## Harmonics in transmission power systems

Research output: Book/Report › Ph.D. thesis

### Abstract

Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need to perform more detailed harmonic studies emerged. Since the transmission network has a complex structure and its impedance varies with frequency in a nonlinear fashion, such harmonic study would require a detailed computer model of the network. Consequently, a PhD project proposal titled "Harmonics in transmission power systems" was formulated.

In this project, the entire 400 kV and 150 kV western transmission network of Energinet.dk is modelled using the simulation software DIgSILENT PowerFactory. A fundamental frequency load-flow model is used as a basis that is to be extended. The model is sought to be applicable for harmonic frequencies in the range from 50 Hz up to 2,5 kHz and should be verified by harmonic measurements.

The task is divided into modelling of the linear transmission network components and modelling of the nonlinear transmission network components that are installed directly on the transmission level, namely the transformer core nonlinearities and the HVDC converters.

While modelling the linear, frequency dependent components in the harmonic domain, priority is given to modelling the transmission lines, especially the effects of distributed parameters, the skin effect, the non-ideal ground return, the line unbalance and the sag of the conductors. The solution for the skin effect involves Bessel series and for the non-ideal ground it involves Carson series. Both aspects can be modelled in PowerFactory and are verified in the project by hand calculations. All other shunt and series linear elements are also considered and the aspects that have to be included in the models are pointed out.

The intention is to verify the created linear model of the network by harmonic measurements. Consequently, various verification techniques based on harmonic measurements are investigated. It is concluded that since some background harmonic distortion is practically always present in the network, a method based on variation of harmonic values must be used. The incremental values of harmonic distortion will allow to verify the harmonic model, despite the existence of background harmonic distortion, provided that background harmonic distortion, and the network configuration, are not changing during the measurement.

It is shown that switching of a shunt linear power system component can result in variation of the harmonic levels that can be measured and used to verify the harmonic model of the network. Three novel methods are also proposed, where switching of a series component can be used for the same purpose. Two of these methods are based on the determination of transfer harmonic impedance of the network and the third approach, which is actually used in the project, is based on injection of the incremental values of harmonic currents directly into the created computer model using current sources, and comparing the obtained harmonic voltage increments with the ones measured in reality.

The harmonic increments must be as high as possible, in order to ensure the highest signal-tonoise ratio. Therefore, in order to determine which power system component, when switched, results in the largest change in harmonic levels, some initial harmonic simulations, using the created harmonic model of Energinet.dk transmission network, are performed. The criterion is that the measuring equipment shall not be installed more than 100 km away from the city of Aalborg. The simulations show that in such a case, the largest harmonic increments can be obtained by switching one of the 400 kV transmission lines.

Therefore, the following technique is applied. Harmonic currents and voltages are simultaneously measured using GPS-synchronized OMICRON CMC256 units. Two such units are installed at 400 kV substations at both ends of the disconnected line and a third unit is located at a substation in a distance of 80 km. Time domain "snap-shot" measurements of three-phase voltages and currents are synchronously taken for some period of time. The line is switched out and in, three times in row, and the harmonic currents and voltages are measured. In total, 24 channels are used for voltage and current measurement. 90 snapshot-measurements are performed, during 45 minutes. Harmonic frequencies up to the 50th harmonic are monitored. All of the gathered data are later processed in Matlab.

The results show that the switching of the line affected mainly the levels of higher harmonics; lower order harmonics were not affected as much as the initial simulations indicated. The harmonic increments at higher frequencies are sufficiently large to be used for verification purposes.

The created network model is adjusted using the SCADA measurements of the actual conditions prevailing in the entire network, exactly at the time when the harmonic measurements were performed. These SCADA measurement results, obtained from Energinet.dk, are imported into the PowerFactory network model.

In the next step, the harmonic currents measured at both ends of the line are assigned to current sources and injected into the linear network model. The resultant voltage increments obtained in the simulation are compared with the voltage increments measured in reality. The results of this verification show that the incremental values of the harmonic voltages at three substations obtained in simulations and from the measurements agree for most of the harmonic frequencies. The differences are below 10% and are due to such factors like synchronization error of the measurements. The conclusion is that a key requirement of this technique is a good synchronization of the measurements.

Capacitive voltage transformers installed at the 400 kV substations are not suited to measure higher frequencies and the capacitive taps of the 400 kV/150 kV autotransformer bushings are used. Coaxial cables are lead for hundred of meters through the high voltage switchyard from the capacitive taps to the OMICRON units placed in the control rooms. The electromagnetic environment at a high voltage substation is very hostile, so various grounding techniques of the cables are inspected and measurements prior to the main measurement are performed. Configuration that reduces the level of noise induced in the cables to the possible minimum is found. It is confirmed that a way to reduce the magnetic coupling is to minimize the area of the loop; therefore the measuring circuit must be grounded at one end only so the ground is not used as a return path. A way to reduce the capacitive coupling is to provide shielding.

Harmonic currents are measured using the conventional inductive voltage transformers. Both protective and metering cores were compared if they could be used for harmonic measurements. The comparison shows that results obtained used both types of the cores are the same, so it is concluded that both cores can be used for harmonic measurements. Low-inductance resistors are introduced in the secondary circuits, in series with the metering and protective relaying. On those resistors, the harmonic voltage drop was measured.

The subsequent tasks of the project concern modelling of non-linear components present in the transmission network, HVDC converters and transformer core nonlinearities. Modelling of large frequency dependent linear networks in the time domain involves approximations by rational functions and it is time consuming. The frequency dependent impedances can be best modelled in the frequency domain where exact solution can be calculated. On another hand, modelling of nonlinear components is most precise in the time domain. In this project an iterative, three-phase, hybrid time/frequency method is developed. The method enables to model linear networks in the harmonic domain, and the HVDC converters in the time domain. This developed model is implemented in the PowerFactory software. The results are verified with precise time domain simulations. The method converges after 4 - 6 iterations. It is presently used in the steady-state harmonic calculations, but it is concluded that after some future adjustments it can be used for inter-harmonic simulations and simulations of dynamically varying harmonics, as well.

Implementation of a nonlinear transformer core model [Neves] is shown. The core nonlinearities can be determined using Vrms - Irms curves and the no-load losses. Such data are present in the typical test reports of power transformers. The method is implemented using the DIgSILENT Programming Language (DPL) and verified with the original data from [Neves] and with measurements performed on a low voltage transformer. It is concluded that the method initially designated for single phase transformers, under certain circumstances can be used for modelling nonlinearities of three-phase autotransformers.

In general, it can be stated that the aim of the project is reached. The linear Western transmission network model is examined and models are extended so can be used for harmonic analysis studies. The model is verified by harmonic measurements. Additionally, both the hybrid time/frequency model and the implemented model of nonlinear transformer core are implemented in the PowerFactory software and verified with measurements or time domain simulations.

### Details

Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need to perform more detailed harmonic studies emerged. Since the transmission network has a complex structure and its impedance varies with frequency in a nonlinear fashion, such harmonic study would require a detailed computer model of the network. Consequently, a PhD project proposal titled "Harmonics in transmission power systems" was formulated.

In this project, the entire 400 kV and 150 kV western transmission network of Energinet.dk is modelled using the simulation software DIgSILENT PowerFactory. A fundamental frequency load-flow model is used as a basis that is to be extended. The model is sought to be applicable for harmonic frequencies in the range from 50 Hz up to 2,5 kHz and should be verified by harmonic measurements.

The task is divided into modelling of the linear transmission network components and modelling of the nonlinear transmission network components that are installed directly on the transmission level, namely the transformer core nonlinearities and the HVDC converters.

While modelling the linear, frequency dependent components in the harmonic domain, priority is given to modelling the transmission lines, especially the effects of distributed parameters, the skin effect, the non-ideal ground return, the line unbalance and the sag of the conductors. The solution for the skin effect involves Bessel series and for the non-ideal ground it involves Carson series. Both aspects can be modelled in PowerFactory and are verified in the project by hand calculations. All other shunt and series linear elements are also considered and the aspects that have to be included in the models are pointed out.

The intention is to verify the created linear model of the network by harmonic measurements. Consequently, various verification techniques based on harmonic measurements are investigated. It is concluded that since some background harmonic distortion is practically always present in the network, a method based on variation of harmonic values must be used. The incremental values of harmonic distortion will allow to verify the harmonic model, despite the existence of background harmonic distortion, provided that background harmonic distortion, and the network configuration, are not changing during the measurement.

It is shown that switching of a shunt linear power system component can result in variation of the harmonic levels that can be measured and used to verify the harmonic model of the network. Three novel methods are also proposed, where switching of a series component can be used for the same purpose. Two of these methods are based on the determination of transfer harmonic impedance of the network and the third approach, which is actually used in the project, is based on injection of the incremental values of harmonic currents directly into the created computer model using current sources, and comparing the obtained harmonic voltage increments with the ones measured in reality.

The harmonic increments must be as high as possible, in order to ensure the highest signal-tonoise ratio. Therefore, in order to determine which power system component, when switched, results in the largest change in harmonic levels, some initial harmonic simulations, using the created harmonic model of Energinet.dk transmission network, are performed. The criterion is that the measuring equipment shall not be installed more than 100 km away from the city of Aalborg. The simulations show that in such a case, the largest harmonic increments can be obtained by switching one of the 400 kV transmission lines.

Therefore, the following technique is applied. Harmonic currents and voltages are simultaneously measured using GPS-synchronized OMICRON CMC256 units. Two such units are installed at 400 kV substations at both ends of the disconnected line and a third unit is located at a substation in a distance of 80 km. Time domain "snap-shot" measurements of three-phase voltages and currents are synchronously taken for some period of time. The line is switched out and in, three times in row, and the harmonic currents and voltages are measured. In total, 24 channels are used for voltage and current measurement. 90 snapshot-measurements are performed, during 45 minutes. Harmonic frequencies up to the 50th harmonic are monitored. All of the gathered data are later processed in Matlab.

The results show that the switching of the line affected mainly the levels of higher harmonics; lower order harmonics were not affected as much as the initial simulations indicated. The harmonic increments at higher frequencies are sufficiently large to be used for verification purposes.

The created network model is adjusted using the SCADA measurements of the actual conditions prevailing in the entire network, exactly at the time when the harmonic measurements were performed. These SCADA measurement results, obtained from Energinet.dk, are imported into the PowerFactory network model.

In the next step, the harmonic currents measured at both ends of the line are assigned to current sources and injected into the linear network model. The resultant voltage increments obtained in the simulation are compared with the voltage increments measured in reality. The results of this verification show that the incremental values of the harmonic voltages at three substations obtained in simulations and from the measurements agree for most of the harmonic frequencies. The differences are below 10% and are due to such factors like synchronization error of the measurements. The conclusion is that a key requirement of this technique is a good synchronization of the measurements.

Capacitive voltage transformers installed at the 400 kV substations are not suited to measure higher frequencies and the capacitive taps of the 400 kV/150 kV autotransformer bushings are used. Coaxial cables are lead for hundred of meters through the high voltage switchyard from the capacitive taps to the OMICRON units placed in the control rooms. The electromagnetic environment at a high voltage substation is very hostile, so various grounding techniques of the cables are inspected and measurements prior to the main measurement are performed. Configuration that reduces the level of noise induced in the cables to the possible minimum is found. It is confirmed that a way to reduce the magnetic coupling is to minimize the area of the loop; therefore the measuring circuit must be grounded at one end only so the ground is not used as a return path. A way to reduce the capacitive coupling is to provide shielding.

Harmonic currents are measured using the conventional inductive voltage transformers. Both protective and metering cores were compared if they could be used for harmonic measurements. The comparison shows that results obtained used both types of the cores are the same, so it is concluded that both cores can be used for harmonic measurements. Low-inductance resistors are introduced in the secondary circuits, in series with the metering and protective relaying. On those resistors, the harmonic voltage drop was measured.

The subsequent tasks of the project concern modelling of non-linear components present in the transmission network, HVDC converters and transformer core nonlinearities. Modelling of large frequency dependent linear networks in the time domain involves approximations by rational functions and it is time consuming. The frequency dependent impedances can be best modelled in the frequency domain where exact solution can be calculated. On another hand, modelling of nonlinear components is most precise in the time domain. In this project an iterative, three-phase, hybrid time/frequency method is developed. The method enables to model linear networks in the harmonic domain, and the HVDC converters in the time domain. This developed model is implemented in the PowerFactory software. The results are verified with precise time domain simulations. The method converges after 4 - 6 iterations. It is presently used in the steady-state harmonic calculations, but it is concluded that after some future adjustments it can be used for inter-harmonic simulations and simulations of dynamically varying harmonics, as well.

Implementation of a nonlinear transformer core model [Neves] is shown. The core nonlinearities can be determined using Vrms - Irms curves and the no-load losses. Such data are present in the typical test reports of power transformers. The method is implemented using the DIgSILENT Programming Language (DPL) and verified with the original data from [Neves] and with measurements performed on a low voltage transformer. It is concluded that the method initially designated for single phase transformers, under certain circumstances can be used for modelling nonlinearities of three-phase autotransformers.

In general, it can be stated that the aim of the project is reached. The linear Western transmission network model is examined and models are extended so can be used for harmonic analysis studies. The model is verified by harmonic measurements. Additionally, both the hybrid time/frequency model and the implemented model of nonlinear transformer core are implemented in the PowerFactory software and verified with measurements or time domain simulations.

Original language | English |
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Place of Publication | Aalborg |
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Publisher | Institut for Energiteknik, Aalborg Universitet |

Number of pages | 281 |

ISBN (Print) | 87-89179-69-2 |

State | Published - 2006 |

Publication category | Research |