FACTS Implementation

1. Equivalent Converter Branch

Generally speaking, when considering of load flow model, a FACTS device can be treated as electric circuit constructed by power electronic-controlled active branches and ancillary elements. In principle, each converter can be treated as a controlled voltage source in series with fixed impedance, as shown in Figure 1.

Figure 1. Equivalent Converter branch

The topology of the entire equivalent circuit depends on the configuration of the FACTS device as well as the function and related physical constraints, which will be discussed in detail in the following sections. Please notice that the controlled voltage is a complex value, meaning that there are two controllable variables (real part/imaginary part or magnitude/phase angle). However, there is ususally an additional constraint to counteract one of the two freedoms. For example, a SVC/STATOM can only generate reactive power, which means that the real part of the converter branch power flow should always be zero. Thus each equivalent converter branch has one degree of freedom for control via tuning the controlled voltage source. From the point of view of the FACTS device, the load flow calculation is to find out the exact value of the controlled voltage to simulate the external characteristic of the device.

2. External Characteristic of a FACTS device

The external characteristic of a FACTS device can usually be written into a set of equations and inequalities.

2.1. Control Objectives

As mentioned before, the control objectives are described by a set of equations, the number of equations equals to the number of converters inside the FACTS device. For example, a STATCOM can behave as a PV bus with zero active power generation, a constant reactive power injection, or a constant shunt reactance, each of the three objectives can be written into an equation.

2.2. Constraints

Those related inequalities are all called constraints of the certain FACTS devices. In general, the inequality constraints can be described on the voltage-current characteristic. For example, the inequality constraints of a typical SVC can be found from Figure 2.

Figure 2. Voltage-current characteristic of SVC

In Figure 2, line sections AC and BD correspond to the maximum inductive and capacitive reactance the SVC device can retrieve, thus the constraints are inequalities.

However, not all the constraints are inequalities. In fact, when the FACTS device is operated under normal conditions (for example, line section AB in Figure 2), it always corresponds to an equation. For instance, since AB always intersects with the V axis at 1.0 p.u., the equation of straight line can be defined whenever the slope of AB is known. Furthermore, some intrinsic behaviors can also be written into equations, such as the zero active power constraint of a SVC.

For a FACTS model in load flow calculations, one of the most important tasks is to define all of the equations and inequalities related to the certain FACTS model. In fact, those equations and inequalities form exactly the external characteristic of the FACTS device in load flow.

3. Violation of Inequality Constraints

In general load flow algorithm, buses are usually separated into three groups: (1) PQ bus, (2) PV bus and (3) swing bus. Those buses behave well under normal conditions. However, type conversions are required when inequality constraints of some buses are violated under some critical conditions. The possible inequality constraints might be

for PV buses, or

for important PQ buses. Under those critical conditions, for example, when the load flow solution requires the reactive power output of a generator to exceed its maximum limit, the original PV bus should be converted into a PQ bus, since the reactive power output can only be fixed at the maximum limit of the generator, thus both P and Q are known for the load flow calculations.

Things are similar for FACTS load flow models. An example can be shown from the SVC model in Figure 2. The operation point of a normal SVC usually locates on AB, and then the behavior of the SVC is determined by its control objective, as discussed in section 1.2.1.. However, if the operation point reaches the two terminals of AB, model conversion is required to convert the SVC into a constant reactance. It might be more complex for multiple-converter FACTS devices, but the idea should be the same.

Type conversion of typical buses is popular for traditional power flow algorithms. It should be reasonably generalized to be suitable for power flow calculations with FACTS models.

4. General FACTS model in InterPSS

Since InterPSS is inherently object-oriented, it is easy to incorporate FACTS models via object-oriented modeling. A typical UML model of an abstract FACTS device is shown in Figure 3.

(TODO)

Figure 3. UML model of an abstract FACTS device

4.2. Functions

a) Control objectives, which can be defined by an enumeration class.

b) Constraints, including both inequality constraints and equation constraints (intrinsic constraints and operation constraints).

4.3. Incorporation of FACTS model with load flow algorithm

Each converter will be modelled by two additional equations, accompanied with two additional rows and two additional columns of the Jacobian matrix. The remain part of the system model will not be changed.

The shadowed parts of the augmented modification linear equation are related with normal load flow equations.

Any type of FACTS device should be inherited from this abstract FACTS model.