Implement phasor model of three-phase static synchronous compensator
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The Static Synchronous Compensator (Phasor Type) block models a static synchronous compensator (STATCOM) shunt device of the Flexible AC Transmission Systems (FACTS) family using power electronics to control power flow and improve transient stability on power grids [1]. The STATCOM regulates voltage at its terminal by controlling the amount of reactive power injected into or absorbed from the power system. When system voltage is low, the STATCOM generates reactive power (STATCOM capacitive). When system voltage is high, it absorbs reactive power (STATCOM inductive).
The variation of reactive power is performed by means of a Voltage-Sourced Converter (VSC) connected on the secondary side of a coupling transformer. The VSC uses forced-commutated power electronic devices (GTOs, IGBTs, or IGCTs) to synthesize a voltage, V2, from a DC voltage source. The principle of operation of the STATCOM is explained on the figure below, which shows the active and reactive power transfer between sources V1 and V2. In this figure, V1 represents the system voltage to be controlled and V2 is the voltage generated by the VSC.
Operating Principle of the STATCOM
This model is represented by the equation:
P = ( V _{1} V _{2} )sin δ / X , Q = V _{1} ( V _{1} – V _{2} cos δ ) / X
where:
Symbol | Meaning |
---|---|
V_{1} | Line to line voltage of source 1 |
V_{2} | Line to line voltage of source 2 |
X | Reactance of interconnection transformer and filters |
δ | Phase angle of V_{1} with respect to V_{2} |
In steady state operation, the voltage, V2, which is generated by the VSC, is in phase with V1 (δ=0), so that only reactive power is flowing (P=0). If V2 is lower than V1, Q is flowing from V1 to V2 (STATCOM is absorbing reactive power). On the reverse, if V2 is higher than V1, Q is flowing from V2 to V1 (STATCOM is generating reactive power). The amount of reactive power is given by:
Q = ( V _{1} ( V _{1} – V _{2} )) / X .
A capacitor connected on the DC side of the VSC acts as a DC voltage source. In steady state, the voltage V2 has to be phase shifted slightly behind V1 in order to compensate for transformer and VSC losses and to keep the capacitor charged. Two VSC technologies can be used for the VSC:
VSC using GTO-based square-wave inverters and special interconnection transformers. Typically four three-level inverters are used to build a 48-step voltage waveform. Special interconnection transformers are used to neutralize harmonics contained in the square waves generated by individual inverters. In this type of VSC, the fundamental component of voltage V2 is proportional to the voltage Vdc. Therefore, Vdc has to be varied to control the reactive power.
VSC using IGBT-based PWM inverters. This type of inverter uses a Pulse-Width Modulation (PWM) technique to synthesize a sinusoidal waveform from a DC voltage source with a typical chopping frequency of a few kilohertz. Harmonic voltages are cancelled by connecting filters at the AC side of the VSC. This type of VSC uses a fixed DC voltage Vdc. The voltage V2 is varied by changing the modulation index of the PWM modulator.
The Static Synchronous Compensator (Phasor Type) block models an IGBT-based
STATCOM (fixed DC voltage). However, as details of the inverter and harmonics are not
represented, it can be also used to model a GTO-based STATCOM in transient stability
studies. A detailed model of a GTO-based STATCOM is found in the
power_statcom_gto48p
example.
The figure below shows a single-line diagram of the STATCOM and a simplified block diagram of its control system.
Single-line Diagram of a STATCOM and Its Control System Block Diagram
The control system consists of:
A phase-locked loop (PLL) that synchronizes on the positive-sequence component of the three-phase primary voltage, V1. The output of the PLL (angle Θ=ωt) is used to compute the direct-axis and quadrature-axis components of the AC three-phase voltage and currents (labeled as Vd, Vq or Id, and Iq on the diagram).
Measurement systems measuring the d and q components of the AC positive-sequence voltage, currents to be controlled, and the DC voltage Vdc.
An outer regulation loop consisting of an AC voltage regulator and a DC voltage regulator. The output of the AC voltage regulator is the reference current Iqref for the current regulator, where Iq is the current in quadrature with voltage that controls reactive power flow. The output of the DC voltage regulator is the reference current Idref for the current regulator, where Id is the current in phase with voltage that controls active power flow.
An inner current regulation loop consisting of a current regulator. The current regulator controls the magnitude and phase of the voltage generated by the PWM converter (V2d and V2q) from the Idref and Iqref reference currents produced respectively by the DC voltage regulator and the AC voltage regulator (in voltage control mode). The current regulator is assisted by a feed-forward-type regulator that predicts the V2 voltage output (V2d and V2q) from the V1 measurement (V1d and V1q) and the transformer leakage reactance.
The STACOM block is a phasor model that does not include detailed representations of the
power electronics. You must use it with the phasor simulation method, activated by
setting the Simulation type parameter of a Powergui
block to Phasor
. It can be used in three-phase power systems
together with synchronous generators, motors, dynamic loads, and other FACTS and
Renewable Energy systems to perform transient stability studies and observe impact of
the STATCOM on electromechanical oscillations and transmission capacity at fundamental
frequency.
The STATCOM can be operated in two different modes:
In voltage regulation mode (the voltage is regulated within limits as explained below)
In var control mode (the STATCOM reactive power output is kept constant)
When the STATCOM is operated in voltage regulation mode, it implements the following V-I characteristic:
STATCOM V-I characteristic
As long as the reactive current stays within the minimum and minimum current values (-Imax and Imax) imposed by the converter rating, the voltage is regulated at the reference voltage Vref. However, a voltage droop is normally used (usually between 1% and 4% at maximum reactive power output), and the V-I characteristic has the slope indicated in the figure. In the voltage regulation mode, the V-I characteristic is described by the following equation:
V = V _{ref} + Xs I
where,
V | Positive sequence voltage (pu) |
I | Reactive current (pu/Pnom) (I > 0 indicates an inductive current) |
Xs I | Slope or droop reactance (pu/Pnom) |
Pnom | Three-phase nominal power of the converter specified in the block dialog box |
The STATCOM performs the same function as the SVC. However, at voltages lower than the normal voltage regulation range, the STATCOM can generate more reactive power than the SVC. This is due to the fact that the maximum capacitive power generated by an SVC is proportional to the square of the system voltage (constant susceptance) while the maximum capacitive power generated by a STATCOM decreases linearly with voltage (constant current). This ability to provide more capacitive reactive power during a fault is one important advantage of the STATCOM over the SVC. In addition, the STATCOM normally exhibits a faster response than the SVC because with the VSC, the STATCOM has no delay associated with the thyristor firing (in the order of 4 ms for a SVC).
[1] N. G. Hingorani, L. Gyugyi, “Understanding FACTS; Concepts and Technology of Flexible AC Transmission Systems,” IEEE^{®} Press book , 2000.