5.2 Problem Formulation for Transient Stability
Figure 5.1: The overall system model of TDS
generator, δk is rotor angle ofkth generator. The deviation between generator rotor angles with reference to timet can be found by using the set of swing Equations 5.1, 5.2 and 5.3.
In the projectile transient phenomena, inertial center of system is taken as reference frame for calculations. The generators’ rotor angles with respect to center of inertia (COI) [269] are used to detect whether the system is stable or not. For a system havingNG-generators with inertia constant Mj and rotor angles δj of jth generator then the inertial center δCOI is determined by Equation 5.4.
δCOI(t) = 1 Mtotal
NG
X
j=1
Mjδj(t) (5.4)
5.2.2 Proposed Transient Stability Assessment
With the wide application of the Phasor Measurement Units (PMU) and Wide Area Measurement System (WAMS) in power system, TSA is possible in real time.
The real time measurements based transient instability detection methods used to employ the post fault power angle trajectories for many decades [263]. The power angle deviation is used as transient stability indicator. If it increases monotonically and cross the predefined threshold value, then power system is transiently unstable.
Figure 5.2: Proposed transient stability assessment model
The frame structure of real time power system TSA model mainly consists of two systems, viz. hardware system and software system as shown in Figure 5.2.
Hardware includes the master server, the visual work station and communication interface as well as control action actuating devices. Software system includes the data acquisition system, the power system monitoring system, the generator rotor angle prediction system, the transient instability identifier system and the preven- tive/emergency control action system.
A numerical integration technique such as Runge-Kutta method can be used to solve swing equation. The T/S status is determined by monitoring the swing in rotor angle trajectories and deviation in rotor angle with respect to the constraint for transient instability is given as Equation 5.5.
∆δj, COI =|δj−δCOI| ≤δmax j = 1,2, . . ., NG (5.5) Hereδmaxis maximum allowable value of relative rotor angle for secure operation.
The PMUs are installed on the high side of generating buses to monitor generator rotor angles [270]. The data are transferred to the central control location every cycle with 1-µs accuracy and is utilized for real-time calculations for this study. During the case of disturbance if relative rotor angle ∆δj, COI violates ∆δj,COI(≥δmax) in a time interval [0, tmax], the system is considered as insecure (1) else is considered
secure (0). For this work maximum allowable value of relative rotor angle for secure operationδmax is taken as 1200 [271–273].
5.2.3 Proposed Transient Stability Index
Rotor angle trajectory of any generator is a replica of transient behavior of that generating unit. Application of PMUs and WAMS makes it possible to determine rotor angle values which can be used to detect the synchronism state of a generating unit in real time. The synchronism status of the generating machines for every inse- cure contingency needs to be discovered with less computational burden and time.
Therefore, the rotor angle trajectory based severity index, called Transient Stability Index (TSI) is proposed in this chapter to assess the severity of any operating con- dition following a disturbance. TSI is determined from TDS and defined for any jth generator as:
T SIj = 1− δmax−∆δj,COI(τ)
|δmax+ ∆δj,COI(τ)| (5.6)
Where, ∆δj,COI(τ) is the final value of rotor angle deviation in degrees at the end of simulation time.
TSI can be used to assess the stability of power system, to rank the criticality and individual stability status of the generators and coherency among generators. Hence, it indicates the synchronizing condition of the system for a given hard contingency.
The numerical value of TSI is an indicator of the unstable or stable system state of the power system respectively.
Generator Stability Status =
(U nstable if T SI ≥1
Stable if T SI <1 (5.7)
5.2.4 Proposed Methodology for Online TSA using ANN
TDS is the well established and accurate method for TSA. It can handle detailed modeling of the system and provides most accurate information of power system variables in post-disturbance scenarios but it is computationally very demanding.
Moreover, the TDS methods requires complete information about all the dynamic
and static variables of power system to predict the security status of a current oper- ating state. Modern power systems are large and complex therefore, it is not possible to keep a track of all minor changes occurring in topology and control variables and therefore TDS methods are not suitable for on-line applications. However, these methods can be used to generate accurate off-line data covering wide range of op- erating scenarios for training ANN. ANN has widely used for the TSA as reported in the literature. The proposed method is used an predictor, which predict the TSI values. These predicted TSI values employed to classifies the operating states of a power system into secure and insecure classes. In this thesis, a more efficient TSA scheme is proposed which determines the on-line transient stability state of the system for probable disturbance through Transient Stability Index (TSI), which is based on the rotor angle deviations using Radial basis function Neural Network (RBFNN). The development of RBFNN topology capable of predicting the post- disturbance severity from pre-contingent data for TSA is proposed in this section.
The method can be used on-line for the unseen operating scenarios when the system is still in secure state and rank the possible contingencies for particular operating conditions in decreasing order of the severity through predicted values of the TSI.
5.2.5 Data Generation
The primary objective of data generation is to obtain all possible operating states of the power system. The off-line database consists of large number of randomly varied load patterns covering wide range of scenarios for credible contingencies.
The selection of critical contingencies depends upon the knowledge of the operator about the probability of their occurrence and severity. The rotor angle values of the generator after fault clearing time i.e. (FCT+0.01s to FCT+0.05s) are considered as input features of the neural network and the values of TSI at the end of the simulation and out of step time are taken as output targets. The steps for generating offline data using TDS for online TSA are as follows:
Step 1 Run Optimal Power Flow (OPF) on the given test system at base case, obtain and set the optimal generation.
Step 2 Set random total load of the system between 95%-105% of the base case.
Step 3 Set pattern I = 1.
Step 4 Randomly vary the real and reactive load of each bus of the system.
Step 5 Create a thre phase fault, perform TDS for given load pattern.
Step 6 Record the rotor angles with respect to COI, δj, COI(t)(g = 1,2, ..., NG) at each time step during simulation.
Step 7 According to theδj, COI(t) TSI is calculated.
Step 8 Isδj, COI(t)>1200orT SI >1, the system for the given operating conditions contingency J is transient unstable (1) otherwise transient stable (0).
Step 9 Is pattern count =max? Yes, go to next step (x) else I = I+ 1 and go to step (iv).
Step 10 All cases simulated? Yes, divided the total patterns into train set and test set for RBFNN otherwise, Increase the total load by 2.5% and go to step 3.