Investigation of Oscillation and Resonance in the Renewable Integrated DC-Microgrid
Abstract
:1. Introduction
- A comprehensive analytical model for investigating high-frequency oscillations and resonance has been developed. The impedance analysis and eigenvalue-based method are used simultaneously to identify the source of oscillation/instability in the DC microgrid.
- Most of the prior studies have considered a constant power load for the high-frequency and resonance assessment of DC microgrids. This work has considered the various types of loads in the DC microgrid and their impact on the overall high-frequency oscillations and resonance.
- A semi-global sensitivity analysis technique has been used to rank the most critical parameters of the DC microgrid, considering the cross-coupling of various parameters and uncertainties.
- Three control synthesis methods are described and compared in their suitability to the conventional PI controller in terms of high-frequency oscillations and resonance.
2. Oscillation Challenges in DCMG
3. Methodology and Modelling
3.1. State Space Modelling
3.2. Analytical Expression for Impedance Scanning
3.3. Sensitivity Analysis
3.4. Overview of Control Tuning
4. Numerical Analysis and Discussion
4.1. Impedance Analysis
4.2. Eigenvalue Analysis
4.2.1. Case Study 1 (Parameter Variation in 12-kW Boost Converter)
4.2.2. Case Study 2 (Parameter Variation in Buck Converter)
4.2.3. Case Study 3 (Variation in DC-Link Capacitance)
4.2.4. Case Study 4 (Variation in Load Power)
4.2.5. Case Study 5 (Variation in Inductance Parameter)
4.3. Time-Domain Simulations and Experimental Studies
4.4. Critical Parameter Ranking
4.5. Control Performance Assessment
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Variables | |
BESS | Battery energy storage system |
DCMG | DC microgrid |
EMI | Electromagnetic interference |
EV | Electric vehicle |
GM | Gain margin |
HF | High frequency |
HVDC | High-voltage DC |
LF | Low frequency |
LQR | Linear Quadratic Regulator |
MVDC | Medium voltage DC |
PI | Proportional integral |
PID | Proportional integral derivative |
PM | Phase margin |
PV | Photovoltaic |
PWM | Pulse-width modulated |
RESs | Renewable energy sources |
SSS | Small-signal stability |
Appendix A
Parameter | Symbol | Value |
---|---|---|
Boost converter source voltage | ||
Boost converter inductor and capacitor | & | |
Parasitic inductor resistor | ||
Boost converter output voltage | ||
DC link voltage | ||
Switching frequency | ||
Proportional and integral gain of PI controller in boost converter | ||
Input voltage of buck converter | ||
Buck converter output voltage | ||
Boost converter inductor and capacitor | ||
Proportional and integral gain of PI controller in buck converter | ||
Switching frequency | ||
Load | ||
Rated output power |
Converter | PI | LQR | IP | PI+clegg |
---|---|---|---|---|
1 | Proportional: 0.9 Integral: 0.005 | Proportional: 0.0011 Integral: 1.73 | Proportional: 0.0013 Integral: 0.707 | Proportional: 0.0015 Integral: 1.25 |
2 | Proportional: 0.9 Integral: 0.005 | Proportional: 0.0011 Integral: 1.73 | Proportional: 0.0012 Integral: 0.707 | Proportional: 0.0012 Integral: 1.23 |
3 | Proportional: 0.9 Integral: 0.005 | Proportional: 0.0011 Integral: 1.73 | Proportional: 0.0011 Integral: 0.707 | Proportional: 0.0012 Integral: 1.22 |
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Reference | Detailed Load Model | Sensitivity Analysis | Key Parameter Identification | Control Method |
---|---|---|---|---|
[13] | ✓ | ✓ | ✕ | ✓ |
[14] | ✓ | ✓ | ✕ | ✕ |
[15] | ✕ | ✓ | ✕ | ✕ |
[16] | ✕ | ✓ | ✕ | ✕ |
[17] | ✓ | ✓ | ✕ | ✕ |
[20] | ✕ | ✓ | ✕ | ✕ |
[21] | ✕ | ✕ | ✕ | ✓ |
This work | ✓ | ✓ | ✓ | ✓ |
Parameter | Symbol | Value |
---|---|---|
Rated power of the simulated system | 20 kW | |
Rated power of boost converter 1 | 12 kW | |
Rated power of boost converter 2 | 8 kW | |
Rated power of buck converter 1 | 10 kW | |
Rated power of buck converter 2 | 5 kW | |
Rated power of buck converter 3 | 1 kW | |
Boost converter source voltage | 375 V | |
Boost converter output voltage | 750 V | |
DC link voltage | 750 V | |
Switching frequency of boost converters | 20 kHz | |
Switching frequency of buck converter | 10 kHz | |
20 kHz | ||
20 kHz | ||
Input voltage of buck converter | 750 V | |
Buck converter output voltage | 400 V |
Boost Converter 1 | Boost Converter 2 | ||
---|---|---|---|
Vs = 375 V | L = 157 µH | Vs = 400 V | L = 147 µH |
V0 = 750 V | R = 47 Ω | V0 = 750 V | R = 70 Ω |
D = 0.5 (no unit) | C = 1000 µF | D = 0.5 (no unit) | C = 1000 µF |
Kp = 0.005 pu | Ki = 0.003 pu | Kp = 0.005 pu | Ki = 0.003 pu |
Parameters | Converter 1 | Converter 2 | Converter 3 |
---|---|---|---|
Input voltage (V) | 750 | 750 | 750 |
Output voltage (V) | 400 | 400 | 400 |
Inductance (H) | 0.00428 | 0.0044 | 0.0033 |
Resistance (ohm) | 16 | 145 | 147 |
Duty cycle | 0.5 | 0.5 | 0.5 |
Proportional gain (pu) | 0.9 | 0.9 | 0.9 |
Integral gain (pu) | 0.005 | 0.005 | 0.005 |
Critical Mode | Damping (%) | f (Hz) | Associated Mode | Remarks |
---|---|---|---|---|
−0.83 ± j953 | 0.09 | 151 | Controller | Boost converter |
−7.91 ± j1443 | 0.55 | 230 | Controller | Boost converter |
−7.33 ± j18,080 | 0.04 | 2878 | Controller | Buck converter |
−66.48 ± j57,931 | 0.11 | 9224 | Controller | Buck converter |
−17.36 ± j14,184 | 0.12 | 2258 | Controller | Buck converter |
Load Type | Damping of Mode 1 | Damping of Mode 2 | Damping of Mode 3 | Damping of Mode 4 | Damping of Mode 5 |
---|---|---|---|---|---|
Constant P | 0.091 | 0.56 | 0.041 | 0.112 | 0.121 |
Constant I | 0.092 | 0.55 | 0.038 | 0.111 | 0.122 |
Constant Z | 0.093 | 0.55 | 0.039 | 0.113 | 0.122 |
ZIP | 0.091 | 0.54 | 0.041 | 0.114 | 0.121 |
Ranking | OAT | Morris | Pearson |
---|---|---|---|
1 | |||
2 | |||
3 | |||
4 | DC-link |
Mode | Damping with PI | Damping with PI+clegg | Damping with IP | Damping with LQR |
---|---|---|---|---|
1 | 0.091 | 0.122 | 0.105 | 0.11 |
2 | 0.551 | 0.593 | 0.573 | 0.57 |
3 | 0.041 | 0.071 | 0.055 | 0.054 |
4 | 0.112 | 0.134 | 0.123 | 0.115 |
5 | 0.122 | 0.151 | 0.134 | 0.125 |
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Habibullah, M.; Mithulananthan, N.; Shah, R.; Islam, M.R.; Muyeen, S.M. Investigation of Oscillation and Resonance in the Renewable Integrated DC-Microgrid. Electronics 2023, 12, 1574. https://doi.org/10.3390/electronics12071574
Habibullah M, Mithulananthan N, Shah R, Islam MR, Muyeen SM. Investigation of Oscillation and Resonance in the Renewable Integrated DC-Microgrid. Electronics. 2023; 12(7):1574. https://doi.org/10.3390/electronics12071574
Chicago/Turabian StyleHabibullah, Mohammad, Nadarajah Mithulananthan, Rakibuzzaman Shah, Md Rabiul Islam, and S. M. Muyeen. 2023. "Investigation of Oscillation and Resonance in the Renewable Integrated DC-Microgrid" Electronics 12, no. 7: 1574. https://doi.org/10.3390/electronics12071574