A Simplified Microgrid Model for the Validation of Islanded Control Logics
Abstract
:1. Introduction
- (a)
- Provide a simple but reliable model for islanded MGs, characterized by all the generation interfaced to the AC part of the MG by means of power electronic devices;
- (b)
- Running the model does not require a dedicated, often licensed, specific software, a relevant time to set up the model and a high computational effort;
- (c)
- The model is presented as a system of ODE that does not need too many input parameters and can be used to design different controllers and tune their parameters.
2. The Savona Campus Smart Polygeneration Microgrid
- The public grid connected to a switchgear (SG) Q1;
- Three photovoltaic (PV) units connected through a unique cable to the SG Q1, namely PV1;
- One PV unit (with its inverter and transformer) connected to SG Q2, namely PV2;
- The storage unit produced by FIAMM (with its DC/DC converter, inverter and transformer) connected to SG Q2;
- Resistive-inductive loads connected to SG Q2.
3. MG Sources and Main Elements
3.1. PV Units Model
3.2. Electric Storage Model
3.3. Inverter Model
3.4. DC/DC Converter Model
4. The Simplified Model
- Each input/output power electronic converter relationship neglects the presence of the higher order harmonics;
- The shunt sections of the inverter AC filters are neglected for simplicity (indeed it can be noted from Table 3 that the shunt filter impedance at the fundamental frequency is more than 3 kΩ). If one considered this, it would imply only an enlargement of the network admittance matrix Y without changing the model structure;
- The AC-side portion of the MG (as well as the inverter filter) is supposed to be at a steady state (assuming that both the angular frequency of the sources and their voltage amplitude can vary), while all the DC dynamics are accounted;
- The loads are described with a constant impedance model. Consequently, as typical in RMS transients, they are inserted in the network model, giving rise to the so-called extended admittance matrix YE [47].
- Define the MG topology, parameters (rated data of cables, transformers, sources etc.) and admittance matrix;
- Define the sources and their characteristic (power–irradiance for PV, power-wind velocity for wind generator, V-SOC for chemical storage etc.);
- Define the all the state variables and write the resulting ODEs;
- Define an equilibrium point of the system zeroing all of the time derivatives;
- Define a contingency;
- Solve the resulting ODE system and get the involved variable dynamics.
5. Controllers
5.1. DC/DC Converter Controller
5.2. Droop Control
5.3. Isochronous (Master/Slave) Control
6. Simulations
- Validating the developed simplified model comparing its results with the ones provided by the complete model implemented in PSCAD-EMTDC;
- Assessing the possibility of interfacing the developed power system model with different controller structures. This will be done considering the two control logics summarized in the previous sections (droop and isochronous).
6.1. Droop Control Simulations
6.1.1. Active Power Increasing Simulation (S1)
6.1.2. Active Power Decreasing Simulation (S2)
6.2. Isochronous Control Simulations
6.2.1. Active Power Increasing Simulation (S3)
6.2.2. Double Perturbation Simulation (S4)
7. Conclusions
Author Contributions
Conflicts of Interest
Nomenclature
Acronyms | |
SQ | Switchgear |
PV | Photovoltaic source |
SPM | Smart Polygeneration Microgrid |
Variables | |
α | Solar irradiation |
T | External temperature |
SOC | State of charge |
δk | Angle of the k-th source |
φk | Phase of the k-th source |
ωk | Angular frequency of the k-th source |
mk | Modulation index of the k-th source |
Voltage phasor of the k-th source | |
Current phasor of the k-th source | |
VDC,k | Voltage across the capacitor |
IST | LST current |
E | Storage internal e.m.f. |
VMPP | Maximum power point voltage at specified conditions |
χ1 | Integrator control output of boost level of DC/DC converter |
χ2 | Integrator control output of buck level of DC/DC converter |
η1,k | Integrator control output of active power control of the k-th source |
η2,k | Integrator control output of reactive power control of the k-th source |
YE | Extended admittance matrix |
Gi,k | Real part of the i-k-th element of YE |
Bi,k | Imaginary part of the i-k-th element of YE |
VDC,k | Voltage across the Ck |
Constants | |
Rint | Internal resistance of the chemical storage |
LST | Storage side inductance filter of DC/DC converter |
Ck | DC capacitor of the k-th inverter |
mD,k | Active power droop coefficient of the k-th source |
nD,k | Reactive power droop coefficient of the k-th source |
NCC | Storage nominal current capacity |
Indices | |
k | Index of sources; 1 refers to PV1, 2 to PV2, 3 to storage |
i | Auxiliary index for k |
Functions | |
f | Function describing ODE system without control |
fD | Function describing ODE system with droop logic |
fI | Function describing ODE system with isochronous logic |
gD | Function describing algebraic equations subsystem with droop logic |
gI | Function describing algebraic equations subsystem with isochronous logic |
KST | Voltage DC/DC converter transfer function |
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Photovoltaic (PV) 1 | PV 2 | Storage | Load | |
---|---|---|---|---|
Rated Power | 3 × 5 kWp | 77 kWp | 62 kW | |
Cable resistance to Q2 | 157.2 mΩ | 20.8 mΩ | 43.5 mΩ | 181 mΩ |
Cable inductance to Q2 | 3023.7 μH | 14.15 μH | 12.42 μH | 14.59 μH |
PV Module Parameters | ||
---|---|---|
Short circuit current in Standard Test Conditions (STC) | 8.75 A | |
Rated external temperature | 25 °C | |
Temperature coeff. of the short circuit current | 0.06 | |
Temperature coeff. of the open module voltage | −0.31 | |
Minimum solar radiation to supply energy | 0.2 kW/m2 | |
Maximum solar radiation to supply energy | 1 kW/m2 | |
Open voltage module at | 35 V | |
Open voltage module at | 37.11 V | |
Maximum power point voltage in STC | VMPP | 29.7 V |
Maximum power in STC | PMPP | 240 W |
[A] | a6 | a5 | a4 | a3 | a2 | a1 | a0 |
---|---|---|---|---|---|---|---|
0 [A] | 1.6 × 10−11 | −4 × 10−9 | 6 × 10−7 | −3.3 × 10−5 | 7.5 × 10−4 | 5.2 × 10−4 | 2.42 |
Lse | Rse | Lsh | Csh | Rsh |
---|---|---|---|---|
1 mH | 0.314 mΩ | 0.0166 mH | 1 µF | 2.61 kΩ |
Proportional Gain | Integral Time Constant | |
---|---|---|
Boost | KP_BOOST = 1.438 × 10−4 | TBOOST = 8.749 (s) |
Buck | KP_BUCK = 1.667 × 10−4 | TBUCK = 10 (s) |
Proportional Gain | Integral Time Constant | |
---|---|---|
phase | KP,phase = 5 × 10−4 | Tphase = 10 (s) |
mod_index | KP,mod_index= 2 × 10−6 | Tmod_index= 2.5 103 (s) |
PV1 | PV2 | Storage | |
---|---|---|---|
Pn | 15 kW | 77 kW | 62 kW |
m | −1.000 × 10−4 rad/sW | −0.187 × 10−4 rad/sW | −0.242 × 10−4 rad/sW |
Qn | 7.265 kVAr | 38.746 kVAr | 30.03 kVAr |
n | −1.000 × 10−4 V/VAr | −0.187 × 10−4 V/VAr | −0.242 × 10−4 V/Var |
PV1 | PV2 | Storage | DC/DC Converter |
---|---|---|---|
VDC,1 = 783.8 V | VDC,2 = 854.8 V | VDC,3 = 750.0 V | χ1 = 0.153 |
IST = 6.4 (A) | χ2 = 0.847 | ||
SOC = 80% | |||
ψ1 = 0.0524 rad | ψ2 = 0.0524 rad | ψ3 =0 rad | |
φ1 = 0 | φ2 = 0 | φ3 = 0 |
PV1 | PV2 | Storage | DC/DC Converter |
---|---|---|---|
VDC,1 = 659.4 V | VDC,2 = 712.8 V | VDC,3 = 750.0 V | χ1 = 0.093 |
η11 = 0.2234 | η12 = 0.2478 | IST = −66.5 A | χ2 = 0.907 |
η21 = 1.01 | η22 = 0.94 | SOC = 10% | |
ψ1 = 0 rad | ψ2 = 0 rad | ψ3 = 0 rad |
PV1 | PV2 | Storage | DC/DC Converter |
---|---|---|---|
VDC,1 = 659.4 V | VDC,2 = 712.8 V | VDC,3 = 750.0V | χ1 = 0.023 |
η11 = 0.2595 | η12 = 0.2889 | IST = −72.07 A | χ2 = 0.977 |
η21 = 0.99 | η22 = 0.90 | SOC = 80% | |
ψ1 = 0 rad | ψ2 = 0 rad | ψ3 = 0 rad |
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Bonfiglio, A.; Brignone, M.; Invernizzi, M.; Labella, A.; Mestriner, D.; Procopio, R. A Simplified Microgrid Model for the Validation of Islanded Control Logics. Energies 2017, 10, 1141. https://doi.org/10.3390/en10081141
Bonfiglio A, Brignone M, Invernizzi M, Labella A, Mestriner D, Procopio R. A Simplified Microgrid Model for the Validation of Islanded Control Logics. Energies. 2017; 10(8):1141. https://doi.org/10.3390/en10081141
Chicago/Turabian StyleBonfiglio, Andrea, Massimo Brignone, Marco Invernizzi, Alessandro Labella, Daniele Mestriner, and Renato Procopio. 2017. "A Simplified Microgrid Model for the Validation of Islanded Control Logics" Energies 10, no. 8: 1141. https://doi.org/10.3390/en10081141