# Static Synchronous Compensator (Phasor Type)

Implement phasor model of three-phase static synchronous compensator

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• Simscape / Electrical / Specialized Power Systems / FACTS / Power-Electronics Based FACTS

## Description

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 1V 2 cos δ ) / X

where:

SymbolMeaning
V1 Line to line voltage of source 1
V2 Line to line voltage of source 2
X Reactance of interconnection transformer and filters
δ Phase angle of V1 with respect to V2

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 1V 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.

### STATCOM V-I Characteristic

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

### Differences Between STATCOM and SVC

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).

## Ports

### Input

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Trip signal to disable the STATCOM, specified as a logical. When this input is high, the STATCOM is disconnected and its control system is disabled. Use this input to implement a simplified version of the protection system.

Simulink® input of the external reference voltage signal.

#### Dependencies

To enable this port, on the Controller tab, select External.

### Output

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Measurements, returned as a 16-element vector of STATCOM internal signals. These signals are either voltage and current phasors (complex signals) or control signals. They can be individually accessed by using the Bus Selector block. They are, in order:

Signal

Signal Group

Signal Names

Definition

1-3

Power Vabc (cmplx)

Va_prim (pu) Vb_prim (pu)
Vc_prim (pu)

Phasor voltages (phase to ground) Va, Vb, and Vc at the STATCOM primary terminals (pu)

4-6

Power Iabc (cmplx)

Ia_prim (pu)
Ib_prim (pu) Ic_prim (pu)

Phasor currents Ia, Ib, and Ic flowing into the STATCOM (pu)

7

Power

Vdc (V)

DC voltage (V)

8

Control

Vm (pu)

Positive-sequence value of the measured voltage (pu)

9

Control

Vref (pu)

Reference voltage (pu)

10

Control

Qm (pu)

STATCOM reactive power. A positive value indicates inductive operation.

11

Control

Qref (pu)

Reference reactive power (pu)

12

Control

Id (pu)

Direct-axis component of current (active current) flowing into STATCOM (pu). A positive value indicates active power flowing into STATCOM.

13

Control

Iq (pu)

Quadrature-axis component of current (reactive current) flowing into STATCOM (pu). A positive value indicates capacitive operation.

14

Control

Idref (pu)

Reference value of direct-axis component of current flowing into STATCOM (pu)

15

Control

Iqref (pu)

Reference value of quadrature-axis component of current flowing into STATCOM (pu)

16

Control

modindex

The modulation index, m, of the PWM modulator. A positive number such that 0<m<1. m=1 corresponds to the maximum voltage V2 that can be generated by the VSC without overmodulation.

### Conserving

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Specialized electrical conserving port associated with the electrical terminal of phase A.

Specialized electrical conserving port associated with the electrical terminal of phase B.

Specialized electrical conserving port associated with the electrical terminal of phase C.

## Parameters

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### Power

The nominal line-to-line voltage in Vrms and the nominal system frequency in hertz.

The nominal power of the converter in VA.

The positive-sequence resistance and inductance of the converter, in pu, based on the nominal power and voltage ratings. R and L represent the resistance and leakage inductance of the coupling transformer and the resistance and inductance of the series filtering inductors connected at the VSC output.

The initial value of the positive-sequence current phasor (with the magnitude in pu and phase in degrees). If you know the initial value of the current corresponding to the STATCOM operating point, you can specify it to start simulation in steady state. If you don't know this value, you can leave [0 0]. The system will reach steady-state after a short transient.

The nominal voltage of the DC link in volts.

The total capacitance of the DC link in farads. This capacitance value is related to the STATCOM rating and to the DC link nominal voltage. The energy stored in the capacitance (in joules) divided by the STATCOM rating (in VA) is a time duration that is usually a fraction of a cycle at nominal frequency. For example, for the default parameters, (where C=375 µF, Vdc=40 000 V, and Snom=100 MVA) this ratio, $\left(C\cdot {V}_{\text{dc}}^{2}/2\right)/{S}_{\text{nom}}$, is 3.0 ms, which represents 0.18 cycle for a 60 Hz frequency. If you change the default values of the nominal power rating and DC voltage, you should change the capacitance value accordingly.

### Controller

Specifies the STATCOM mode of operation.

Reference voltage, in pu, used by the voltage regulator.

#### Dependencies

To enable this parameter, set Mode to `Voltage regulation` and clear the External check box.

When External is selected, a Simulink input port named Vref appears on the block, allowing you to control the reference voltage from an external signal (in pu). The Reference voltage Vref parameter is therefore disabled.

Maximum rate of change of the reference voltage, in pu/s, when an external reference voltage is used.

#### Dependencies

To enable this parameter, set Mode to `Voltage regulation`.

Droop reactance, in pu, which defines the slope of the V-I characteristic.

#### Dependencies

To enable this parameter, set Mode to `Voltage regulation`.

Gains of the AC voltage PI regulator. Specify the proportional gain Kp, which is calculated by (pu of I)/(pu of V). Specify the integral gain, Ki, which is calculated as (pu of I)/(pu of V)/s, where V is the AC voltage error and I is the output of the voltage regulator.

#### Dependencies

To enable this parameter, set Mode to `Voltage regulation`.

Reference reactive power, in pu, when the STATCOM is in `Var Control` mode.

#### Dependencies

To enable this parameter, set Mode to `Var Control`.

Maximum rate of change of the reference reactive power, in pu/s.

#### Dependencies

To enable this parameter, set Mode to `Var Control`.

Gains of the DC voltage PI regulator, which controls the voltage across the DC bus capacitor. Specify the proportional gain, Kp, which is calculated by (pu of I)/Vdc. The integral gain, Ki, is calculated as (pu of I)/Vdc/s, where Vdc is the DC voltage error and I is the output of the voltage regulator.

Gains of the inner current regulation loop. Specify the proportional gain, Kp, which is calculated as (pu of V)/(pu of I). The integral gain, Ki, is calculated as (pu of V)/(pu of I)/s. The feed forward gain, Kf, is calculated as (pu of V)/(pu of I), where V is the output V2d or V2q of the current regulator and I is the Id or Iq current error.

For optimal performance, the feed forward gain should be set to the converter reactance (in pu) given by parameter L in the Converter impedance [R(pu),L(pu)] parameter.

## References

[1] N. G. Hingorani, L. Gyugyi, “Understanding FACTS; Concepts and Technology of Flexible AC Transmission Systems,” IEEE® Press book , 2000.