Therefore the exact measurement of the grid impedance is necessary

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(1)Grid Impedance Determination - Relevancy for Grid Integration of Renewable Energy Systems Hauke Langkowski, Trung Do Thanh, Klaus-Dieter Dettmann, Detlef Schulz Helmut-Schmidt-University, Faculty of Electrical Power Systems, Holstenhofweg 85, 22043 Hamburg, Germany hauke.langkowski@hsu-hh.de, trung.dothanh@hsu-hh.de, kd.det@hsu-hh.de, detlef.schulz@hsu-hh.de. Abstract—As the power of renewable energy plants is increasing, their impact on the power quality becomes more and more important. The occurring grid feedback is related to the grid impedance. Therefore the exact measurement of the grid impedance is necessary. In this paper simulations of a windfarm grid integration scenario are presented that show the advantages of a grid impedance measurement in context of harmonics. In addition methods to determine the frequency dependent grid impedances are outlined and the influence of the virtual-starpoint on the calculations is examined. Based on the examinations a novel method to identify the real grid impedances is proposed.. I. I NTRODUCTION With growing installed power the impact on the power quality of renewable energy systems using power converters cannot be neglected. Current harmonics caused by the converters possibly cause undesired over-voltages at resonance points in the grid. Due to this effect the isolations of connected electrical equipments could be damaged. For that reason the behavior of the grid impedance is important when evaluating the power quality. There are many grid impedance identification methods in time and in frequency domain. It is distinguished between the identification at low- and at medium-/high-voltage level. Since at medium- and high-voltage level only a three-phase three-wire-system exists most identification methods use the transformation of the line to line voltages to virtual-starpoint voltages to determine the grid impedances. In a balanced grid and in grids with slightly asymmetrical grid impedances these identification methods produce nearly accurate results. But if the grid is unbalanced to higher degree only virtual grid impedances can be calculated that do not comply with the real grid impedance values. For that reason this paper investigates the accuracy of the grid impedance calculation by means of virtual voltages. Furthermore a novel method to identify the real grid impedances at medium- and high-voltage level respectively is proposed. A further aspect that is considered in this paper is the improvement of the grid integration of renewable energy systems by means of grid impedance measurement. In order to get access permission for renewable energy systems at the medium- and high-voltage level the given grid codes of local power utilities have to be fulfilled. This involves in certain cases high costs, which can be reduced with grid simulations before the energy systems are connected to the power supply. For the simulations the real grid structure at the PCC (Point of Common Coupling) should be known. In reality the grid. 978-1-4244-4649-0/09/$25.00 ©2009 IEEE. structure is very complex and it is impossible to set it up in a simulation. Therefore the grid impedance should be measured to predict the influence of renewable energy systems that are planned to be connected to the grid. Using the grid simulation program DIgSILENT Power Factory the necessity of grid impedance measurement is shown by a windfarm grid integration example. Resonance points in the grid can be detected which help to optimize the filter dimensioning at the PCC. By that way the capacity of the access point can be used in an optimal way allowing maybe the connection of additional wind energy converters (WECs). II. I MPROVED GRID INTEGRATION BY MEANS OF GRID IMPEDANCE MEASUREMENT. Currently, at the Helmut-Schmidt-University Hamburg a novel grid impedance measurement device is in development that is able to determine the grid impedance in dependency of frequency and time. Using the measured shape of the grid impedance, effects when connecting WECs to the power grid could be predicted. The improved grid integration procedure could be: 1) Measurement of the source voltage at the PCC and identification of the present harmonic spectrum 2) Measurement of the grid impedance at the PCC using the novel measurement device 3) Set up of a mathematical model that includes the frequency behavior of the grid impedance 4) Determination of the required cable length and type for the WECs 5) Simulation of the network using the specifications in the certificate of the WECs and the models of cable and grid impedance 6) Identify possible problems at resonance frequencies 7) Optimization of filter dimensioning With the determined shape of the grid impedance resonance peaks are read off. These peaks can be suppressed by appropriate compensation networks. In this way it can be ensured that the power quality limits are held. Unnecessary retrofits of transmission systems can be avoided. The procedure named above is illustrated in the following simulations. Fig. 1 shows a windfarm with five 2 MW WECs planned to be connected over a 7 km medium-voltage cable with the power distribution grid. The windfarm shares the PCC. 516.

(2) with a parallel medium-voltage consumer grid that supplies an industrial consumer and a small village.. Voltage Level [p.u.]. .

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(6). . . Relevant limitation values PCC − disconnected wind−farm PCC − connected wind−farm. 0. 10. −1. 10. −2. 10. −3. 10. . ! −4. 10. . 4. 6. 8. 10. 12. 14. Fig. 3: Harmonics voltages at the PCC before and after WECs are connected. Before the windfarm is connected to the PCC two resonance points at 680 Hz and 1350 Hz can be identified (Fig. 2). These resonance points result from the grid transformer, connected cables and loads. When the WECs are connected to the PCC the resonance points are shifted to lower frequencies due to the additional cable 1. The first resonance point is shifted to 650 Hz and meets the 13th harmonic.. 1000. It can be observed that the limitation values are exceeded if the WECs are connected to the PCC. With this knowledge the windfarm owners can optimize integrated filters of their WECs. This process allows to forecast, if existing standards will be held, since there is more data available for simulations. The grid integration is improved, since possible problems can be avoided in advance. If different PCCs are available, a suitable one can be chosen. Additionally it will be possible to allocate the origin of disturbing harmonics. III. M ETHOD FOR IDENTIFICATION OF GRID IMPEDANCES A. General Method There are several methods that can be used to determine the grid impedance. The general method can be seen in Fig. 4 where a resistive load is switched on and off in order to get two different load situations of the circuit. When the switch is off (subscript 1), no current flows (i1 = 0) and the measured voltage equals to the phase grid voltage (v1 = vG ). In the next case when the switch is on (subscript 2), the current equals to i2 and the measured voltage equals to the load voltage v2 .. |Z| at PCC before |Z| at PCC after. 800. Grid impedance [Ohm]. 2. Order of Harmonics. Fig. 1: Windfarm simulation setup. 900. 0. 700 600 500 400 300 200 100 0. 0. 500. 1000. 1500. 2000. Frequency [Hz]. Fig. 2: Frequency shape of the grid impedance at PCC before and after connection of the windfarm. The voltage levels of certain harmonics as well as the limitation values are shown in Fig. 3 before and after the connection of the WECs. The black bars represent relevant limitation values. The gray bars show the values before the windfarm is connected and the white bars show the values after the windfarm is connected to the PCC.. 978-1-4244-4649-0/09/$25.00 ©2009 IEEE. Fig. 4: Equivalent circuit for a single-phase impedance measurement In order to consider the frequency dependent grid impedances the measured currents and voltages are transformed into the frequency domain using the FFT-algorithm. In the frequency domain the grid impedance can be calculated as follows:. 517.

(7) ZG = RG + jωLG =. V1 − V2 ΔV ΔV = = ΔI I1 − I2 I2. (1). B. Grid Impedance Measuring at Low-Voltage Level At the low-voltage level the grid impedance can be measured in single-phase and three-phase systems. Looking at the fact that at the low-voltage level a four-wire system is installed, the grid impedance can be calculated with unbalanced grid voltages, too. In Fig. 5 the four-wire measuring circuit at the 0.4 kV level is shown. Kirchhoff’s laws are applied to meshes ”a-N”,”b-N” and ”c-N” for two different cases. At first, all switches are open (subscript 1) and then, all switches are closed (subscript 2). From the first set of equations results that the grid voltages V Ga , V Gb and V Gc are equal to the terminal voltages V 1,Na , V 1,Nb and V 1,Nc . The latter are used to substitute the grid voltages in the second set of equations. In this way three linearly independent equations are obtained for calculating the three unequal phase grid impedances:. −V 1,Na + I 2,a · Z Ga + V 2,Na −V 1,Nb + I 2,b · Z Gb + V 2,Nb. = =. 0 0. −V 1,Nc + I 2,c · Z Gc + V 2,Nc. =. 0. Fig. 5: Three-phase four-wire equivalent circuit C. Grid Impedance Measuring at Medium- and High-Voltage Level In contrast to the low-voltage level a three-phase four-wire system does not exist at the medium- and high-voltage level. For a three-wire grid the measurement circuit is shown in Fig. 6.. (2). Fig. 6: Three-phase three-wire equivalent circuit Evaluating equation (2) using the abbreviation V 1,a − V 2,a = ΔV a , the equations ⎤ ⎡ I 2,a ΔV a ⎣ ΔV b ⎦ = ⎣ 0 ΔV c 0 ⎡. 0. I 2,b 0. ⎤ ⎡ ⎤ 0 Z Ga 0 ⎦ · ⎣ Z Gb ⎦ Z Gc I 2,c. (3). In this circuit the line to line voltages are measured, because the neutral point’s potential at the loads is undefined. Therefore it fluctuates and cannot be used as a reference point. Applying Kirchhoff’s laws to the two meshes ”a-b” and ”b-c” in Fig. 6 while the switches are on, two linear independent equations can be found: I 2,a · (Z Ga + RLa ) − I 2,b · (Z Gb + RLb ) = V 1,ab I 2,b · (Z Gb + RLb ) − I 2,c · (Z Gc + RLc ) = V 1,bc. result. This set of equations can be rearranged to calculate the grid impedances: ⎡. ⎤ Z Ga ⎣ Z Gb ⎦ = ⎢ ⎣ Z Gc ⎡. 1 I 2,a. 0. 0. 0. 0. 1 I 2,b. 0. 0. 1 I 2,c. ⎤ ⎡ ⎤ ΔV a ⎥ ⎣ ⎦ · ΔV b ⎦ ΔV c. (4). With only two equations the three unknown grid impedances cannot be calculated explicitly. Therefore a third condition is required to set up a third equation. For this purpose most identification methods introduce a virtual-starpoint as reference point that has not the same potential as the starpoint of the three loads. For any n-line current system with the currents i1 , i2 ,. . . ,in ,whose sum is always zero:. The grid impedance in each phase is only dependent on the current and voltage of the same phase. In this case a calculation of grid impedances is possible by a synchronous switching of three loads. The voltages and currents are transformed into the frequency domain and the grid impedances are calculated as quotients of the complex voltages and currents which have the same frequency.. 978-1-4244-4649-0/09/$25.00 ©2009 IEEE. (5). 518. n . Iμ = 0. (6). μ=1. the condition is defined as follows: n μ=1. V μ0 = 0. (7).

(8) By that way a system of n-virtual-starpoint voltages is introduced. With this third condition (7) the virtual-starpoint voltages can be calculated from the measured line to line voltages: V μ0. n 1 = V n μ=1 μn. ⎡. (9). The transformation of line to line voltages to virtualstarpoint voltages is applied for both situations when the switches are synchronously switched on and off. The difference of both voltage situations equals to [ΔV a0 , ΔV b0 , ΔV c0 ]. After transforming these virtual-terminal-voltages and the measured terminal currents respectively into the frequency domain and inserting them into the following matrix the socalled ”virtual grid impedances” are determined to: ⎤ ⎡ Z Ga0 ⎣ Z Gb0 ⎦ = ⎢ ⎣ Z Gc0 ⎡. 1 I 2,a. 0. 0. 0. 0. 1 I 2,b. 0. 0. 1 I 2,c. ⎤ ⎡ ⎤ ΔV a0 ⎥ ⎣ ⎦ · ΔV b0 ⎦ ΔV c0. μ=a. (10). c . V μ0 = 0 =. μ=a. V μN + 3 · V N0. (12). allows to obtain: c . (8). Applying this condition for a three-wire-system the virtual starpoint voltages result to: ⎡ ⎤ ⎡ ⎤ ⎤ 1 0 −1 V ab V a0 ⎣ V b0 ⎦ = 1 · ⎣ −1 1 0 ⎦ · ⎣ V bc ⎦ 3 V c0 V ca 0 −1 1. c . μ=a. V μN = −3 · V N0. (13). It can be seen that theoretically there are infinitely many solutions for equation (13), if the grid is unbalanced. In this case the reference point (0) and the starpoint (N) do not have the same potential. Therefore only virtual grid impedances are calculated dependently on the grid situation. For that reason a new method has to be applied in order to calculate the real grid impedances even in cases of unbalanced grids. This method is described in the following part. D. Novel Grid Impedance Measuring Method at Medium- and High-Voltage Level The two linearly independent equations, see (6), cannot be solved explicitly when the grid impedances are asymmetric. To set up three linearly independent equations, the described asymmetrical switching of two loads has to be repeated for the other two meshes in a cyclic manner. For example in order to get the first equation the switches in phases ”a” and ”b” are switched on while in phase ”c” the switch is off. Repeating the above steps for phases ”b-c” and ”a-c” respectively, three linearly independent equations result:. Because these virtual impedances are dependent on the arbitrary chosen virtual-starpoint they do not comply with the real grid impedances if the grid is unbalanced. In Fig. 7 voltages of a three-phase three-wire system at virtual-starpoint (0) can be seen.. V 1,ab (jω) − I 2,ab (jω) · (Z Ga + Z Gb +RLa + RLb ). =. 0. V 1,bc (jω) − I 2,bc (jω) · (Z Gb + Z Gc +RLb + RLc ). =. 0. V 1,ac (jω) − I 2,ac (jω) · (Z Ga + Z Gc +RLa + RLc ). =. 0. (14). With the knowledge of: V 2,ab (jω) = (RLa (jω) + RLb (jω)) · I 2,ab (jω). (15). and V 1,ab (jω)−V 2,ab (jω) = ΔV ab (jω) the system of equations (14) can be extracted, which leads to the individual grid impedances :. Fig. 7: Voltages at virtual-starpoint According to Fig. 7 the virtual-starpoint voltages are calculated to: V a0 V b0. = V aN + V N = V bN + V N. V c0. = V cN + V N. The equation:. 978-1-4244-4649-0/09/$25.00 ©2009 IEEE. (11). Z Ga Z Gb Z Gc. ⎡ 1⎢ = ⎣ 2. 1 I 2,ab 1 I 2,ab −I 1 2,ab. −I. 1. 2,bc. 1. I 2,bc 1 I 2,bc. 1 I 2,ac −I 1 2,ac 1 I 2,ac. ⎤ ⎥ ⎦·. ΔV a ΔV b ΔV c. (16). For this asymmetrical switching sequence a certain amount of time is necessary. If the grid conditions change significantly within this switching period, the measuring process has to be canceled and restarted. In order to identify the real grid impedances the method of asynchronous switching has to be applied. However this. 519.

(9) method is complex because many switching procedures have to be done. The following section investigates the accuracy of both grid impedance identification methods.. Absolute value Deviation [%]. MEASUREMENT. In the following the two grid impedance identification methods from the previous section are compared. The first method determines the grid impedance by means of virtual-starpoint voltages. In this method the loads are switched synchronously. The second method applies asynchronous switching of the loads in order to set up three linearly independent equations. Ideal three-phase voltage sources are used with specified grid impedances Z a , Z b and Z c to simulate the line to line voltages and line currents in case of connected resistive loads Ra , Rb and Rc . The obtained voltages and currents are used as original data in order to calculate the grid impedances with both methods. The grid impedances determined with the first method are called ”Z star ”, since they depend on the virtualstarpoint voltages. Additionally an index for the referred line is used for this method. The grid impedances of the second method will be named ”Z asyn ”. Next different grid situations are considered.. (17). (18). with their R/X-ratio set to 0.1. Z c is scaled from Z down to 0.5 · Z. The connected loads used in the simulation are:. 978-1-4244-4649-0/09/$25.00 ©2009 IEEE. 10 5 0. (19). 1. 0.9. 0.8. |Z c /Z|. 0.7. 0.6. 0.5. . Z a-star . Z b-star . Z c-star . Z asyn. Phase Deviation [%]. 10. 5. 0. −5. −10. −15. from the real grid impedance values of both methods are shown in Fig. 8 and Fig. 9. The calculated values using the described methods are compared with the real grid impedances for increasing degree of asymmetry in line c. The grid impedances used in the simulation are:. Ra = Rb = Rc = 200 · |Z|.. 15. 15. If the grid impedances used in the simulation are not symmetric the first method does not result in the exact values. The normalized deviations:. Za = Zb = Z. 20. Fig. 8: Deviation of virtual-starpoint (|Z star |) and asynchronous switching (|Z asyn |) methods for asymmetrical grid impedances and symmetrical loads. B. Asymmetrical grid impedances - symmetrical loads:. (Z) − (Z real ) (Z real ). 25. −10. The determined grid impedances of both methods are equal in absolute value and phase if the real grid impedances of the simulation are balanced. An asymmetry in the loads Ra , Rb and Rc does not have influence on the calculated grid impedances if the grid impedances specified in the simulation are symmetric.. . |Z asyn|. |Z c-star|. −5. A. Symmetrical grid impedances:. and. |Z b-star|. 30. IV. I NFLUENCE OF ASYMMETRY ON GRID IMPEDANCE. |Z| − |Z real | |Z real |. |Z a-star|. 35. 1. 0.9. 0.8. |Z c /Z|. 0.7. 0.6. 0.5. Fig. 9: Deviation in phase: asymmetrical grid impedances with symmetrical loads In Fig. 8 it can be seen that asynchronous switching does not have any deviation as expected in contrast to the other method which does not result in the specified real grid impedance values. The absolute value of the calculated grid impedances is too high in line c, which includes the scaled asymmetry, and too low in lines a and b (overlapping) in contrast to the real grid impedances. An asymmetry in line c of 0.5 leads to 33 % deviation in the absolute value of the calculated grid impedance in line c and -7 % in lines a and b, if virtualstarpoint voltages are used. The method using virtual-starpoint voltages leads to no phase deviation in line c, but to 2 % in line b and -11 % in line a for an asymmetry of 0.5 in line c, see Fig. 9. The phase deviation is almost linear to the asymmetry. C. Asymmetrical grid impedances - asymmetrical loads: In this part additionally to the unbalanced grid impedances also unbalanced loads are chosen:. 520.

(10) Ra /2 = Rb = Rc = 200 · |Z|.. (20). The resulting deviations in absolute value and phase can be seen in Fig. 10 and Fig. 11. |Z a-star|. 35. |Z b-star|. |Z asyn|. |Z c-star|. Absolute value Deviation [%]. 30 25 20 15 10 5. V. C ONCLUSION The grid impedance has to be considered when renewable energy converters are connected to the grid. The power quality underlies certain limitation values that must not be exceeded. Since most renewable energy converters contain power electronics that feed harmonic currents into the grid the frequency shape of the grid impedance is of interest. Resonance peaks at the PCC could be determined in advance allowing power plant operators to optimize the integrated filters. A further aspect in this paper introduces and compares two different methods that allow the determination of the grid impedances. The first method uses asynchronous switching of resistive loads while the second method uses virtualstarpoint voltages. Both methods produce the same results if the grid is balanced. In cases when the grid is unbalanced only the method with asynchronous switching determines the real grid impedances. With simulations it is shown that a strong asymmetry in the grid impedances results in large deviations of the determined grid impedances. In this case the method of asynchronous switching should be used. However in case of slightly unbalanced grid impedances only small deviations in the range of 2-5% occur, which can be neglected related to the measuring uncertainties of the measuring transformers.. 0 −5 −10 −15. 1. 0.9. 0.8. |Z c /Z|. 0.7. 0.6. 0.5. Fig. 10: Deviation in absolute value: asymmetrical grid impedances - asymmetrical loads . 10. Z a-star . Z b-star . Z c-star . Z asyn. 5. Phase Deviation [%]. D. Interpretation of results: In the simulations above it can be seen that the method of asynchronous switching results in the real grid impedances, while the determination of the grid impedance using virtualstarpoint voltages shows deviations. Considering the figures it can be observed that larger asymmetries in line c lead to exponential dependence on the asymmetry. In practice the medium- and high-voltage grids are assumed as balanced because their electrical components are assembled symmetrically. Strong asymmetries, as in the simulation, usually do not occur in normal operation, so the method using virtual-starpoint voltages can be applied without wrong interpretation of the real grid situation. In case of large deviations the method of asynchronous switching should be preferred since the real grid impedances are determined.. 0. −5. −10. −15. −20. R EFERENCES 1. 0.9. 0.8. |Z c /Z|. Fig. 11: Deviation in phase: impedances - asymmetrical loads. 0.7. 0.6. asymmetrical. 0.5. grid. It can be observed in Fig. 10 that the assumed asymmetrical loads result in shifted deviations in lines a and b compared to the previous simulation. The absolute values of the calculated grid impedances are deviated by about 5.3 % in line a and 12.5 % in line b for the method using virtual-starpoint voltages and an asymmetry of 0.5 in line c. Asynchronous switching leads to the expected grid impedances, again. The phases of the calculated grid impedances are deviated by about 8 % in line b and 17.5 % in line a for an asymmetry of 0.5 in line c, see Fig. 11. The deviations of the phases are almost linear to the asymmetry, as in the previous simulation.. 978-1-4244-4649-0/09/$25.00 ©2009 IEEE. [1] T. Do Thanh, S. Schostan, K. Dettmann and D. Schulz, ”Nonsinusoidal Power Caused by Measurements of Grid Impedances at Unbalanced Grid Voltages,” IEEE, Lagow, Poland, 2008. [2] D. Schulz, ”Power Quality - Theory, Simulation, Measurement and Assessment,” (in German), VDE-Verlag, Offenbach, Germany, 2004. [3] K. Heuck, K.-D. Dettmann and D. Schulz, ”Electrical Power Systems,” (in German), Vieweg, 7th Edition, Wiesbaden, Germany, 2007. [4] T. Tischbein, ”Identification of Harmonic Impedance of Medium-Voltage Grids,” (in German), VAB, Aachen, Germany, 1997. [5] BDEW, ”Technical Guideline: Power Plants at Medium-Voltage Grid,” (in German), BDEW, Berlin , Germany, 2008. [6] DIN 40110-1, ”Quantities used in alternating current theory,” (in German), part 1, ”two-line circuits”, (in German), 1994. [7] DIN 40110-2, ”Quantities used in alternating current theory,” (in German), part 2, ”Multi-conductor circuits,” (in German), 2002. [8] J. Schlabbach and W. Mombauer, ”Power Quality,” (in German), VDE Verlag, Berlin, Germany, 2008. [9] R. Dib and A. Breitstadt, ”Measurements in low-voltage networks and transformers in the range of up to 20 kHz,” Elektrizitätswirtschaft 97 (1998), no. 21, pp. 15-18.. 521.

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