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Impact of current-controlled voltage source converters on power system stability
Tokyo, Japan, September 4-6, 2018 10th IFAC Symposium on Control of Power and Energy Systems 10th IFAC Symposium on 4-6, Control andonline EnergyatSystems Available www.sciencedirect.com Tokyo, Japan, September 2018of Power Tokyo, Japan, September 2018of 10th IFAC IFAC Symposium on 4-6, Control of Power Power and and Energy Energy Systems Systems 10th Symposium on Control Tokyo, Tokyo, Japan, Japan, September September 4-6, 4-6, 2018 2018
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IFAC PapersOnLine 51-28 (2018)source 570–575converters on power system stability Impact of current-controlled voltage Impact of current-controlled source H. converters power system stability C. Schöll*,voltage J. Lehner**, Lens* on Impact of current-controlled voltage source converters on power system stability Impact source converters power system stability C. Schöll*,voltage J. Lehner**, Lens* on Impact of of current-controlled current-controlled source H. converters C. Schöll*,voltage J. Lehner**, H. Lens* on power system stability
C. J. H. C. Schöll*, Schöll*, J. Lehner**, Lehner**, H. Lens* Lens* (IFK), Department Power Generation and *University of Stuttgart, Institute of Combustion and Power Plant Technology Automatic Control, Pfaffenwaldring 23, 70569 Stuttgart, Germany (e-mail: [email protected]; *University of Stuttgart, Institute of Combustion and Power Plant Technology (IFK), Department Power Generation and *University of Stuttgart, Institute of Combustion and Power Plant Technology (IFK), Department Power Generation and [email protected]). Automatic Control, Pfaffenwaldring 23, 70569 Stuttgart, Germany (e-mail: [email protected]; *University of Stuttgart,Pfaffenwaldring Institute of Combustion Combustion and Power Plant Technology (IFK), Department Power Generation Generation and and Automatic Control, 23, 70569 Stuttgart, Germany (e-mail:(e-mail: [email protected]; *University Stuttgart, Institute of and Power Plant Technology (IFK), Department Power ** of TransnetBW GmbH, Osloerstr. 15-17, 70173 Stuttgart, Germany [email protected]) [email protected]). Automatic Control, Control, Pfaffenwaldring Pfaffenwaldring 23, 23,[email protected]). 70569 Stuttgart, Stuttgart, Germany Germany (e-mail: (e-mail: [email protected]; [email protected]; Automatic 70569 ** TransnetBW GmbH, [email protected]). 15-17, 70173 Stuttgart, Germany (e-mail: [email protected]) ** TransnetBW GmbH, [email protected]). 15-17, 70173 Stuttgart, Germany (e-mail: [email protected]) ** TransnetBW TransnetBW GmbH, GmbH, Osloerstr. Osloerstr. 15-17, 15-17, 70173 70173 Stuttgart, Stuttgart, Germany Germany (e-mail: (e-mail: [email protected]) [email protected]) ** Abstract: It is known that current-controlled voltage source converters do not contribute to the inertia of power systems, leading a higher rate of change frequency in case imbalances. Another Abstract: It is known thattocurrent-controlled voltageofsource converters do of notpower contribute to the inertia of Abstract: It iseffect known that current-controlled voltage source converters doofnot contribute to the inertia of fundamental becomes apparent in case of large phase angleinjumps the gridimbalances. voltage. Such phase power systems, leading to a higher rate of change of frequency case of power Another Abstract: It is ismay known that current-controlled voltageofsource source converters do of not contribute to the the converter inertia of power systems, leading tocurrent-controlled aexample, higher rate of change frequency in case power imbalances. Another Abstract: It known that voltage converters do not contribute to inertia of angle jumps occur, for in ofphase a system The power infeed of fundamental effect becomes apparent inconsequence case of large anglesplit. jumps of the grid voltage. Such phase power systems, leading to a higher rate of change of frequency in case of power imbalances. Another fundamental effect becomes apparent inand, case of large angleinfluenced of the voltage. delay Such phase power systems, leading tophase aexample, higher rate of change ofofphase frequency injumps case ofpower power imbalances. Another depends on the estimated angle hence, is transiently by grid theinfeed inherent of its angle jumps may occur, for in consequence a system split. The of the converter fundamental effectoccur, becomes apparent in inconsequence case of large large phase angle jumps of the grid voltage. Such phase angle jumpsusually may for example, ofphase a system split. The power infeed ofPLL the converter fundamental effect becomes apparent in case of angle jumps of the grid voltage. Such phase estimation, by a phase-locked loop (PLL). This paper investigates the effect of the dynamics depends on the estimated phase angleinand, hence, isoftransiently influenced by theinfeed inherent delay of its angle jumps mayestimated occur, for forand example, consequence system split. split. The power of the the converter depends on the phase and, hence, isoftransiently influenced by theinfeed inherent delay its angle may occur, example, in consequence aa system The power of converter on thejumps converter behavior itsangle impact on(PLL). transmission voltage and frequency stability. Toofthis estimation, usually by a phase-locked loop This paper investigates the effect of the PLL dynamics depends on the estimated phase angle and, hence, is transiently influenced by the inherent delay of its estimation, usually by a phase-locked loop (PLL). This paper investigates the effect of the PLL dynamics depends on the estimated phase angle and, hence, is transiently influenced by the inherent delay of its end,the islanding scenarios ofand a grid lines loaded beyondsystem their natural are considered. Sensitivity on converter behavior its with impact on(PLL). transmission voltagepower and frequency stability. To this estimation, usually by a phase-locked loop This paper investigates the effect of the PLL dynamics on the converter behavior and its impact on transmission system voltage and frequency stability. To this estimation, usually by a phase-locked loop (PLL). This paper investigates the effect of the PLL dynamics analyses of thescenarios PLL parameters show noticeable effects ontheir voltage and power frequency stability depending on end, islanding ofand a grid with lines loaded beyond natural are considered. Sensitivity on the converter behavior itsthe impact onloaded transmission system voltagepower and frequency frequency stability. To this this end, islanding scenarios ofand a grid with lines beyondsystem their natural are considered. Sensitivity on converter behavior its impact on transmission voltage and stability. To the the dynamic parameterization of PLL. analyses of the PLL parameters show noticeable effects on voltage and frequency stability depending on end, islanding islanding scenarios of aa grid gridshow with noticeable lines loaded loaded beyond their natural power are considered. considered. Sensitivity analyses of thescenarios PLL parameters effects ontheir voltage and power frequency stability depending on end, of with lines beyond natural are Sensitivity the dynamic parameterization of the PLL. Keywords: angle jumps, Phase-locked loop, Voltage stability, Voltage SourceLtd. Converter. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier All rights reserved. on analyses of Phase the PLL parameters show noticeable effects on voltage voltage and frequency stability depending on the dynamic parameterization of the PLL. analyses of the PLL parameters show noticeable effects on and frequency stability depending Keywords: Phase angle jumps, Phase-locked loop, Voltage stability, Voltage Source Converter. the dynamic parameterization of the PLL. the dynamicPhase parameterization the PLL. loop, Voltage stability, Voltage Source Converter. Keywords: angle jumps, of Phase-locked Keywords: Phase angle jumps, Phase-locked Keywords:1.Phase angle jumps, Phase-locked loop, loop, Voltage Voltage stability, stability, Voltage Voltage Source Source Converter. INTRODUCTION with PLL may even resultConverter. in local stability issues (Duckwitz 1. INTRODUCTION Synchronous generators of conventional power plants 1. INTRODUCTION substantially contribute to system stability. Their 1. Synchronous generators ofpower conventional power plants 1. INTRODUCTION INTRODUCTION Synchronous generators of due conventional power source plants stabilizing characteristics are to their voltage substantially contribute toofpower system stability. Their Synchronous generators conventional power plants substantially contribute toofpower system stability. Their Synchronous conventional power plants behavior and togenerators the rotational energy stored in the rotating stabilizing characteristics are due to their voltage source substantially contribute to power system stability. Their stabilizing characteristics are due to their voltage source substantially contribute to power system stability. Their mass of generator androtational turbine. energy Sudden stored changes phase behavior and to the in in thetherotating stabilizing characteristics are due to their voltage source behavior and to the rotational energy stored in the rotating stabilizing characteristics are due to their voltage source angle of generator the grid voltage, for example caused by an active mass of androtational turbine. Sudden stored changes in the phase behavior and to to the the energy in the rotating mass ofimbalance generator and turbine. Sudden lead changes in therotating phase behavior and rotational energy stored the power involtage, the overall system, to in anby injection or angle of the grid for example caused an active mass of and turbine. Sudden changes in the phase angle of generator the grid voltage, for (Kundur, example caused This by an active mass of generator and turbine. Sudden changes in the phase absorption of rotational energy 1994). behavior power imbalance in the overall system, lead to an injection or angle of the grid voltage, for example caused an active power imbalance in theany overall system, lead to anby injection or angle of the grid voltage, for example caused by an active is independent of automatic control mechanism. absorption of rotational energy (Kundur, 1994). This behavior power imbalance in the overall system, lead to an injection or absorption of rotational energy (Kundur, 1994). This behavior power imbalance in the overall system, lead to an injection or Consequently, present power system stability is based on the is independent of any automatic control mechanism. absorption of rotational energy (Kundur, 1994). This behavior is independent of any automatic control mechanism. absorption of rotational energy (Kundur, 1994). This behavior intrinsic behavior of synchronous generators. Consequently, powerautomatic system stability based on the is independent independentpresent of any any controlis mechanism. Consequently, present powerautomatic system stability is based on the is of control mechanism. intrinsic behavior of synchronous generators. In contrast, most renewable energy sources (RES) are Consequently, present power stability intrinsic behavior of synchronous generators. Consequently, present power system system stability is is based based on on the the connected to the grid via current-controlled voltage source intrinsic behavior of synchronous synchronous generators. In contrast, mostof renewable energy sources (RES) are intrinsic behavior generators. In contrast, most(ENTSO-E, renewable2017). energy sources (RES)active are converters (VSC) In order tovoltage deliver connected to the grid via current-controlled source In contrast, most renewable energy sources (RES) are connected to the grid via current-controlled voltage source In contrast, most(ENTSO-E, renewable energy sources (RES) are and reactive power properly, 2017). these concepts depend on the converters (VSC) In order tovoltage deliver active connected to the grid via current-controlled source converters (VSC) (ENTSO-E, 2017). In order to deliver active connected to the grid via current-controlled voltage source synchronization with an existing grid. To this end, the phase and reactive power properly, 2017). these concepts on the converters (VSC) (ENTSO-E, In order order todepend deliver active and reactive power properly, these concepts depend the converters (ENTSO-E, 2017). In to deliver active angle has to(VSC) be estimated, which usually is this done withthe a on phasesynchronization with an existing grid. To end, phase and reactive power properly, these concepts depend on the synchronization with an existing grid. To this end, the phase and reactive power properly, these concepts depend on the lockedhas loop (S.-K.Chung, 2000). In to protect angle to (PLL) be estimated, which usually is order doneend, with a phasesynchronization with an existing grid. To this the phase angle has to be estimated, which usually is done with a phasesynchronization with an existing grid. To this end, the phase converter from overcurrent, converters fororder REStousually are lockedhas loop (PLL) (S.-K.Chung, 2000). In protect the angle to be which usually is done with aa phaselocked loop (PLL) (S.-K.Chung, 2000). to protect the angle has to be aestimated, estimated, which usually is done with phaseequipped with fast current control. AsIn a order consequence, their converter from overcurrent, converters for RES usually are locked loop (PLL) (S.-K.Chung, 2000). In order protect the converter from overcurrent, converters for RESto usually are locked loop (PLL) (S.-K.Chung, 2000). In order to protect the behavior is fundamentally different from synchronous equipped with a overcurrent, fast current control. As for a consequence, their converter from converters RES usually are equipped with a fast current control. As a consequence, their converter from overcurrent, converters for RES usually are machines. They are not capable of island operation and do not behavior is fundamentally different from synchronous equipped with aasystem fast current control. As consequence, their behavior is fundamentally different from synchronous equipped with fastnot current control. As aaoperation consequence, support power stability intrinsically. Suitable machines. They are capable of island andcontrol dotheir not behavior is fundamentally different from synchronous machines. They are not capable of island operation and do not behavior is fundamentally different from synchronous algorithms can system be used in order to supportSuitable power control system support power stability intrinsically. machines. They are not capable of island operation and do not support power system stability intrinsically. Suitable control machines. They are not capable of island operation and do not stability withcan VSC, e.g.in(Liu & Lindemann, 2017), they algorithms be see used order to supportSuitable power but system support power system stability intrinsically. control algorithms can be used in order to support power system support power system stability intrinsically. Suitable control can onlywith do so if the RES is equipped with sufficient energy stability VSC, see e.g.in(Liu & Lindemann, 2017), but they algorithms be used order to power system stability withcan VSC, see e.g.in(Liu & Lindemann, 2017), but they algorithms can be used order to support support power system storage capacity. Even then, power system stability support of can only do so if the RES is equipped with sufficient energy stability with VSC, see e.g. (Liu & Lindemann, 2017), but they can only do so ifequivalent the RES istoequipped with of sufficient energy stability with VSC, see e.g. (Liu & Lindemann, 2017), but they VSC cannot be the behavior a synchronous storage capacity. Even then, power system stability support of can do the is equipped with sufficient energy storage capacity. Even then, system support of can only only do so so if the RES RES istopower equipped withstability sufficient energy machine due to if inevitable delays inbehavior measurement and control. VSC cannot be equivalent the of a synchronous storage capacity. Even then, power system stability support of VSC cannot be equivalent to the behavior of a synchronous storage Evenconcepts then, power system stabilityand support of In fact, capacity. some control based on frequency estimation machine due be to inevitable delays inbehavior measurement control. VSC cannot equivalent to the of a synchronous machine due to inevitable delays in measurement and control. VSC cannot be equivalent to the behavior of a synchronous In fact, some control concepts based on frequencyand estimation machine due to to inevitable delays in measurement measurement control. In fact, some control concepts based on frequencyand estimation machine due inevitable delays in control. In In fact, fact, some some control control concepts concepts based based on on frequency frequency estimation estimation
& Fischer, 2017). with PLL may even result in local stability issues (Duckwitz with PLL may even result in local stability issues (Duckwitz & Fischer, 2017). As synchronous generators inverter-based with PLL may may even result in in are local stability issues (Duckwitz & Fischer, 2017). with PLL even result localreplaced stabilityby issues (Duckwitz generation, their stabilizing effect diminishes. In the German & Fischer, 2017). As synchronous generators are replaced by inverter-based & Fischer, 2017). As synchronous generators area replaced inverter-based control areas, with low sharebyofIn synchronous generation, theirsituations stabilizing effect diminishes. the German As synchronous generators are replaced by inverter-based generation, their stabilizing effect diminishes. In thesufficient German As synchronous generators are replaced by inverter-based generators can situations already bewith observed. As long as control areas, a low share of synchronous generation, their stabilizing effect diminishes. In the German control areas, situations with a low share of synchronous generation, their stabilizing effect diminishes. In the German synchronouscan generators connected in control generators already are bewith observed. Asneighboring long as sufficient control areas, situations a low share of synchronous generators can already be observed. As long as sufficient control areas, situations with a low share of synchronous areas, the impact on overall power system stability remains synchronous generators are connected in neighboring control generators can already be observed. As long sufficient synchronous generators are in control generators can already be connected observed. Asneighboring long as sufficient limited.theHowever, inverter-based generation is as expected to areas, impact on overall power system stability remains synchronous generators are connected in neighboring control areas, the at impact on overall power system stability remains synchronous generators are connected in neighboring control dominate, least temporarily, the generation mix of the whole limited.theHowever, inverter-based generation is expected to areas, impact on overall power system stability remains limited. generation is expected to areas, theHowever, impact oninverter-based overall power system Europe stability remains interconnected power system of continental (ENTSOdominate, at least temporarily, the generation mix of the whole limited. However, inverter-based generation is expected to dominate, at least temporarily, the generation mix of the whole limited. inverter-based generation is expected to E, 2017),However, with power significant impact on the dynamic behavior. interconnected system of continental Europe (ENTSOdominate, at least temporarily, the generation mix of the whole interconnected power system of continental Europe (ENTSOdominate, at least temporarily, the generation mix of the whole Obviously, power systems can cope with a certain share of E, 2017), with power significant impact on the dynamic behavior. interconnected system of continental continental Europe (ENTSOE, 2017), with power significant impact on ittheis dynamic behavior. interconnected system of Europe RES connected with VSC. However, not clear(ENTSOwhat Obviously, power systems can cope with a certain sharethe of E, 2017), with significant impact on the dynamic behavior. Obviously, power systems can cope with a certain share of E, 2017), with significant impact on the dynamic behavior. critical thresholdwith of this share is with respect toclear power system RES connected VSC. However, it is not what the Obviously, power systems can cope with a certain share of RES connected with VSC. However, it is not clear what the Obviously, power systems can cope with a certain share of stability. The stability of theispower systemtoispower particularly critical threshold of this share with respect system RES connected with VSC. However, it is not what the critical threshold of this share is with respect toclear power system RES connected with VSC. However, it is not clear what the important in exceptional situations. Therefore, this paper stability. The stability of theispower systemtoispower particularly critical this share with system stability. The stability theispower systemtoispower particularly critical threshold threshold ofhigh this of share withofrespect respect system presents effects ofof penetration VSC-based generation important in exceptional situations. Therefore, this paper stability. The stability of the power system is particularly important in exceptional situations. Therefore, this papera stability. The stability of the power system is particularly with fast current control after a severe disturbance with presents effects of high penetration of VSC-based generation important in exceptional situations. Therefore, this paper presents effects of high penetration of VSC-based generation important in exceptional situations. Therefore, this with papera particular focus oncontrol the roleafter of thea PLL dynamics. with fasteffects current severe disturbance presents of control high penetration penetration of VSC-based VSC-based generation with fasteffects currentof after a severe disturbance with a presents high of generation particular the role of fundamental the PLL dynamics. The focus of theon is on effects. Therefore, with fast focus current control after severe disturbance with a particular focus onpaper the role of thea PLL dynamics. the paper concentrates on the commonly used Synchronous particular the role of fundamental the PLL dynamics. The focus focus of theonpaper is on effects. Therefore, The focus Frame of the paper is on fundamental effects. (Blaabjerg, Therefore, Reference Phase-Locked Loop (SRF-PLL) the paper concentrates on thefundamental commonly used Synchronous of the paper is on effects. Therefore, The focus the paper concentrates on the commonly used Synchronous of Liserre, the paper on fundamental effects. Therefore, Teodorescu, &isTimbus, 2016) and overall system Reference Frame Phase-Locked Loop (SRF-PLL) (Blaabjerg, the paper concentrates on the commonly used Synchronous Reference Frame Phase-Locked Loop (SRF-PLL) (Blaabjerg, the paper concentrates on the commonly used Synchronous behavior of the transmission system. A dynamic model of Teodorescu, Liserre, & Timbus,Loop 2016) and overall system Reference Frame Phase-Locked (SRF-PLL) (Blaabjerg, Teodorescu, Liserre, & Timbus, 2016) andis overall system Referencewith Frame Phase-Locked Loop (SRF-PLL) (Blaabjerg, inverters current control and SRF-PLL introduced and dynamic model of behavior of the transmission system. A Teodorescu, Liserre, & 2016) overall system behavior of the transmission system. dynamic model of Teodorescu, Liserre, & Timbus, Timbus, 2016)A and and overall system its behavior after phase angle jumps for different PLL inverters with current control and SRF-PLL is introduced and behavior of transmission system. A dynamic model of inverters with current control and SRF-PLL is introduced and behavior of the the transmission system. dynamic modelPLL of parameterizations is phase compared in Section its behavior after angle jumpsA 3.for different inverters with current control and SRF-PLL is introduced and its behavior after phase angle jumps foris introduced different PLL inverters with current control and SRF-PLL and parameterizations is compared in Section 3. different PLL its angle jumps parameterizations compared in Section its behavior behavior after afteris phase phase angle jumps 3.for for different PLL parameterizations parameterizations is is compared compared in in Section Section 3. 3.
Copyright © 2018 IFAC 570 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright 2018 responsibility IFAC 570Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 570 10.1016/j.ifacol.2018.11.764 Copyright © 2018 IFAC 570 Copyright © 2018 IFAC 570
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DC Circuit Inverter
Grid
𝑢𝑢
Converter 𝑢𝑢
𝑖𝑖
𝜑𝜑 PLL
V ~ Source
pmd
pmq abc dq
𝑖𝑖
𝑖𝑖
𝑢𝑢
,
PI
𝑖𝑖
b) After the grid voltage phase angle jump = 0 𝑈𝑈Grid
𝑈𝑈Grid
𝜑𝜑
𝐼𝐼Inverter
0°
𝐼𝐼Inverter
𝐼𝐼P
𝐼𝐼Q
Fig. 2: Phasor diagrams of a current-controlled inverter a) right before and b) after a grid voltage phase angle jump. 𝐾𝐾
𝐾𝐾
(2)
In order to do so, the inverter control works in dq-coordinates. As shown in Fig. 1, active power is controlled by controlling the DC voltage 𝑢𝑢dc to a constant set-point 𝑢𝑢dc,ref . To this end, the PI-controller modifies the set-point for the d-axis current 𝑖𝑖d,ref . The set-point value for the q-axis current, 𝑖𝑖q,ref , typically is zero for RES, but a further PI controller (not shown) could be used to provide a nonzero 𝑖𝑖q,ref .
𝜑𝜑 = 0°
abc 𝑢𝑢 dq
𝑄𝑄Inverter = 3 𝑈𝑈Grid 𝐼𝐼Inverter sin Δ𝜑𝜑,
In this paper, the current control of the inverter is assumed to be sufficiently fast such that the controlled inverter can be considered as a current source. Hence, after a jump of the phase angle 𝜑𝜑𝑈𝑈Grid , the inverter continues to feed the same current. Now, Δ𝜑𝜑 ≠ 0° and the inverter current can be divided into an active component 𝐼𝐼𝑃𝑃 and a reactive component 𝐼𝐼𝑄𝑄 , see Fig. 2b. As a result, active power is reduced in favor of capacitive or inductive reactive power after a positive or a negative phase angle jump, respectively. Of course, this is only the case at first instance, since the inverter controller modifies the current set-points to return to the desired active and reactive power.
,
Fig. 1: Voltage orientated control of current-controlled inverter based generation (Wessels, 2012).
𝑢𝑢
(1)
,
𝑖𝑖
a) Before the grid voltage phase angle jump = 0 −
𝑃𝑃Inverter = 3 𝑈𝑈Grid 𝐼𝐼Inverter cos Δ𝜑𝜑,
where all values are root mean square (RMS) values and Δ𝜑𝜑 = 𝜑𝜑𝑈𝑈Grid − 𝜑𝜑𝐼𝐼Inverter is the phase angle difference. Fig. 2a shows the case of a pure active power infeed. The grid voltage 𝑈𝑈Grid and the inverter current 𝐼𝐼Inverter are in phase, i.e. Δ𝜑𝜑 = 0°. In the following, we define the phase angle 𝜑𝜑𝑈𝑈Grid as the reference angle.
PI
PI
571
𝜔𝜔
The current control uses the actual values 𝑖𝑖d and 𝑖𝑖q . These are computed by applying a Park transformation (Park, 1927) on the measured inverter currents 𝑖𝑖abc . The transformation depends on 𝜑𝜑PLL , which is an estimation of the reference angle 𝜑𝜑𝑈𝑈Grid , determined by the PLL. In two further controllers, the Pulse-Width-Modulation (PWM) signals pmq und pmd are calculated in order to switch the transistors of the inverter.
𝜑𝜑
Fig. 3: Block diagram of the SRF-PLL. In Section 4, the fundamental impact on power system stability is analyzed based on a simplified, highly loaded grid. This simplified grid model is based on the transmission grid of the transmission system in South-West Germany. The scenario considers islanding of the grid, resulting in large phase angle jumps with subsequent over- and under-frequency. The focus of the analysis lies on the transient behavior immediately after the phase angle jump and the related impact on voltage and frequency stability.
2.2. Phase-locked loop The reference angle is estimated by a PLL (Teodorescu, Liserre, & Rodríıguez, 2011). The most common type is the Synchronous Reference Frame PLL (SRF-PLL), shown in Fig. 3. The measured three-phase voltage 𝑢𝑢abc is transformed using a Park transformation on the basis of the estimated reference angle 𝜑𝜑PLL . The control loop of the PLL drives the q-axis component 𝑢𝑢q to zero. In its simplest form, it consists of a PI controller with the parameters 𝐾𝐾P and 𝐾𝐾I . The estimated reference angle 𝜑𝜑PLL and the grid frequency 𝜔𝜔PLL are the outputs of the SRF-PLL. As shown in Fig. 3, the control loop has no direct feedthrough. Therefore, changes in the grid voltage phase angle can only be estimated with a time delay. If the grid voltage phase angle changes, the estimated reference angle is not correct and the computed 𝑖𝑖d and 𝑖𝑖q do not match the real actual values during the transient behavior of the PLL. The dynamic performance of the PLL – meaning how fast the estimation error is controlled to zero – depends on the parameters 𝐾𝐾P and 𝐾𝐾I .
2. DYNAMIC INVERTER MODEL 2.1. General model structure Fig. 1 shows a model of a VSC inverter with a direct current capacity and voltage-orientated current control. It consists of two VSC that are connected via a direct current (DC) voltage link circuit. The converter feeds the power of the source – here shown as a voltage source – into the DC circuit. The inverter feeds this power into the grid by providing a current 𝐼𝐼Inverter with phase angle 𝜑𝜑𝐼𝐼Inverter at a given grid voltage 𝑈𝑈Grid with phase angle 𝜑𝜑𝑈𝑈Grid . Considering symmetric three phase power flow, active and reactive power of the inverter are given by 571
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572
due to the overshoot of 𝜑𝜑PLL . After the decay of the PLL phase angle error, pure active power is fed in again. As a conclusion, the PLL parameterization influences the feed-in behavior of current-controlled inverters after a grid voltage phase angle jump. Furthermore, electromagnetic transient (EMT) simulations show that simulating the PLL in the RMS domain is sufficiently accurate, even for large phase angle jump. The response of the PLL to a symmetrical phase angle jump of 30° in the input variable 𝑢𝑢abc is almost identical in the EMT and the RMS domains. 3. TRANSMISSION GRID INVESTIGATIONS The impact of the PLL parameterization on grid behavior and stability is investigated by means of simulations. They consider an islanding scenario in order to generate sufficiently large phase angle jumps. The simulation model used is a simplified benchmark model based on assumptions of future developments of the transmission grid of the federal state of Baden-Württemberg, Germany. The generation and consumption forecast is based on the German network development plan (NEP2013), see Table 2. The scenario features low synchronous generation and high shares of inverter-based generation. It is assumed that two feeding high voltage direct current (HVDC) connections are in operation. Furthermore, the scenario has a large supply of RES in Germany as a whole, resulting in significant active power transit over the transmission grid. The total transit is assumed to be 4.5 GW and runs from north to south. Run-of-river power stations and conventional generation feed in with synchronous generators.
Fig. 4: RMS Simulation results of two different PLL parameterizations, PLLA (⋯) and PLLB (– –). In order to investigate the influence of the PLL speed on the inverter infeed behavior, two different PLL parameterizations are considered as shown in Table 1. While other PLL algorithms with higher performance exist (Karimi-Ghartema, 2014), SRF-PLL is a widespread technique. The parameters given in Table 1 are chosen based on assumptions, literature, and information from inverter manufacturers. PLLA represents a parameterization resulting in realistic dynamics of the PLL itself. The parameters of PLLB represent a considerably slower behavior, taking additional measurement delays into account. However, this does not mean that these parameters are representative. The purpose is to analyze fundamental effects of PLL dynamics. It is also worth noting that the model does not contain any filtering of 𝑢𝑢abc , which may be necessary for faster PLL parametrizations.
Table 2. Conditions for the investigated scenario. All units in GW. AC Import Total load RES Baden-Württemberg RES Germany Conventional Generation Run-of-River power plants HVDC feed in
Table 1. PLL-Parameters PLLA (fast) PLLB (slow)
𝐾𝐾P 10 3
𝐾𝐾I 50 0 (P-controller)
Fig. 4 illustrates the difference between the parameterizations given in Table 1. For simplicity, the DC capacitor is assumed to have infinite capacitance, hence the DC voltage is assumed to be constant. Furthermore, to isolate the influence of the PLL, the inverter has no active or reactive power control and initially provides active power only.
1.57 12.42 6.13 80.85 0.16 0.56 4
3.1. Modelling of the benchmark model The benchmark network shown in Fig. 5 is a simplified model of the transmission grid of Baden-Württemberg, Germany, consisting of nine 380 kV nodes.
At the beginning, the PLL is synchronous with the reference angle. At = 0 s, the reference angle jumps by 30° at constant frequency. PLLA detects the grid voltage angle faster than PLLB, but also shows a significant overshoot. Due to the fact that the PLL has no direct feedthrough, the initial estimation error and the behavior of the inverter immediately after the phase angle jump do not depend on the parameters of the PLL. The angle 𝜑𝜑PLL converges to the actual value with different dynamic performance, depending on the parameterization. In particular, PLLA causes the reactive power to change its sign 572
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SG
~
3.2.2 Sources
Synchronous Generator
In the benchmark network, a remaining portion of synchronous generators is assumed at nodes A, B, C, and G with a total apparent power of 6 GVA. The respective generator parameters, as well as the turbine and voltage controllers used have also been approximated realistically (IEEE, 1973). All HVDC and RES are represented by an aggregated model, based on the model shown in Section 3. The model of RES is not equipped with frequency containment reserve but with an over-frequency control namely limited frequency sensitive mode – over-frequency (LFSM-O) (ENTSO-E, 2012). This control reduces active power as a linear function of frequency in the range of 50.2 Hz to 51.5 Hz. It is assumed that, in contrast to HVDC systems, RES do not provide any AC voltage control. The RES feed-in power is distributed evenly across all nodes of the benchmark network. A full nonlinear SRF-PLL model has been implemented, as for our analysis, a linearization as in (Hans, Schumacher, & Harnefors, 2018) is not necessary. All RES have identical PLL and control parameters. The current control of all inverters is very fast and uniformly parameterized, so that the inverters approximately behave as current sources. The power of the HVDCs is divided equally. The HVDCs each have the same parameterization of the PLL and current controller.
External Grid
G
H
I
SG
~
HVDC Connection E D
Load
B
SG
~
A
Renewable Energy Source
F
SG
~
C
SG
~
Shunt Capacitor
Fig. 5: Simplified benchmark network of the transmission grid of the federal state of Baden-Württemberg, Germany. 3.2 Modelling of the network elements 3.2.1 Network model The number and length of the overhead lines are modeled close to reality of the transmission grid, see Table 3. All specific line parameters are identical: AC-resistance 𝑅𝑅′ = 0.03 Ω⋅km−1 , reactance 𝑋𝑋′ = 0.26 Ω⋅km−1 , and capacitance 𝐶𝐶′ = 4 nF⋅km−1 .
3.2.3 Loads The total load is distributed equally among all nodes of the benchmark model. To model the behavior of active and reactive power consumption, a dynamic voltage- and frequency dependent model is used (Hall, 1993). All loads perform frequency-dependent load shedding. The loads in the considered scenario are shed according to the UFLS plan 14 (ENTSO-E, 2014). According to the plan, a frequency below 49 Hz triggers an instantaneous load shedding of 5% every 0.1 Hz with 10 steps in total up to 48.1 Hz. The switching time of the load shedding relay is modeled with a dead time of 150 ms.
Table 3. Number and length of the benchmark network lines. Line NodeNode A-B A-D A-E B-C C-F D-G E-H F-H F-I G-H H-I
Length in km 50 150 158,11 50 150 150 150 158,11 150 50 50
573
Number of parallel lines 2 3 2 2 2 3 2 2 1 2 2
3.2.4 Shunt Capacitors The shunt capacitors at nodes D, E, and F are implemented with a capacitive nominal reactive power of 250 Mvar each at a rated voltage of 380 kV. Furthermore, they are equipped with an automatic over-voltage disconnection. 3.3 Simulative Investigations 3.3.1 Study Cases
For the analysis of the results, the nodes are clustered in a southern (nodes A, B, and C), center (nodes D, E, and F) and northern cluster (nodes G, H, and I). This is admissible because the electrical state variables of nodes in one cluster have almost identical values due to their small mutual electrical distance. Nodes A, C, G, H, and I are connected to external networks. In order to implement the assumed transit, 4.5 GW are imported from the external grid in the north and exported in the south. In addition, 1.57 GW are imported from the north. All power flows are evenly distributed among the corresponding nodes.
In this paper, two cases are examined on basis of the developed benchmark network: In case A, all inverters are equipped with PLLA, in case B with PLLB. At the beginning of the simulation, several lines are heavily loaded by transit power flows. The current-dependent reactive power load of the north-south lines have to be compensated by the shunt capacitors and synchronous generators in order to counteract a power flow dependent voltage drop.
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Fig. 7: a) Sum of all RES reactive power case A (—) and B (-), b) sum of all RES active power outputs A (—) and B (--). Fig. 6: a) Case A and b) case B: phase angle differences Δ𝜑𝜑 = 𝜑𝜑𝑈𝑈Grid − 𝜑𝜑𝐼𝐼Inverter north (⋯), center (– –) and south (—). At = s, all AC couplings are disconnected simultaneously in order to cause large phase angle jumps and an active power imbalance. Due to the elimination of transit and import power flows, the electrical conditions change instantaneously, which can be seen in the phase angle differences, shown in Fig. 6. The largest phase angle differences occur at the northern nodes. The change decreases towards the southern nodes. Analogously to Fig. 4, PLLA follows the grid voltage phase angle faster than PLLB in case B, but also shows a significant overshoot. 3.3.2 Voltage / Reactive Power Behavior Due to the delayed detection of the grid voltage phase angle by the PLL, the inverter-based elements no longer provide active and reactive power according to their set-points. This is clearly visible from the feed-in behavior of the RES, which feed in large amounts of inductive reactive power into the network immediately after islanding, see Fig. 7a. The inductive reactive power feed-in by the RES lasts significantly longer in case B than in case A. The latter even has a temporary phase of capacitive reactive power feed-in. Fig. 7b shows a drop in the active power feed-in in case A at = 2.6 s as the over-frequency control of RES is triggered and thus reduce their active power output.
Fig. 8: a) Case A and b) case B: Grid voltages north (⋯), center (– –) and south (—). of 𝜑𝜑PLL in case A, the RES temporarily feed in capacitive reactive power, thus increasing the grid voltages further. In case B, the longer duration of inductive reactive power temporarily compensates parts of the excess of capacitive reactive power, see Fig. 8b. The shunt capacitors are disconnected from the grid in both cases after = .6 s due to overvoltage. This leads to a drop in the grid voltages and after that to a new stationary state in both cases.
The load of the north-south lines drops significantly in both cases. As a result, their current-dependent reactive power consumption changes instantly. Thus, after islanding they act as a capacitance and the grid voltages increase.
3.3.3 Frequency / Active Power Behavior Due to the loss of imported active power, the frequency drops almost linearly at all nodes, see Fig. 9a. Despite having an identical import in both cases, the frequency drops faster in case A. This is caused by the voltage-dependent active power demand of loads. Their active power demand increase temporarily, caused by the increasing voltages, in both cases due to overvoltage, see Fig. 9b. The frequency drops below 49 Hz in both cases, so that loads are shed according to the frequency-dependent load shedding plan. Caused by the higher frequency gradient, the cumulative load shedding is 20 % of total load in case A. In case B on the other hand, only 10 % of the total load is disconnected. This is of crucial importance for the subsequent frequency response after the automatic
The reactive power jumps of the RES and the lines dominate the grid voltage curves in both cases, see Fig. 8. All grid voltages are in steady state at the beginning of the simulation an in a narrow voltage band between 407 and 413 kV. Immediately after islanding, the grid voltages jump in negative direction in both cases due to the described jump in inductive reactive power feed-in of the RES inverters. Thereupon, the effect of the capacitive north-south lines together with the shunt capacitors still connected becomes dominant and leads to an increase in grid voltages. This voltage increase is more pronounced in case A, see Fig. 8a. Due to the overshoot 574
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Duckwitz, D., & Fischer, B. (2017). Modeling and Design of df/dt-Based Inertia Control for Power Converters. IEEE Journal of Emerging and Selected Topics in Power Electronics, 5(4), pp. 1553 - 1564. ENTSO-E. (2012). Network Code for Requirements for Grid Connection Applicable to all Generators. ENTSO-E. (2014). Technical background for the Low Frequency Demand Disconnection requirements. ENTSO-E. (2017). High Penetration of Power Electronic Interfaced Power Sources (HPoPEIPS). Hall, B. (1993). Experimentelle Untersuchung zur frequenzund spannungsabhängigen Leistungsaufnahme elektrischer Verbraucherteilnetze. Stuttgart: MediaDruck Wiesinger.
Fig. 9: a) Frequency in case A (—) and case B (– –), b) total load in case A (—) and case B (– –). disconnection of the shunt capacitors at = .6 s and the resulting normalization of the grid voltages. In case A, the increased active power demand of the loads is temporarily higher after islanding. This is why the load shedding in case A overreacts. Therefore, the frequency increases much more after t = .6 s in case A than in case B. The under-frequency problem turns into an over-frequency problem that can only be stabilized by the RES LFSM-O.
Hans, F., Schumacher, W., & Harnefors, L. (2018). SmallSignal Modeling of Three-Phase Synchronous Reference Frame Phase-Locked Loops. In IEEE Transactions on Power Electronics (pp. 5556-5560). Boston, MA: IEEE Power Electronics Society. IEEE. (1973). Dynamic Models for Turbine-Governors in Power System Studies. IEEE Trans. Power App. Syst., PAS-92(6), pp. 1904 - 1915.
In the shown islanding scenario, the slower PLLB stabilizes the grid voltage due to a longer inductive reactive power feed-in which temporarily compensates reactive power demand of the lines and shunt capacitors. However, in case of an export scenario PLLB would lead to increasing grid voltage due to capacitive reactive power feed-in.
Karimi-Ghartema, M. (2014). Enhanced Phase-Locked Loop Structures for Power and Energy Applications (1. ed.). Hoboken, New Jersey: Wiley-IEEE Press. Kundur, P. (1994). Power System Stability And Control (1. ed.). New York City: McGraw-Hill.
4. CONCLUSIONS AND OUTLOOK
Liu, X., & Lindemann, A. (2017). Control of VSC-HVDC Connected Offshore Windfarms for Providing Synthetic Inertia. IEEE Journal of Emerging and Selected Topics in Power Electronics(99), pp. 1-1.
In this paper, the feed-in behavior of inverter-based generation is explained theoretically in case of grid voltage phase jumps. The effects on voltage stability are investigated by simulations. The effects on grid voltages are analyzed based on an islanding scenario of a simplified model of the transmission grid of Baden-Württemberg, Germany, with high penetration of inverter-based generation. Sensitivity analyses of the PLL parameters show that inverters with the described current controlled control algorithm can significantly influence voltage and frequency stability of the power system, especially in case of islanding and system split scenarios with significant phase angle jumps of the grid voltage.
Park, R. H. (1927). Two-Reaction Theory of Synchronous Machines. Transactions of the American Institute of Electrical Engineers, 48(3), pp. 716 - 727. S.-K.Chung. (2000). Phase-locked loop for grid-connected three-phase power conversion systems. United Kingdom: IEE Proc-Electr. Power Appl. Teodorescu, R., Liserre, M., & Rodríıguez, P. (2011). Grid Converters For Photovoltaic And Wind Power Systems. United Kingdom: John Wiley & Sons.
All simulations shown in this paper are based on RMS simulations. In a next step it has to be proved if a stable system operation can be achieved for different penetration levels of current-controlled voltage source converters at all, using EMT simulation. Future investigations will also cover grid-forming converters, which can be seen as voltage-controlled voltage source converters. REFERENCES Blaabjerg, F., Teodorescu, R., Liserre, M., & Timbus, A. (2016). Overview of Control and Grid Synchronization for Distributed Power Generation Systems. pp. 1398-1409.
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IFAC PapersOnLine 51-28 (2018)source 570–575converters on power system stability Impact of current-controlled voltage Impact of current-controlled source H. converters power system stability C. Schöll*,voltage J. Lehner**, Lens* on Impact of current-controlled voltage source converters on power system stability Impact source converters power system stability C. Schöll*,voltage J. Lehner**, Lens* on Impact of of current-controlled current-controlled source H. converters C. Schöll*,voltage J. Lehner**, H. Lens* on power system stability
C. J. H. C. Schöll*, Schöll*, J. Lehner**, Lehner**, H. Lens* Lens* (IFK), Department Power Generation and *University of Stuttgart, Institute of Combustion and Power Plant Technology Automatic Control, Pfaffenwaldring 23, 70569 Stuttgart, Germany (e-mail: [email protected]; *University of Stuttgart, Institute of Combustion and Power Plant Technology (IFK), Department Power Generation and *University of Stuttgart, Institute of Combustion and Power Plant Technology (IFK), Department Power Generation and [email protected]). Automatic Control, Pfaffenwaldring 23, 70569 Stuttgart, Germany (e-mail: [email protected]; *University of Stuttgart,Pfaffenwaldring Institute of Combustion Combustion and Power Plant Technology (IFK), Department Power Generation Generation and and Automatic Control, 23, 70569 Stuttgart, Germany (e-mail:(e-mail: [email protected]; *University Stuttgart, Institute of and Power Plant Technology (IFK), Department Power ** of TransnetBW GmbH, Osloerstr. 15-17, 70173 Stuttgart, Germany [email protected]) [email protected]). Automatic Control, Control, Pfaffenwaldring Pfaffenwaldring 23, 23,[email protected]). 70569 Stuttgart, Stuttgart, Germany Germany (e-mail: (e-mail: [email protected]; [email protected]; Automatic 70569 ** TransnetBW GmbH, [email protected]). 15-17, 70173 Stuttgart, Germany (e-mail: [email protected]) ** TransnetBW GmbH, [email protected]). 15-17, 70173 Stuttgart, Germany (e-mail: [email protected]) ** TransnetBW TransnetBW GmbH, GmbH, Osloerstr. Osloerstr. 15-17, 15-17, 70173 70173 Stuttgart, Stuttgart, Germany Germany (e-mail: (e-mail: [email protected]) [email protected]) ** Abstract: It is known that current-controlled voltage source converters do not contribute to the inertia of power systems, leading a higher rate of change frequency in case imbalances. Another Abstract: It is known thattocurrent-controlled voltageofsource converters do of notpower contribute to the inertia of Abstract: It iseffect known that current-controlled voltage source converters doofnot contribute to the inertia of fundamental becomes apparent in case of large phase angleinjumps the gridimbalances. voltage. Such phase power systems, leading to a higher rate of change of frequency case of power Another Abstract: It is ismay known that current-controlled voltageofsource source converters do of not contribute to the the converter inertia of power systems, leading tocurrent-controlled aexample, higher rate of change frequency in case power imbalances. Another Abstract: It known that voltage converters do not contribute to inertia of angle jumps occur, for in ofphase a system The power infeed of fundamental effect becomes apparent inconsequence case of large anglesplit. jumps of the grid voltage. Such phase power systems, leading to a higher rate of change of frequency in case of power imbalances. Another fundamental effect becomes apparent inand, case of large angleinfluenced of the voltage. delay Such phase power systems, leading tophase aexample, higher rate of change ofofphase frequency injumps case ofpower power imbalances. Another depends on the estimated angle hence, is transiently by grid theinfeed inherent of its angle jumps may occur, for in consequence a system split. The of the converter fundamental effectoccur, becomes apparent in inconsequence case of large large phase angle jumps of the grid voltage. Such phase angle jumpsusually may for example, ofphase a system split. The power infeed ofPLL the converter fundamental effect becomes apparent in case of angle jumps of the grid voltage. Such phase estimation, by a phase-locked loop (PLL). This paper investigates the effect of the dynamics depends on the estimated phase angleinand, hence, isoftransiently influenced by theinfeed inherent delay of its angle jumps mayestimated occur, for forand example, consequence system split. split. The power of the the converter depends on the phase and, hence, isoftransiently influenced by theinfeed inherent delay its angle may occur, example, in consequence aa system The power of converter on thejumps converter behavior itsangle impact on(PLL). transmission voltage and frequency stability. Toofthis estimation, usually by a phase-locked loop This paper investigates the effect of the PLL dynamics depends on the estimated phase angle and, hence, is transiently influenced by the inherent delay of its estimation, usually by a phase-locked loop (PLL). This paper investigates the effect of the PLL dynamics depends on the estimated phase angle and, hence, is transiently influenced by the inherent delay of its end,the islanding scenarios ofand a grid lines loaded beyondsystem their natural are considered. Sensitivity on converter behavior its with impact on(PLL). transmission voltagepower and frequency stability. To this estimation, usually by a phase-locked loop This paper investigates the effect of the PLL dynamics on the converter behavior and its impact on transmission system voltage and frequency stability. To this estimation, usually by a phase-locked loop (PLL). This paper investigates the effect of the PLL dynamics analyses of thescenarios PLL parameters show noticeable effects ontheir voltage and power frequency stability depending on end, islanding ofand a grid with lines loaded beyond natural are considered. Sensitivity on the converter behavior itsthe impact onloaded transmission system voltagepower and frequency frequency stability. To this this end, islanding scenarios ofand a grid with lines beyondsystem their natural are considered. Sensitivity on converter behavior its impact on transmission voltage and stability. To the the dynamic parameterization of PLL. analyses of the PLL parameters show noticeable effects on voltage and frequency stability depending on end, islanding islanding scenarios of aa grid gridshow with noticeable lines loaded loaded beyond their natural power are considered. considered. Sensitivity analyses of thescenarios PLL parameters effects ontheir voltage and power frequency stability depending on end, of with lines beyond natural are Sensitivity the dynamic parameterization of the PLL. Keywords: angle jumps, Phase-locked loop, Voltage stability, Voltage SourceLtd. Converter. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier All rights reserved. on analyses of Phase the PLL parameters show noticeable effects on voltage voltage and frequency stability depending on the dynamic parameterization of the PLL. analyses of the PLL parameters show noticeable effects on and frequency stability depending Keywords: Phase angle jumps, Phase-locked loop, Voltage stability, Voltage Source Converter. the dynamic parameterization of the PLL. the dynamicPhase parameterization the PLL. loop, Voltage stability, Voltage Source Converter. Keywords: angle jumps, of Phase-locked Keywords: Phase angle jumps, Phase-locked Keywords:1.Phase angle jumps, Phase-locked loop, loop, Voltage Voltage stability, stability, Voltage Voltage Source Source Converter. INTRODUCTION with PLL may even resultConverter. in local stability issues (Duckwitz 1. INTRODUCTION Synchronous generators of conventional power plants 1. INTRODUCTION substantially contribute to system stability. Their 1. Synchronous generators ofpower conventional power plants 1. INTRODUCTION INTRODUCTION Synchronous generators of due conventional power source plants stabilizing characteristics are to their voltage substantially contribute toofpower system stability. Their Synchronous generators conventional power plants substantially contribute toofpower system stability. Their Synchronous conventional power plants behavior and togenerators the rotational energy stored in the rotating stabilizing characteristics are due to their voltage source substantially contribute to power system stability. Their stabilizing characteristics are due to their voltage source substantially contribute to power system stability. Their mass of generator androtational turbine. energy Sudden stored changes phase behavior and to the in in thetherotating stabilizing characteristics are due to their voltage source behavior and to the rotational energy stored in the rotating stabilizing characteristics are due to their voltage source angle of generator the grid voltage, for example caused by an active mass of androtational turbine. Sudden stored changes in the phase behavior and to to the the energy in the rotating mass ofimbalance generator and turbine. Sudden lead changes in therotating phase behavior and rotational energy stored the power involtage, the overall system, to in anby injection or angle of the grid for example caused an active mass of and turbine. Sudden changes in the phase angle of generator the grid voltage, for (Kundur, example caused This by an active mass of generator and turbine. Sudden changes in the phase absorption of rotational energy 1994). behavior power imbalance in the overall system, lead to an injection or angle of the grid voltage, for example caused an active power imbalance in theany overall system, lead to anby injection or angle of the grid voltage, for example caused by an active is independent of automatic control mechanism. absorption of rotational energy (Kundur, 1994). This behavior power imbalance in the overall system, lead to an injection or absorption of rotational energy (Kundur, 1994). This behavior power imbalance in the overall system, lead to an injection or Consequently, present power system stability is based on the is independent of any automatic control mechanism. absorption of rotational energy (Kundur, 1994). This behavior is independent of any automatic control mechanism. absorption of rotational energy (Kundur, 1994). This behavior intrinsic behavior of synchronous generators. Consequently, powerautomatic system stability based on the is independent independentpresent of any any controlis mechanism. Consequently, present powerautomatic system stability is based on the is of control mechanism. intrinsic behavior of synchronous generators. In contrast, most renewable energy sources (RES) are Consequently, present power stability intrinsic behavior of synchronous generators. Consequently, present power system system stability is is based based on on the the connected to the grid via current-controlled voltage source intrinsic behavior of synchronous synchronous generators. In contrast, mostof renewable energy sources (RES) are intrinsic behavior generators. In contrast, most(ENTSO-E, renewable2017). energy sources (RES)active are converters (VSC) In order tovoltage deliver connected to the grid via current-controlled source In contrast, most renewable energy sources (RES) are connected to the grid via current-controlled voltage source In contrast, most(ENTSO-E, renewable energy sources (RES) are and reactive power properly, 2017). these concepts depend on the converters (VSC) In order tovoltage deliver active connected to the grid via current-controlled source converters (VSC) (ENTSO-E, 2017). In order to deliver active connected to the grid via current-controlled voltage source synchronization with an existing grid. To this end, the phase and reactive power properly, 2017). these concepts on the converters (VSC) (ENTSO-E, In order order todepend deliver active and reactive power properly, these concepts depend the converters (ENTSO-E, 2017). In to deliver active angle has to(VSC) be estimated, which usually is this done withthe a on phasesynchronization with an existing grid. To end, phase and reactive power properly, these concepts depend on the synchronization with an existing grid. To this end, the phase and reactive power properly, these concepts depend on the lockedhas loop (S.-K.Chung, 2000). In to protect angle to (PLL) be estimated, which usually is order doneend, with a phasesynchronization with an existing grid. To this the phase angle has to be estimated, which usually is done with a phasesynchronization with an existing grid. To this end, the phase converter from overcurrent, converters fororder REStousually are lockedhas loop (PLL) (S.-K.Chung, 2000). In protect the angle to be which usually is done with aa phaselocked loop (PLL) (S.-K.Chung, 2000). to protect the angle has to be aestimated, estimated, which usually is done with phaseequipped with fast current control. AsIn a order consequence, their converter from overcurrent, converters for RES usually are locked loop (PLL) (S.-K.Chung, 2000). In order protect the converter from overcurrent, converters for RESto usually are locked loop (PLL) (S.-K.Chung, 2000). In order to protect the behavior is fundamentally different from synchronous equipped with a overcurrent, fast current control. As for a consequence, their converter from converters RES usually are equipped with a fast current control. As a consequence, their converter from overcurrent, converters for RES usually are machines. They are not capable of island operation and do not behavior is fundamentally different from synchronous equipped with aasystem fast current control. As consequence, their behavior is fundamentally different from synchronous equipped with fastnot current control. As aaoperation consequence, support power stability intrinsically. Suitable machines. They are capable of island andcontrol dotheir not behavior is fundamentally different from synchronous machines. They are not capable of island operation and do not behavior is fundamentally different from synchronous algorithms can system be used in order to supportSuitable power control system support power stability intrinsically. machines. They are not capable of island operation and do not support power system stability intrinsically. Suitable control machines. They are not capable of island operation and do not stability withcan VSC, e.g.in(Liu & Lindemann, 2017), they algorithms be see used order to supportSuitable power but system support power system stability intrinsically. control algorithms can be used in order to support power system support power system stability intrinsically. Suitable control can onlywith do so if the RES is equipped with sufficient energy stability VSC, see e.g.in(Liu & Lindemann, 2017), but they algorithms be used order to power system stability withcan VSC, see e.g.in(Liu & Lindemann, 2017), but they algorithms can be used order to support support power system storage capacity. Even then, power system stability support of can only do so if the RES is equipped with sufficient energy stability with VSC, see e.g. (Liu & Lindemann, 2017), but they can only do so ifequivalent the RES istoequipped with of sufficient energy stability with VSC, see e.g. (Liu & Lindemann, 2017), but they VSC cannot be the behavior a synchronous storage capacity. Even then, power system stability support of can do the is equipped with sufficient energy storage capacity. Even then, system support of can only only do so so if the RES RES istopower equipped withstability sufficient energy machine due to if inevitable delays inbehavior measurement and control. VSC cannot be equivalent the of a synchronous storage capacity. Even then, power system stability support of VSC cannot be equivalent to the behavior of a synchronous storage Evenconcepts then, power system stabilityand support of In fact, capacity. some control based on frequency estimation machine due be to inevitable delays inbehavior measurement control. VSC cannot equivalent to the of a synchronous machine due to inevitable delays in measurement and control. VSC cannot be equivalent to the behavior of a synchronous In fact, some control concepts based on frequencyand estimation machine due to to inevitable delays in measurement measurement control. In fact, some control concepts based on frequencyand estimation machine due inevitable delays in control. In In fact, fact, some some control control concepts concepts based based on on frequency frequency estimation estimation
& Fischer, 2017). with PLL may even result in local stability issues (Duckwitz with PLL may even result in local stability issues (Duckwitz & Fischer, 2017). As synchronous generators inverter-based with PLL may may even result in in are local stability issues (Duckwitz & Fischer, 2017). with PLL even result localreplaced stabilityby issues (Duckwitz generation, their stabilizing effect diminishes. In the German & Fischer, 2017). As synchronous generators are replaced by inverter-based & Fischer, 2017). As synchronous generators area replaced inverter-based control areas, with low sharebyofIn synchronous generation, theirsituations stabilizing effect diminishes. the German As synchronous generators are replaced by inverter-based generation, their stabilizing effect diminishes. In thesufficient German As synchronous generators are replaced by inverter-based generators can situations already bewith observed. As long as control areas, a low share of synchronous generation, their stabilizing effect diminishes. In the German control areas, situations with a low share of synchronous generation, their stabilizing effect diminishes. In the German synchronouscan generators connected in control generators already are bewith observed. Asneighboring long as sufficient control areas, situations a low share of synchronous generators can already be observed. As long as sufficient control areas, situations with a low share of synchronous areas, the impact on overall power system stability remains synchronous generators are connected in neighboring control generators can already be observed. As long sufficient synchronous generators are in control generators can already be connected observed. Asneighboring long as sufficient limited.theHowever, inverter-based generation is as expected to areas, impact on overall power system stability remains synchronous generators are connected in neighboring control areas, the at impact on overall power system stability remains synchronous generators are connected in neighboring control dominate, least temporarily, the generation mix of the whole limited.theHowever, inverter-based generation is expected to areas, impact on overall power system stability remains limited. generation is expected to areas, theHowever, impact oninverter-based overall power system Europe stability remains interconnected power system of continental (ENTSOdominate, at least temporarily, the generation mix of the whole limited. However, inverter-based generation is expected to dominate, at least temporarily, the generation mix of the whole limited. inverter-based generation is expected to E, 2017),However, with power significant impact on the dynamic behavior. interconnected system of continental Europe (ENTSOdominate, at least temporarily, the generation mix of the whole interconnected power system of continental Europe (ENTSOdominate, at least temporarily, the generation mix of the whole Obviously, power systems can cope with a certain share of E, 2017), with power significant impact on the dynamic behavior. interconnected system of continental continental Europe (ENTSOE, 2017), with power significant impact on ittheis dynamic behavior. interconnected system of Europe RES connected with VSC. However, not clear(ENTSOwhat Obviously, power systems can cope with a certain sharethe of E, 2017), with significant impact on the dynamic behavior. Obviously, power systems can cope with a certain share of E, 2017), with significant impact on the dynamic behavior. critical thresholdwith of this share is with respect toclear power system RES connected VSC. However, it is not what the Obviously, power systems can cope with a certain share of RES connected with VSC. However, it is not clear what the Obviously, power systems can cope with a certain share of stability. The stability of theispower systemtoispower particularly critical threshold of this share with respect system RES connected with VSC. However, it is not what the critical threshold of this share is with respect toclear power system RES connected with VSC. However, it is not clear what the important in exceptional situations. Therefore, this paper stability. The stability of theispower systemtoispower particularly critical this share with system stability. The stability theispower systemtoispower particularly critical threshold threshold ofhigh this of share withofrespect respect system presents effects ofof penetration VSC-based generation important in exceptional situations. Therefore, this paper stability. The stability of the power system is particularly important in exceptional situations. Therefore, this papera stability. The stability of the power system is particularly with fast current control after a severe disturbance with presents effects of high penetration of VSC-based generation important in exceptional situations. Therefore, this paper presents effects of high penetration of VSC-based generation important in exceptional situations. Therefore, this with papera particular focus oncontrol the roleafter of thea PLL dynamics. with fasteffects current severe disturbance presents of control high penetration penetration of VSC-based VSC-based generation with fasteffects currentof after a severe disturbance with a presents high of generation particular the role of fundamental the PLL dynamics. The focus of theon is on effects. Therefore, with fast focus current control after severe disturbance with a particular focus onpaper the role of thea PLL dynamics. the paper concentrates on the commonly used Synchronous particular the role of fundamental the PLL dynamics. The focus focus of theonpaper is on effects. Therefore, The focus Frame of the paper is on fundamental effects. (Blaabjerg, Therefore, Reference Phase-Locked Loop (SRF-PLL) the paper concentrates on thefundamental commonly used Synchronous of the paper is on effects. Therefore, The focus the paper concentrates on the commonly used Synchronous of Liserre, the paper on fundamental effects. Therefore, Teodorescu, &isTimbus, 2016) and overall system Reference Frame Phase-Locked Loop (SRF-PLL) (Blaabjerg, the paper concentrates on the commonly used Synchronous Reference Frame Phase-Locked Loop (SRF-PLL) (Blaabjerg, the paper concentrates on the commonly used Synchronous behavior of the transmission system. A dynamic model of Teodorescu, Liserre, & Timbus,Loop 2016) and overall system Reference Frame Phase-Locked (SRF-PLL) (Blaabjerg, Teodorescu, Liserre, & Timbus, 2016) andis overall system Referencewith Frame Phase-Locked Loop (SRF-PLL) (Blaabjerg, inverters current control and SRF-PLL introduced and dynamic model of behavior of the transmission system. A Teodorescu, Liserre, & 2016) overall system behavior of the transmission system. dynamic model of Teodorescu, Liserre, & Timbus, Timbus, 2016)A and and overall system its behavior after phase angle jumps for different PLL inverters with current control and SRF-PLL is introduced and behavior of transmission system. A dynamic model of inverters with current control and SRF-PLL is introduced and behavior of the the transmission system. dynamic modelPLL of parameterizations is phase compared in Section its behavior after angle jumpsA 3.for different inverters with current control and SRF-PLL is introduced and its behavior after phase angle jumps foris introduced different PLL inverters with current control and SRF-PLL and parameterizations is compared in Section 3. different PLL its angle jumps parameterizations compared in Section its behavior behavior after afteris phase phase angle jumps 3.for for different PLL parameterizations parameterizations is is compared compared in in Section Section 3. 3.
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DC Circuit Inverter
Grid
𝑢𝑢
Converter 𝑢𝑢
𝑖𝑖
𝜑𝜑 PLL
V ~ Source
pmd
pmq abc dq
𝑖𝑖
𝑖𝑖
𝑢𝑢
,
PI
𝑖𝑖
b) After the grid voltage phase angle jump = 0 𝑈𝑈Grid
𝑈𝑈Grid
𝜑𝜑
𝐼𝐼Inverter
0°
𝐼𝐼Inverter
𝐼𝐼P
𝐼𝐼Q
Fig. 2: Phasor diagrams of a current-controlled inverter a) right before and b) after a grid voltage phase angle jump. 𝐾𝐾
𝐾𝐾
(2)
In order to do so, the inverter control works in dq-coordinates. As shown in Fig. 1, active power is controlled by controlling the DC voltage 𝑢𝑢dc to a constant set-point 𝑢𝑢dc,ref . To this end, the PI-controller modifies the set-point for the d-axis current 𝑖𝑖d,ref . The set-point value for the q-axis current, 𝑖𝑖q,ref , typically is zero for RES, but a further PI controller (not shown) could be used to provide a nonzero 𝑖𝑖q,ref .
𝜑𝜑 = 0°
abc 𝑢𝑢 dq
𝑄𝑄Inverter = 3 𝑈𝑈Grid 𝐼𝐼Inverter sin Δ𝜑𝜑,
In this paper, the current control of the inverter is assumed to be sufficiently fast such that the controlled inverter can be considered as a current source. Hence, after a jump of the phase angle 𝜑𝜑𝑈𝑈Grid , the inverter continues to feed the same current. Now, Δ𝜑𝜑 ≠ 0° and the inverter current can be divided into an active component 𝐼𝐼𝑃𝑃 and a reactive component 𝐼𝐼𝑄𝑄 , see Fig. 2b. As a result, active power is reduced in favor of capacitive or inductive reactive power after a positive or a negative phase angle jump, respectively. Of course, this is only the case at first instance, since the inverter controller modifies the current set-points to return to the desired active and reactive power.
,
Fig. 1: Voltage orientated control of current-controlled inverter based generation (Wessels, 2012).
𝑢𝑢
(1)
,
𝑖𝑖
a) Before the grid voltage phase angle jump = 0 −
𝑃𝑃Inverter = 3 𝑈𝑈Grid 𝐼𝐼Inverter cos Δ𝜑𝜑,
where all values are root mean square (RMS) values and Δ𝜑𝜑 = 𝜑𝜑𝑈𝑈Grid − 𝜑𝜑𝐼𝐼Inverter is the phase angle difference. Fig. 2a shows the case of a pure active power infeed. The grid voltage 𝑈𝑈Grid and the inverter current 𝐼𝐼Inverter are in phase, i.e. Δ𝜑𝜑 = 0°. In the following, we define the phase angle 𝜑𝜑𝑈𝑈Grid as the reference angle.
PI
PI
571
𝜔𝜔
The current control uses the actual values 𝑖𝑖d and 𝑖𝑖q . These are computed by applying a Park transformation (Park, 1927) on the measured inverter currents 𝑖𝑖abc . The transformation depends on 𝜑𝜑PLL , which is an estimation of the reference angle 𝜑𝜑𝑈𝑈Grid , determined by the PLL. In two further controllers, the Pulse-Width-Modulation (PWM) signals pmq und pmd are calculated in order to switch the transistors of the inverter.
𝜑𝜑
Fig. 3: Block diagram of the SRF-PLL. In Section 4, the fundamental impact on power system stability is analyzed based on a simplified, highly loaded grid. This simplified grid model is based on the transmission grid of the transmission system in South-West Germany. The scenario considers islanding of the grid, resulting in large phase angle jumps with subsequent over- and under-frequency. The focus of the analysis lies on the transient behavior immediately after the phase angle jump and the related impact on voltage and frequency stability.
2.2. Phase-locked loop The reference angle is estimated by a PLL (Teodorescu, Liserre, & Rodríıguez, 2011). The most common type is the Synchronous Reference Frame PLL (SRF-PLL), shown in Fig. 3. The measured three-phase voltage 𝑢𝑢abc is transformed using a Park transformation on the basis of the estimated reference angle 𝜑𝜑PLL . The control loop of the PLL drives the q-axis component 𝑢𝑢q to zero. In its simplest form, it consists of a PI controller with the parameters 𝐾𝐾P and 𝐾𝐾I . The estimated reference angle 𝜑𝜑PLL and the grid frequency 𝜔𝜔PLL are the outputs of the SRF-PLL. As shown in Fig. 3, the control loop has no direct feedthrough. Therefore, changes in the grid voltage phase angle can only be estimated with a time delay. If the grid voltage phase angle changes, the estimated reference angle is not correct and the computed 𝑖𝑖d and 𝑖𝑖q do not match the real actual values during the transient behavior of the PLL. The dynamic performance of the PLL – meaning how fast the estimation error is controlled to zero – depends on the parameters 𝐾𝐾P and 𝐾𝐾I .
2. DYNAMIC INVERTER MODEL 2.1. General model structure Fig. 1 shows a model of a VSC inverter with a direct current capacity and voltage-orientated current control. It consists of two VSC that are connected via a direct current (DC) voltage link circuit. The converter feeds the power of the source – here shown as a voltage source – into the DC circuit. The inverter feeds this power into the grid by providing a current 𝐼𝐼Inverter with phase angle 𝜑𝜑𝐼𝐼Inverter at a given grid voltage 𝑈𝑈Grid with phase angle 𝜑𝜑𝑈𝑈Grid . Considering symmetric three phase power flow, active and reactive power of the inverter are given by 571
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due to the overshoot of 𝜑𝜑PLL . After the decay of the PLL phase angle error, pure active power is fed in again. As a conclusion, the PLL parameterization influences the feed-in behavior of current-controlled inverters after a grid voltage phase angle jump. Furthermore, electromagnetic transient (EMT) simulations show that simulating the PLL in the RMS domain is sufficiently accurate, even for large phase angle jump. The response of the PLL to a symmetrical phase angle jump of 30° in the input variable 𝑢𝑢abc is almost identical in the EMT and the RMS domains. 3. TRANSMISSION GRID INVESTIGATIONS The impact of the PLL parameterization on grid behavior and stability is investigated by means of simulations. They consider an islanding scenario in order to generate sufficiently large phase angle jumps. The simulation model used is a simplified benchmark model based on assumptions of future developments of the transmission grid of the federal state of Baden-Württemberg, Germany. The generation and consumption forecast is based on the German network development plan (NEP2013), see Table 2. The scenario features low synchronous generation and high shares of inverter-based generation. It is assumed that two feeding high voltage direct current (HVDC) connections are in operation. Furthermore, the scenario has a large supply of RES in Germany as a whole, resulting in significant active power transit over the transmission grid. The total transit is assumed to be 4.5 GW and runs from north to south. Run-of-river power stations and conventional generation feed in with synchronous generators.
Fig. 4: RMS Simulation results of two different PLL parameterizations, PLLA (⋯) and PLLB (– –). In order to investigate the influence of the PLL speed on the inverter infeed behavior, two different PLL parameterizations are considered as shown in Table 1. While other PLL algorithms with higher performance exist (Karimi-Ghartema, 2014), SRF-PLL is a widespread technique. The parameters given in Table 1 are chosen based on assumptions, literature, and information from inverter manufacturers. PLLA represents a parameterization resulting in realistic dynamics of the PLL itself. The parameters of PLLB represent a considerably slower behavior, taking additional measurement delays into account. However, this does not mean that these parameters are representative. The purpose is to analyze fundamental effects of PLL dynamics. It is also worth noting that the model does not contain any filtering of 𝑢𝑢abc , which may be necessary for faster PLL parametrizations.
Table 2. Conditions for the investigated scenario. All units in GW. AC Import Total load RES Baden-Württemberg RES Germany Conventional Generation Run-of-River power plants HVDC feed in
Table 1. PLL-Parameters PLLA (fast) PLLB (slow)
𝐾𝐾P 10 3
𝐾𝐾I 50 0 (P-controller)
Fig. 4 illustrates the difference between the parameterizations given in Table 1. For simplicity, the DC capacitor is assumed to have infinite capacitance, hence the DC voltage is assumed to be constant. Furthermore, to isolate the influence of the PLL, the inverter has no active or reactive power control and initially provides active power only.
1.57 12.42 6.13 80.85 0.16 0.56 4
3.1. Modelling of the benchmark model The benchmark network shown in Fig. 5 is a simplified model of the transmission grid of Baden-Württemberg, Germany, consisting of nine 380 kV nodes.
At the beginning, the PLL is synchronous with the reference angle. At = 0 s, the reference angle jumps by 30° at constant frequency. PLLA detects the grid voltage angle faster than PLLB, but also shows a significant overshoot. Due to the fact that the PLL has no direct feedthrough, the initial estimation error and the behavior of the inverter immediately after the phase angle jump do not depend on the parameters of the PLL. The angle 𝜑𝜑PLL converges to the actual value with different dynamic performance, depending on the parameterization. In particular, PLLA causes the reactive power to change its sign 572
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SG
~
3.2.2 Sources
Synchronous Generator
In the benchmark network, a remaining portion of synchronous generators is assumed at nodes A, B, C, and G with a total apparent power of 6 GVA. The respective generator parameters, as well as the turbine and voltage controllers used have also been approximated realistically (IEEE, 1973). All HVDC and RES are represented by an aggregated model, based on the model shown in Section 3. The model of RES is not equipped with frequency containment reserve but with an over-frequency control namely limited frequency sensitive mode – over-frequency (LFSM-O) (ENTSO-E, 2012). This control reduces active power as a linear function of frequency in the range of 50.2 Hz to 51.5 Hz. It is assumed that, in contrast to HVDC systems, RES do not provide any AC voltage control. The RES feed-in power is distributed evenly across all nodes of the benchmark network. A full nonlinear SRF-PLL model has been implemented, as for our analysis, a linearization as in (Hans, Schumacher, & Harnefors, 2018) is not necessary. All RES have identical PLL and control parameters. The current control of all inverters is very fast and uniformly parameterized, so that the inverters approximately behave as current sources. The power of the HVDCs is divided equally. The HVDCs each have the same parameterization of the PLL and current controller.
External Grid
G
H
I
SG
~
HVDC Connection E D
Load
B
SG
~
A
Renewable Energy Source
F
SG
~
C
SG
~
Shunt Capacitor
Fig. 5: Simplified benchmark network of the transmission grid of the federal state of Baden-Württemberg, Germany. 3.2 Modelling of the network elements 3.2.1 Network model The number and length of the overhead lines are modeled close to reality of the transmission grid, see Table 3. All specific line parameters are identical: AC-resistance 𝑅𝑅′ = 0.03 Ω⋅km−1 , reactance 𝑋𝑋′ = 0.26 Ω⋅km−1 , and capacitance 𝐶𝐶′ = 4 nF⋅km−1 .
3.2.3 Loads The total load is distributed equally among all nodes of the benchmark model. To model the behavior of active and reactive power consumption, a dynamic voltage- and frequency dependent model is used (Hall, 1993). All loads perform frequency-dependent load shedding. The loads in the considered scenario are shed according to the UFLS plan 14 (ENTSO-E, 2014). According to the plan, a frequency below 49 Hz triggers an instantaneous load shedding of 5% every 0.1 Hz with 10 steps in total up to 48.1 Hz. The switching time of the load shedding relay is modeled with a dead time of 150 ms.
Table 3. Number and length of the benchmark network lines. Line NodeNode A-B A-D A-E B-C C-F D-G E-H F-H F-I G-H H-I
Length in km 50 150 158,11 50 150 150 150 158,11 150 50 50
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Number of parallel lines 2 3 2 2 2 3 2 2 1 2 2
3.2.4 Shunt Capacitors The shunt capacitors at nodes D, E, and F are implemented with a capacitive nominal reactive power of 250 Mvar each at a rated voltage of 380 kV. Furthermore, they are equipped with an automatic over-voltage disconnection. 3.3 Simulative Investigations 3.3.1 Study Cases
For the analysis of the results, the nodes are clustered in a southern (nodes A, B, and C), center (nodes D, E, and F) and northern cluster (nodes G, H, and I). This is admissible because the electrical state variables of nodes in one cluster have almost identical values due to their small mutual electrical distance. Nodes A, C, G, H, and I are connected to external networks. In order to implement the assumed transit, 4.5 GW are imported from the external grid in the north and exported in the south. In addition, 1.57 GW are imported from the north. All power flows are evenly distributed among the corresponding nodes.
In this paper, two cases are examined on basis of the developed benchmark network: In case A, all inverters are equipped with PLLA, in case B with PLLB. At the beginning of the simulation, several lines are heavily loaded by transit power flows. The current-dependent reactive power load of the north-south lines have to be compensated by the shunt capacitors and synchronous generators in order to counteract a power flow dependent voltage drop.
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Fig. 7: a) Sum of all RES reactive power case A (—) and B (-), b) sum of all RES active power outputs A (—) and B (--). Fig. 6: a) Case A and b) case B: phase angle differences Δ𝜑𝜑 = 𝜑𝜑𝑈𝑈Grid − 𝜑𝜑𝐼𝐼Inverter north (⋯), center (– –) and south (—). At = s, all AC couplings are disconnected simultaneously in order to cause large phase angle jumps and an active power imbalance. Due to the elimination of transit and import power flows, the electrical conditions change instantaneously, which can be seen in the phase angle differences, shown in Fig. 6. The largest phase angle differences occur at the northern nodes. The change decreases towards the southern nodes. Analogously to Fig. 4, PLLA follows the grid voltage phase angle faster than PLLB in case B, but also shows a significant overshoot. 3.3.2 Voltage / Reactive Power Behavior Due to the delayed detection of the grid voltage phase angle by the PLL, the inverter-based elements no longer provide active and reactive power according to their set-points. This is clearly visible from the feed-in behavior of the RES, which feed in large amounts of inductive reactive power into the network immediately after islanding, see Fig. 7a. The inductive reactive power feed-in by the RES lasts significantly longer in case B than in case A. The latter even has a temporary phase of capacitive reactive power feed-in. Fig. 7b shows a drop in the active power feed-in in case A at = 2.6 s as the over-frequency control of RES is triggered and thus reduce their active power output.
Fig. 8: a) Case A and b) case B: Grid voltages north (⋯), center (– –) and south (—). of 𝜑𝜑PLL in case A, the RES temporarily feed in capacitive reactive power, thus increasing the grid voltages further. In case B, the longer duration of inductive reactive power temporarily compensates parts of the excess of capacitive reactive power, see Fig. 8b. The shunt capacitors are disconnected from the grid in both cases after = .6 s due to overvoltage. This leads to a drop in the grid voltages and after that to a new stationary state in both cases.
The load of the north-south lines drops significantly in both cases. As a result, their current-dependent reactive power consumption changes instantly. Thus, after islanding they act as a capacitance and the grid voltages increase.
3.3.3 Frequency / Active Power Behavior Due to the loss of imported active power, the frequency drops almost linearly at all nodes, see Fig. 9a. Despite having an identical import in both cases, the frequency drops faster in case A. This is caused by the voltage-dependent active power demand of loads. Their active power demand increase temporarily, caused by the increasing voltages, in both cases due to overvoltage, see Fig. 9b. The frequency drops below 49 Hz in both cases, so that loads are shed according to the frequency-dependent load shedding plan. Caused by the higher frequency gradient, the cumulative load shedding is 20 % of total load in case A. In case B on the other hand, only 10 % of the total load is disconnected. This is of crucial importance for the subsequent frequency response after the automatic
The reactive power jumps of the RES and the lines dominate the grid voltage curves in both cases, see Fig. 8. All grid voltages are in steady state at the beginning of the simulation an in a narrow voltage band between 407 and 413 kV. Immediately after islanding, the grid voltages jump in negative direction in both cases due to the described jump in inductive reactive power feed-in of the RES inverters. Thereupon, the effect of the capacitive north-south lines together with the shunt capacitors still connected becomes dominant and leads to an increase in grid voltages. This voltage increase is more pronounced in case A, see Fig. 8a. Due to the overshoot 574
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Duckwitz, D., & Fischer, B. (2017). Modeling and Design of df/dt-Based Inertia Control for Power Converters. IEEE Journal of Emerging and Selected Topics in Power Electronics, 5(4), pp. 1553 - 1564. ENTSO-E. (2012). Network Code for Requirements for Grid Connection Applicable to all Generators. ENTSO-E. (2014). Technical background for the Low Frequency Demand Disconnection requirements. ENTSO-E. (2017). High Penetration of Power Electronic Interfaced Power Sources (HPoPEIPS). Hall, B. (1993). Experimentelle Untersuchung zur frequenzund spannungsabhängigen Leistungsaufnahme elektrischer Verbraucherteilnetze. Stuttgart: MediaDruck Wiesinger.
Fig. 9: a) Frequency in case A (—) and case B (– –), b) total load in case A (—) and case B (– –). disconnection of the shunt capacitors at = .6 s and the resulting normalization of the grid voltages. In case A, the increased active power demand of the loads is temporarily higher after islanding. This is why the load shedding in case A overreacts. Therefore, the frequency increases much more after t = .6 s in case A than in case B. The under-frequency problem turns into an over-frequency problem that can only be stabilized by the RES LFSM-O.
Hans, F., Schumacher, W., & Harnefors, L. (2018). SmallSignal Modeling of Three-Phase Synchronous Reference Frame Phase-Locked Loops. In IEEE Transactions on Power Electronics (pp. 5556-5560). Boston, MA: IEEE Power Electronics Society. IEEE. (1973). Dynamic Models for Turbine-Governors in Power System Studies. IEEE Trans. Power App. Syst., PAS-92(6), pp. 1904 - 1915.
In the shown islanding scenario, the slower PLLB stabilizes the grid voltage due to a longer inductive reactive power feed-in which temporarily compensates reactive power demand of the lines and shunt capacitors. However, in case of an export scenario PLLB would lead to increasing grid voltage due to capacitive reactive power feed-in.
Karimi-Ghartema, M. (2014). Enhanced Phase-Locked Loop Structures for Power and Energy Applications (1. ed.). Hoboken, New Jersey: Wiley-IEEE Press. Kundur, P. (1994). Power System Stability And Control (1. ed.). New York City: McGraw-Hill.
4. CONCLUSIONS AND OUTLOOK
Liu, X., & Lindemann, A. (2017). Control of VSC-HVDC Connected Offshore Windfarms for Providing Synthetic Inertia. IEEE Journal of Emerging and Selected Topics in Power Electronics(99), pp. 1-1.
In this paper, the feed-in behavior of inverter-based generation is explained theoretically in case of grid voltage phase jumps. The effects on voltage stability are investigated by simulations. The effects on grid voltages are analyzed based on an islanding scenario of a simplified model of the transmission grid of Baden-Württemberg, Germany, with high penetration of inverter-based generation. Sensitivity analyses of the PLL parameters show that inverters with the described current controlled control algorithm can significantly influence voltage and frequency stability of the power system, especially in case of islanding and system split scenarios with significant phase angle jumps of the grid voltage.
Park, R. H. (1927). Two-Reaction Theory of Synchronous Machines. Transactions of the American Institute of Electrical Engineers, 48(3), pp. 716 - 727. S.-K.Chung. (2000). Phase-locked loop for grid-connected three-phase power conversion systems. United Kingdom: IEE Proc-Electr. Power Appl. Teodorescu, R., Liserre, M., & Rodríıguez, P. (2011). Grid Converters For Photovoltaic And Wind Power Systems. United Kingdom: John Wiley & Sons.
All simulations shown in this paper are based on RMS simulations. In a next step it has to be proved if a stable system operation can be achieved for different penetration levels of current-controlled voltage source converters at all, using EMT simulation. Future investigations will also cover grid-forming converters, which can be seen as voltage-controlled voltage source converters. REFERENCES Blaabjerg, F., Teodorescu, R., Liserre, M., & Timbus, A. (2016). Overview of Control and Grid Synchronization for Distributed Power Generation Systems. pp. 1398-1409.
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