kaiserstraße 2 24143 kiel
TRANSCRIPT
Chair of Power Electronics
Christian-Albrechts-Universität zu Kiel
Kaiserstraße 2
24143 Kiel
Chair of Power Electronics
Christian-Albrechts-Universität zu Kiel
Kaiserstraße 2
24143 Kiel
Prof. Marco Liserre, PhD, IEEE fellow
Head of the Chair of Power Electronics
MV Grid Identification (Impedance and Voltage-sensitivity)
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 3
Background (Impedance)
Increase of nonlinear loads and power converters leads to the deterioration of the utility grid
Resonance problem arises due to the increased number of filters and length of cables
Grid impedance is the key factor for the grid stabilization.
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 4
Background (Voltage sensitivity)
The Voltage sensitivity describe how a network react to a change in the injected power and viceversa how a variation of voltage change the power absorbed/injected by a grid
The knowledge of voltage sensitivity can help in controlling the grid but also in assessing how much reactive power is needed in case of a grid fault
Sensitivities calculation methods require high computational effort and/or large field measurements/data history
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 5
Outline
Impedance analysis approach, vector fitting and applications
MV-Analyzer in the Field
Control for wide-frequency grid impedance measurement
Identification of the Voltage sensitivity
Conclusions
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 6
Impedance measurement
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 7
Impedance-based stability analysis
The grid impedance measurement is important for stability
problem. The VSC-grid system is stable if the Nyquist plots of
the loop gain:
g oL(s) = Z (s)Y (s)
does not encircle the critical point (-1, j).
Re-shaping of the output virtual admittance
Yo on the bases of the estimated Zg in order
to guarantee the stability in case of grid
variations.
Equivalent network of a grid connected inverter
for small signal analysis.
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 8
Resonance Identification inSmart Transformer-fed Grid
• Mono-frequency excitation ranging from 150 Hz to 1500 Hz is implemented together with voltage control and active damping;
• The frequency sweep procedure will be repeatedly carried on in order to obtain the grid characteristics in real time.
Z. Zou, G. Buticchi and M. Liserre, "Grid Identification and Adaptive Voltage Control
in a Smart Transformer-fed Grid," in IEEE Transactions on Power Electronics.
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 9
LV Grid Impedance Identification
• By using time-domain data, the transfer function of impedance can be obtained by vector fitting method;
• The main idea is to use a rational function to approximate poles {am};
N is the approximation order,
d and e are optional for the rational functionAn example of measured & estimated grid impedance
in LV German grid
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 10
Case of study: Public LV grid Northern Germany
Magnitude and Phase angle of grid impedance versus time and frequency measured in public LV grid northern Germany.
• Night: resonance at 1.8 kHz with a magnitude |Zg|= 1.3Ω
• Day: the magnitude at 1.8 kHz is |Zg|=0.5Ω due to the changing operation of loads and generators by the grid customers.
• The grid impedance angle ψg is about 20° at 50 Hz, grid is predominant resistive at 50 Hz
• The measurements show that the grid impedance phase angle is temporarily capacitive in afrequency range between 1.6kHz and 4.8kHz.
L. Jessen and F. W. Fuchs, "Modeling of inverter output impedance for stability analysis in combination with measured grid
impedances," 2015 IEEE 6th International Symposium on PEDG, Aachen
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 11
Adaptive Active Damping
Current sensors on the grid side
• LCL-filter effectiveness changes with the grid stiffness
• If the grid impedance Zg is time variant, it influences the resonance frequency of the LCL filter
• The tuning of the active damping parameters can be online adapted as a tradeoff between robustness and resonance damping
• E.s. Notch filter is tuned at the resonance frequency.
Current sensors on the converter side
J. Dannehl, M. Liserre, F. Fuchs, F.; , "Filter-based Active Damping of Voltage Source
Converters with LCL-filter," IEEE Transactions on Industrial Electronics.
2 2
2 2
2( )
2
z NF NFNF
p NF NF
s sG s
s s
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 12
EEMSWEA:Medium Voltage Grid Analyser
• Aim: Analysis of the electrical properties
of medium-voltage networks with regard
to an optimization at high feed-in from
wind energy plants and improvement of
the harmonic load
• Realization: Development of a mobile
measurement and analysis system for
feeding harmonic currents and
measuring the network impedance
• Project volume: € 3.8 million (overall)
• 2.9 million € (Kiel University)
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 13
MV Analyzer System Description
Pos. Description
A MV-switchgear room
B Auxiliary power transformer
C MV-transformer room
D Inverter room
E Measurement room
F Cooling System
Transformer Container
Inverter Container
3D-Rendering of the MV Analyzer System
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 14
Specifications of the single Transformer
Rated power per transformer 1000 kVA
Rated current per transformer 1077 A
Rated voltage 20 kV / 536 V
Rel. short-circuit voltage 2.5 %
Number of transformers 2
Rated current (overall) 2154 A
Rated power (overall) 2000 kVA
Transformer Container
Two MV-transformers MV-Switchgear
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 15
Inverters Container
6 NPC-Inverters Control CabinetSpecifications of the single inverter
Nominal power 478 kVA
Nominal voltage (interl.) 920 V
Nominal current 300 A
Inductive filter 25 µH
DC link voltage 1500 V
DC link capacity 55.2 µF/A (2x)
Power feed 265 kVA
Switching frequency (nom.) 15 kHz
max. Switching frequency 30 kHz
Dimensions (100 x 200 x 80) cm
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 16
EEMSWEA-PROJEKT
MITTEL SPANNUNGS NETZ ANALYSATOR
Grid impedance identification
-High-frequency current injection (100 Hz…10 kHz)
-Total system: 1.6 MVA; single inverter: 480 kVA
-FPGA-based control system (master-slave configuration)
Inverter Filter Cable Transformer MV-Grid
Overall Power: 2 MVA
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 17
Impedance Identification through mono-Frequency Current Injection
MV grid impedance analyzer uses mono-frequency current injection in a wide rangebetween 100 Hz÷10 kHz to excite the MV grid.
, 2
cos cos
2 cos 1
s res res res s
RES
res s
T z z TG z
z z T
Internal Model Principle
To track a sinusoidal reference the harmonic model of the reference need to be added in the direct branch of the current loop.
Discretization method
Resonant controller must have infinite gain at thedesired frequency: deviation leads to tracking error.
Computation and PWM delay compensation
2 2 ( )
32 ( )
2 2
res res s res co s
res res s res co s
T f T
T f T
Phase lead compensation φres due to the delay phase lag: stability and robustness
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 18
Resonant Discretization for High Frequency Current Control
P+RES Controller
2 2P RES p i
res
sG s K K
s
1
f fL s R
+
-
*
g si kT
PWM
gi
RES
convv *
conv sv kT
RESG z
pK+
+
g si kTDigital Controller
skT
Filter
iK
Plant model in Z – time domain
1 f S f
f S f
R T Ln
T R T L
f
z eG z
R z e
Discretization Z
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 19
Resonant Discretization for High Frequency Current Control
SOGI
Gain/phase deviation at high frequency
Simple implementation
Impulsive invariant
Perfect tracking at every frequency
More computational burden
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 20
Experimental Results
αβ grid current and current error at 1kHz injection with
SOGI
αβ grid current and current error at 1kHz injection with Z {cos(ωRest)}
S. Brüske, S. Pugliese, S. Flacke and M. Liserre, "High-Frequency Grid Current Control of Parallel Inverters," IECON 2018 - Washington
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 21
Computation and PWM delayphase compensation
Kp tradeoff between high bandwidth and optimal damping
Kp =Lf /3Ts damping factor ξ=0.7
PM = 60° crossover frequency fco=1/6πTs.
System delay causes instability when the resonant frequency is over the bandwidth of the system!
φres should compensate the delay introduced by the plant GT(z)
φres = -GT(z)
2-sample phase lead
3 2
,2 2
4cos 3cos 1 2cos
2 cos 1
s res s res s s res s
RES Ts
res s
T z T T T TG z
z z T
3
2 2res res sT
Linear phase compensation of GT(z)
moving the zero of the transfer function with a two-step prediction
for frequencies higher than f90 = 5Rf /πLf
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 22
Nyquist Stability Criterion in Open-Loop Bode Diagram
Open-loop Bode diagram with linear phase delay compensation.Open-loop Bode diagram with 2-sample phase delay compensation.
Nyquist stability criterion counts –π crossings, in the open-loop Bode diagram, in the frequency range
where the magnitude is above 0 dB. N+ and N- number of positive/negative crossings.
No unstable open-loop poles and (N- - N+) = 0 Stable system
S. Pugliese, S. Flacke, Z. Zou and M. Liserre, "High-Frequency Harmonic Current Control of Power Converters," 2019 IEEE ECCE, Baltimore
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 23
Zone-phase based delay compensation
2 2
32
2 2
res res s res co
res res s res co
T f
T f
High PMs provided by the linear
compensation in high frequencies
Stability provided by the 2-sample delay method in low frequencies
fco = 1/6πTs (crossover frequency)
+
Stability margins at different fres in case of linear, 2-sample and zone-phase delay compensation
Open-loop Bode diagrams with zone-phase delay compensation
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 24
MV Grid-Impedance Analyzer Setup
Symbol Description Value
LV (rms) LV grid side 510 V / 50Hz
MV (rms) MV grid side 20 kV
Lf AC Inductor filter 25 uH
Rf AC Resistive filter 2.6mΩ
vDC DC-Link voltage 1200 V
fsw Switching frequency 30 kHz
Kp Proportional gain 0.25
Ki,50 Integral gain at 50Hz 62.5
Ki,res Integral gain at fres 62.5 / 125 / 250 / 375
`
NPC 1-4
Control Cabinet 1, 2
Control Cabinet 3
NPC 5,6
500A/div 4 ms/div
200A/div 500Hz/div
fres = 250Hz
iabc,1
iabc,2
iabc,tot
fres = 5kHz
10A/div 500Hz/div
20A/div 1 ms/div
Single NPC-converter: 30Apeak
at 5kHz grid current injection
2-parallel NPC converters: 800Apeak
at 250Hz grid current injection.
Table: power stage and current controller parameters used in simulations and experiments.
Experimental setup: 1.6 MVA MV grid impedance analyzer based on 6-parallel 3phase-NPC converters.
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 25
Simulation and Experimental Results
100A/div 20 ms/div
3
2 2res res sT
2res res sT
50A/div 1 ms/div
3
2 2res res sT
2res res sT
300Apeak /250Hzgrid current injection when switching the delay compensation from the 2-sample based method to the linear formulation.
30Apeak /5kHz grid current injection when switching the delay compensation from the 2-sample based method to the linear formulation.
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 26
MV-Analyzer in the Wind-park field
Field measurement on northern Germany's north coast
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 27
Messtechnische Einbindung
110 kV 20 kV
𝐼𝜈,𝑀𝑒𝑠𝑠𝑡𝑟𝑜𝑚
𝐼𝜈,𝐿𝑎𝑠𝑡+𝐸𝑟𝑧𝑒𝑢𝑔𝑒𝑟
𝐼𝜈
𝑍𝜈,𝑁𝑒𝑡𝑧
Messeinrichtung
𝑍𝜈,𝐴𝑛𝑙𝑎𝑔𝑒
𝑍𝜈,𝑁𝑒𝑡𝑧 ≪ 𝑍𝜈,𝐴𝑛𝑙𝑎𝑔𝑒
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 28
MittelspannungFrequenzgangmessung
Samples during a 250 Hz filter test
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 29
MittelspannungFrequenzgangmessung
Frequency response measurement, magnitude values
Frequency response measurement,
phase values
Medium voltage mains impedance measurement
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 30
Voltage Sensitivity Measurement
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 31
Example: Voltage sensitivity in UK
Tests performed in UK show that the active power sensitivity to voltage varies mostly during the day between constant current and constant impedancebehavior.
A. Ballanti, L. Ochoa, “Off-Line Capability Assessment”, WP2 Part A – Final Report.
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 32
𝑃 = 𝑃0𝑉
𝑉0
𝐾𝑝
1 + 𝐾𝑓𝑝𝑓 − 𝑓0𝑓0
𝑄 = 𝑄0𝑉
𝑉0
𝐾𝑞
1 + 𝐾𝑓𝑞𝑓 − 𝑓0𝑓0
The load can be represented with an exponential model for the voltage and with a linear dependency from the frequency
• Independent of initial voltage and does not require initialization
• Only one parameter is needed for active and one for reactive power.
• The exponent is equal to load sensitivity to voltage.
G. De Carne, M. Liserre, C. Vournas, "On-Line Load Sensitivity Identification in LV Distribution Grids," in IEEE
Transactions on Power Systems, vol. 32, no. 2, pp. 1570-1571, March 2017.
Voltage Sensitivity Identification
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 33
𝑃0 = 𝑃𝐿 − 𝑃𝐺 > 0 (7)
Let us suppose that the DG works at unity power factor and that the following assumption holds:
Where P0 is the net power, PL is the passive load power and PG is the DG power.The passive load has a normalized sensitivity equal to:
𝐾𝑝 =Τ∆𝑃𝐿 𝑃𝐿Τ∆𝑉 𝑉0
∆𝑃=∆𝑃𝐿 = 𝐾𝑝,𝐿 Τ∆𝑉 𝑉0 𝑃𝐿
Considering that the DG power output is invariant to the voltage, the previous equation becomes:
(8)
(9)
Voltage Sensitivity Identification: Influence of DG on the identification
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 34
Integrating eq. (9) in eq. (4) we obtain:
𝐾𝑝 =Τ∆𝑃 𝑃0Τ∆𝑉 𝑉0
= 𝐾𝑝,𝐿𝑃𝐿
𝑃𝐿 − 𝑃𝐺(10)
The net load reacts in different way depending on the presence of DG.
Example:
𝐾𝑝 = 11
1 − 0= 1
𝑃𝐿 = 1, 𝑃𝐺 = 0 → 𝑃0 = 1𝐾𝑝,𝐿 = 1
𝑃𝐿 = 1.5, 𝑃𝐺 = 0.5 → 𝑃0 = 1𝐾𝑝,𝐿 = 1
𝐾𝑝 = 11.5
1.5 − 0.5= 1.5
𝑃 = 𝑃0𝑉
𝑉0
1
𝑃 = 𝑃0𝑉
𝑉0
1.5Linear
responseMore than linear
response
Voltage Sensitivity Identification: Influence of DG on the identification
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 35
The Voltage sensitivity can beevaluated applying a controlledvoltage disturbance and measuringthe power or the opposite
Simple and low-computationalcost
Updates in real time (every few minutes)
Consider the power influence ofDG
Helps in assessing how muchpower need really to be injected
Main grid
0
1.0 ind
Q (
p.u
.)
Time0.95
1.0
P (
p.u
.)Time
0.95
1
V (
p.u
.)
Time
0
1.0 ind
Q (
p.u
.)
Time
0.95
1.0
P (
p.u
.)
Time
0.95
1
V (
p.u
.)
Time
Voltage Sensitivity Potential
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 36
The load sensitivity to voltage can be used to shape the load consumption varying the ST voltage output
𝑽
𝑉0= 1 +
∆𝑷
𝑃𝑲𝒑
Sensitivity coefficients for each phase
ST bus
0.93 pu
Furthest bus
0.90 pu
ST voltage and lowest grid voltage
5%
Load reduction (%)
Desired power
variation
Active power
sensitivity to voltage
New voltage
set-point
Voltage Sensitivity Potential in ST application
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 37
This features enables the Smart Transformer to offer services to the grid, such as primary frequency supportH
V F
req
uen
cy
+200mHz
Voltage Sensitivity Potential in ST application
Sensitivity coefficients for each phase
ST bus
0.93 pu
Furthest bus
0.90 pu
ST voltage and lowest grid voltage
5%
Load reduction (%)
Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 38
Impedance knowledge helps in Wind Turbine park integration
Active filter, active damping and Low Voltage Ride Through could be improved
EEMSWEA Project: 2MVA MV-grid impedance analyzer
Impedance Identification through mono-Frequency Current Injection in MV grid is analyzed:
- the effects of the discretization in the accuracy of current control
- the effects of computation/PWM delay compensation in the stability of current control.
Voltage sensitivity can be used by influencing load consumption and in defining the power to be injected into the grid for supporting the voltage and the primary frequency
Conclusions