• Hydrogen storage VS no hydrogen storage
• Slightly higher flow in storage case, increased flow on average by:
– EV: 0.38 % – S120: 0.70 % – PI: 1.21 %
• The system already has high flexibility from hydro power
• Hydrogen load could be placed better or distributed to give more effect
• No storage results in rationing of 9.8 MW in all cases
13
Conclusion
• A rolling horizon model was developed for assessing the value of including stochastic wind power in a regional power system with hydrogen production
• Case study shows:
– Reduced costs of 5.6% compared to deterministic solution – Potential of reducing costs in stochastic solution up to 37.6%
– Lower regulation cost and higher import for the better solutions – Similar solutions for more than 60 wind samples
– More flow on the transmission lines when storage is included, better improvement for better uncertainty representation
– Storage helps to avoid very expensive rationing
Small Signal Modelling and Eigenvalue Analysis of Multiterminal HVDC Grids
Salvatore D'Arco, Jon Are Suul SINTEF Energi AS
SINTEF Energy Research
• Power systemstability is commonly assessed by eigenvalueanalysis
• Enables analysis and mitigation of oscillatory behaviour or instability due to system configuration,systemparameters and controller settings
• VSCHVDCsystems has different dynamics compared to traditional generators
• Models of MMCHVDCterminals arecurrently under development
• State-spacemodels for HVDCsystems can beused for multiplepurposes
• Analysis, identification and mitigation of oscillations and small-signal instability mechanisms in HVDCtransmission schemes
• Analysis of controller tuning and interaction between control loops in HVDCterminals
• Integration in larger power systemmodels for assessment of howHVDCtransmission will influenceoverall small signal stability and oscillation modes
2
Eigenvalue based small signal analysis
SINTEF Energy Research 3
Protection and Fault Handling in Offshore HVDC grids
Objectives: Establish tools and guidelines to support the design of multi-terminal offshore HVDC grids in order to maximize system availability. Focus will be on limiting the effects of failures and the risks associated to unexpected interactions between components.
• Develop mmodels of offshore grid components (cables, transformers, AC and DC breakers, HVDC converters) for electromagnetic transient studies.
• Define guidelines to reduce the risks of uunexpected interactions between components during normal and fault conditions.
• Define strategies for pprotection and fault handling to improve the availability of the grid in case of failures.
• DDemonstrate the effectiveness of these tools with numerical simulations (PSCAD, EMTP), real time simulations (RTDS, Opal-RT) and experimental setups.
• Expand the kknowledge base on offshore grids by completion of two PhD degrees / PostDoc at NTNU and one in RWTH.
SINTEF Energy Research
Overview of models and methods for stability analysis
4 Detailed Circuit Model
(including IGBT’s)
Mathematical model with discontinuous switching functions
Average model with continuous insertion indices, and time-periodic solutions in
steady-state
Average model with continuous insertion indices, and time-invariant solutions in
steady-state
Piecewise (linear) models
Linearized SSTP models
Impedance Representation
(seq. domain)
Linearized SSTI models x Computationally intensive,
time-consuming EMT simulation studies for large signal stability.
x Search for a Lyapunov function to prove large-signal stability.
x Estimate of regions of attraction as a measure of the system large-signal stability robustness.
Lyapunov methods for piecewise linear models:
x Common quadratic Lyapunov function, x Switched quadratic Lyapunov function x Multiple Lyapunov functions Ly
L L x xx
Small-signal stability assessment via time-periodic theory:
x Poincaré multipliers S
t x
Small-signal stability assessment via traditional eigenvalue-based methods x Eigenvalue plots x Parametric sensitivity x Participation factor analysis S
t x xx
Small-signal stability assessment via by means of Nyquist criteria.
Impedance Representation (dq
domain) Impedance Representation
(seq. domain) Impedance Representation (dq
domain)
SINTEF Energy Research 6 GSC
Grid #1 WFC Offshore Onshore
Qg1*
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Frequency-Dependent State-Space modelling of HVDC cables
7
• The modelling approach is based on a lumped circuit and constant parameters – Parallel branches allow for capturing the frequency dependent behavior of the cable – Compatible with a state space representation in the same way as classical models with simple
Ɏsections
– Model order depends on the number of parallel branches and the number of Ɏsections
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State-space frequency-dependent Ɏsection modelling
8
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Behavior in a point to point HVDC transmission scheme
9
Interaction modes All modes
5Ɏsections 5 parallel branches
5Ɏsections classical
Eigenvalue trajectory for a sweep of dc voltage controller gain
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Main conclusions related to cable modelling
10
• ULM is established for EMT simulations
• Traditional Ɏ-section models of HVDC cables are not suitable for dynamic simulation or stability-assessment of HVDC systems
• Single inductive branches imply significant under-representation of the damping in the system
• Frequency-dependent (FD) Ɏ-model for small-signal stability analysis
• For simplified models, representation of cables by equivalent resistance and capacitance can be sufficient
• Developed Matlab-code and software tool for generating FD-Ɏmodels
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• Advantages
• Modularity
• Scalability
• Redundancy
• Low losses
• DC-capacitor is not required
• Disadvantages
• High number of switches
• Large total capacitance
• Complexity
• Sub-module Capacitors will have steady-state voltage oscillations and internal currents can have corresponding frequency components
11
3-phase MMC: Basic Topology
SM
Main challenge for small-signal modelling
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Classification of MMC Modelling for eigenvalue analysis
12
MMC Small-Signal Modelling
Phasor Modelling:
U. Aberdeen / NCEPU/Manitoba
Approach Two-Level VSC
Equivalent
MMC Complete Power Balance
Circulating
(Jovcicet al. & Li et al.)
NO
(Deoreet al.) IIT Mumbai Approach (Trinh et al.)
(Liu et al.)
(Adam et al.) (Bergna et al.)
Voltage Aggregation:
SINTEF'S Approach (Bergna et al.)
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Compensated vs. Uncompensated Modulation
13 signals are divided by the actual arm voltage
Voltage references are divided by a
MMC output voltage component will be approximately equal to the reference
Non-linear relationship between reference and
"real" driving voltages
The control output is modified by the energy information in each arm/phase Appropriate for energy-based modelling
Energy-based modelling is not suitable for this case
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Main conclusions related to MMC modelling
16
• The internal energy storage dynamics of MMCs must be represented for obtaining accurate models
• Established models of 2-Level VSCs should not be used for studying fast dynamics in HVDC systems
• Models assuming ideal power balance between AC- and DC-sides can only be used for studying phenomena at very low frequency
• Two cases of MMC modelling
• Compensated modulation with Energy-based modelling
• Un-compensated modulation with Voltage-based modelling
Energy-based model
Voltage-based model
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Generation of a small signal model for MT HVDC
• A modular approach was developed to generate the small signal model of MT HVDC transmission system
– Decompose the HVDC MT into predefined modular blocks (cable, converters) – Modules can be customized by modifying the parameters but not the structure of the
subsystem
– Several blocks are developed for the converters reflecting the topology and the control – Steady state conditions (linearization points) for each block were precalculated as a function of
the input
– Steady state conditions for the entire system were obtained by implementing a dc loadflow
17
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Definition of subsystem interfaces
18 CONVERTER A
CONVERTER C
CONVERTER B
CONVERTER D CABLE AB
CABLE BC CABLE BD
CABLE CD
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Definition of subsystem interfaces
19 CONVERTER A
CONVERTER C
CONVERTER B
CONVERTER D CABLE AB
CABLE BC
CABLE BD
CABLE CD ADDING
NODE
ADDING NODE ADDING NODE
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Workflow for generating the small signal model
20 Definition of the grid
topology
Input components parameters
dc Load flow
Calculation steady state conditions for the
submodules
Calculation state space matrices for the
submodules
Assemble submodules matrices into system
matrices Export data
Data input Calculation steady
state conditions Calculation state space matrices
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Screenshot of the GUI after generating the small signal model
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• Modes associated with thecablearequitequickly damped
• One oscillatory mode and one real pole are slightly dependent on operating conditions Systemis stableand well-damped in thefull rangeof expected operating conditions
23
MMC-based point-to-point transmission scheme
-8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 -4000
Trajectory of critical eigenvalue with power reference is varied from -1.0 to 1.0 pu Eigenvalues of MMC HVDC point-to-point
scheme
SINTEF Energy Research
• Variables of small-signal model can accurately represent the nonlinear system model for variables at both terminals
24
Time-domain verification of point-to-point MMC scheme
DC voltage [pu]
Active current Id[pu]
DC voltage controlled terminal
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
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Aggregated participation factor analysis
26
• Approach proposed for identifying interactions in an interconnected system
• An interaction mode is defined as an eigenvalue having participation ȡhigher than a threshold ɖfrom both parts of the interconnected system
• Interaction modes identified as shown below for ɖ= 0.20
• Close correspondence can be identified between identified interaction modes and eigenvalues that are significantly influenced by the interconnection
-1000-1 -800 -600 -400 -200 0
4 Eigenvalues - 3T system
real
4 Eigenvalues - Interaction modes
real
cumulative participation in system S1
,
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• More interaction modes compared to case with 2LVSCs
• In total 14 eigenvalues - 12 oscillatory modes (6 pairs) and two real poles.
• A first group is defined as those well damped oscillatory modes (real part smaller than -200).
• A second group of interaction modes is found much closer to the imaginary axis
• Oscillatory mode (39-40)
• Two real eigenvalues (48 and 49)
27
Interaction modes –MMC HVDC point-to-point scheme
-400 -350 -300 -250 -200 -150 -100 -50 0
4000 eigenvalues of interarea modes
8
30 eigenvalues of interarea modes
39
40
48 49
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• For fast interaction modes:
• Balanced participation from the two converter stations
• High participation from the cable in the fastest modes
• Slow interaction modes
• Dominant participation from the DC-voltage controlled terminal in oscillatory modes
• Low participation from the cable, especially for the two real poles
• Depending on the eigenvalue, one station will have a higher participation
28
Interaction modes –Aggregated participation factor analysis
Aggregated participation factor analysis of interarea modes of theMMC-HVDCpoint-to-point scheme
–blue:DCVoltagecontrollingstation –green:power controllingstation –brown:dc cable
SINTEF Energy Research
• The fast oscillatory modes (8-9, 10-11, and 14-15)
• Related to dc voltages at both cable ends
• Associated with cable dynamics
• Modes 21-22 and 25-26
• "DC-side" interactions
• Almost no participation from the AC-sides
• Associated with the MMC energy-sum wand the circulating current ic,z.
29
Participation Factor Analysis of Interaction Modes
vodvoq ild ilqgamdgamqiod ioqphid phiqvplldvpllqepsplldthetapllvdcvdcfrhopacmiczwSigmaKappaSigma Xiz
0 0.05 0.1 0.15 0.2
0.25 mode 8, with eigenvalue at -397.87635+3360.0213i
conv 1 conv 2
vodvoq ild ilqgamdgamqiod ioqphid phiqvplldvpllqepsplldthetapllvdcvdcfrhopacmiczwSigmaKappaSigma Xiz
0
0.4 mode 10, with eigenvalue at -355.55027+3025.4561i
conv 1 conv 2
vodvoq ild ilqgamdgamqiod ioqphid phiqvplldvpllqepsplldthetapllvdcvdcfrhopacmiczwSigmaKappaSigma Xiz
0 0.05 0.1 0.15 0.2
0.25 mode 14, with eigenvalue at -282.05785+2005.4132i
conv 1 conv 2
vodvoq ild ilqgamdgamqiod ioqphid phiqvplldvpllqepsplldthetapllvdcvdcfrhopacmiczwSigmaKappaSigma Xiz
0
0.4 mode 21, with eigenvalue at -238.34277+1138.0026i
conv 1
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• Oscillatory mode given by eigenvalues 39-40
• Interaction modes associated with the power flowcontrol in the system
• Associated with the integrator state of the DCvoltage controller,ɏ
• Real poles 48 and 49
• Associated with integrator states of the PI controllers for the circulating current, Ɍz,
• The interaction of both stations in these eigenvalues is mainly due to the power transfer through the circulating current.
• Small participation of the cable since the dynamics are slow and the equivalent parameters of the arm inductors dominate over the equivalent DC parameters of the cable
30
Participation Factor Analysis of Interaction Modes
vodvoq ild ilqgamdgamqiod ioq phidphiqvplldvpllqepsplldthetapllvdcvdcfrhopacmiczwSigmaKappaSigma Xiz
0
mode 39, with eigenvalue at -12.3531+24.6583i
conv 1 conv 2
vodvoq ild ilqgamdgamqiod ioqphidphiq vplldvpllqepsplldthetapllvdcvdcfrhopacmiczwSigmaKappaSigma Xiz
0
1 mode 48, with eigenvalue at -10.2218
conv 1 conv 2
vodvoq ild ilqgamdgamqiod ioqphidphiqvplldvpllqepspll dthetapllvdcvdcf rhopacmiczwSigmaKappaSigma Xiz
0
mode 49, with eigenvalue at -9.2989
conv 1 conv 2
vod voqild ilqgamdgamqiod ioq phidphiqvplldvpllqepsplldthetapllvdcvdcf rhopacmiczwSigmaKappaSigma Xiz
0
0.45 mode 25, with eigenvalue at -222.2334+683.0681i
conv 1
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Main conclusions related to interaction analysis
33
• Small-signal eigenvalue analysis can be utilized to reveal the properties of modes and interactions in the system
• Participation and sensitivity of all oscillations and small-signal stability problems can be analyzed
• Suitable for system design, controller tuning and screening studies based on open models
• Aggregated participation factor analysis can reveal interaction between different elements or sub-systems
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