations with IMSC equal to 12•IR, the minimum current is 99 % for a halfsized generator and 96 % for a double-sized generator. These results show that during a fault IG remains high when an induction generator is used locally. As a result, the ground current can be used to detect a single line-to-ground fault. E. Number of Generators The simulations discussed so far concern a distribution system with one four-pole generator. In order to investigate the effect of increasing the number of generators while keeping the generated power constant, additional simulations are conducted with modified systems. These systems consist of eight combinations, marked by X in Fig. 3. The double-sized generator is replaced by two unit-sized or four half-sized generators. The generators are located at the same node. Each generator is connected to the feeder through an individual transformer. The results are compared to the results for the double-sized generator. For all configurations, the effect of increasing the number of generators, on detected fault current is weak. If the instant at 0.1 s is considered, the maximum increase is 1.3 % (single line-to-ground fault, IMSC = 6•IR) and the maximum decrease is 1.6 % (three-phase fault, IMSC = 12•IR), compared to the maximum detected current with one generator. At 0.2 s the maximum increase is 2.7 % (threephase fault, IMSC = 6•IR) and the maximum decrease is 1.2 % (line-to-line fault, IMSC = 6•IR). In all of these cases, the number of generators is four. The maximum increases are found for the configurations with a cable of 240 mm2. The maximum decreases are found for the configurations with a cable of 16 mm2.
IV. CONCLUSION A study has been presented, concerning the effect of an embedded induction generator on the current detected by a relay at the beginning of a distribution feeder during a fault situation. If this current is lower than the tripping current of the definite-time characteristic of the circuit breaker, protection schemes of feeders have to be adapted when embedded generators are installed. By varying the values of the system parameters in a structured way, a large number of system configurations are covered. It is assumed a three-phase relay and circuit breaker are used. In order to assess the effect on fault detection, the currents in the affected phases have to be considered simultaneously. If the current in one phase remains sufficiently high, the fault will be detected fast enough. Among the low-current situations, the following maximum decreases in detected current are found: 0.19 p.u. for the threephase fault, 0.15 p.u. for the line-to-line fault, 0.1 p.u. for the double line-to-line fault and 0.2 p.u. for the single line-toground fault. In all of these cases, IMSC is equal to 6•IR. A comparison of the detected currents with IMSC shows that for the three-phase fault and the double line-to-ground fault, one phase current is always sufficiently high. When these faults occur, an embedded induction generator does not pose a detection problem. For the line-to-line fault, a problem can arise when a double-sized generator is used at node 1 (10 and 16 mm2 / IMSC = 12•IR). The largest decrease is 12 %. For the single phase-toground fault, the minimum current is 81 % of IMSC. This decrease can pose a problem. With measurement of the ground current, this problem can be solved. Investigation of the effect of the number of generators shows that increasing the number up to four does not strengthen the effect of decreased currents; the maximum decrease is 1.6 %. V. APPENDIX Equations for the induction generator in an arbitrary reference frame [23] (pp. 147, 150, 154, 157): voltage equations for stator (1) and rotor (2), flux linkages of stator (3) and rotor (4), electromagnetic torque and mechanical equation (5), inertia constant (6). The stator windings are ungrounded, therefore the zero-sequence currents are zero. vqs = rsiqs + ωλds + pλqs
vds = rsids − ωλqs + pλds
vqr′ = rr′iqr′ + (ω − ωr ) λdr′ + pλqr′
vdr′ = rr′idr′ − (ω − ωr ) λqr′ + pλdr′ (2)
λqs = Llsiqs + LM ( iqs + iqr′ )
λds = Llsids + LM ( ids + idr′ )
(3)
λdr′ = Llr′ idr′ + LM ( ids + idr′ )
(4)
λqr′ = Llr′ iqr′ + LM ( iqs + iqr′ )
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Te =
3P LM ( iqsidr′ − ids iqr′ ) 22
(Te − TL )
1 § 2 · J ωb2 H= ¨ ¸ 2 © P ¹ SB
P = pωr 2J
(1)
(5)
2
(6)
Symbols: P: number of poles, p: differential operator, Ll: leakage inductance, LM: main inductance, Ȧ: electric speed of reference frame, Ȧr: electrical rotor speed, J: inertia, H: inertia constant, SB: base power, Ȧb: base frequency.
[14]
[15] TABLE III FOR SIX CABLE SIZES: RATED CURRENT IR OF FEEDER AND DATA OF HALF AND DOUBLE -SIZED GENERATORS: APPARENT POWER S AND I NERTIA CONSTANT H.
AC (mm2) 10 25 50 120 185 300
IR (A) 81 135 185 310 396 522
Half-sized generator S (kVA) H (s) 28 0.19 47 0.25 64 0.28 107 0.30 137 0.36 181 0.36
[16] [17] [18]
Double-sized generator S (kVA) H (s) 112 0.31 187 0.36 256 0.41 430 0.47 549 0.58 723 0.50
[19] [20] [21] [22] [23]
VI. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[24]
P. Dondi, D. Bayoumi, C. Haederli, D. Julian, and M. Suter, “Network integration of distributed power generation,” Journal of Power Sources, vol. 106, pp. 1-9, 2002. M. Megdiche, Y. Besanger, J. Aupied, R. Garnier, and N. Hadjsaid, “Reliability assessment of distribution systems with distributed generation including fault location and restoration process,” in Proc. 2003 CIRED, 17th International Conference on Electricity Distribution, Barcelona, Spain, 12-15 May. F. M. Gatta, F. Iliceto, S. Lauria, and P. Masato, “Behaviour of dispersed generation in distribution networks during system disturbances. Measures to prevent disconnection,” in Proc. 2003 CIRED, 17th International Conference on Electricity Distribution, Barcelona, Spain, 12-15 May. R. C. Dugan and T. E. McDermott, “Operating conflicts for distributed generation interconnected with utility distribution systems,” IEEE Industry Applications Magazine, pp. 19-25, MarchApril, 2002. N. Hadjsaid, J. Canard, and F. Dumas, “Dispersed generation increases the complexity of controlling, protecting and maintaining the distribution system,” IEEE Computer Applications in Power, pp. 2328, April, 1999. C. J. Mozina, “Interconnection protection of IPP generators at commercial/industrial facilities,” IEEE Transactions on Industry Applications, vol. 37 (3), pp. 681-688, 2001. S. Stieb, A. Wildenhein, and W. Zimmermann, “Connection of cogeneration plants with the medium voltage network of public utilities,” in Proc. 1999 CIRED, 15th International Conference on Electricity Distribution, Nice, France, 1-4 June. S. M. Brahma and A. A. Girgis, “Microprocessor-based reclosing to coordinate fuse and recloser in a system with high penetration of distributed generation,” in Proc. 2002 IEEE Power Engineering Societ, Summer Meeting, vol. 1, pp. 453-458, 21-25 July. M. E. Baran and I. El-Markaby, “Fault analysis on distribution feeders with distributed generators,” IEEE Transactions on Power Systems, vol. 20 (4), pp. 1757-1764, 2005. T. M. de Britto, D. R. Morais, M. A. Marin, J. G. Rolim, H. H. Zürn and R. F. Buendgens, “Distributed generation impacts on the coordination of protection systems in distribution networks,” in Proc. 2004 IEEE Power Engineering Societ, Transmission and Distribution Latin América, São Paulo, pp. 623-628. S. M. Brahma and A. A. Girgis, “Development of adaptive protection scheme for distribution systems with high penetration of distributed generation,” IEEE Transactions on Power Delivery, vol. 19 (1) pp. 56-63, January 2004. I. Chilvers, N. Jenkins and P. Crossley, “Development of distribution network protection schemes to maximize the connection of distributed generation,” in Proc. 2003 CIRED, 17th International Conference on Electricity Distribution, Barcelona, 12-15 May. M. Baran and I. El-Markabi, “Adaptive over current protection for distribution feeders with distributed generators,” in Proc. 2004 IEEE
[25] [26]
Power Engineering Society Power Systems Conference and Exposition, pp. 715-719. B. de Metz-Noblat, F. Dumas and C. Poulain, “Cahier Technique no. 158: Calculation of Short-Circuit Currents,” September 2005 [Online]. Available: http://www.schneider-electric.com P. M. Anderson, Power System Protection, New York: McGraw-Hill, 1999, p. 149. G. G. Seip (editor), Electrical Installations Handbook, 3rd ed., Chichester (United Kingdom): Wiley, 2000, pp. 285 – 288. Cable series: EXVB 4 x … mm2 [Online]. Available: http://eservice.nexans.com R. Bartnikas and K. D. Srivastava (editors), Power and Communication Cables - Theory and Applications, Piscataway (New Jersey): IEEE Press, 2000, p. 179, pp. 460 – 461. L. Heinhold, Kabel und Leitungen für Starkstrom, Berlin: Siemens Aktiengesellschaft, 1965, p. 20. J. J. Grainger and W. D. Stevenson, Power System Analysis, New York: McGraw-Hill, Inc., 1994, p.155. W. H. Kersting, Distribution System Modeling and Analysis, Boca Raton (Florida): CRC Press, 2002, p. 77. IEC standard voltages, IEC 60038 Ed. 6.2, 2002, p. 11. P. C. Krause, O. Wasynczuk and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, 2nd ed., Piscataway (New Jersey): IEEE Press, 2002. P. M. Anderson, Analysis of Faulted Power Systems, Ames (Iowa): The Iowa State University Press, 1973, p. 225. Low Voltage General Purpose Motors, ABB, pp. 88 – 91, 2005 [Online]. Available: http://www.abb.com Short-Circuit Currents in Three-phase A.C. Systems, International Standard IEC 60909, Geneva (Switzerland), 2001.
VII. BIOGRAPHIES
Pieter Vermeyen (S’06) was born in Belgium in 1979. He graduated as an electrical engineer in 2002 at the Katholieke Universiteit Leuven (KULeuven). He started working as a member of ELECTA, a research group of the KULeuven, participating in various projects. In 2003 he started his own research project, in order to obtain a Ph. D. degree. His main fields of interest are electrical safety and protection of power systems.
Johan Driesen (S’93–M’97) was born in 1973 in Belgium. He received the M.Sc. degree in 1996 as Electrotechnical Engineer from the K.U. Leuven, Belgium. He received the Ph.D. degree in Electrical Engineering at K.U.Leuven in 2000 on the finite element solution of coupled thermal-electromagnetic problems and related applications in electrical machines and drives, microsystems and power quality issues. Currently he is an associate professor at the K.U.Leuven and teaches power electronics and drives. In 2000-2001 he was a visiting researcher in the Imperial College of Science, Technology and Medicine, London, UK. In 2002 he was working at the University of California, Berkeley, USA. Currently he conducts research on distributed generation, including renewable energy systems, power electronics and its applications, for instance in drives and power quality.
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Ronnie Belmans (S’77-M’84-SM’89-F’05) received the M.S. degree in electrical engineering in 1979, the Ph.D. in 1984, and the Special Doctorate in 1989 from the K.U.Leuven, Belgium and the Habilitierung from the RWTH, Aachen, Germany, in 1993. Currently, he is full professor with K.U.Leuven, teaching electrical machines and variable speed drives. He is appointed visiting professor at Imperial College in London. He is also President of UIE. He was with the Laboratory for Electrical Machines of the RWTH, Aachen, Germany (Von Humboldt Fellow, Oct.’88-Sept.’89). Oct.’89-Sept.’90, he was visiting associate professor at Mc Master University, Hamilton, Ont., Canada. During the academic year 1995-1996 he occupied the Chair at the London University, offered by the Anglo-Belgian Society. Dr. Belmans is a fellow of the IEE (United Kingdom). He is the chairman of the board of Elia, the Belgian transmission grid operator.
Daniel Van Dommelen (M '70, SM '78) graduated as electrotechnical engineer from the K.U.Leuven in Belgium, holds an M.Sc. in Electrical Engineering (U. Wisc.), and a PhD from the K.U.Leuven. Since 1977 he is full professor at this university, where he teaches both undergraduate and graduate courses in Power Systems, High Voltage and Electroheat. He is the author of a book on Production, Transmission and Distribution of Electric Power, presently in its fully revised second edition after five reprints, and of numerous publications in both national and international journals. He is a Belgian representative in the Committee for Education and Research in Electroheat of the UIE. He initiated Electrabel’s Interuniversity Chair in Electroheat. He has been chairman and is presently SAC for the IEEE Benelux Section. He is a distinguished member of CIGRE, a senior member of the IEEE and of the French SEE and a member of national engineering societies.
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