ECN-RX--06-018
A METHOD FOR OPERATIONAL GRID AND LOAD IMPEDANCE MEASUREMENTS K. Visscher P.J.M. Heskes
This paper was presented at the Future Power Systems 2005 (Meeting the challenges of a reliable and sustainable power supply) inAmsterdam, The Netherlands, November 16-18, 2005
JANUARY 2006
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A method for operational grid and load impedance measurements K. Visscher and P. J. M. Heskes, Energy research Center of the Netherlands (ECN), P.O. Box 1, 1755 ZG Petten, The Netherlands, (e-mail:
[email protected] and
[email protected] website: http://www.ecn.nl/) Abstract--A method is proposed to simultaneously measure the small signal grid impedance and load impedance as a function of frequency under operational conditions. The method is tested before experiment by means of simulation. Index Terms-- Impedance measurement, conditions, Phase locked amplifiers
Operational
I. INTRODUCTION
II. THE METHOD OF PHASE SENSITIVE DETECTION The measurement method is based on the use of double phase locked amplifiers. The principle of a double phase locked amplifier is depicted in Figure 1. A sine wave and a cosine wave of a certain frequency ω are simultaneously multiplied with a signal S (see Figure 1). The sine wave is used as a reference signal to be added to an experimental setup being investigated.
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n order to assess stability problems due to harmonics generation in various loads, the complex impedances of the grid and the load as a function of frequency have to be determined simultaneously under working conditions. The loads considered include passive as well as "active" loads like solar arrays and combined heat and power generators. Examples of the stability problems caused by harmonics generation are overloading of neutral lines in three phase systems, generation of counteracting torques in three phase motors, undesired tripping of inverters for solar arrays and amplification of harmonics due to resonance. In general harmonics are generated by non-linear effects which occur in grid elements like transformers and electronic switching component, e.g. electronic inverters for solar cells and for combined heat and power generation. In order to assess the stability of such systems, the small-signal complex impedance under operational conditions is required. Stability problems due to harmonics generation and amplification have been the subject of earlier work of one of the authors [1,2,3,4]. However, similar impedance measurements did take place in a laboratory environment and could not be extended to situations under operational conditions in practice. In this article a method is proposed to simultaneously measure the small signal impedance of grid and load under operational conditions. The method is based on the use of double phase locked amplifiers. No other means of passive or active filtering is used. This makes it possible to leave the electric properties of the grid and load virtually unaltered during the measurements. Further, the voltage over and the current through the impedance considered are measured directly, thereby avoiding phase errors due to nonlinear behavior of the electrical signal sources. This work was supported by the Dutch Ministry of Economic Affairs through the SenterNovem agency under Grant EOSLT01021.
1 S_ref sin(wt)
2 a
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Bus Creator
Cosine Wave
Mean
Time averaging
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Figure 1 Working principle of a double phase locked amplifier
The multiplied signal is averaged over a relatively long period, resulting in a complex representation a + i⋅b of the part of the signal S with frequency ω. From the coefficients a and b the amplitude and phase of the detected signal can be calculated. The strength of the method lies in the relatively long time averaging process, which annihilates noise almost completely. A disadvantage is that smooth periodic disturbance signals like voltages and currents at grid frequency are difficult to cancel out. For this to achieve, special measures are to be taken. Because in a double phase locked amplifier a separate sine and cosine wave are used as reference signals instead of just a single sine wave, the phase of the reference signal does not have to be adjusted in order to find the maximum amplitude of the signal detected. Instead, the amplitude and phase of the signal are found in one step. III. OPERATIONAL MEASUREMENT METHOD The measurement method is depicted in Figure 2. A probe signal with frequency ω is injected to the grid and to the load under normal working conditions. The signal voltages and currents originating from the signal injector are small compared to the nominal grid voltage and grid current. Further, the voltage drop over the signal injector at the grid frequency is low compared to the nominal grid voltage.
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S_ref
the case without window optimization in the dual phase locker.
Dual Phase Locker
1 V_ac(+)
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IV. SIMULATION The basic measurement method has been tested by simulation with the SimPowerSystems block set in the simulation environment Matlab/Simulink [5]. The results are to be used in experiments being set-up by ECN within the FLEXIBEL project (EOSLT01021). The basic measurement method depicted in Figure 2 in fact just is the graphical representation of the system in Simulink. The "loads" block in Figure 2 is a so-called "configurable subsystem", which means that several types of loads can be chosen in a drop-down menu of this block. The advantage of the use of the configurable subsystem is that the loads chosen are simulated in exactly the same simulation environment. In this way it is easy to get a reliable comparison between results for the different loads chosen. In all load cases an example grid impedance of Rs=0.1 Ω and Ls=44.6 µH is used. The grid voltage is 230 Vrms and the grid frequency is 50 Hz. The frequency range of the test signal injected into the system is 10 Hz to 2500 Hz. The frequency points taken are roughly logarithmically spaced within this frequency interval. A. Passive load case For the passive load in Figure 3 the measurement method proposed was carried out. This was done for the case with and
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Imaginary [Ω ]
A basic problem is to device the signal injector in such a way that not most of the signal is injected into either the grid or the load, leaving respectively the load and the grid with too low a signal. This is achieved by using an appropriate combination of controlled voltage and current sources, fed by the very same reference signal with frequency ω. The small signal impedance of the grid and the load are determined by measuring the resulting voltage and current at frequency ω for the grid and the load separately. This is accomplished by using double phase locked amplifiers. To average-out the grid frequency and attain maximum accuracy, the window width of the "Time averaging" block in Figure 1 is optimized depending on the test frequency. Therefore the window width must be an integral multiple of the grid periodic time. Further, in order to filter out the test frequency ω at maximum accuracy, the window width must also be an integer multiple of the periodic time of the test frequency ω.
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Figure 4 Complex impedance plot of the grid, measured without the use of window width optimization. (Circles: calculated. Stars: simulated). 90
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Figure 2 Operational measurement method.
Figure 3 Reference RLC-network as a passive load. (C=4 µF, R=33.063 Ω, L=31.83 mH)
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Figure 5 Complex impedance plot of passive load, measured without the use of window width optimization. (Circles: calculated. Stars: simulated).
As can be seen in Figure 4 and Figure 5, the lack of window optimization leads to rather scattered impedance plots.
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B. Active load case As an example active load an existing model of a pulse width modulated current regulated inverter is used. The same example grid impedance as in the case of the passive load is applied. The inverter delivers a constant power of 1600 W to the grid. 1 V_ac(+) Voltage Measurement
+
Controlled Current Source
power
+ v -
C -
p_ac_rel
s
The grid impedance measurement in Figure 4 (without window optimization) does not give any reliable results, as all impedance values measured in the simulation are much larger than and scattered around the calculated values. As a result the calculated values all reside in the center of the plot. Applying window optimization in the dual phase locker in the very same simulation setting gives the plots in Figure 6 and Figure 7. Now the impedance plots are much smoother and in accordance with the values expected. From the figures it follows that the load impedance can be measured more accurately than the grid impedance.
current
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V_ac(-)
60 PWM current regulated inverter
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Figure 8 Inverter at constant power as an active load. C=4 µF.
0.2 Imaginary [Ω ]
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terminal voltage
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As can be seen from Figure 9, the measured grid impedance as a function of frequency is in accordance with the values calculated. This shows that the measurement method for the active load seems to work properly. 90
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Figure 6 Complex impedance plot of the grid (passive load case), measured with the use of window width optimization. (Circles: calculated. Stars: simulated).
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Figure 7 Complex impedance plot of passive load, measured with the use of window width optimization. (Circles: calculated. Stars: simulated).
Figure 9 Complex impedance plot of the example grid (active load case), with Rs=0.1 Ω and Ls=44.6 µH. (Circles: calculated. Stars: simulated).
The measured impedance of the example inverter load however gives scattered results below a frequency of roughly 150 Hz, which is at the left end of the smooth arc of nonscattered points in Figure 10. This is probably due to actions of the power regulating part of the active circuit in the inverter. The impedance curve lies in the negative real part of the polar plane, which means that power can be delivered to the grid at the corresponding test frequencies. In other words: this inverter type is able to reduce circuit damping at harmonic frequencies [3]. For higher frequencies the impedance tends to that of the capacitor alone, as to be expected. In order to calculate the impedance curve, it is necessary to make a
4 harmonics due to the use of small micro generators with inverters". ECN report: ECN-C--04-87, 2004.
dynamic model of the inverter. This has not been done in the current investigation.
Papers from Conference Proceedings (Published):
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Enslin, J.H.R., Hulshorst, W.T.J., Atmadji, A.M.S., Heskes, P.J.M., Kotsopoulos, A., Cobben, J.F.G., van der Sluis, P.: Harmonic Interaction between Large Numbers of Photovoltaic Inverters and the Distribution Network, In proceedings IEEE PowerTech 2003, Bologna, Italy, 2003.
Software:
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[5]
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The Mathworks Inc., Matlab and Simulink version 7.01, Natick, Massachusetts, USA, 2005. http://www.mathworks.com
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VIII. BIOGRAPHIES 330
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Figure 10 Complex impedance plot of the example inverter load with output capacitor C=4 µF. (Circles: calculated for the capacitor alone. Stars: simulated).
V. CONCLUSIONS The measurement method proposed gives good results for the operational determination of passive grid and load impedances. However, for the example active load, no consistent impedance values seem to be acquired for frequencies up to about 2 to 3 times the grid frequency, which is up to 150 Hz. This is probably due to actions of the power regulating part of the active circuit in the inverter. Further investigations, including an experimental test with the measurement method proposed on an actual inverter, might shed light on the underlying reason for this behavior. VI. ACKNOWLEDGMENT The example inverter model used was built and kindly made available by Andrew Kotsopoulos from the Department of Electrical Engineering of the Technical University of Eindhoven, The Netherlands. VII. REFERENCES Periodicals: [1]
[2]
A. Kotsopoulos, P.J.M. Heskes, M.J. Jansen: Zero-Crossing Distortion in Grid-Connected PV Inverters, IEEE Transactions on industrial electronics, Vol. 52, no. 2, April 2005. P.J.M. Heskes, J.F.G. Cobben, H.H.C. de Moor: “Harmonic distortion in residential areas due to large scale PV implementation is predictable”, Intern. Journal of Distributed Energy Resourses, Vol.1, Number 1, 2005, pages 17-32.
Technical Reports: [3]
P.J.M. Heskes, P.M. Rooij, J.F.G. Cobben, H.E. Oldenkamp: "Estimation of the potential to pollute the electricity network with
Klaas Visscher studied electrical engineering at the former higher technical college (HTS) in Zwolle, The Netherlands, before he went to university in 1982. He received his Master's degree in Applied Physics from Twente University, Enschede, The Netherlands, in 1988. Next he did his PhD-research in Rheology at the faculty of Applied Physics of Twente University, where he received his Doctor's degree in 1993. After working several years in automation projects in his own consultancy, he completed a one-year MBA-program on environmental business administration at the Center for Clean Technology and Environmental Policy of Twente University in 1998. He joined the Energy Research Centre of The Netherlands (ECN), Petten, The Netherlands, in 1999. There he worked for several years on heat storage and thermal processes for renewable energy applications in the built environment. In time his research shifted towards distributed combined heat and power generation. The main topics of his current research are control and stability of distributed electricity generation systems in the built environment.
Peter J.M. Heskes received the Electronic Engineer degree from the University of Professional Technical Education (formerly the Institute of Technology, HTS), The Hague, The Netherlands, in 1980. From 1980 to 1999, he was with a large Dutch electronic-product manufacturer for the military and professional market, where he started as a Product Designer and became a Product Manager of the power-electronic department. His work was related to inverter technology and power supplies. He is currently a Project Co-ordinator with Intelligent Energy Management, Energy Research Centre of The Netherlands (ECN), Petten, The Netherlands. His current work is related to inverter technology in grid-connected distributed energy systems. Recently he finished his sixth research project on inverter interactions with the public electricity grid. Mr. Heskes is a Member of the Netherlands National Committee of the IEC: NEC82, where he is working on standardization.
