**2. Voltage instability phenomena**

Several theories have been proposed to understand the mechanism of voltage instability. Voltage instability leading to collapse is system instability in that it involves many power system components and their variables at once. There are several system changes that can contribute to voltage collapse [4] such as increase in loading, SVC reaching reactive power limits, action of tap changing transformers (LTCs), load recovery dynamics, line tripping and generator outages. Most of the above mentioned system changes have a large effect on reactive power production or transmission. To discuss voltage collapse some notion of time scales is needed that accounts for fast acting variables in time scales of the order of seconds such as induction motors, SVCs to slow acting variables having long term dynamics in hours such as LTCs, load evolution etc.

## **2.1. Role of induction motors**

158 Induction Motors – Modelling and Control

the conclusions.

**2. Voltage instability phenomena** 

hours such as LTCs, load evolution etc.

control action and have better controllability and repeatability of operation. While MSCs are able to strengthen a power system against long term voltage instability issues [1], transient voltage dip and slow voltage recovery issues (influenced by electric load dynamics) is most effectively addressed by fast responding dynamic VAR sources [10, 11, 12]. While, past methods allocate static and dynamic VAR sources sequentially for one contingency at a time, the key to solving transmission system problems in the most cost-effective way will be to coordinate reactive power requirements simultaneously under many contingencies for both static and dynamic problems. The RPP should therefore identify the right mix of VAR

In this chapter, we present a long term VAR planning algorithm, which coordinates between network investments that most effectively address steady-state voltage instability and those which most effectively address transient voltage recovery problems under severe contingencies. The study takes into account the induction motor dynamic characteristics, which influence the transient voltage recovery phenomenon. The algorithm is applied on a portion of a large scale system consisting of 16173 buses representing the US eastern interconnection. The planning method is a mixed integer programming (MIP) based optimization algorithm that uses sensitivity information of performance measures with

The remaining parts of this chapter are organized as follows. In section 2, we discuss the very important role played by induction motor loads in the voltage stability phenomena. Section 3 sheds focus on the models used to build a base case for voltage stability assessment, and on appropriate performance criteria and solution strategies used in this chapter to devise the proposed coordinated planning. A summary of proposed RPP algorithm that considers both static as well as dynamic reactive resources in a coordinated planning framework, together with the various stages of planning are presented in Section 4. Section 5 illustrates the influence of induction motors on voltage stability phenomenon under severe contingencies, and demonstrates application of the coordinated VAR planning method on a large scale system to effectively avoid induction motor trips. Section 6 presents

Several theories have been proposed to understand the mechanism of voltage instability. Voltage instability leading to collapse is system instability in that it involves many power system components and their variables at once. There are several system changes that can contribute to voltage collapse [4] such as increase in loading, SVC reaching reactive power limits, action of tap changing transformers (LTCs), load recovery dynamics, line tripping and generator outages. Most of the above mentioned system changes have a large effect on reactive power production or transmission. To discuss voltage collapse some notion of time scales is needed that accounts for fast acting variables in time scales of the order of seconds such as induction motors, SVCs to slow acting variables having long term dynamics in

devices, good locations and appropriate capacities for their installation.

respect to reactive devices to plan for multiple contingencies simultaneously.

A major factor contributing to voltage instability is the voltage drop that occurs when active and reactive power flow through inductive reactance of the transmission network; which limits the capability of the transmission network for power transfer and voltage support [13]. The power transfer and voltage support are further limited when some of the generators hit their field or armature current time-overload capability limits. Under such stressed conditions, the driving force for voltage instability is usually the inductive loads that try to recuperate after a disturbance. For instance, in response to a disturbance, power consumed by the induction motor loads tends to be restored by the action of motor slip adjustment, distribution voltage regulators, tap-changing transformers, and thermostats [6]. Restored loads increase the stress on the high voltage network by increasing the reactive power consumption and causing further voltage reduction. A run-down situation causing voltage instability occurs when load dynamics attempt to restore power consumption beyond the capability of the transmission network and the connected generation to provide the required reactive support.

The publication [14] corroborates this voltage instability phenomenon by means of a powervoltage (PV) curve, as shown in Figure 1. For a particular system and loads considered, the normal system can be stable with both resistive and motor loads at points where load curves and system curves intersect. However, when the system becomes stressed, with increased system reactance, it can only have a stable operating point with a resistive load. Due to lack of reactive power support that limits the transfer capability or loadability of the system, there is no intersection of system and load curves for the induction motor load since there is no stable operating point.

**Figure 1.** Stability and Load Characteristics

### **2.2. A typical scenario of slow voltage recovery leading to collapse**

Heavily loaded transmission lines during low voltage conditions can result in operation of protective relays causing some transmission lines to trip in a cascading mode. A common scenario is a large disturbance such as a multi-phase fault near a load center that decelerates induction motor loads. Following fault clearing with transmission outages, motors draw very high current while simultaneously attempting to reaccelerate, as discussed in previous section, thereby making slowing down the voltage recovery process. A typical slow voltage recovery phenomenon following a disturbance is indicated in Figure 2 [15]. While trying to recover, if the voltage drops to a very low point for a sustained duration due to system's inability to provide reactive support, some motors may stall. Such drastic stalling of motor further exacerbates the conditions by increasing the reactive power requirements quickly, and the rate of voltage decline can accelerate catastrophically [6, 7, 16]. Massive loss of load and possibly area instability and voltage collapse may follow.

Role of Induction Motors in Voltage Instability and Coordinated Reactive Power Planning 161

system P-V curve and the sensitivity information derived from the power flow jacobian are used to assess and plan for voltage instability. But the realization that voltage stability is a dynamic phenomenon has led to dynamic formulations of the problem and application of dynamic analysis tools [18] that uses time-domain simulations to solve nonlinear system

A pre-contingency steady state base case is required for the voltage stability study to be performed, which is usually generated from real-time sequence control (State estimator solution), or via an already recorded power flow solution. In the case of a base case for dynamics study, as discussed in previous section, the dynamic phenomenon of voltage stability is largely determined by load characteristics and the available means of voltage control. The response speeds of these loads may be comparable to the speed of response of the dynamic voltage control equipment. So in such studies involving dynamic phenomena, using static models will give forth dubious results. So it is very important to properly model dynamic behavior of such large, small and trip induction motor loads; along with that of relevant voltage controls. Investigating the post-fault dynamic system response and effective planning to prevent a voltage collapse depends on inclusion of relevant system

This section presents the various components and their relevant models that are required to build a suitable base case for comprehensive voltage stability assessment and planning.

1. **Transmission lines** are represented as pi-sections, possibly with unsymmetrical line charging; accompanying data include line pi-section impedances/admittances data; line

2. **Transformers** represented as pi-sections whereby the various impedance/admittance components may be explicit functions of tap settings; three winding transformers must be properly modeled. The data also include transformer limits under normal/emergency cases. **Phase-shifting transformers** are represented by complex tap

3. **Generators** as real-power source together with a reactive power capability curve as a function of terminal voltage; The required generator static data include minimum and maximum ratings, nominal terminal voltage and reactive power capability curve as a

4. **Shunt elements** by their impedance/admittance and Static Var compensators by static

5. **Loads** by ZIP model, i.e., as a combination of constant impedance (Z), constant current (I), and constant real/reactive injection (P) components; The data necessary are default ZIP load partition ratios at nominal voltage, load limits and default power factors

ratios, allowing both shift in angle and change in voltage magnitude;

differential algebraic equations.

component models.

**3.1. System component models** 

function of terminal voltage

gain and maximum/minimum limits

thermal limit both normal and emergency.

*3.1.1. Static device models* 

**Figure 2.** Post-Fault Transient Voltage Characteristics

There are several works [10] that have documented many short-term (few seconds) voltage collapse incidents with loss of load. In all cases, adequate dynamic reactive power support was not available which resulted in a large loss of load.

All the above discussions give a physical sense of how the problem of voltage instability occurs, and shed importance on the requirement of study techniques and good models, especially of induction motor dynamics as they are particularly hazardous from the viewpoint of voltage stability.
