ABSTRACT:
The analysis of the small-signal stability of
conventional power systems is well established, but for inverter based microgrids
there is a need to establish how circuit and control features give rise to
particular oscillatory modes and which of these have poor damping. This paper
develops the modeling and analysis of autonomous operation of inverter-based
microgrids. Each sub-module is modeled in state-space form and all are combined
together on a common reference frame. The model captures the detail of the
control loops of the inverter but not the switching action. Some inverter modes
are found at relatively high frequency and so a full dynamic model of the
network (rather than an algebraic impedance model) is used. The complete model is
linearized around an operating point and the resulting system matrix is used to
derive the eigenvalues. The eigenvalues (termed “modes”) indicate the frequency
and damping of oscillatory components in the transient response. A sensitivity
analysis is also presented which helps identifying the origin of each of the
modes and identify possible feedback signals for design of controllers to improve
the system stability. With experience it is possible to simplify the model
(reduce the order) if particular modes are not of interest as is the case with
synchronous machine models. Experimental results from a microgrid of three
10-kW inverters are used to verify the results obtained from the model.
KEYWORDS:
1.
Inverter
2.
Inverter model
3.
Microgrid
4.
Power control
5.
Small-signal
stability
SOFTWARE: MATLAB/SIMULINK
BLOCK DIAGRAM:
Fig.
1. Typical structure of inverter-based microgrid.
Fig.
2. Active power (filtered) response of micro-sources with 3.8 kW of step
change
in load power at bus 1.
Fig.
3. Reactive power exchange between the micro sources with 3.8 kW of
step
change in load power at bus 1 (Initial values: Q1 =0, Q2 = 200, Q3 =
+200;
Final values: Q1 = +600, Q2 = 300, Q3 = 200).
Fig.
4. Active power (filtered) response of micro-sources with 16.8 kW and
12
kVAR RL load step change at bus 1.
Fig.
5. Reactive power (filtered) response of micro-sources with 16.8 kW and
12
kVAR RL load step change at bus 1.
Fig.
6. Output voltage (d-axis) response with 27 kW of step change in load
power
at bus 1.
Fig.
7. Inductor current (d-axis) response with 27 kW of step change in load
power
at bus 1.
CONCLUSION:
In this paper, a small-signal state-space model of a
microgrid is presented. The model includes inverter low frequency dynamics dynamics,
high frequency dynamics, network dynamics, and load dynamics. All the
sub-modules are individually modeled and are then combined on a common
reference frame to obtain the complete model of the microgrid.
The model was analyzed in terms of the system
eigenvalues and their sensitivity to different states. With the help of this analysis
the relation between different modes and system parameters was established. It
was observed that the dominant low-frequency modes are highly sensitive to the
network configuration and the parameters of the power sharing controller of the
micro sources. The high frequency modes are largely sensitive to the inverter
inner loop controllers, network dynamics, and load dynamics.
Results obtained from the model were verified
experimentally on a prototype microgrid. It was observed that the model
successfully predicts the complete microgrid dynamics both in the low and high
frequency range.
Small signal modeling has had a long history of use
in conventional power systems. The inverter models (and the inclusion of
network dynamics) illustrated in this paper allow microgrids to be designed to
achieve the stability margin required of reliable power systems.
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