Abstract and Figures

The virtual synchronous machine concept (VSM) has been developed initially to reproduce the synchronous machine stabilizing effect by providing inertia with the emulation of swing equation, whereas droop control is developed initially to ensure load sharing and has no inertia. An introduction of a low pass filter to droop control has been motivated to filter the active power measurement and ensures a time decoupling with the inner control loops, whereas, this low-pass filter can also provide inertia to the system. This functionality is limited due to its negative impact on the active power dynamic. This paper proposes an analysis of the conventional droop control by showing its limitations and proposes an improved inertial droop control that allows providing the inertia to the system and ensures a good dynamic behavior of the active power at once in simple manner, and without modifying the load sharing capability. The results obtained are compared to the conventional method (Droop control and VSM) in various topologies in order to show the relevance of the proposed method.
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Inertia effect and load sharing capability of grid forming
converters connected to a transmission grid
T. Qoria*, F. Gruson*, F. Colas*, G. Denis , T. Prevost , X. Guillaud*
* Univ. Lille, Centrale Lille, Arts et Métiers Paris Tech, HEI,
EA 2697 - L2EP - Laboratoire d’Electrotechnique et d’Electronique de Puissance, F-59000 Lille, France
Réseau de Transport d’Electricité, Versailles, France
Keywords: Grid-forming converter, improved droop control,
inertia emulation, active power dynamic, power sharing
The virtual synchronous machine concept (VSM) has been
developed initially to reproduce the synchronous machine
stabilizing effect by providing inertia with the emulation of
swing equation, whereas droop control is developed initially
to ensure load sharing and has no inertia. An introduction of a
low pass filter to droop control has been motivated to filter
the active power measurement and ensures a time decoupling
with the inner control loops, whereas, this low-pass filter can
also provide inertia to the system. This functionality is limited
due to its negative impact on the active power dynamic. This
paper proposes an analysis of the conventional droop control
by showing its limitations and proposes an improved inertial
droop control that allows providing the inertia to the system
and ensures a good dynamic behavior of the active power at
once in simple manner, and without modifying the load
sharing capability. The results obtained are compared to the
conventional method (Droop control and VSM) in various
topologies in order to show the relevance of the proposed
1 Introduction
Electrical machines have the physical property of storing
kinetic energy in their mechanical part; this energy
contributes essentially to the stability of the electrical grid.
In case of failure, the inertia is able to compensate
immediately the power imbalance and limits the frequency
variations which help the system to remain stable.
In recent years, renewable energy sources have been steadily
increasing, these latter are interfaced to the AC system
through power converters. Currently these converters are
controlled to inject active and reactive power by relying on
the voltage formed by the AC grid; this control strategy is
well-known as grid-following control.
This project has received funding from the European Union’s Horizon 2020
research and innovation program under grant agreement No 691800. This
paper reflects only the author’s views and the European Commission is not
responsible for any use that may be made of the information it contains.
A rise of renewable energy sources based on grid-following
control causes a significant reduction of the total electrical
grid inertia [1]. It induces a faster dynamic response of the
frequency since they do not naturally bring this inertia effect
[2]. Therefore the reaction time of the primary control
becomes slower than the frequency response time which may
lead to an unstable operation. This low-Inertia phenomenon is
already noticed in several areas, such as Ireland and UK.
More details about those data are published by ENTSOE [3].
It is possible to modify the active power with respect to the
derivative of the frequency to mimic the inertial effect. But
this supposes to measure the frequency and operate a
derivation which may induce some time delay and frequency
oscillations [2], [4].
Because of these limitations, new control laws are needed in
order to emulate the inertia effect. This subject has been
widely discussed in the literature, which has led to the
development of the grid forming control[5]- [6] that induces
more natural inertia effect linked with the way to synchronize
the converter to the grid. This has been largely documented
on various publications dealing with virtual synchronous
machine, synchronverter, virtual synchronous generator
(VSG) or VISMA [7][13]. Some of these concepts emulate
the electrical behavior of the real synchronous machine in
order to enhance the load sharing transient; others imitate the
stabilizing effect by reproducing only the swing equation
effect. The virtual synchronous machine concept has been
developed also to ensure a self-synchronization to the main
AC grid [11].
From another side, the principle of the droop control is also
linked with the synchronous behavior of synchronous
generators. Lots of classical synchronous generators have a
static droop control that adjusts their mechanical power
injection with respect to the frequency variation, and thus
compensate for power unbalance. The static proportional
relationship between power and frequency creates a
mechanism of load sharing between generation units. This
effect can be reproduced by the droop control applied to the
grid forming converter, this concept has been widely
discussed in the context of micro-grids [14][17] and
uninterruptible power supply [18], [19]. The droop control is
also known in the literature as Power Synchronization
Method (PSM) [20]. The droop control principle has been
developed for a variety of applications. Then, it has been
improved in order to achieve a good decoupling between
active and reactive power, to guarantee an accurate reactive
power sharing by introducing virtual impedances, and also to
ensure a good transient behavior by filtering the oscillations
around the grid frequency [20].
Although conceptually these two concepts are used for
different reasons .i.e. droop control ensures the power sharing
between units in parallel operation, while VSM provides
inertia and damping; it has been shown in this context that the
two approaches are mathematically equivalent [21]. In some
papers the load sharing using the VSM concept is ensured by
an extra loops, thus the model become more complex and
require additional loops [8], [22][24].
This paper aims to combine the inertial effect of a VSM and
the load sharing capability of a droop control in a single
algorithm without adding any more loops or complexities.
In this paper, small-signal model for conventional droop
control is presented in order to show its limitations and
propose a new simple control strategy that provides inertia;
ensure a better active power transient and load sharing.
In order to simplify the study, only the average VSC model is
used in the development and the DC bus is considered as an
Ideal DC voltage source.
The inertia effect will be analyzed, improved and simulated in
various grid topologies (e.g. grid connected mode and parallel
The reminder of this paper is structured as follows. In
Section.2, a mathematical comparison between droop control
and VSM is presented with reference to the shortcomings of
droop control. Section.3 presents the proposed inertial droop
control with its design method. Section.4 shows a
comparative synthesis between the proposed method and
conventional control techniques.
2 Droop control and VSM comparison
2.1 Recall on classical algorithms
The choice of the droop control is motivated by its capacity to
interact with other units without dedicated communication
link. The architecture is presented in Figure 1. This controller
is responsible for power regulation and load sharing through
the parameter which defines the maximum variation of
the frequency for a nominal power of the AC source. Usually
the droop control gain is set to 5%. This means that for a
maximum variation of the active power, the frequency will
decrease by 5%.
Figure 1: Droop control.
A low-pass filter is often added on the power measurement or
on the frequency derivation as shown in figure 1 for dynamic
decoupling with inner loops, active power noises filtration,
and to avoid frequency jump.
The architecture of the VSM is presented in figure 2. This
concept is mainly chosen because it reproduces the
synchronous machine stabilizing effect by introducing inertial
effect of the synchronous machine. More complex models
have been also developed to mimic also the electrical
behavior of the synchronous machine as mentioned in the
Figure 2: VSM for virtual inertia and damping
2.2 Mathematical equivalence
The transfer function of the droop control is expressed in per-
unit as follow:
  
  
Where , and  are respectivey the set-point active
power, the set-point frequency and the output converter
Note that the red expression in the equation above can be
neglected as the set-point  is constant.
The transfer function of the VSM is expressed in per-unit as
       (2)
Whereand are respectively the inertia constant and
damping coefficient, while  can be a constant frequency
set-point or a grid frequency estimation depending on the
mode operation (i.e. power regulator of frequency regulator)
Equivalence between both approaches exists and can be
expressed by:
 
  (3)
However, the aim of these two approaches is slightly
different. The VSM is mainly focused on bringing an inertial
effect to the grid. The coefficient is chosen first (e.g. =
5s) and then the coefficient is choosen to give a stable
From the analogy between equations (1) and (2), it is clear
that the droop control can provide inertia such as VSM thanks
to the low-pass filter dynamic where the inertia constant can
be tuned through the decrease of the filter cut-frequency.
While the decrease of induces oscillations on the active
power. In [25], must fulfills the following condition to
maintain a stable operation:
  
Hence, with the classical parameters, the inertia provided by
this control is limited to  . If more inertia is needed,
these approaches need to be improved.
3 Proposed inertial droop control
In control theory, a derivative action aims to stabilize the
system and to control the undesirable overshoot; however a
lead-lag filter is generally used to overcome the numerical
issue linked to the derivative computation.
The proposed idea is to add a lead-lag controller on the active
power measurement in order to damp the active power
oscillations. The expression of this lead-lag action is
presented in (5).
 (5)
The interval of should not be chosen too high in order to
ensure a proper operation in practice and to avoid soliciting
much derivative action.
Figure 3: The proposed inertial droop control
To tune the lead controller, the root-locus method based on
sensitivity analysis is used. A linear model in equation 6 has
been developed for the system presented below:
Figure 4: Grid-forming VSC connected to an infinite bus.
The system contains 5 state variables which are respectively
the grid currents dynamics, the converter output frequency,
the converter angle and the filter active power measurement.
     
 
 
 
  
 
 
 
 
 
    
    
    
    
    
  (6)
The analysis will be interested only on dominant oscillatory
modes shown in Figure 5 for   that corresponds
to  .
Figure 5: Lead-lag controller design
Using an iterative variation of the controller parameters, the
obtained results in figure 5 show that for a given lead-lag
controller frequency variation
 [1 60] rad/s range, the
active power modes become more damped when the value of
increases. It means that the proposed control improves
widely the active power dynamic for large inertia constant
H=5s. A comparison between modes related to active power
dynamic with and without lead-lag controller is presented in
the table.1.
Table 1: The active power dynamic improvement
Inertia constant H = 5s
Droop with LP filter
Proposed Droop control
  
  
  
  
The improvements brought by the developed control are
checked with time domain simulations in figure 6. A step on
the active power ( ) is applied at t =1s.
Figure 6: comparison of active power dynamics between
conventional droop control and the proposed droop control.
(a) VSC Frequency, (b) Active Power
System parameters:    
       
 
The next section presents a modified AC grid model with
variable frequency that behaves similarly to the traditional
synchronous machine response in order to show the active
power dynamic, load sharing and the inertia contribution of
the proposed control.
4 Comparison with other control techniques
Till now, the frequency of the voltage source modelling the
grid has been considered as fixed. In this section, a variable
frequency is considered in order to assess the behavior of this
source with respect to frequency variation. The studied
system is presented in figure 7. The rated power of the
converter and the grid are considered identical ( Power
Electronics integration). The system parameters are described
in Table 2.
The objective of this test case is to validate the proposed
method and to compare it with other control strategies by
showing the frequency variation; load sharing and the active
power dynamic (e.g. load variation for different nominal
power of the converter and the equivalent AC grid).
The AC grid frequency is driven by a model representing a
kind of simplified equivalent synchronous machine with a
droop control. Where , , and are respectively the
droop gain, the inertia constant, the lead time constant and the
lag time constant. The lead-lag component aims to reproduce
the synchronous machine frequency dip behavior.
Figure 7: Controlled voltage source connected to an infinite
AC grid with variable frequency
(a) (b) (c)
(a) (b) (c)
Figure 8: Comparison of the proposed method to conventional ones (a) Conventional droop control with H=5s, (b) VSM
with high damping coefficient , (c) VSM with a small damping coefficient equivalent to the droop gain.
Table 2: System parameters
  
  
 
  
 
  
  
 
  
 
 
   
 
 
  
  
The developed control is compared to the control strategies of
figures 1 and figure 2. In simulations of figure 8, a load
variation is applied at t=5s.
In figure (8.a), the conventional droop is parametrically
adapted to obtain an inertia constant of =5s. In these
conditions, the conventional droop control shows a good
frequency response and power sharing in steady state,
however, the active power dynamic remains very oscillatory.
Comparing to the proposed method, this latter ensures at once
a good active power dynamic, power-sharing capability and
inertia providing.
Comparing the proposed method to the VSM and according
to the function that VSM should ensure, the value of can be
adapted to obtain a good damping [26], in this case, the VSM
cannot ensure any more the power sharing capability since the
droop gain of the two AC source is completely different as
shown in figure (8.b), this operation mode is not acceptable in
large power transmission grid. Or, the parameter is adapted
to ensure power sharing and in this situation we fall back on
the same problematic of the conventional droop as shown in
figure (8.c) (oscillatory active power). In both cases the
developed control remains advantageous since it fulfills the
requested specifications (.i.e. Load sharing capability, good
active power dynamic and inertia providing).
It is possible to add two additional loops to the VSM (i.e. PLL
and classic frequency droop control) in order to ensure
separately the functionalities needed, where the PLL is
required for frequency measurement and the classical droop
for frequency regulation. The principle of this control is
similar conceptually to the one of the real synchronous
machine (Figure.8), while the implementation remains
Figure 9: VSM with frequency droop
Taking into account these changes, the results obtained by
VSM in figure 9 remains nearly the same to the proposed
method as shown in the figure 10. In the following simulation
the response time of the PLL is 50ms.
If the PLL dynamic is chosen slower (e.g.  ), the
frequency response will change and the active power dynamic
also (Figure 11), therefore, the control parameters require a
new tuning in order to get acceptable performances.
Moreover, PLLs introduce a non-negligible delay in practice
which can limit the performance of the controllers that
depend on the frequency estimation of the PLL. Recent
publications have recognized the impact of PLLs in the
regulation provided by non-synchronous devices, but also the
potential instabilities that these devices can cause to power
converter [27], hence the advantage of the proposed method
which remains very simple to implement without additional
measurement or control complexity.
Figure 10: Comparison of the proposed method to the VSM
with frequency droop. (a) The frequency. (b) The active
power of the VSC and the AC grid
Figure 11: Comparison of the proposed method to the VSM in
case of PLL dynamic change. (a) The frequency. (b) The
active power of the VSC and the AC grid
5 Conclusion
In this paper, a mathematical comparison between
conventional droop and VSM is presented to show the
similarity of the two control strategies. Subsequently the
limitations of the conventional droop in terms of inertia
providing is highlighted, which led to the development of a
new control law based on droop control principle that ensure
a good dynamic behavior (Frequency and active power) and
also static one (power sharing capability).
In order to show the relevance of the proposed method, this
latter has been compared with conventional methods such as
droop control, VSM and VSM + Frequency Droop.
From a perspective point of view, this technique will be
analyzed in case of several converters to show its impact on
the system stability taking into account all converter
dynamics (i.e. LC filters).
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... Even if a significant effort has been done to identify and classify the different grid-forming schemes [4][5][6][7][8][9][10][11][12][13][14][15][16], and to designate specifications and definitions of the behaviour of a grid-forming controlled power converter [17][18][19][20][21][22], a generalized formulation of the power-angle control for grid-forming converters has not been fully investigated. The motivation of this work is to address this point formulating a general law for the power-angle control, introducing a discussion about the physical realization and the feasibility of a grid-forming control, and describing an assessment of these aspects with an analytical approach. ...
... The expression of K share derived in (21) can be used to assess or to design the power sharing characteristics of the grid-forming control. Using (21), it is possible to identify specific conditions related to the actual realization of a feasible power sharing: ...
... The expression of K share derived in (21) can be used to assess or to design the power sharing characteristics of the grid-forming control. Using (21), it is possible to identify specific conditions related to the actual realization of a feasible power sharing: ...
Several control schemes have been recently proposed and studied as grid-forming controls for power converters. In all these schemes, the power-angle control loop is the part which defines the fundamental capabilities of the grid-forming control: that control loop governs in fact the inherent synchronization mechanism of the power converter, the power sharing with the other generation sources in the system and the oscillatory characteristics of the converter-based resource. This article introduces a general formulation for the power-angle control characterizing the grid-forming concept for power converters. The generalized power-angle control is based on a polynomial fraction formulation, and it is arranged according to physical requirements and constraints. The structural analysis provides an insight into the capabilities and the design of the power-angle control loop of a grid-forming scheme. The generalized formulation is eventually applied to some common grid-forming controls like the power-synchronization control and the virtual synchronous machine, showing how the proposed generalized power-angle control can effectively realize different control structures.
... The root cause of the observed instability can be ultimately identified in the time constant T pf of the LPF applied on the active power measurement of the converter. This is a known issue with LPF and active power control in grid-forming converters [36][37][38][39]. For a better illustration of this issue, the simple case of a single oscillator connected to an infinite bus can be used as illustrative example ( Figure 6). ...
... As observed in the previous analysis, all these factors can have a critical impact on the system stability. The aspects related to damping and oscillatory stability of power systems dominated by power converters are addressed in several works [36][37][38][39]41,42]. In [41], it is remarked that grid-forming controls should be properly implemented, as they could result in a poorly damped closed-loop system. ...
... In [36], the effects related to LPF within the active power loop of the converter control are analytically investigated and recognized as a potential source of a critical lack of damping, leading to instability and loss of synchronization. Other works and research propose specific solutions to this problem [37][38][39]. More generally, the issue of damping provision by power converters is widely discussed in several papers and technical reports [42][43][44][45][46][47][48][49][50][51]. ...
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The operation of a power system with 100% converter-interfaced generation poses several questions and challenges regarding various aspects of the design and the control of the system. Existing literature on the integration of renewable energy sources in isolated systems mainly focuses on energy aspects or steady-state issues, and only a few studies examine the dynamic issues of autonomous networks operated with fully non-synchronous generation. A lack of research can be found in particular in the determination of the required amount of grid-forming power, the selection of the number and rated power of the units which should implement the grid-forming controls, and the relative locations of the grid-forming converters. The paper aims to address those research gaps starting from a theoretical point of view and then by examining the actual electrical network of an existing island as a case study. The results obtained from the investigations indicate specific observations and design opportunities, which are essential for securing the synchronization and the stability of the grid. Possible solutions for a fully non-synchronous operation of autonomous systems, in terms of dynamic characteristics and frequency stability, are presented and discussed.
... This reduction in the filter cut-off frequency results in power oscillations. Therefore, an additional damping (e.g., a derivative action on the measured active power [60]) has to be utilized to mitigate these oscillations. ...
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The rapid development of converter-based devices such as converter-interfaced renewable generations and high-voltage direct-current (HVDC) transmission links is causing a profound change into the very physics of the power system. In this scenario, the power generation is shifted from the pollutant synchronous generators based on nuclear or fossil fuels to converter-based renewable resources. The modeling, control, and stability of the power converters are now one of the focuses of attention for researchers. Today, power converters have the main function of injecting power into the utility grid, while relying on synchronous machines that ensure all system needs (e.g., ancillary services, provision of inertia and reliable power reserves). This operation mode of power converters is called "Grid-following". Grid-following converters have several limitations, such as: inability to operate in a standalone mode, stability issues under weak grids and faulty conditions and also, negative side effect on the system inertia. To tackle these challenges, the grid-forming control as an alternative has shown its appropriate performance that could make this kind of control a promising solution to respond to the system needs and to allow a stable and safe operation of power system with high penetration rate of power electronic converters. In this thesis, a fundamental description of grid-forming control with a simplified quasi-static modeling approach aiming to regulate the converter active power by a voltage source behavior is presented. From the description, several variants of grid-forming strategies are identified that represent some differences in terms of active power dynamic behavior, inertia emulation capability and system frequency support. Hence, the presented grid-forming variants are then classified according to their capabilities/functionalities. From the small-signal stability and robustness point of view, the studied grid-forming controls, which are implemented to a 2-level VSC at first, show their ability to operate under very weak grid conditions. Moreover, the ancillary services such as inertial response and frequency support are appropriately provided to the AC grid. The questions of the grid-forming converters protection against overcurrent and their post-fault synchronization while considering the current limitation are investigated and a new method is proposed to enhance the transient stability of the system. All the obtained results are then extended to a modular multi-level converter (MMC) topology successfully. The use of a grid forming control in an HVDC converter is interesting for the grid to which it is connected due to the inertial effect that can be induced. Therefore, the final part of this thesis evaluates the dynamic performance of an HVDC link interconnecting two AC grids and highlights the proper strategy and requirements for inertia provision.
... In particular, the aspects related to the synchronization mechanism of grid-forming converters are the focus of several studies [9]- [19]. Some works investigated the interactions between grid-forming and synchronous machines [20] [21], while other works focused on mutual interactions between grid-forming and conventional grid-following converters [22]. In the field of power-frequency dynamics and synchronizing interactions between different grid-forming converters, it appears instead to be only limited research. ...
... The equivalent AC grid consists of an inertial AC voltage source in series with its impedance, which is driven by a model representing the equivalent dynamic behavior of a large system. It consists of a swing equation and a lead-lag filter, which is a simplified model of the turbine dynamics [11]. A governor is added to support the grid frequency. ...
This paper assesses the performance of a high-voltage direct-current (HVDC) interconnection for providing virtual inertia to the power system. The impact of inertia provision on the DC bus dynamics and system frequency when one or both converter terminals are controlled with a virtual synchronous machine (VSM) based grid-forming strategy is evaluated. It has been demonstrated that an identical inertial support cannot be provided to both terminals due to a fundamental conflict between the DC voltage control and inertia emulation tasks. Therefore, it has been proposed to integrate a storage device (e.g. flywheel energy storage system (FESS)) with an additional converter to the DC link in order to control the DC voltage. Doing so, the DC voltage control is not couple with the inertia emulation at each substation and the obtained results have shown that a good performance in the DC voltage control as well as a proper inertia support provision are achieved. Finally, a discussion on a simplified approach to size the storage system is presented.
... It is essential to acknowledge that different implementations of the converter control scheme can indeed modify the oscillatory characteristics offered by the given control scheme, such as, for instance, the addition of transient damping terms [28,29], the implementation of inertial effect and fast frequency response directly with the PLL [30], or the application of lead-lag filters and phase compensation in the synchronisation loop [31][32][33]. The considerations about the expected different impacts of grid-following and grid-forming converters on the oscillatory characteristics of the system remain valid, however, since they refer to fundamental traits of grid-following and grid-forming common to the different control schemes. ...
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The oscillatory behaviour of the power system is an aspect that is significantly affected by the increasing integration of converter-based generation sources. Several works address the impact of non-synchronous generation on the operation of the system from different points of view, but only a few studies focus on power-frequency oscillations with a prevalence of generation sources interfaced through power electronics. A lack of research can be found in particular in the comparative analysis of the two main control strategies for power converters, namely grid-following and grid-forming. The article aims to contribute to this direction, starting from a theoretical analysis of the two control structures and then examining the case study of an existing transmission system. The research provides a specific insight into the fundamental aspects related to synchronisation mechanism and inertial capabilities of both grid-following with synthetic inertia and grid-forming controls. The difference in the relationship between synchronisation unit and inertial capability is recognised as the fundamental aspect determining the different impacts on the oscillatory characteristics of the system. The observation derived in the theoretical analysis is then applied to an actual power system with a high predominance of converter-based generation, considering the Colombian interconnected national system as a case study.
Type-IV wind turbines can experience torsional vibrations in the drivetrain structure. This can lead to additional stress on turbine components. Vibrations are mostly induced by fast variations of the electromagnetic torque depending on the control of a back-to-back converter. A number of studies have presented methods to mitigate drivetrain vibrations. However, the research was dedicated to cases where the converter, interfacing a wind turbine to the grid operates in a grid-following mode. A wind turbine can also be interfaced to a grid-forming converter. In this case, there is a strong link between the electromagnetic torque and grid dynamics, so the abovementioned problem remains relevant. Recent works have introduced methods to damp torsional vibrations in grid-forming wind turbines. However, based on their results, there is still a lot to improve to achieve suppressed vibrations without significant impact on wind turbine’ electrical infrastructure. Therefore, this paper proposes an improved solution to effectively mitigate torsional vibrations in a grid-forming wind turbine. The solution relies on the input shaping method. Simulation results prove the effectiveness of the damping. In addition, the negative impact of the damping on system behavior with respect to other parameters is analyzed and options for its minimization are suggested.
The recent engagements of many national governments backed by the United Nations push for introducing more and more renewable energy in the power systems in an attempt to mitigate global warming. Most of the renewable sources other than hydro power, such as wind turbines (except directly connected) or solar PV systems, depend on Power Electronics (PE) converters for their interconnection with the grid. Thus, the PE-based sources are becoming more and more prevalent in the current power systems and bring brand-new features in the grid. We observe this tendency both at the distribution level where the decentralized production units such as residential solar PV are gaining popularity, and at the transmission level as well where large energy sources such as Offshore Wind Farms (OWF) start to be interconnected with the grid using High-Voltage Direct Current (HVDC) technology.This PhD thesis addresses some of the future grid challenges of replacing existing Synchronous Generators (SG) by PE-based interfaces and focuses more specifically on Voltage Source Converters (VSC) and their associate control strategies. This work focuses on the transmission grid level and investigates the control of VSCs interfacing renewable sources in hybrid power systems where PE and SG coexist.In the first part of the work, the different ancillary services provided by SGs are listed and an overview of the existing VSC-based solutions is given, including the so-called grid-following and grid-forming controls. These two approaches are compared in terms of performances and constraints. Next, these types of controls are studied regarding the maximum allowable limit of PE and their interactions with nearby SGs in hybrid systems. It was shown that switching the VSC control mode from grid-following to grid-forming mode can allow a higher penetration rate of PE-based sources, even though some interactions with the remaining SGs must be taken care of.In the second part of this work, we focus on the application of grid-forming control to Modular Multilevel Converters (MMC) for the integration of OWF in AC grids. The impacts of the DC-grid dynamics on the behavior of the grid-forming controlled MMC are assessed when the station must ensure the stability of the DC grid at the same time. In this context, a method is also proposed to estimate the energy requirements of the MMC submodules to provide AC-grid related synthetic inertia. The corresponding control proposed is compatible with the state-of-the-art grid-forming control and is validated by simulations in a multi-machine system. To complement, a control solution that enhances the AC/DC support of such stations based on a MIMO-oriented Model Predictive Control (MPC) is proposed. It shows a better handling of the MMC internal energy as well as robustness against parameter uncertainties when compared to the existing SISO-based dual PI structure that relies on a theoretical decoupling between the AC and DC dynamics.Finally, the proposed MPC-based control is applied to a real MMC. It is validated using an experimental setup which involves a mockup of an MMC of 6 kVA and 60 submodules. The grid-forming control and the proposed MPC are implemented into an Opal RT target and tested with success in real-time conditions to validate the approach developed in this thesis.
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In the context of renewable energy and HVDC links development in power systems, the present work concerns the technical operations of such systems. As wind power, solar photovoltaics andHVDC links are interfaced to the transmission grid with power-electronics, can the system be operated in the extreme case where the load is fed only through static converters? Driving a power system only based on power electronic interfaced generation is a tremendous change of the power system paradigm that must be clearly understood by transmission grid operators. The traditional “grid-feeding” control strategy of inverters exhibits a stability limit when their proportion becomes too important. The inverter control strategy must be turned into a “parallel grid-forming” strategy. This thesis �rst analyses the power system needs, proposes the requirements for “parallel grid-forming” converters and describes the associated challenges. Accordingly, the thesis gives a method for designing a stable autonomous synchronization controls so that grid-forming sources can operate in parallel with a good level of reliability. Then, a method is proposed to design a voltage control for a grid-forming PWM source taking into account the limited dynamic of powerful converters. The robustness of the solution is discussed for di erent con�guration of the grid topology. A current limiting strategy is presented to solve the current sensitivity issue of grid-forming converters, subject to di erent stressing events of the transmission grid. The ideas developed on a single converter are then applied on small grids with a limited number of converters to allow a physical interpretation on the simulation results.
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In recent researches on inverter-based distributed generators, disadvantages of traditional grid-connected current control, such as no grid-forming ability and lack of inertia, have been pointed out. As a result, novel control methods like droop control and virtual synchronous generator (VSG) have been proposed. In both methods, droop characteristics are used to control active and reactive power, and the only difference between them is that VSG has virtual inertia with the emulation of swing equation, whereas droop control has no inertia. In this paper, dynamic characteristics of both control methods are studied, in both stand-alone mode and synchronous-generator-connected mode, to understand the differences caused by swing equation. Small-signal models are built to compare transient responses of frequency during a small loading transition, and state-space models are built to analyze oscillation of output active power. Effects of delays in both controls are also studied, and an inertial droop control method is proposed based on the comparison. The results are verified by simulations and experiments. It is suggested that VSG control and proposed inertial droop control inherits the advantages of droop control, and in addition, provides inertia support for the system.
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This study addresses the development and operation of the European continental electricity system with a high penetration of wind and photovoltaic (PV) generation. The main focus of the work is the assessment of the impact of inertia reduction, due to wind and PV power electronics interface, on frequency stability indicators, as the rate of change of frequency and the frequency nadir following a large generation loss. The analysis is based on dynamic frequency stability studies, performed for every hour of the year and over a large number of weather scenarios. The outputs of these simulations are used to perform statistical analysis of these indicators and to estimate the critical instantaneous penetration rate of wind and PV, which the European continental synchronous area can accommodate from a system dynamics point of view. The results show that a single critical instantaneous penetration rate cannot be defined, since the frequency dynamic behaviour depends on parameters that change from one period to the following. Instead, this critical penetration rate should be calculated for every dispatch period. This study also highlights the growing importance of load self-regulating effect's contribution to frequency stability in the future system.
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The concept of Virtual Synchronous Machines (VSMs) is emerging as a flexible approach for controlling power electronic converters in grid-connected as well as in stand-alone or microgrid applications. Several VSM implementations have been proposed, with the emulation of inertia and damping of a traditional Synchronous Machine (SM) as their common feature. This paper investigates a VSM implementation based on a Voltage Source Converter (VSC), where a virtual swing equation provides the phase orientation of cascaded voltage and current controllers in a synchronous reference frame. The control system also includes a virtual impedance and an outer loop frequency droop controller which is functionally equivalent to the governor of a traditional SM. The inherent capability of the investigated VSM implementation to operate in both grid-connected and islanded mode is demonstrated by numerical simulations. Then, a linearized small-signal model of the VSM operated in islanded mode while feeding a local load is developed and verified by comparing its dynamic response to the time-domain simulation of a nonlinear system model. Finally, this small-signal model is applied to identify the dominant modes of the system and to investigate their parametric sensitivity.
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Control structures containing cascaded loops are used in several applications for the stand-alone and parallel operation of three-phase power electronic converters. Potential interactions between these cascaded loops and the complex functional dependence between the controller parameters and the system dynamics prevent the effective application of classical tuning methods in the case of converters operating with a low switching frequency. A tuning approach guided by the eigenvalue parametric sensitivities calculated from a linearized model of the converter and its control system is proposed in this paper. The method is implemented in the form of an iterative procedure enforcing the stability of the system and ensuring that the system eigenvalues are moved away from critical locations. Numerical simulations in the time domain are presented to verify the improvement in the dynamic performance of the system when tuned with the presented algorithm compared with a conventional rule-based tuning method.
Conference Paper
From the origin of the grid, energy has been delivered to electrical loads mainly by synchronous machines. All the main rules to manage the grid have been based on the electromechanical behavior of these machines which have been extensively studied for many years. Due to the increase of HVDC link and renewable energy sources as wind turbine and PV, power converters are massively introduced in the grid with a fundamentally different dynamic behavior. Some years ago, they were connected as simple power injector. Then, they were asked to provide some ancillary services to the grid, in the future, grid forming capability will be required. Even if gridforming converters had been extensively studied for microgrids and offshore grids, it has to be adapted to transmission grid where the topology may be largely modified. This paper presents an algorithm for calculating the controller parameters of a gridforming converter which guarantee a stable behavior for many different configurations of the grid.
In a DC microgrid (DC-MG), the dc bus voltage is vulnerable to power fluctuation derived from the intermittent distributed energy or local loads variation. In this paper, a virtual inertia control strategy for DC-MG through bidirectional grid-connected converters (BGCs) analogized with virtual synchronous machine (VSM) is proposed to enhance the inertia of the DC-MG, and to restrain the dc bus voltage fluctuation. The small-signal model of the BGC system is established, and the smallsignal transfer function between the dc bus voltage and the dc output current of the BGC is deduced. The dynamic characteristic of the dc bus voltage with power fluctuation in the DC-MG is analyzed in detail. As a result, the dc output current of the BGC is equivalent to a disturbance, which affects the dynamic response of the dc bus voltage. For this reason, a dc output current feed-forward disturbance suppressing method for the BGC is introduced to smooth the dynamic response of the dc bus voltage. By analyzing the control system stability, the appropriate virtual inertia control parameters are selected. Finally, simulations and experiments verified the validity of the proposed control strategy.
In this paper, a reactive power sharing strategy that employs communication and the virtual impedance concept is proposed to enhance the accuracy of reactive power sharing in an islanded microgrid. Communication is utilized to facilitate the tuning of adaptive virtual impedances in order to compensate for the mismatch in voltage drops across feeders. Once the virtual impedances are tuned for a given load operating point, the strategy will result in accurate reactive power sharing even if communication is disrupted. If the load changes while communication is unavailable, the sharing accuracy is reduced, but the proposed strategy will still outperform the conventional droop control method. In addition, the reactive power sharing accuracy based on the proposed strategy is immune to the time delay in the communication channel. The sensitivity of the tuned controller parameters to changes in the system operating point is also explored. The control strategy is straightforward to implement and does not require knowledge of the feeder impedances. The feasibility and effectiveness of the proposed strategy are validated using simulation and experimental results from a 2-kVA microgrid.
The virtual synchronous generator (VSG) is a control scheme applied to the inverter of a distributed generating unit to support power system stability by imitating the behavior of a synchronous machine. The VSG design of our research incorporates the swing equation of a synchronous machine to express a virtual inertia property. Unlike a real synchronous machine, the parameters of the swing equation of the VSG can be controlled in real time to enhance the fast response of the virtual machine in tracking the steady-state frequency. Based on this concept, the VSG with alternating moment of inertia is elaborated in this paper. The damping effect of the alternating inertia scheme is investigated by transient energy analysis. In addition, the performance of the proposed inertia control in stability of nearby machines in power system is addressed. The idea is supported by simulation and experimental results, which indicates remarkable performance in the fast damping of oscillations.
To address inaccurate power sharing problems in autonomous islanding microgrids, an enhanced droop control method through online virtual impedance adjustment is proposed. First, a term associated with DG reactive power, imbalance power, or harmonic power is added to the conventional real power-frequency droop control. The transient real power variations caused by this term are captured to realize DG series virtual impedance tuning. With the regulation of DG virtual impedance at fundamental positive sequence, fundamental negative sequence, and harmonic frequencies, an accurate power sharing can be realized at the steady state. In order to activate the compensation scheme in multiple DG units in a synchronized manner, a low-bandwidth communication bus is adopted to send the compensation command from a microgrid central controller to DG unit local controllers, without involving any information from DG unit local controllers. The feasibility of the proposed method is verified by simulated and experimental results from a low-power three-phase microgrid prototype.