Measurement of the Harmonic Impedance of the Aggregated Distribution Network

Measurement of the Harmonic Impedance of the Aggregated Distribution Network V. Ćuk, F. Ni, W. Jin, J.F.G. Cobben A. Jongepier H.E. van den Brom, G. Rietveld, M. Ačanski Eindhoven University of Technology Enduris B.V. VSL Eindhoven, the Netherlands Goes, the Netherlands Delft, the Netherlands Abstract--This paper presents a method for measurement of the harmonic impedance of an aggregated distribution network using multiple Phasor Measurement Units (PMUs) with the additional capability of synchronized voltage and current spectrum measurement. The perturbations of the harmonic voltages which originate from the higher voltage levels are distinguished based on the measurements from multiple busbars, and used as the input for the calculation. Results of a test case using measurements from a 5 kv network are given to illustrate the method. Index Terms Power Quality, Power system harmonics, Impedance measurement, Harmonic impedance, Load modeling, Phasor measurement units. T I. INTRODUCTION o perform studies of harmonic distortion propagation in an electricity grid, the impedance information of the network is needed as well as information on the emission of disturbing loads. For network elements such as transformers, lines, cables and capacitor banks, harmonic impedance models are considered to be mature knowledge and are standardly used as such for system studies. The two main challenges in the modeling of harmonic impedances are: modeling of the aggregated upstream network (e.g. the high voltage network when analyzing the distribution system) and modeling of the aggregated loads which may have a known or unknown composition. In an early CIGRE report [1], three approaches to the modeling of aggregated loads are proposed: - Representing them only with equivalent resistance, where the value is obtained from the fundamental active power value (measured or assumed) and a scaling factor to take skin-effect into account, - Complementary to the equivalent resistance, using a parallel inductive reactance, with the value determined based on the short-circuit impedance of assumed motor loads in service, This work is carried out as part of a joint European research project called Measurement Tools for Smart Grid Stability and Supply Quality Management. The project is part of the European Metrology Research Program (EMRP), which is jointly funded by the EMRP participating countries within EURAMET and the European Union. Additional funding is received from the Dutch Ministry of Economic Affairs. - Using a generalized impedance equivalent, as shown in Figure 1, with values of components derived from field measurements. In the third method, the values of the equivalent resistance R, the series harmonic reactance X sh and the shunt harmonic reactance X ph are calculated using: = (1) =.73 h (2) h = 6.7 (3).74 where U is the nominal voltage of the observed system, P 1 is the measured fundamental active power, h is the harmonic order and Q 1 is the measured fundamental reactive Figure 1.Generalized harmonic load equivalent, as proposed in [1], with the values of components based on field measurements. An overview of alternative aggregated equivalents is given in [2], where it was discussed that most of the equivalents used differ only in coefficients, namely the way motor loads are taken into account. There are two reasons to assume that the generality of these equivalents is limited. The first one is that the network composition (share of overhead lines and cables) and load composition (types of loads and consumption profiles) differ per country and per region. The second reason is that the loads are evolving in time, in particular the share of power electronic loads is considerably larger than in the time these equivalents were developed and measurements were made, which was the end of 197s and early 198s. 978-1-59-3792-6/16/$31. 216 IEEE 834

The reliability of these equivalents is difficult to assess, as the simulation results are also dependent on the way the emission is modeled. One approach to analyze the uncertainty of the models is to use new measurement results, which can also include the dependency to the measured power levels. This paper proposes a method to measure the equivalent harmonic impedance of the loads from synchronously measured spectra of voltages and currents on consecutive busbars in the network. In Chapter II, the general approaches to load impedance measurement are introduced, and the differences to measurement of the upstream network impedance. In Chapter III the proposed method is introduced and in Chapter IV the test case, measurements from a 5 kv network in the Netherlands, is introduced. Measurement results and discussion are presented in Chapter V, followed by the conclusions in Chapter VI. II. MEASUREMENT OF HARMONIC IMPEDANCE Measurement of harmonic impedances is addressed in a number of papers, with a summary given in [3]. The basic approach of all of the mentioned methods is: = (4) where Z h is the harmonic impedance of the order h, ΔU h is change of the h th harmonic voltage and ΔI h is the change of the h th harmonic current. The reason to use changes of the spectrum, instead of simply measurements of a single moment in time, is to reduce the uncertainty which comes from the fact that distortion is caused by multiple sources operating at the same time. In particular, if the loads downstream from the measurement point are causing most of the voltage distortion (or its change), we are able to calculate the supply impedance. In this case the background distortion originating in the upstream part of the system is a source of measurement error. Conversely, if we want to calculate the equivalent impedance of the loads, the upstream distortion should is the dominant source of information, and the emission of loads downstream become a source of error. Many of the practical applications utilize injection of harmonic or inter-harmonic perturbations into the network, and then calculate the harmonic impedances based on the differences of voltage and current spectra before and during the perturbation [4] [7], whereas other methods make use of load changes, transients or data selection for this purpose [8] [11]. With the exception of the work in [7], the other papers are addressing the measurement of the supply side impedance, with the challenge of reducing the impact of supply side distortion. For the measurement of load side impedance, which is the topic of this paper, one of the main challenges is to reduce the impact of load side emissions, i.e. using the changes of distortion which originate from the upstream network. In [7], this problem was dealt with by using the current and voltage waveforms during a deliberately induced switching transients (capacitor bank switching), upstream from the observed distribution system feeders. The results showed good matching with the excepted (calculated) results. The aim of this paper is to propose a method which can effectively identify upstream network induced changes of distortion, e.g. due to load variations, and calculate the equivalent harmonic impedance of loads based on measured spectra rather than waveforms. III. PROPOSED METHODOLOGY As discussed in the previous chapter, one of the main challenges in determining the load side impedance is the identification of the changes in the voltage and current spectra which are caused by variations on the supply side (large load or generation changes in the upstream network). For this reason, in this paper it is proposed to use synchronized voltage spectrum measurements e.g. using synchronized measurement data from PMUs with additional harmonic spectrum functionality on several consecutive busbars, to identify time moments when harmonic voltages are changing by (almost) equal amounts on all of them. If there are time moments when: (5) where the underscore designates the complex value, and ΔU hi is the change of the harmonic voltage on busbar i, we can conclude that the change is caused by the upstream system. These changes will differ from each other due to the measurement uncertainty and simultaneous changes caused by the loads and generators downstream from each of the busbars. The threshold for considering the changes close enough is debatable; in this paper the approach is to calculate the vectorial difference between each two busbar voltage changes and compare the magnitude of this difference to a threshold set e.g. to the class of voltage transformers used.5 %. After the perturbations originating from the upstream network are identified, the simultaneous changes of the voltage and current harmonicsof the harmonic current flowing downstream are calculated, and the impedance is calculated based on the identified simultaneous changes of voltage harmonics and current harmonics using (4). IV. TEST CASE To test the methodology, a 5 kv network from Enduris in the Netherlands is used, where PMUs are installed in five consecutive substations. The PMUs have the capability of measuring the voltage and current spectrum at time intervals of 1 s, next to the normal PMU functionality of measuring the fundament voltage and current phasors [12], [13]. The schematic of the test network is shown in Figure 2. The currents of aggregated loads flowing through the 5 kv/1 kv transformers, are not measured directly, but can be calculated based on the currents of the incoming and outgoing 5 kv feeders. In some of the feeders the current measurement is placed on the other end of the feeder. This results in an 835

extra uncertainty of the transformers current calculation, additional to the uncertainty caused by the current transformers and PMUs. Current transformers on the feeder Zierikzee Oosterland (according to Figure 2) are of Class 1 and the current transformer in the feeder Oosterland Tholen is of Class.1. Voltage transformers at substation Oosterland are of Class.5 and voltage transformers at substation Zierikzee and Tholen are of class 1. The influence of frequency on the uncertainty of instrument transformers is not characterized, but for the observed harmonic orders (up to the 17 th ) it is expected that there is no influence of the first parallel resonance [14]. the relevant changes of harmonic voltages (caused by the upstream network) are selected based on the following criteria: - changes of harmonic voltages at the observed substation and two neighboring substations do not differ by more than.5 % in magnitude, - voltage changes lower than.1% of the nominal voltage are not taken into account for sensitivity reasons, - current changes lower than.1 A are not taken into account, also due to the sensitivity;.1 A also roughly corresponds to.1 % of the nominal fundamental current. Figure 2. Schematic of the 5 kv test network. Measurement of the aggregated load impedances are calculated for substation Oosterland i.e. for the loads connected to the 5 kv/1 kv transformer, including the transformer and outgoing 1 kv feeders (in this case cables). Unlike the IEC 61-4-7 compliant power quality devices, which use data windows of 1/12 cycles of the fundamental frequency and starting at zero crossings for spectral measurements, the PMUs in this study use 1 ms data windows triggered by 1-pulse-per-second GPS-based clock signals. So the length of the measurement is not dependent on the fundamental frequency and its start is not synchronized to the signals zero crossing. This means that the angles of spectral components are not relative to any reference electrical grid signal typically the fundamental voltages. Additionally, the angles of harmonic components do not include any form of averaging over the 1 s time intervals the results of each 1 s measurement is in fact the result of a single 1 ms data window within the 1 s [15]. This makes the angle information unreliable for time intervals which include (significant) changes over the 1 ms data windows. For magnitudes, time aggregation is used, which reduces the effect of variations on results (averaging of 1 ms resutls). For this reason, in this paper only the magnitude of the impedance is calculated. The analysis of the real and imaginary components of the impedance will be the objective of future work, which could further process the measured phase angles to determine reliable changes of the angle within the 1 s time intervals. The test case uses the measurements over one week in total about 6, measurement points. From these points, V. RESULTS AND DISCUSSION Over the observed time period, only five out of the 25 measured harmonic orders had voltage and current changes which satisfy all of the mentioned criteria the 5 th, 7 th, 11 th, 13 th and 17 th (which also have the highest levels for harmonic voltages in general). From the one week time period, up to 4 changes between 1 s time intervals could be used for impedance calculation in the light of the given criteria. The measured impedance values for the 5 th, 11 th and 13 th order against the active and reactive power values are given in Figure 3 - Figure 8. These orders are chosen as they have the most measured points. It can be observed that the impedance values are highest at the 11 th harmonic order, and have the highest number of selected observation intervals (due to the highest signal to noise ratio). If the impedance of the upstream system shows such behavior, it would indicate the first parallel resonance at the 11 th order. However, the effect is different for the load impedances. As the upstream system act closer to an ideal voltage source than an ideal current source, this impedance does not lead to very high harmonic voltages. In fact, it reduces the secondary emission of loads). The change of the 11 th harmonic voltage in notable, as shown in Figure 9 for. The maximal value is around.5 % of the nominal fundamental voltage. Impedance 5 th order [Ω] 8 7 6 5 4 3 2 1-6 -4-2 2 4 6 Active power [W] Figure 3. Dependency between the 5 th harmonic impedance and active 836

Impedance 5 th order [Ω] 8 7 6 5 4 3 2 Impedance 13 th order [Ω] 2 15 1 5 1.5 1 1.5 2 2.5 3 3.5 4 Reactive power [var] Figure 4. Dependency between the 5 th harmonic impedance and reactive -6-4 -2 2 4 6 Active power [W] Figure 7. Dependency between the 13 th harmonic impedance and active Impedance 11 th order [Ω] 1 8 6 4 2 Impedance 13 th order [Ω] 2 15 1 5-8 -6-4 -2 2 4 6 Active power [W] Figure 5. Dependency between the 11 th harmonic impedance and active 1 2 3 4 5 Reactive power [var] Figure 8. Dependency between the 13 th harmonic impedance and reactive Impedance 11 th order [Ω] 1 8 6 4 2 11 th harmonic voltage [V] 16 14 12 1 8 6 4 2-1 1 2 3 4 5 Reactive power [var] Figure 6. Dependency between the 11 th harmonic impedance and reactive 1 2 3 4 5 6 Time [s] x 1 5 Figure 9. Magnitudes of the 11 th harmonic voltage in during the one week measurement. 837

For the 11 th and 13 th orders, a connection between the power levels and impedance magnitude can be observed, with some points which seem to be different from the trend. A fitted relation would however not be sufficient to define a load model, until the resistive and reactive components of the impedance are calculated. As a more general description of the aggregated impedance, in Figure 1 the mean value, 5 % and 95 % nonexceeded values of impedances are shown. Harmonic Ipedance [Ω] 35 3 25 2 15 1 5 5 % Average 95 % 4 6 8 1 12 14 16 18 Harmonic order [-] Figure 1. Mean values and 5 % and 95 % non-exceeded values of harmonic impedances for all analyzed orders. The validation of results is not possible at this stage, until the real and imaginary parts of the impedance are derived. Additionally, the connections between powers and impedance values are to be re-examined with the results, so the existing ones cannot be used as a reference with the measured power in general conditions. To validate the results, the following steps are proposed: - Derive the real and imaginary parts of the impedance, - Derive the connection between power and resistance/reactance for a known loading condition e.g. near zero loading (transformer losses), or at a location with a capacitor bank or shunt reactor connected. For further research and improvements of this analysis, the following aspects can be considered: - To better define the uncertainty of the calculation, the instrument transformers should be characterized over the frequency range of interest (which is limited by the magnitudes of variations in operation, in this case up to the 17 th harmonic order), - To further improve the calculation accuracy it would be beneficial to measure the transformer currents directly, preferably on the low-voltage side; alternatively, if the transformer currents are is to be calculated based on ingoing and outgoing feeders, it is beneficial to measure all currents in the observed substation (due to the capacitive leakage between the substations, especially for cable networks), - To determine the resistive and reactive components of the harmonic impedances, the phase-angle aggregation needs to be resolved (a single 1 ms data window representing the whole 1 s time interval). One possibility is to use the 2 ms fundamental voltage/current measurements of the PMU to filter out the time intervals in which the measurements are not (relatively) stable over the 1 s time intervals, - Once the resistive and reactive components are determined, the connection between the results and the measured active and reactive powers can be further analyzed, e.g. to evaluate the performance of the generalized model given in (1) (3). VI. CONCLUSIONS This paper presents a method for the measurement of harmonic impedances of aggregated loads based on synchronized spectrum measurements using the (almost) equal perturbations of harmonic voltages of nearby substations to identify the changes originating from the upstream network. The method is demonstrated on a test case of a 5 kv network from Enduris in the Netherlands, with results for the magnitudes of the harmonic impedances presented. The magnitude of the aggregated 1 kv network impedance at this location showed close values for the 5 th, 7 th, 13 th and 17 th harmonic. At the 11 th harmonic a peak is observed, indicating that the transformer, cables and loads have a parallel resonance at this frequency observed without the upstream network. The limitations of the method and the setup used in the test case are discussed and propositions for improvements and further analysis are given: characterizing the instrument transformers over the analyzed frequency range, adding additional current measurement points and determining the parameters of the aggregated load model based on more advanced phase angle analysis. VII. ACKNOWLEDGMENT The authors would like to thank Joeri van Seters and Marco Visser from Enduris B.V., the Netherlands, for providing the measurement data to perform this study. VIII. 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