Implement phasor model of three-phase static synchronous compensator

FACTS/Power-Electronics Based FACTS

The Static Synchronous Compensator (STATCOM) is a 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 showing the active and reactive power transfer between a source V1 and a source 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**

*P* =
(*V*_{1}*V*_{2})sin*δ*
/ *X *, *Q* =
*V*_{1}(*V*_{1} –
*V*_{2}cos*δ*) /
*X*

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 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 for controlling the reactive power.

VSC using IGBT-based PWM inverters. This type of inverter uses 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. Voltage V2 is varied by changing the modulation index of the PWM modulator.

The STATCOM (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 provided in the FACTS example library (`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) which 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, Iq on the diagram).

Measurement systems measuring the d and q components of AC positive-sequence voltage and currents to be controlled as well as 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 (Iq = current in quadrature with voltage which controls reactive power flow). The output of the DC voltage regulator is the reference current Idref for the current regulator (Id = current in phase with voltage which 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 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 which predicts the V2 voltage output (V2d V2q) from the V1 measurement (V1d V1q) and the transformer leakage reactance.

The STACOM block is a phasor model which does not include detailed representations of the power electronics. You must use it with the phasor simulation method, activated with the Powergui block. 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, 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 | 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 a 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 will 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).

The STATCOM parameters are grouped in two categories: ```
Power
data
```

and `Control parameters`

. Use the **Display** listbox to select which group of parameters
you want to visualize.

**Nominal voltage and frequency**The nominal line-to-line voltage in Vrms and the nominal system frequency in hertz. Default is

`[ 500e3, 60 ]`

.**Converter rating**The nominal power of the converter in VA. Default is

`100e6`

.**Converter impedance**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. Default is

`[ 0.22/30, 0.22 ]`

.**Converter initial current**The initial value of the positive-sequence current phasor (Magnitude in pu and Phase in degrees). If you know the initial value of the current corresponding to the STATCOM operating point you may specify it in order 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. Default is

`[0, 0 ]`

.**DC link nominal voltage**The nominal voltage of the DC link in volts. Default is

`40000`

.**DC link total equivalent capacitance**The total capacitance of the DC link in farads. Default is

`750e-6/2`

. 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 which is usually a fraction of a cycle at nominal frequency. For example, for the default parameters, (C=375 µF, Vdc=40 000 V, 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.

**Mode**Specifies the STATCOM mode of operation. Select either

`Voltage regulation`

(default) or`Var Control`

.**Reference voltage Vref**This parameter is not visible when the

**Mode**parameter is set to`Var Control`

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

`1.00`

.**External**When

**External**is selected, a Simulink^{®}input 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 dimmed. Default is cleared.**Maximum rate of change of reference voltage**This parameter is not visible when the

**Mode**parameter is set to`Var Control`

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

`10`

.**Droop (pu):**This parameter is not visible when the

**Mode**parameter is set to`Var Control`

.Droop reactance, in pu/converter rating Snom, defining the slope of the V-I characteristic. Default is

`0.03`

.**Vac Regulator gains: [Kp Ki]**This parameter is not visible when the

**Mode**parameter is set to`Var Control`

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

`[5, 1000]`

.**Reactive power setpoint Qref**This parameter is not visible when the

**Mode**parameter is set to`Voltage Control`

.Reference reactive power, in pu, when the STATCOM is in

`Var Control`

. Default is`0`

.**Maximum rate of change of reactive power setpoint Qref**This parameter is not visible when the

**Mode**parameter is set to`Voltage Control`

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

`2`

.**Vdc Regulator gains: [Kp Ki]**Gains of the DC voltage PI regulator which controls the voltage across the DC bus capacitor. Specify proportional gain Kp in (pu of I)/Vdc, and integral gain Ki, in (pu of I)/Vdc/s, where Vdc is the DC voltage error and I is the output of the voltage regulator. Default is

`[0.1e-3, 20e-3]`

.**Current Regulators gains: [Kp Ki Kf]**Gains of the inner current regulation loop. Default is

`[0.3, 10, 0.22]`

.Specify proportional gain Kp in (pu of V)/(pu of I), integral gain Ki, in (pu of V)/(pu of I)/s, and feed forward gain Kf in (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**parameters.

`A B C`

The three terminals of the STATCOM.

`Trip`

Apply a Simulink logical signal (0 or 1) to this input. 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.

`Vref`

Simulink input of the external reference voltage signal.

This input is visible only the

**External control of reference voltage Vref**parameter is checked.`m`

Simulink output vector containing 16 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, 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, 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 0<m<1. m=1 corresponds to the maximum voltage V2 which can be generated by the VSC without overmodulation.

See the `power_statcom`

example which illustrates
the steady-state and dynamic performance of a STATCOM regulating voltage
on a 500 kV, 60 Hz, system. The example also compares the performance
of the STACOM with an SVC having the same rating.

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

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