*3.1.2. Dynamic device models*


Induction motor and SVC modeling will be discussed further in this section. In addition to all the system/device data, other system data include convergence parameters such as threshold and maximum iteration counts for static power flow studies, and also various other solution parameters used for the dynamic time domain simulation.

### *3.1.2.1. Induction motor modeling*

As mentioned earlier large induction motor loads generally affect the voltage recovery process after voltage sag has been incepted due to system faults, and in many occasions due to extended voltage sag secondary effects such as stalling or tripping of sensitive motors might happen leading to massive load disruption. So, it is very vital to represent large, small and trip induction motor loads in various combinations in the system, so that we capture the stalling phenomenon of induction motor load, the real and reactive power requirements in the stalled state, and the tripping caused by thermal protection.

The induction motor load must be modeled such that it is sensitive to dynamic variations in voltage and frequency, and emulates the typical characteristic of consuming more power at increased speeds. Equation (1) shows the modeling of mechanical torque (*Tload*) as a function of speed deviation from nominal and motor load torque at synchronous speed (*Tnom*).

$$T\_{load} = T\_{nom} (1 + \Delta o)^D \tag{1}$$

Role of Induction Motors in Voltage Instability and Coordinated Reactive Power Planning 163

*B*svc

*B*

In the study done in this chapter we employ SVC as an effective means to mitigate transient voltage dip problem by providing fast responding dynamic reactive power support. The SVC is modeled as shown in the figure 3, with a non-windup limit *Bsvc* (in MVAR) on the SVC output, which constrains the SVC output B. At its limit, SVC output is non-controllable and functions as a shunt capacitor. Hence, the ability of an SVC to provide dynamic support for mitigating the transient voltage dip problems depends on the SVC's capacitive limit (size) Bsvc, which also increases the SVC cost. The RPP finds the optimum rating of SVC that

0

Some of the main parameters include voltage limits *VMAX* and *VMIN* to specify the active range of the voltage control, a time constant (of about 0.05 sec. or less) to model the delay in reactor's response, a steady-state voltage control gain K of about 100, and the time constant

Once the voltage stability base case is ready, next system analysis has to be performed to check the severity of the contingencies that need planning. So the next vital step in the

In order to effectively plan against steady state and dynamic voltage stability problems under a certain set of contingencies, we need to identify proper performance criteria. Voltage stability of the power system should be assessed based on voltage security criteria

As far as the steady state performance criteria are concerned, there are many criteria such as reactive reserve in different parts of the system, post-contingency voltage, Eigenvalues, etc. that enable to quantify the severity of a contingency with respect to voltage stability. In this work we utilize the most basic and widely accepted criteria, namely, post-contingency voltage stability margin [21, 22] for steady state performance assessments. Voltage stability margin, a steady state performance criterion, is defined as the amount of additional load in a specific pattern of load increase that would cause voltage instability. Contingencies such as

**3.2. Post-contingency performance criteria for voltage stability assessment** 

K s

ܭ ܶݏͳ

*3.1.2.2. Static VAR compensator modeling* 

is economical and enhances system reliability.

*V*ref

T of about 0.01 to provide transient gain reduction in the control loop.

planning procedure is voltage stability assessment of contingencies.

<sup>+</sup> \_ <sup>∑</sup>

*V*

**Figure 3.** Static VAR compensator model

of interest to, and accepted by, the utility.

Some of the primary model parameters include stator and rotor resistances and inductances, mutual inductance, saturation components, MVA base, intertia (H), per unit voltage level below which the relay to trip the motor will begin timing (*VT*), time in cycles for which the voltage must remain below the threshold for the relay to trip (*CT*), breaker delay time in cycles, nominal torque (*Tnom*), load damping factor (*D*) etc.

There are new composite load models developed by WECC LMTF [19] that improves the representation of induction motor load dynamics, and thereby more closely captures the critical role played by such loads in delayed voltage recovery events. These composite loads are represented by CMLD models in PSS/E and CMPLDW models in PSLF [20].

### *3.1.2.2. Static VAR compensator modeling*

162 Induction Motors – Modelling and Control

*3.1.2. Dynamic device models* 

used in most cases.

SVC etc. are also required.

*3.1.2.1. Induction motor modeling* 

1. **Machine** mechanical dynamic equation (swing with damping) and machine electrical dynamic equations; machine mechanical parameters such as inertia constant and damping co-efficient and machine electrical parameters such as transient/sub-transient reactances and time constants etc are required. Saturation model data is also very vital. 2. **Excitation systems** of various types; the data for each model available in standard power system stability analysis programs such as EPRI's ETMSP, PTI's PSS/E etc are

3. **Governor systems** of various types; Again the necessary data for each model are

5. Models for selected prime mover, power system stabilizers, and control devices such as

Induction motor and SVC modeling will be discussed further in this section. In addition to all the system/device data, other system data include convergence parameters such as threshold and maximum iteration counts for static power flow studies, and also various

As mentioned earlier large induction motor loads generally affect the voltage recovery process after voltage sag has been incepted due to system faults, and in many occasions due to extended voltage sag secondary effects such as stalling or tripping of sensitive motors might happen leading to massive load disruption. So, it is very vital to represent large, small and trip induction motor loads in various combinations in the system, so that we capture the stalling phenomenon of induction motor load, the real and reactive power requirements in

The induction motor load must be modeled such that it is sensitive to dynamic variations in voltage and frequency, and emulates the typical characteristic of consuming more power at increased speeds. Equation (1) shows the modeling of mechanical torque (*Tload*) as a function

(1 )*<sup>D</sup>*

(1)

of speed deviation from nominal and motor load torque at synchronous speed (*Tnom*).

*load nom T T*

Some of the primary model parameters include stator and rotor resistances and inductances, mutual inductance, saturation components, MVA base, intertia (H), per unit voltage level below which the relay to trip the motor will begin timing (*VT*), time in cycles for which the voltage must remain below the threshold for the relay to trip (*CT*), breaker delay time in

There are new composite load models developed by WECC LMTF [19] that improves the representation of induction motor load dynamics, and thereby more closely captures the critical role played by such loads in delayed voltage recovery events. These composite loads

are represented by CMLD models in PSS/E and CMPLDW models in PSLF [20].

usually available in standard power system stability analysis programs.

4. **Load modeling** is very vital for performing a voltage stability study.

other solution parameters used for the dynamic time domain simulation.

the stalled state, and the tripping caused by thermal protection.

cycles, nominal torque (*Tnom*), load damping factor (*D*) etc.

In the study done in this chapter we employ SVC as an effective means to mitigate transient voltage dip problem by providing fast responding dynamic reactive power support. The SVC is modeled as shown in the figure 3, with a non-windup limit *Bsvc* (in MVAR) on the SVC output, which constrains the SVC output B. At its limit, SVC output is non-controllable and functions as a shunt capacitor. Hence, the ability of an SVC to provide dynamic support for mitigating the transient voltage dip problems depends on the SVC's capacitive limit (size) Bsvc, which also increases the SVC cost. The RPP finds the optimum rating of SVC that is economical and enhances system reliability.

**Figure 3.** Static VAR compensator model

Some of the main parameters include voltage limits *VMAX* and *VMIN* to specify the active range of the voltage control, a time constant (of about 0.05 sec. or less) to model the delay in reactor's response, a steady-state voltage control gain K of about 100, and the time constant T of about 0.01 to provide transient gain reduction in the control loop.

Once the voltage stability base case is ready, next system analysis has to be performed to check the severity of the contingencies that need planning. So the next vital step in the planning procedure is voltage stability assessment of contingencies.
