Unified Power Flow Controller (UPFC) device is applied to control power flow in transmission lines. Supplementary damping controller can be installed on any control channel of the UPFC inputs to implement the task of Power Oscillation Damping (POD) controller. In this paper, we have presented the simultaneous coordinated design of the multiple damping controllers between Power System Stabilizer (PSS) and UPFC-based POD or between different multiple UPFC-based POD controllers without PSS in a single-machine infinite-bus power system in order to identify the design that provided the most effective damping performance. The parameters of the damping controllers are optimized utilizing a Chaotic Particle Swarm Optimization (CPSO) algorithm based on eigenvalue objective function. The simulation results show that the coordinated design of the multiple damping controllers has high ability in damping oscillations compared to the individual damping controllers. Furthermore, the coordinated design of UPFC-based POD controllers demonstrates the superiority over the coordinated design of PSS and UPFC-based POD controllers for enhancing greatly the stability of the power system.
When large power systems are interconnected through weak tie lines, Low Frequency Oscillations (LFO) in the range of 0.1–3 Hz are observed. These oscillations may sustain and grow to cause system separation if no adequate damping is available [
The installation of a Power System Stabilizer (PSS) appears as a simple and inexpensive technique for many years to produce an amount of damping torque through the injection of a supplementary stabilizing signal at a voltage reference input of an Automatic Voltage Regulator (AVR), which has increased the stability of the power system. However, their performance deteriorated when the system operating conditions varied widely [
Unified Power Flow Controller (UPFC) is one of the most important FACTS device families. Its primary function is to control and optimize the real and reactive power flow in a given line, voltage, and current at the UPFC bus [
To improve general power system performance, possible interactions between PSSs and FACTS-damping controllers are considered, but uncoordinated local design of PSS and FACT-damping controller may cause destabilizing interaction on the damping of system oscillations [
Several researches have been carried out for the coordination between PSSs and FACTS damping controllers. Some of these researches were depending on the complex nonlinear simulation while the others based on the linearized model for power system [
Recently, Particle Swarm Optimization (PSO) technique has appeared as a useful tool for engineering global optimization. PSO is a population-based stochastic optimization method, which employs the swarm intelligence produced by the cooperation and rivalry between the particles in a swarm. PSO is unlike the other evolutionary algorithms having many advantages. The major advantages are as follows: it is fast and simple, does need to apply operators such as GA algorithm, and is easy to be implemented [
In this paper, we present the results of our comprehensive comparison and assessment of the damping function of multiple damping stabilizers using different coordinated designs in order to identify the design that provided the most effective damping performance. The two alternative designs we evaluated are listed below: coordinated design between PSS and any one out of the four input control channels of the series and shunt structure of UPFC device because any control loop can superimpose a supplementary damping controller to implement the required damping, coordinated design between any two out of the four input control channels of the series and shunt structure of UPFC device as a multiple damping controller without using PSS.
The parameters of the damping controllers for individual and coordinated design are optimized utilizing CPSO technique based on eigenvalue objective function. The simulation results of the individual damping controllers show the best damping effects resulting from using the POD controllers
Figure
SMIB power system equipped with UPFC.
The structure of the UPFC controller is shown in Figure
UPFC with damping controller.
UFPC with dc voltage regulator and damping controller.
Referring to Figure
By applying Park’s transformation and ignoring the resistance and transient of the UPFC transformers, equations (
The nonlinear dynamic equations of the SMIB system shown in Figure
The excitation system is represented by a first-order model (IEEE type—ST1) [
The output power of the generator can be expressed in terms of the
Linear dynamic model of the power system is obtained by linearizing the nonlinear equations (
Referring to Figure
In addition, from Figure
Equation (
The structure of the matrices
The modified Phillips-Heffron transfer function model including UPFC has 28 constants; on the other hand, the Phillips-Heffron model has only 6 constants as shown in Figure
Modified Phillips-Heffron transfer function model of SMIB system with UPFC.
For nominal operating condition, the dynamic behavior of the system is recognized through the eigenvalues of the system matrix
It is clearly seen from eigenvalues of the matrix
In order to overcome the LFO problem, supplemental control action is applied to the generator excitation in the form of PSS or UPFC device as POD controller. The four main control parameters of the UPFC (
The POD controller has a structure similar to that of the PSS. Figure
Structure of the supplementary damping stabilizers (PSS or POD).
The main objective of optimization technique is to improve the dynamic stability of the power system against disturbances at different loading conditions. It can be achieved by suitable tuning of damping controller parameters.
The supplementary damping stabilizer (lead-lag type) can be described mathematically as
The goal of optimization process is to maximize
Typical ranges of the optimized parameters are 0.01–100 for
The problem of tuning the parameters for individual and coordinated design for multiple damping controllers, which would ensure maximum damping performance, was solved via a PSO optimization procedure that appeared to be a promising evolutionary technique for handling optimization problems. PSO is a population-based, stochastic-optimization technique that was inspired by the social behavior of flocks of birds and schools of fish [
The advantages of PSO algorithm are that it is simple and easy to implement and it has a flexible and well-balanced mechanism to enhance the local and global exploration capabilities. Recently, it has acquired wide range of applications in solving optimization design problems featuring nonlinearity, nondifferentiability, and high dimensionality in many area search spaces [
In the PSO, each possible solution is represented as a particle, and each set of particles comprises a population. Each particle keeps its position in hyperspace, which is related to the fittest solution it ever experiences in a special memory called
PSO algorithm for the tuning parameters of an individual and coordinated design.
The main disadvantage of the simple PSO algorithm is that the performance of it greatly depends on its parameters and it is not guaranteed to be global convergent. In order to improve the global searching ability and prevent a slide into the premature convergence to local minima, PSO and chaotic sequence techniques are combined to form a chaotic particle swarm optimization (CPSO) technique, which practically combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. The logistic equation employed for constructing hybrid PSO is described as [
To improve the global searching capability of PSO, we have to introduce a new velocity update equation as follows:
We have observed that the proposed new weight decreases and oscillates simultaneously for total iteration, whereas the conventional weight decreases monotonously from
In this section, the ability of UPFC in damping system oscillation and the dynamic interactions of UPFC-POD controllers are investigated intensively. The CPSO technique has been applied to design individual and coordinated damping controllers. To evaluate the performance of the proposed simultaneous coordinated design approaches, the responses with the proposed controllers were compared with the responses of the individual design of the PSS and UPFC-POD controllers for two schemes. The resultant optimal parameters of the individual controllers and coordinated designs are given in Tables
The optimal parameters of the individual controllers.
Individual controllers | Type of algorithm | Optimal values | ||
---|---|---|---|---|
|
|
|
||
|
CPSO | 38.8433 | 0.2490 | 0.2490 |
PSO | 12.2151 | 0.8227 | 0.8227 | |
|
CPSO | 26.1560 | 0.8812 | 0.0015 |
PSO | 31.5718 | 0.3635 | 0.0344 | |
|
CPSO | 11.5577 | 0.1960 | 0.0331 |
PSO | 12.1740 | 0.2143 | 0.0028 | |
|
CPSO | 66.2928 | 0.0011 | 0.2369 |
PSO | 75.4243 | 0.0998 | 0.3171 | |
|
CPSO | 99.6244 | 0.7206 | 0.0017 |
PSO | 25.4779 | 0.0307 | 0.5386 |
The optimal parameters of the coordinated designs between PSS and UPFC-POD controllers.
Coordinated designs | Type of algorithm | Optimal values | |||||
---|---|---|---|---|---|---|---|
|
|
|
|
|
|
||
|
CPSO | 45.5204 | 0.0418 | 0.2659 | 38.3455 | 0.0316 | 0.6943 |
PSO | 44.0127 | 0.2628 | 0.0613 | 52.8507 | 0.5057 | 0.0072 | |
|
CPSO | 8.1683 | 0.2501 | 0.1518 | 10.0208 | 0.1993 | 0.0361 |
PSO | 5.2118 | 0.7275 | 0.0301 | 10.9942 | 0.1579 | 0.0284 | |
|
CPSO | 57.2645 | 0.1963 | 0.1756 | 54.6790 | 0.1057 | 0.2037 |
PSO | 61.6657 | 0.2949 | 0.4783 | 59.6813 | 0.3536 | 0.0816 | |
|
CPSO | 63.0262 | 0.2377 | 0.2371 | 3.9384 | 0.7395 | 0.9415 |
PSO | 15.2002 | 0.9788 | 0.0074 | 0.3729 | 0.5007 | 0.5611 |
The optimal parameters of the coordinated designs between different UPFC-POD controllers.
Coordinated designs | Type of algorithm | Optimal values | |||||
---|---|---|---|---|---|---|---|
|
|
|
|
|
|
||
|
CPSO | 50.7479 | 0.6966 | 0.0656 | 8.0139 | 0.0513 | 0.0530 |
PSO | 57.7561 | 0.4707 | 0.0895 | 7.9823 | 0.0460 | 0.0136 | |
|
CPSO | 97.9661 | 0.0014 | 0.0019 | 69.2724 | 0.0022 | 0.1816 |
PSO | 68.0064 | 0.2596 | 0.0413 | 42.4356 | 0.2982 | 0.0070 | |
|
CPSO | 26.1813 | 0.0081 | 0.8276 | 2.3838 | 0.6509 | 0.4527 |
PSO | 41.5012 | 0.9941 | 0.0023 | 0.1583 | 0.8581 | 0.0941 | |
|
CPSO | 89.0042 | 0.0735 | 0.0087 | 63.4526 | 0.0490 | 0.2352 |
PSO | 4.7214 | 1.0000 | 0.6398 | 11.4511 | 0.1435 | 0.7305 | |
|
CPSO | 99.9911 | 0.2171 | 0.0407 | 81.5964 | 0.0005 | 0.0063 |
PSO | 17.2632 | 0.1916 | 0.8990 | 87.1383 | 0.1447 | 0.0056 | |
|
CPSO | 57.8685 | 0.0530 | 0.2428 | 10.5448 | 0.0462 | 0.0788 |
PSO | 65.7520 | 0.1876 | 0.0403 | 10.7924 | 0.0619 | 0.0561 |
Figures
System eigenvalues of the individual controllers.
|
|
|
|
|
---|---|---|---|---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
19.17 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
System eigenvalues of the coordinated designs between PSS and UPFC-POD controllers.
|
|
|
|
---|---|---|---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Speed variation responses for individual damping controllers (PSS,
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Figure
Figures
In this scheme, the power system is considered to possess a UPFC device without PSS. Figures
System eigenvalues of the coordinated designs between different UPFC-POD controllers.
|
|
|
|
|
|
---|---|---|---|---|---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
Speed variation responses for individual damping controllers
From Figures
This paper is concerned with the damping of LFO via PSS and UPFC-POD controllers applied independently and also through the simultaneous coordinated designs in a SMIB power system. To improve the global searching ability and prevent a slide into the premature convergence to local minima, PSO and chaos theory are combined to form a CPSO. For the proposed controller design problem, a CPSO algorithm was used as the optimization technique to search for the optimal damping controller parameters in both the individual and the coordinated designs. The simulation results of the individual damping controllers showed the best damping effects resulting from using
Power system parameters (resistance and reactance are in p.u. and time constants are in second): Generator: Excitation: Transmission line: UPFC transformers: Operating condition: UPFC: DC link parameter: DC voltage regulator: