UPTEC E 20006
Examensarbete 30 hp
Juni 2020
Modeling and comparative analysis
of different grid-forming converter
control concepts for very low
inertia systems
Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student
Abstract
Modeling and comparative analysis of different
grid-forming converter control concepts for very low
inertia systems
Martin Westman & Ellen Nordén
As renewable power from DC sources are constantly increasing their power generation share compared to the high inertia generators that provide robustness to the grid, the overall stability of the grid decreases. Grid forming converter could be the solution to this problem.
This thesis includes a pre-study of grid forming control methods, implementation of the most promising and relevant methods in a generic PSCAD modeling environment for comparative analysis and for
establishing pros and cons. Lastly, studying the system impact of each grid forming control method through small-signal stability and fault analysis.
Four methods of grid forming were implemented and evaluated during the course of the thesis, which were: Droop control, Virtual Synchronous Generator control, Power Synchronization control and Synchronous Power control. All methods fulfilled the criteria for successful
implementation with good results. For further developments, we would recommend Synchronous Power control and Virtual Synchronous Generator control for their development potential and operational width.
Examinator: Mats Ekberg
Popul¨
arvetenskaplig sammanfattning
Dagens eln¨at f˚ar idag sin stabilitet och robusthet av bland annat de synkrona maskinerna som tillf¨or sv¨angmassa och effekt till n¨atet. Ett stabilt eln¨at inneb¨ar att frekvensen p˚a n¨atet h˚alls konstant, kring det riktv¨ardet varje land har. Ett instabilt n¨at skulle orsaka enorma problem f¨or samh¨allet som helhet, p˚a grund av att vi idag ¨ar beroende av en p˚alitlig eltillf¨orsel till samh¨allets alla delar.
Historiskt sett har eln¨atet ¨over de flesta delar av v¨arlden genererats av f¨orbr¨anning av fossila br¨anslen som skapat energi fr˚an roterande massor som i sin tur genererar elektricitet. En vanligt f¨orekommande energik¨alla ¨ar kolkraft, som bland annat orsakar massiva koldioxidutsl¨app som i sin tur bidrar till den globala uppv¨armningen. Detta har i sin tur lett till att forskning inom f¨ornyelsebar elgenerering har ¨okat enormt. Man har sett en stor uppg˚ang f¨or implementering av energik¨allor som vind- och solkraft p˚a senare ˚ar. Dessa k¨allor ¨ar kopplade till n¨atet via v¨axelriktare och bidrar d¨arf¨or inte idag till n¨atstabilitet s˚asom roterande maskiner g¨or. Dessa f¨ornyelsebara energik¨allor st¨odjer effekttillf¨orseln och d¨armed frekvensstabiliteten som de roterande maskinerna ger n¨atet. Ett s¨att f¨or att veta n¨ar n¨atet beh¨over mer effekt ¨ar via frekvensm¨atning som ges av de roterande maskinerna, och skulle dessa f¨orsvinna m˚aste andra l¨osningar hittas.
En av dessa l¨osningar ¨ar ett koncept som kallas grid-forming converters. Tanken med dessa ¨ar att uppfylla eln¨atets effektbehov utan att m¨ata den befintliga frekvensen. Detta g¨ors d˚a ist¨allet via kontrollalgoritmer som kollar p˚a effektbehov och tillf¨orsel p˚a n¨atet. Detta g¨or det m¨ojligt att styra n¨atet ist¨allet f¨or att f¨olja det.
M˚alet med detta exjobb ¨ar att utforska vilka metoder som forskats p˚a, implementera fyra av dessa som verkar visa goda egenskaper i ett simuleringsprogram. Simuleringsprogrammet heter PSCAD och ¨ar ett av utvecklingsverktygen som anv¨ands p˚a ABB f¨or systemtester. M˚alet ¨ar ¨aven att utf¨ora tester f¨or att kunna j¨amf¨ora dessa metoder mot varandra f¨or att till sist g¨ora en analys kring metodernas f¨ordelar och nackdelar.
Acknowledgments
Firstly, we would like to extend our gratitude to our supervisor Pinaki Mitra for his time invested in helping and discussing problems and ideas during the entirety of the thesis project. We would also like to thank the department of System Design at ABB G&PQS for they warm welcome and support during the thesis.
Contents
1 Introduction 1 1.1 Background . . . 1 1.1.1 Collaborators . . . 1 1.2 Project goals . . . 1 1.3 Delimitation . . . 2 1.4 Work division . . . 2 2 Theory 3 2.1 Electrical Concepts . . . 32.1.1 Voltage Source Converters (VSC) . . . 3
2.1.2 PWM . . . 3
2.1.3 SPWM control scheme for VSCs . . . 3
2.1.4 Per Unit System . . . 4
2.1.5 Three-phase system representations . . . 4
2.1.6 Clarke & Park Transformations . . . 5
2.1.7 Electrical Faults . . . 6
2.1.8 Overcurrent protection . . . 8
2.1.9 RMS Fault ride-through method . . . 8
2.1.10 Inertia . . . 8
2.1.11 Power grid system . . . 9
2.2 Automatic Control . . . 10
2.2.1 PID controllers . . . 10
2.2.2 Transient Response . . . 10
2.2.3 Control system filtering . . . 11
2.3 Grid Converters . . . 12
2.3.1 Grid Following Converter . . . 12
2.3.2 Grid Forming Converter . . . 13
2.3.3 Control Loops . . . 14
2.4 Grid forming control methods . . . 16
2.4.1 Droop Control . . . 16
2.4.2 Virtual Synchronous Generator (with inertia) . . . 17
2.4.3 Virtual Synchronous Machine, without inertia (VSM0H) . . . 19
2.4.4 Power Synchronization Control . . . 19
2.4.5 Synchronous Power Control . . . 21
2.4.6 Virtual Oscillator Control . . . 23
3 Method 24 3.1 Software . . . 24
3.1.1 PSCAD modeling and testing . . . 24
3.2 Pre-study . . . 25
3.2.1 Choice of Grid Forming Converter-methods . . . 25
3.3 Implementation . . . 27
3.3.1 Modeling of converters in PSCAD . . . 27
3.3.2 Tuning of controllers . . . 29
3.3.3 Simulations in PSCAD . . . 29
3.3.4 Small Signal Analysis . . . 30
3.3.5 Short Circuit analysis . . . 30
4 Results 32 4.1 Final models . . . 32
4.1.1 General system model . . . 32
4.1.2 Inner Control loop . . . 35
4.1.3 Droop Control . . . 35
4.1.4 Virtual Synchronous Generator Control . . . 36
4.1.5 Power Synchronization Control . . . 37
4.1.6 Synchronous Power Control . . . 37
4.1.7 Fault detection and handling . . . 39
4.2 Small Signal analysis . . . 40
4.2.1 Droop Control . . . 40
4.2.2 Virtual Synchronous Generator . . . 43
4.2.3 Power Synchronization Control . . . 46
4.2.4 Synchronous Power Control . . . 48
4.2.5 Inner loop performance . . . 55
4.2.6 Comparative result . . . 56
4.3 Fault behavior . . . 58
4.3.1 Droop Control . . . 58
4.3.2 Virtual Synchronous Generator . . . 58
4.3.3 Power Synchronization Control . . . 59
4.3.4 Synchronous Power Control . . . 62
4.3.5 Comparative result . . . 64 5 Discussion 66 5.1 System analysis . . . 66 5.2 Test configuration . . . 68 5.3 Droop control . . . 69 5.3.1 Model design . . . 69
5.3.2 Small Signal analysis . . . 69
5.3.3 Fault analysis . . . 69
5.4 Virtual Synchronous Generator Control . . . 70
5.4.1 Model design . . . 70
5.4.2 Small Signal analysis . . . 70
5.4.3 Fault analysis . . . 70
5.5 Power Synchronization Control . . . 71
5.5.1 Model design . . . 71
5.5.2 Small Signal analysis . . . 71
5.5.3 Fault analysis . . . 71
5.6 Synchronous Power Control . . . 72
5.6.1 Model design . . . 72
5.6.2 Small Signal analysis . . . 72
5.6.3 Fault analysis . . . 72
5.7.1 Small Signal analysis . . . 73
5.7.2 Fault analysis . . . 73
6 Conclusions 74 7 Appendix 79 7.1 MATLAB-code . . . 79
7.2 Fault analysis - Droop control . . . 80
7.3 Fault analysis - VSG . . . 82
7.4 Fault analysis - PSC . . . 84
Nomenclature
DC Direct Current
GFC Grid forming converter HPF High pass filter
HVDC High-voltage direct current IGBT Insulated-gate bipolar transistor IPL Instantaneous Penetration Limit LPF Low pass filter
p.u. Per Unit
PCC Point of Common Coupling PLC Power loop controller PLL Phase Locked Loop
PSC Power Synchronization Control
PSCAD Power System Computer Aided Design PSL Power synchronization loop
PWM Pulse Width Modulation SCR Short Circuit Ratio SG Synchronous Generator SM Synchronous Machine SPC Synchronous Power Control
SPWM Sinusoidal Pulse Width Modulation VA Virtual Admittance
VOC Virtual Oscillator Control VSC Voltage Source Converter VSG Virtual Synchronous Generator
1.
Introduction
1.1
Background
The electric power system over the world is currently going through an immense change - with the growing need for electricity and the fact that greenhouse gas emissions globally need to be reduced. Over the past 20 years the energy consumption of renewable sources as solar- and wind power has increased and considering modern renewables was the total share of the energy consumption globally in 2018 almost 11 %, and the share is expected to grow over 15 % by 2030 [1].
This implies that the amount of installed non-synchronous based generation is increasing at a significant rate while the amount of installed synchronous generation relative to the non-synchronous generation, decrease. This entails challenges concerning the grid and its stability and the impact on the system is increasing as the renewable penetration grows. Renewable sources like wind and solar power, are to a high extent connected to the grid via electronic power converters, which does not contribute to inertia in the system and it will cause a greater rate of change in the frequency, hence they cannot contribute to grid stability. Furthermore, the current power electronic converters struggle to operate under highly variable conditions. Therefore, the instantaneous penetration limit on the grid that can be achieved is constrained due to the existing converter technology [2].
A possible solution to attain higher levels of renewable power generation while still preserving the grid stability, could be grid forming converters. Grid forming converters are voltage source converters that can reliably operate and maintain a stiff voltage even during highly variable conditions. The main mission of a grid forming converter is to replicate the behavior of the synchronous machine via different control strategies. Additionally, they can contribute to grid stability by providing voltage and frequency support [3].
1.1.1
Collaborators
This thesis has been done at ABB Power Grids Sweden - Grid & Power Quality Solutions. They have provided deep knowledge in the respective area, as well as guidance and some research materials.
1.2
Project goals
1.3
Delimitation
This Master thesis investigates six different grid forming converters that have been researched on, but the development of functioning models is limited to four converter control methods. The control methods are Droop control, Virtual Synchronous Generator, Power Synchronization Control and Synchronous Power Control. The systems studies are limited to an average voltage source system and source harmonics are therefore neglected. The average converter used are one where the six switches are replaced with three ideal ac voltage sources.
The control methods will be evaluated in the aspects of signal dynamics, transient behavior and fault ride through capabilities. The fault study will be limited to the symmetrical three phase fault. The study as a whole will be an empirical one, with no development of state space models as the thesis goal describes a general study of grid forming models.
1.4
Work division
The main work was to implement, test and analyze four different grid forming converters, and the work was naturally divided for Martin and Ellen to be responsible for two methods each, including implementation, test, discussion and conclusion. Pre-study, comparison and conclusion were performed together, but the rest of the report and work was divided as follows;
Ellen was responsible for: • Grid dimensioning
• Power Synchronization Control • Synchronous Power Control
Martin was responsible for: • Fault detection and handling • Droop Control
2.
Theory
2.1
Electrical Concepts
2.1.1
Voltage Source Converters (VSC)
A Voltage Source Converters’ basic principle is that it converts DC to AC voltage. The VSC consists of an n amount of switches (IGBTs or Thyristors for example) which are oriented in an H-bridge configuration that are switched on an off according to a predefined control scheme. This control flexibility allows for control of voltage magnitude, phase angle and frequency at its output [4].
2.1.2
PWM
Pulse Width Modulation (PWM) is a method that can adjust average voltage output signal. The PWM signal is generally a control signal that enables switching of switches with varying duty cycle, which is the ratio of on time of the switch. With a lower duty cycle, the switch is conducting a smaller fraction of the period, resulting in a decrease of voltage. [5]
2.1.3
SPWM control scheme for VSCs
The VSC:s are generally switched with a Sinusoidal-PWM switching scheme, which is a softer switching scheme than pure PWM. It consists of a sinusoidal reference waveform with grid frequency and amplitude Vref. This sinusoidal is compared to a triangular carrier waveform with constant amplitude Vtriand frequency
ftri, which also is the switching frequency of the VSC. There are also two modulation ratios connected to
SPWM, frequency modulation ratio mf and amplitude modulation ratio ma, and they are calculated as
stated in equation 2.1 and 2.2.
mf= ftri f1 (2.1) ma = Vref Vtri (2.2)
Figure 2.1: The control scheme of bipolar SPWM.
If the amplitude modulation ratio exceeds 1 the system becomes over modulated, and the peaks of the output sinusoidal from the VSC becomes ”chopped off”, and we lose linearity as well as introduce unwanted low-frequency harmonics.
In order to increase the modulation ratio, and thereby increase the output voltage as well as decrease the THD in the output current, Common-mode injection can be implemented [6].
2.1.4
Per Unit System
The Per Unit system is a way of expressing the system parameters in a normalized unit. This Per Unit (p.u. in short) normalization applies for power, voltage, current and impedance. The conversion between regular units and p.u. is done by dividing the regular unit by the systems rated unit magnitude as seen in equation 2.3.
per-unit quantity = actual quantity
base value of quantity (2.3) The base value is calculated with Ohm’s law.
This conversion greatly simplifies the overview between systems by normalizing the system units, even though they have different ratings. Since nominal values of systems parameters hover around 1, implementation of regulators and its parameters are also kept around 1, which cuts down on regulator tuning complexity [7].
2.1.5
Three-phase system representations
The dq-frame is a rotating frame which is rotating with the magnetic field, hence the magnitude of the phasors becomes constant. When synchronous the rotation is perpendicular to either the d or q axis, which results in one of the axes being around zero as the other changes in amplitude (as seen in figure 2.2). This can be used for simplifying a sinusoidal problem to an equivalent DC-command problem. This entails that PID-regulators can be used for the control.
The αβ-frame is a stationary frame where its magnitude has a sinusoidal behavior. The two phases are placed perpendicular to each other and are in the same plane as the three-phase (ABC) reference frame [8].
Figure 2.2: Representation of the different reference frames [9].
2.1.6
Clarke & Park Transformations
The Clarke and Park transformations are used to change the representation of three phase phasors in order to simplify the analysis and control of a three phase system. The Clarke and Park transformations are widely used in control system because of their simplification of the three phase system.
The Clark transformation converts the three-phase quantities (ABC vectors) into balanced two-phase quadrature quantities (αβ). The αβ-frame is a stationary frame where its magnitude has a sinusoidal behavior. The two phases are placed perpendicular to each other and are in the same plane as the three-phase (ABC) reference frame[8]. The transformation from ABC-frame to the αβ-frame can be seen in equation 2.5. In order to transform from αβ-frame to ABC-frame the inverse of the Clarke transformation matrix (eq.2.4) is multiplied with the αβ-frame.
Tαβ= 2 3 1 −1 2 − 1 2 0 √ 3 2 − √ 3 2 1 2 1 2 1 2 (2.4) vα vβ vγ = Tαβ va vb vc (2.5)
This transformation can be utilized in some of the control systems that will be examined in this thesis, but is less used than its counterpart, the Park transformation.
Tθ=
2 3
cos(θ) cos(θ −2π3 ) cos(θ +2π3) −sin(θ) −sin(θ −2π 3 ) −sin(θ + 2π 3) 1 2 1 2 1 2 (2.6) vd vq v0 = Tθ va vb vc (2.7)
The Park transformation is the most common transformation used for grid control systems, which will be clear from the grid forming converter concepts below [9].
2.1.7
Electrical Faults
Electrical failures in an electrical system can arise because of various reasons, for example failure in equipment or environmental conditions such as lightning or earthquakes. These failures often lead to large fault currents (short circuit currents), which for instance can lead to arcing, mechanical stresses, heat, noise or explosions. The resulting fault current is determined by the impedance between the machine voltage and the fault and by the internal voltages of the synchronous machines.
In order to avoid electrical faults, a fault analysis can be made, which reduces the risk of large losses in the system and increases the reliability and safety. Furthermore, it is possible to discover weak points, problem areas and identify solutions to existing problems. Also, one important purpose of doing a fault analysis is to determine the magnitude of the maximum currents generated by the fault, in order to ensure that the equipment in the system can survive a fault.
There are two main types of faults: symmetrical and asymmetrical faults. The main difference between them is that when a symmetrical fault occurs the system will remain in balance, whilst the system becomes unbalanced if an asymmetrical fault arises. The symmetrical fault, being a fault across all phases presents the largest current surges but are relatively rare compared to an asymmetrical fault, but easier to analyze.
There are different types of faults, depending on where the fault occurs. The most common ones are: one phase to ground, phase to phase, two phases to ground and balanced three phase. When doing a fault analysis on an unbalanced fault, a balanced three-phase network can be divided into three sequence networks; positive, negative and zero sequence. These network circuits can then be connected in different ways based on which fault it is, to continue the fault analysis and establish the fault current [10] [11].
Three-phase fault
A three-phase fault is a balanced symmetrical fault, which means that only the positive sequence network needs to be considered. In this type of fault, all three phases are shorted together. It is the least common fault but the one that can cause largest fault current and is therefore a good representation of the worst-case scenario considering faults.
When calculating the fault current, the following assumptions can be made [10]: • Transformers can be represented by their leakage reactances
• Transmission lines are defined by their equivalent series reactances
• Synchronous machines (and often induction motors) are represented by a constant-voltage source behind a subtransient reactance
The three phase fault can be divided into four segments as seen in figure 2.3 and 2.4. Segment 1 shows the nominal voltage/current operation, segment 2; the three phase fault, segment 3; the recovery phase and lastly the system returns to nominal voltage/current operation in segment 4. The current shown in figure 2.4 is the current on the converter side, hence not were the fault occurs on the grid side.
Figure 2.3: The voltage during a three phase fault, with the sequences: (1) nominal operation, (2) the fault, (3) recovery and (4) nominal operation again.
Figure 2.4: The current (on the converter side) during a three phase fault, with the sequences: (1) nominal operation, (2) the fault, (3) recovery and (4) nominal operation again.
2.1.8
Overcurrent protection
In a system with a VSC and control loops, the inner control loop is responsible for the overcurrent projection of the system, since the converters are prone to break upon too high currents. Transients, are a common occurrence on the grid which happen due to unexpected load changes or short circuits for example.
Synchronous generators can handle current spikes of about six times their rating for shorter periods of time, compared to the VSC:s that run nominally closer to their power ratings in order to not over dimension the switches, and are therefore more prone to breaking during these events. Thus, a control system with the capabilities to prevent the destruction of the VSC:s is crucial. This is usually done in the inner control loops which measure current and voltage, and limits these quantities inside their acceptable boundaries. [12]
2.1.9
RMS Fault ride-through method
As power ratings on connected systems increase, so does the electrical faults during power variations. Traditionally synchronous generator-based systems handle variations better because of its physical dampening behavior and the resilience to high current spikes, while VSC-based solutions do not. These systems need smart fault detection methods in order to dampen the power spikes to protect the hardware.
A commonly used fault detection method is by examining the RMS voltage or current at the Point of Common Coupling (PCC), hence at the grid-side, as the RMS value will either drop below or rise above a chosen threshold [13]. This method does however have the downside of needing one cycle to reach the correct RMS value [14]. The reason for this delay being the analytical calculation of RMS values seen below in equation 2.8. VRM S= s 1 T Z T 0 V2cos2(ωt)dt (2.8)
VRM Sis the RMS voltage, V is the sinusoidal voltage and T equals to the period time, and the computation
is done continuously on all phases, on the outlook for deviating behavior.
2.1.10
Inertia
Inertia refers to the resistance to change. In an electricity grid, inertia represents large rotating masses which are the large synchronous generators that are directly connected to the grid. These rotating masses hold a kinetic energy which provides stability. Since their rotating speed is connected to the grid and its frequency, they counteract the change in frequency. This contributes to a mechanical inertia in the system, which helps preventing instability and disturbance.
The frequency in a system shows how well-balanced electricity production and consumption are at every given moment. If the consumption increases, the frequency will decrease (or the opposite if the consumption decreases), but the inertia in the system will make the decrease happen slower. The more inertia in the system, the smaller will the impact between consumption and production have on the frequency [15].
The relationship between the frequency and power balance is described by the Swing equation:
J ω ·dω
dt = ∆P (2.9)
where J is the inertia [kgm2], ω is the rotational speed [rad/s] and ∆P is the difference between current
H = J ω
2 0
2Sbase
(2.10)
The inertia of the synchronous generator is also defined as equation 2.10, where H is the synchronous generators inertial constant, Sbase is the base power rating and ω0 is the generators rotational speed [16].
2.1.11
Power grid system
An electrical grid system is generally consisting of a type of generating station which provides electricity, a transformer, transmission lines and a type of load. A transmission line is generally represented as a series impedance (consisting of an inductance and a resistance), often together with some shunt admittance [17].
When discussing the power grid and different sources of generation, one often used concept is the Instantaneous Penetration Limit (IPL), which can be described by following equation:
IP L = PV SC Pdemand
· 100% (2.11)
which means that the IPL describes how much of the total demand can be delivered by the power from the VSC [18].
Weak vs Strong grid
A grid can either be described as a ’strong’ or a ’weak grid’ and is represented with the Short Circuit Ratio (SCR). A strong grid is more stable and has less impact from disturbances. How strong a grid is can be defined by the capability to maintain a constant voltage independently of the load. In general, a higher value of the inductance and resistance means a higher grid impedance, i.e. a weaker grid. The SCR is defined by:
SCR = Sac Srated (2.12) and SCR = Xgrid Rgrid (2.13)
where Sac is the capacity of ac-short circuit and Srated is the rated capacity. A general guideline to know
2.2
Automatic Control
Control theory is based around the concept of controlling physical phenomena, this encapsulates everything from electrical grid stability to the operation and stability of an aircraft [21]. For this Master thesis control, theory will be used for ensuring fast and stable performance of the systems.
2.2.1
PID controllers
The PID regulator is the most common regulator used in the industry [22]. PID stands for Proportional Integral Derivative and is generally defined as in equation 2.14. Regulators are used to control an output signal according to a signal values, by continuously trying to minimize the error between them. The minimization of the error can be realized in different ways, namely using proportional (P ), integral (I ) and derivative (D ) terms of the error which will result in different response of the regulator system.
u(t) = Kpe(t) + Ki
Z
e(t)dt + Kd
d
dte(t) (2.14)
The error e(t) is defined as the error between the reference signal and the output signal:
e(t) = r(t) − y(t) (2.15)
The goal of the PID controller is to follow a set reference value (r ) as fast and accurately as possible. The different components of the regulator Proportional, Integral and Derivative has different ways of eliminating the control error (e).
The proportional (P) regulator has an output that is proportional to the error (u(t) = Kp(r(t) − y(t))).
This results in a controller that never reaches steady state and often has a steady state error, which is an offset compared to the reference value.
The proportional integral (PI) controller adds the integral action on the error. This will eliminate the steady state error but results in the regulation of the system taking longer to settle.
The last type of regulator is the proportional, integral and derivative (PID) regulator and has the benefits of the PI regulator, with the added benefit of also taking the derivative of the error into account. This can decrease overshoot, decrease settling time and somewhat improve stability of the system [22].
2.2.2
Transient Response
Figure 2.5: Transient response [23].
The main parameters regarded in transient response is as mentioned above; rise time, overshoot and settling time. The rise time is defined as the time it takes for the system to reach 90% of the set point value. The overshoot of a transient is by how much the control signal misses the reference signal as it tries to settle, this quantity is given in percent. The cause of an overshoot is that the system is not dampened enough or that the rise time is too high (slow) for the system to slow down before reaching its set point, therefore overshooting its target. The settling time determines how long it takes for the signal to settle within a error margin to the set point value [24].
2.2.3
Control system filtering
When designing a control system, noisy measurement signals has to be taken into account. If the input signals to the controllers are too noisy, that might result in unstable regulatory conditions. To combat this, filtering can be implemented at the inputs, to ensure a more stable operation. The low-pass filter, which attenuates frequency components above a certain frequency level, as seen in Laplace form in equation 2.16.
H(s) = ωc s + ωc = 1 1 +ωs c = 1 1 + τ s (2.16)
The high-pass filter has the same function as the low-pass filter, only inverted, as it attenuates frequency components below a selected frequency. The Laplace domain representation can be seen in equation 2.17
H(s) = s s + ωc = s ωc 1 +ωs c = τ s 1 + τ s (2.17)
The transfer functions for the given filters consist of controllable parameters, were ωc is the given cutoff
2.3
Grid Converters
As the grid inertia decrease and the steady flow of power to the grid becomes more variable as more renewable energy sources are being deployed, the grid will start using more grid converters in order to control the flow of power to the grid. In table 2.1 a general comparison between two grid converters that will be discussed further in the report is presented [26].
Table 2.1: General comparison between Grid Forming and Grid Following converters. Grid Following Converter Grid Forming Converter
Controls Current and phase angle Controls Voltage magnitude and frequency Cannot operate in standalone-mode Can operate in standalone-mode Cannot achieve 100% grid penetration Can achieve 100% grid penetration
For the definition of what 100 % grid penetration means, see equation 2.11.
2.3.1
Grid Following Converter
Grid Following Converters mimic the instantaneous inertial response of Synchronous Machines. This type of converter can only operate under grid connected mode which follow the grids behavior and injects power when needed. The Grid Following Converter can be modeled as a current source connected in parallel to the grid. The converter synchronizes with the grid frequency utilizing a phase locked loop (PLL), as well as measure phase and voltage amplitude, which is used as the reference to the control system. The control system translates the measurements to inverters control signals, which compensates for possible errors in active and reactive power on the grid. This type of converter is the dominant type present on the grid as of now.
Figure 2.6: The model representation of the Grid Following Converter [27].
These types of converters do however work under the assumption that there is a stable voltage reference to synchronize to (usually from SGs) and will therefore never achieve 100 % penetration on the grid. This poses the largest problem with Grid Following Converters, that if (when) the number of SGs decrease as a consequence of the rise of renewable energy sources, Grid Following converters will not be suitable for use [28].
Phase Locked Loop
Figure 2.7: The general design of the PLL [30].
In figure 2.7 the basic block diagram of the PLL is presented. It inputs the voltage in dq-domain and outputs corresponding phase angle of the grid in dq-form.
2.3.2
Grid Forming Converter
Grid forming converters are much like Grid Following Converters when it comes to the basic hardware concept. However, the major thing that differentiates the two is their manner of operation. The grid forming converter does, opposed to the Grid Following Converter not use the reference frequency of the grid into account, but rather sets its frequency reference to the local grid frequency and outputs the needed active and reactive power in order to stabilize the grid. The grid forming converter proposes to ’lead ’ the grids behavior, rather than to follow it. The grid forming converter can therefore be modeled as a low impedance voltage source with the main goal of enforcing an amplitude and frequency at its output, rather than conforming to the grid’s behavior [31].
The grid forming converter also offers some advantages over the grid following converter, such as a theoretical 100 % penetration level, since the operation of the converter is not dependent on a stable voltage reference since that is set in the converter. Good theoretical black start capability (restoring a part of a grid or an electrical power station without being dependent of the external electric power transmission network) is also a benefit [32].
Grid forming converter do however have some downsides. Since they act as voltage sources overcurrent protection is needed for situations when transients occur (fast load change, short circuit etc...). Some controller-based safety features can however be implemented in order to ameliorate these current spikes [28].
Figure 2.9: The model representation of the Grid Forming Converter [27].
2.3.3
Control Loops
For grid forming and following converters to behave in a sought-after way, different constellations of control loops are needed. These control loops translate measured quantities and reference values to signals that can be used to control the inverter in order to achieve a reference output. Depending on the converter type different amount of control layers will be implemented in order to limit the output current or regulate certain feedback parameters. [27]
Outer Control Loop
The outer-most control loop is commonly the placeholder for the high system level control, which is where the control methods are implemented, which will be discussed further below. The inputs to this control layer often consist of measurements from the PCC and the output of the converter in order to determine power levels as well as sought-after quantities of voltage, current and frequency. The power measurements are calculated using the voltage and current in dq-form as seen below [27].
P = vdid+ vqiq (2.18)
Q = vqid− vdiq (2.19)
The outer control loop will in most control methods output control signals to the inner loop.
Inner Control Loop
As the inner control loop receives reference data from the outer control loop it acts on this information by controlling the VSC:s to achieve the wanted output from the converter. This could include regulating the voltage, current or frequency of the converter. The inner control loop is generally comprised of a voltage control loop and a current control loop. The sampling frequency of the inner loop is much higher than that of the outer control loop (at least 10x). This is to ensure decoupling of the signals.
The voltage control loop typically receives voltage references in dq-form from the outer control loop and is subtracted from the actual d and q component of the output filter to generate the difference between the reference and actual value. The delta is then PI-regulated to reach a stable output [27].
Figure 2.11: The general design of the voltage control loop.
Figure 2.12: The general design of the current control loop.
The current control loop output is fed into a dq to abc transformer, which generates three sinusoidals (ma, mb
and mc) which are used to control the switching generation shown in figure 2.13.
Figure 2.13: The general design of the SPWM switching generation.
The switching traditionally is done according to the SPWM switching scheme seen in figure 2.1, where the generated sinusoidals are compared to a triangle wave in order to switch the inverters switches (S1 to S6) in the correct order.
2.4
Grid forming control methods
2.4.1
Droop Control
Figure 2.14: The general Droop Control scheme [33].
P = vdid+ vqiq (2.20)
Q = vqid− vdiq (2.21)
Equation 2.22 and 2.23 is generally referred to as P-f droop and Q-V droop respectively.
ω = ωref − Kp ωcP s + ωcP (P − Pref) (2.22) V = Vref − (Kqp+ Kqi s ) ωcQ s + ωcQ (Q − Qref) (2.23)
The final control algorithms for frequency (eq.2.22) and voltage (eq.2.23) use the active and reactive power to control the two parameters. A low-pass filter is implemented into both equations in order to avoid high frequency disturbances, which could destabilize the control method [28]. The independent droop gains Kp
and Kqp act as damping factors for the frequency deviations of the system as well as Kqi which is the
integrator term gain.
2.4.2
Virtual Synchronous Generator (with inertia)
The Virtual Synchronous Generator (VSG) is designed to mimic the behavior of a synchronous generator, most importantly its inertial properties. Its working principle is similar to that of the droop control method with P-f and Q-V droop, but with additional control components added to the P-f droop such as virtual inertia and damping factors. There are two main versions of the Virtual Synchronous Generator that is reoccurring in research articles [34][31], which both show promise.
The outputs from the QDroop and the swing equations are utilized to generate control signals (eq. 2.24) to
the voltage loop.
The VSG:s frequency computation is designed having the swing equation in focus (eq. 2.9), as well as the virtual synchronous generator governor, which is the virtual equivalent to a speed controller. In figure 2.15 the general frequency computation is presented. The governor operated by computing the frequency delta, as well as the rate of change of the active power, which has the purpose of damping system overshoot. In the final stage of the governor the frequency delta is subtracted by the active power reference, as well as the rate of change damper to form the output of the governor.
The governor control signal is fed into the swing equation where it is compared to the active power, frequency reference and fed through the virtual inertial block to finally result in an output frequency and phase angle θ. Furthermore, the active power is used to regulate the frequency for simulating the inertia (J ) for resemble the swing equation (eq. 2.9). Q-V droop is implemented by altering the reactive power reference according to the voltage difference. The output reactive power error is then integrated to obtain output V.
Figure 2.15: VSG - Active Power loop version 1[34].
There are two recurring versions of VSG, where the other method can be seen in figure 2.16.
Figure 2.16: VSG - Active Power loop version 2 [31].
θ = 2π Z K
p(f − fref) + Pref − P − Dfref(f − fref)
The control equations for frequency and voltage can be seen in equation 2.25, 2.26 and 2.27. The assumption can be made that fref and Vref are constant, J is the inertia of the VSG, as defined in
equation 2.10.
The inertial constant H which determines the magnitude of the virtual inertia is calculated using equation 2.10, as a higher inertial constant equals more virtual inertia.
2.4.3
Virtual Synchronous Machine, without inertia (VSM0H)
The Virtual Synchronous Machine with zero inertia is a control method closely related to the Virtual Synchronous Generator, with the main difference between the methods being that the VSM0H introduces no virtual inertia. The benefit with this being fast dynamic response of the system [35]. In fact, VSM0H also discards the inner current loop to generate balanced switching signals, but uses an averaging filter applied to the measured active and reactive power, to get stable measurements even in scenarios of system unbalance [35]. As system speed is prioritized, it is assumed that sufficient power can be delivered from the DC bus.
Figure 2.17: The general schematic of the VSM0H.
The main control block as seen in figure 2.17 as Droop controllers are computed as described in equation 2.28 and 2.29, with its corresponding reference values and damping parameters (Df and DV).
f = fref + Df(Pref − P )(1 +
kDs
1 + τkDs
) (2.28)
V = Vref+ DV(Qref− Q) (2.29)
It can also be observed that the VSM0H is similar to Droop control, with the modification of implementing a boxcar filter, that encapsulates one period of the fundamental frequency as well as the removal of the inner current control loop. This would theoretically enable the elimination of harmonics, and faster system.
2.4.4
Power Synchronization Control
Figure 2.18: General design of the Power synchronization loop [37].
The active power output from the VSC is controlled by a Power Synchronization Loop (PSL) (figure 2.18), which is converting the power control error to a frequency deviation between the grid and the VSC. The control law is according to:
∆θ + ωref =
kp
s(Pref− P ) (2.30)
to get the phase angle. Kp is proportional gain, P is the measured power output from the VSC and Pref is
the reference value.
The output θ from the PSL gives the angle for converting the voltage reference from dq-frame to ABC-frame, which then supplies the reference for the VSC. This implies that the PSL is used both for controlling the active power and for maintaining grid synchronization.
The reactive power is controlled by adjusting the voltage magnitude. This entails that an inner current control loop is not necessary. Although, in case of ac-faults, a current control system must be used for preventing over currents. In most solutions is a current-limiter control used together with a back-up PLL to maintain synchronization with the grid. If the converter current is exceeding its maximum current rating is a current limitation controller used to enable switching to the vector-current control and the use of the back-up PLL [37] [38]. To enable the switching between the regular synchronization of PSL and the back-up PLL can be set-up according to figure 2.19.
The angle correction and the feedback part from θv has the function to make it smoother to switch
between the synchronization methods. It causes them to follow whichever one that is active, hence the frequency of the system.
During normal operation, there is a mechanism of limiting current and controlling the voltage output (without the back-up PLL) which could be realized as a standard inner control loop described in section 2.3.3, but often with an added high pass filter to prevent instability and eliminate noise [36].
2.4.5
Synchronous Power Control
The Synchronous Power Control (SPC) utilizes the main working principle of the PSC, but with added damping and inertial characteristics.
Figure 2.20: The general schematic of the SPC [39].
The control of the SPC is multi-layered, as it takes inspiration from several other grid forming control methods. It is based on the synchronous generator with both an electric and a mechanical part with inertia and damping characteristics.
The main design used can be seen in figure 2.20, which is based on reactive and active power control, described as: ωr∗= (P − Pref) · P LC + ωref (2.31) and E∗= (Q − Qref)(Kp+ Ki s ) + Vref (2.32)
where PLC stands for the power loop controller.
The current and voltage are measured at the PCC. The reactive and active power is calculated and is fed into a Droop controller. The voltage and the frequency angle from the power loops are then fed into a voltage controlled oscillator which is generating a sinus voltage signal. The signal, which is supposed to simulate the electromotive force is then fed through the virtual admittance (VA), further to the current controller [39].
There are two main methods used in the active power control loop as the PLC. One where the control is based on the synchronous generator swing equation:
ω = ωref+
Kps + Ki
s + KG
Ki, Kp and KG describes the inertia, damping and droop characteristics. Ki is expressed as: Ki= ωs 2H · SN (2.34) Kp is expressed as: Kp = 2ζ · r ω s 2H · SN · Pmax − 1 2H · Rd· Pmax (2.35)
and KG is expressed as:
KG =
1 2H · Rd
(2.36)
where ζ is the damping factor (normal range: 0.1-1.1), H is the inertia constant (normal range: 1-10), SN
is the nominal power, ωS is the nominal angular speed and Rd is the value of the P-f droop slope that
describes the variance of the frequency in percentage (normal range: 2-5%) [40].
Its control scheme is shown in the figure below.
Figure 2.21: One method of constructing the PLC [40].
The other method which is also often used is a simpler method where the PLC is constructed as in figure 2.22 [40].
Figure 2.22: Another method of constructing the PLC [39].
GP LC(s) =
1 ωs(J s + D)
(2.37)
Here, J is the inertia constant and D represent the damping.
J can be calculated as in 2.10, and D is calculated as:
D = 2ζ ωs
r 2H · SN· Pmax
ωs
(2.38)
The VA is included because of its capacity to ensure a high X/R ratio (SCR) in the system. It is represented as a low pass filter-block with a resistance and inductance as the constants [39]:
V A = 1 Rv+ Lvs
(2.39)
2.4.6
Virtual Oscillator Control
The Virtual Oscillator Control (VOC) differs from the other grid forming methods because of its use of an oscillator to control the VSC parameters, also since it is based on instantaneous time signals, using neither dq nor αβ. The oscillator used can for example be a dead zone or a Van der Pool oscillator and it is designed to perform as a voltage dependent current source, and it is connected to an LCR-filter. L and C are designed to tune the oscillator and the resistance is chosen to ensure a stable operation. Because of its simple design, without conversion between ABC and dq-frame and without regulation parameters, it is fast and acts directly on disturbances [41]. The overall system of the VOC can be seen in figure 2.23.
3.
Method
The method used can be divided into different segments. Firstly, a literature study was completed, reading and gaining knowledge about grid-forming control principles and concepts. Furthermore, studying various control methods including advantages, disadvantages, similarities and differences among them. Thereafter, the four most interesting and most applicable ones out of ABBs point of view were selected and modeled in PSCAD for further study, analysis and comparison.
3.1
Software
Investigating the behavior and prototyping power systems is mainly done by software simulations in power system analysis software. This will, besides the pre-study serve as the majority of the master thesis, as it will be done in software.
3.1.1
PSCAD modeling and testing
The main software that will be used for implementing and modeling the grid forming control methods is PSCAD (Power System Computer Aided Design). PSCAD is used to design and simulate power systems of various sorts. PSCAD has a predefined library of system models and electrical components that enables faster model creation [42]. PSCAD allows for continuous time simulations with great accuracy.
3.1.2
MATLAB
MATLAB will be used for mathematical computations and for final plotting and comparison of the control methods signals. Calculations that are to be made are network parameters, SCR:s and DC voltages.
3.2
Pre-study
3.2.1
Choice of Grid Forming Converter-methods
During this master thesis’ pre-study six grid forming control methods were evaluated at a deep level, as presented in the previous chapter. At the end of the pre-study these control methods were compared with each other on aspects such as performance, complexity and applicability for ABB:s current hardware systems in order to choose which control methods that were to be further investigated. The following section will summarize the considerations that were made for each of the control methods and why they were chosen or not.
Droop Control
The principle of Droop control is based on basic Droop equations which were discussed in the theory section. It turned out that a lot of the control methods that were evaluated were based on, or similar to Droop control. Besides being a method that is similar to others, it also showed promising behavior, despite its simplicity in the articles examined in the pre-study. These factors led to including Droop control in the further investigation and modeling.
Virtual Synchronous Generator (VSG)
The Virtual Synchronous Generator is one of the control methods that mimics the inertial-like behavior of the synchronous generators. As seen in the theory chapter, the VSG has some similarities to Droop control, as the voltage amplitude reference algorithm is identical between the models as well as the rest of the system. The differing factor is the frequency generation, were the VSG is more complex, but also adds more features such as the virtual inertia. The performance of the VSG also shows promise in the stability aspect as well as fault-ride through capabilities in several articles. Being similar to the Droop control method, as well as the performance promise made the VSG the second control method that was to be implemented in PSCAD.
Virtual Synchronous Machine, without inertia (VSM0H)
The Virtual Synchronous Machine without inertia (VSM0H) was a control method whose main advantage was supposed to be fast response and regulation. The main concept of this control method being that of the Virtual Synchronous Generator, but with no virtual inertia as well as the removal of the inner current control. This would in theory make the control system response faster. The conclusion made in the pre-study however is that this system would give a similar behavior to the Droop Control method, as their models are similar, as well as the lack of research that had been made on the control method. Based on these factors, the decision not to move forward with this control was made.
Power Synchronization Control
Synchronous Power Control
The SPC can be seen as a development of PSC, but with elements of other control methods such as VSG and Droop. However, compared to PSC it has been less tested in weak HVDC systems, but has the advantages of the added damping and inertia characteristics. With that in mind, plus the fact that a back-up PLL is not needed, it is chosen to be implemented for further studies.
Virtual Oscillator Control
3.3
Implementation
The pre-study main purpose was to gain knowledge in the relatively new and cutting-edge technology that grid forming converters are. As a consequence, to this technology being new, and not implemented on a large scale, as well as generally only studied on a microgrid level, some generalizations have been done. As a standard does not exist for any of these converters, the decision to change and experiment with the implementations in order to tailor the systems to ABBs needs. The converters as described in the theory are a general or average interpretation of the numerous variants that have been researched in the academic papers that form the base of the theory section.
The performance of the grid forming models are to achieve predetermined criteria in order for implementation of the model to be considered as successful and complete. These are the following criteria:
• The model is able to reach the entire power span of P and Q (-1 to 1 p.u) during nominal operation (IPL=100%)
• All signals of interest follow the control signals with minimal steady-state error • The model has good fault-ride through capabilities
• The model exhibits stable frequency characteristics
The criteria above are specified for very weak grids with an Short Circuit Ratio of 1, but will be evaluated for stronger grids as well to benchmark their operational span.
3.3.1
Modeling of converters in PSCAD
Average inverter model
As one of the goals of the master thesis was to implement generic control method models in PSCAD for comparative analysis the decision to implement an average inverter model was made. The average inverter model is a simplification of the inverter control model, as it is represented with three ideal ac voltage sources with a phase difference of 120 degrees between them, instead of the standard six-switch inverter model. This eliminates harmonics generated from the inverter, thus creating a cleaner output to analyze. The average inverter model can also be seen as an infinite bus, meaning that the available power delivery is infinite. This decision could also enable a more direct comparison between the general behavior of the control methods, putting their dynamics in focus. It has to be noted however that harmonics do matter, but ABB did not feel as this was the main goal of the thesis, as a general behavioral test were to be executed.
The design of the average model can be seen in figure 3.1 and when compared to the standard inverter switching model, as seen in figure 2.13 some simplifications can be seen. The main difference being that the average model controls three voltage sources, and the full model switches the inverters switches in order to generate three voltages.
Grid modeling
The type of grid that the grid forming converter was to be connected to was of great importance in an analytical perspective, as different grid types corresponds to a different system response. The system was therefore altered with respect to the SCR.
The grid voltage across all tests was set to 400kV L-L RMS, as was the converter side voltage. This was done to simplify the analysis, as it meant that the transformer ratio was 1:1. The transformer is in a Y-Y configuration, 50 Hz base frequency, 0.15 p.u. leakage reactance and a power rating of 600 MVA. These values were chosen in cooporation with the supervisor at ABB.
The resistive and inductive components corresponding to a specific SCR was derived and computed in MATLAB using equations 2.12 and 2.13 with respect to the given grid parameters.
The output value of the ac voltage sources in the average model described above, were generated by a DC-voltage multiplied with three generated switching signals. The system was rated for 600 MVA, and since the system had to be able to reach Q = 600 MVAr on the grid side was the DC-voltage required to be a certain value in order to generate large enough ac-voltage. The DC voltage was therefore calculated to be big enough for the system to be able to inject the rated power. The calculations were done in MATLAB.
General system
The general structure of the control system for all the converter methods is the same, regarding conversion between the grid and control parameters and the switching part. Firstly, as described above is the average inverter model used, where the output values were transformed to grid voltage via a transformer. The three phase (abc) voltages and currents were measured after the transformer, at the PCC. All the measured values were converted into p.u. and then converted to dq-frame, according to the equations 2.3 and 2.6. Furthermore, was the active and reactive power at the PCC calculated with equation 2.18 and 2.19. The calculated grid powers were then used for realizing the control of the angle and voltage, which takes place in the outer control loop.
3.3.2
Tuning of controllers
All the grid forming control methods consist of cascaded regulators in different control loops. For the majority of the models P (proportional) or PI (proportional and integrating) regulators have been implemented. As the regulators are in series a proper tuning methodology had to be applied. This procedure involved starting to implement the last regulator in the regulator chain, the current control loops PI regulators. This entailed inputting test values into the input and tuning the parameters until precise output tracking was achieved. This method is applied to the voltage control loop as well, this ensures correct behavior throughout the control loops. How the outer and inner control loops is coupled with P and PI-controllers can be seen in figure 3.2.
Figure 3.2: Cascaded Control loop structure.
Once the inner control loop is tuned, the outer loop has to be tuned. As it proved the inner loop tuning remained the same, with some minor changes done between the different control methods.
3.3.3
Simulations in PSCAD
During the time that the control models were developed, simulations were used to verify their behavior. Subsystems could with ease be individually tested and debugged block-wise, in order to minimize errors when putting all of the subsystems together.
Debugging simulations would include running everything from shorter simulations in order to verify that specific system parameters were behaving as expected to longer stability centered simulations. However, the primary type of simulation that were initially run were tuning simulations, were the developer’s main objective was to try to get the entire system running at a basic level. Because of the systems complexity, small changes could lead to the system not functioning properly, an area were the quick simulation tools of PSCAD came in handy.
When functioning on a fundamental level, the models were given a reference power, to examine what the response to a power order was. Why changing the power reference as a validator to if the system is behaving properly is based on the fact that changing the power (active and reactive) will impact all system parameters which then can be verified to be working properly or not.
When doing the simulations of the grid converter control methods that contained a virtual inertia, both the parameters J and H are mentioned in the theory. How they correlate can be seen in table 3.1.
Table 3.1: Value of J that were utilized and the corresponding H. J 0.0005 0.004 0.005 0.01 1
H 0.63 5 6.3 12.5 1250
3.3.4
Small Signal Analysis
To investigate impact of individual and impactful parameters in a control system, a small signal analysis ought to be performed. In the case of the control methods implemented in this thesis the focus was put on the outer loop parameters (i.e. the control method specific parameters) in order to collect as much data as possible on stability regions and how parameters impact the systems response, which is what will be shown in the small signal analysis result section below.
One of the properties that the grid forming models comparison is based on is their transient behavior, in other words how they behave in sudden operational change. The fundamental way that this is going to be performed is through a step change from 0.95 p.u. to 1 p.u., solely on the active power, seen in table 3.2.
Table 3.2: Step test scenario. Test scenario Start p.u. Stop p.u. Active power step 0.95 1
The reason to not execute the step test on negative steps (-0.95 p.u. to -1 p.u.) as well as reactive power is based on ABB:s guidance, as it can be presumed that the step response is similar on both ends of the spectrum. As mentioned above this impacts all system parameters, and therefore can be used to analyze and compare how systems behave during this change.
The response of the parameters during an active power step will be evaluated based on their; rise time, overshoot and settling time, as being the main parameters discussed in the Transient Response section of the theory. The tuned optimal parameter values will be marked as bold. The sections will also be structured by the presentation of a table that summarizes the tests that have been done, followed by graphical representations of the same tests.
3.3.5
Short Circuit analysis
The models are tested for short circuit resilience using the built in three-phase timed fault logic in PSCAD. The three phase fault duration set to 200 ms for a substantial fault period. The models will be tested under different test environments, as the transient behavior analysis. The following short circuit tests are to be executed:
Table 3.3: Short circuit test scenarios
Test scenario Active Power (P) Reactive power (Q) 1 - Maximum active power 1 0
The short circuits tests are designed to stress test the models as they operate at their limit at the time of the three-phase fault. Successful short circuits tests at the extremes will ensure good performance across the power spectrum for other scenarios that are not tested here. This results in four tests for the non-inertial models and eight for the ones that have. The main parameters that will be examined in the fault tests are is the power (active and reactive, depending on the test scenario), converter-side current (to monitor recovery and current levels over switches) as well as the grid frequency.
RMS fault-ride through method
4.
Results
4.1
Final models
This section will cover the final implementation of the different systems. This will include parameter choices, model design as well as model specific descriptions.
4.1.1
General system model
The four implemented control methods have different control models implemented. However, their general system models are identical, in order to make a comparative analysis. The following description of the grid and converter model will be done from left to right in figure 4.1. At the very left the converter output resides and is represented with three AC voltage sources (Va, Vb, Vc), which have a variable amplitude that
is controlled according to the implemented control method and are electrically phase-shifted by 120 degrees. This is what the implementation defined as the ’Average Switching model ’ as it does not rely on actual switches but generated the sinusoidals expected from the regular switching model, apart from the harmonics generated.
Next comes the filter inductance, which filters the output of the converter. This is also where the filter current and voltages are measured, which are parameters used in the control methods. Next comes the system transformer which has a transformation ratio of 1 for added simplicity in the comparison. The secondary side of the transformer is where the PCC is located, which is where the converter connects to the grid. The grid naturally has a grid impedance and the grid voltage is represented with an AC-source to the very right in figure 4.1.
The table 4.1 represents different grid configurations, namely different ’grid strengths’, which represents the grid impedance. A SCR of 1 represents the weakest grid model (and also the highest impedance) and 5 the strongest in the test setup.
Table 4.1: Different grid parameters.
Grid SCR Resistive component [Ω] Inductive component [H]
5 2.9527 0.1128
4 3.6909 0.1410
3 4.9212 0.1880
2 7.3818 0.2820
1 14.7636 0.5639
The system grid shown in figure 4.1 has the set parameters as shown in table 4.2. These parameters are used during the entirety of the grid forming analysis.
Table 4.2: System parameters.
Component location Parameter name Value DC voltage source Vdc 850 [kV] AC voltage source Vabc Variable [V]
VResistance 0 [Ω]
Filter inductance 0.041 [H] Y-Y transformer Power rating 600 [MVA]
Frequency rating 50 [Hz] Primary voltage 400 [kV] Secondary voltage 400 [kV] Leakage reacteance 0.15 [pu] Other losses None Grid Grid inductance Table 4.1
On a control-based level figure 4.2 shows the generalized picture of what the control methods consist of. Figure 4.2 comprises of ”black boxes” in order to get a better overview of how the models are interconnected, both on the control and grid side.
Figure 4.2: Full developed and generalized grid forming model.
The computational cycle of the grid forming converters that were implemented can be seen in figure 4.3, starting from the top and going clockwise around the figure.
When examining figure 4.2 the first step is the measurement of filter and PCC voltage and currents, as this is converted into dq-domain and the power quantities are computed. Passing the measured powers into the ’Active Power loop’ and ’Reactive Power loops’ to calculate the voltage sinusoidals that are to be passed into the inner control loops. These loops make sure that the voltage and current levels are kept within the specified limits as well as outputting the control parameters needed to feed or absorb the grid with energy. As this cycle repeats, the system continuously controls that the output values are equal to the reference values that are set at any given time.
4.1.2
Inner Control loop
The inner control loop shown in figure 4.4 is the general set-up in all the control methods, although some small changes can occur in the different methods.
Figure 4.4: Inner control loops of the grid forming model.
4.1.3
Droop Control
The Droop control method was implemented as figures 4.5 and 4.6 show below. The model differ somewhat from how the theory defines it. Firstly, both the active and reactive power controls are controlled by a PI controller, compared to that of the P controller in the theory.
Figure 4.5: Droop Control - Active Power loop.
Figure 4.6: Droop Control - Reactive Power loop.
4.1.4
Virtual Synchronous Generator Control
The Virtual Synchronous Generator control model had two versions of the model brought up in the theory section. However, after implementation of both models one of them showed more promise than the other, this is the control scheme shown in figure 4.7. The model is simpler and consists of a virtual inertia block ’1/Js’ and a damping factor ’D ’.
Figure 4.7: Virtual Synchronous Generator Control - Active Power loop.
The reactive power control was implemented in the same way as that of the Droop control, as can be seen below in figure 4.8.
4.1.5
Power Synchronization Control
The power synchronization control was implemented almost as described in the theory as in figure 2.19. What differs was the feedback part in the PSL where the γ was implemented on both sides, instead of one side. Also, a PI-controller was used instead of a P-control. The final active and reactive power loop can be seen in 4.9 and 4.10.
Figure 4.9: Power Synchronization Control - Power synchronization loop.
Figure 4.10: Power Synchronization Control - Reactive Power loop.
The inner loop control was implemented as in 4.4 but with a HPF instead of a LPF when If D and If Q are
added at the voltage control loop. Also, a LPF was implemented when Uf D and Uf Q are subtracted.
4.1.6
Synchronous Power Control
Figure 4.11: Synchronous Power Control - Power Loop Controller.
Figure 4.12: Synchronous Power Control - Reactive Power Control.
4.1.7
Fault detection and handling
The fault detection and handling implementation is nothing but standard, and is therefore not included in the theory section, other than the fact that faults can be detected utilizing the RMS voltage and a threshold value to monitor the state of the system. This is what can be seen in the ’Fault Detection’ box in figure 4.13. This box consists of RMS measurement of all phases and compares these to a set threshold value, that if crossed will output a digital high from the comparator. All of the phase comparators are connected to an AND-gate which outputs a fault detection high if any of the phases fall below their threshold values.
Figure 4.13: Fault detection and recovery handling model. Left: Fault detection for all phases coupled with an AND-gate for minimum detection time. Middle: Selectors for power reference as well as ramp for different fault scenarios. Right: Sign comparator and output for power reference.
4.2
Small Signal analysis
If nothing else is stated, all graphs are showing values in per unit.
4.2.1
Droop Control
The parameters that were deemed to have a significant enough impact (meaning that the parameter impact is non-negligible) on the system behavior on the Droop control method were; Kpp, Kpq, Kip, ωc. Their
response can be seen in table 4.3.
Table 4.3: Droop Control - small signal analysis performance. Parameter Value Rise Time [ms] Overshoot [%] Settling Time [ms]
Kpp 1.2 144 15.6 685 2.2 113 16.9 516 3.2 101 36.9 435 Kpq 0.02 76 30.5 381 0.12 70 16.5 443 0.22 63 9.2 458 Kiq 0.1 49 36.8 366 0.7 67 16.7 443 1.3 70 12.4 535 ωc 5 122 100.2 3630 25 65 10.7 444 45 69 16.5 440
The proportional gain of the active power loop Kpp shows significant impact on the system performance.
With a higher gain the rise time decreases, but with the cost of a much larger overshoot than the optimal value as well as having more oscillations. The settling time for the higher proportional gain was however similar to that of the optimal parameter. The lower Kppexhibits slow overall response, as it has a slower rise
Figure 4.14: Small signal analysis of Kpp. Blue: Active power reference, Red: Proportional gain, active
power loop (1.2), Yellow: Proportional gain, active power loop (2.2), Purple: Proportional gain, active power loop (3.2).
The proportional gain of the reactive power loop Kpq, showed some impact on the system. As can be
observed the tuned parameter value and the higher parameter value showed similar responses during the test, with what looks like a favorable result for the larger value. A Kpq of 0.02 resulted in a response that
was slower, had more overshoot and took longer to settle.
Figure 4.15: Small signal analysis of Kpq. Blue: Reactive power reference, Red: Proportional gain, reactive
The integral gain of the reactive power loop Kiq, presented dynamic change in system response depending
on the chosen parameter. With a small integral gain the step response became oscillative, but did settle in the end. The response of the optimal parameter value compared to the higher value in the interval had a faster rise time, lower overshoot and a faster settling time as shown in figure 4.16.
Figure 4.16: Small signal analysis of Kiq. Blue: Active power reference, Red: Integral gain, reactive power
loop (0.1), Yellow: Integral gain, reactive power loop (0.7), Purple: Integral gain, reactive power loop (1.3).
Figure 4.17: Small signal analysis of ωc. Blue: Active power reference, Red: Cutoff frequency (5 Hz), Yellow:
Cutoff frequency (25 Hz), Purple: Cutoff frequency (45 Hz).
4.2.2
Virtual Synchronous Generator
The parameters that displayed a significant impact on the system dynamics of the Virtual Synchronous Generator control method were; Kpp(D), J, Kpq, Kip. The summarized results of the tests are seen in table
4.4.
Table 4.4: VSG Control - small signal analysis performance. Parameter Value Rise Time [ms] Overshoot [%] Settling Time [ms]
kpp (D) 0.1 - - -2 375 2.6 435 3.9 862 0.9 1658 J 0.0005 389 0.5 468 0.01 382 0.6 459 1 359 5 1194 kpq 0.06 358 1.3 1178 0.26 389 0.4 466 0.46 420 0.3 533 kiq 0.1 467 0.5 760 0.6 397 1.6 470 1.1 397 1.7 464
