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Design of static synchronous series compensator based damping controller employing invasive weed optimization algorithm
- Ashik Ahmed^{1}Email author,
- Rasheduzzaman Al-Amin^{2} and
- Ruhul Amin^{3}
Received: 29 November 2013
Accepted: 14 July 2014
Published: 30 July 2014
Abstract
This paper proposes designing of Static Synchronous Series Compensator (SSSC) based damping controller to enhance the stability of a Single Machine Infinite Bus (SMIB) system by means of Invasive Weed Optimization (IWO) technique. Conventional PI controller is used as the SSSC damping controller which takes rotor speed deviation as the input. The damping controller parameters are tuned based on time integral of absolute error based cost function using IWO. Performance of IWO based controller is compared to that of Particle Swarm Optimization (PSO) based controller. Time domain based simulation results are presented and performance of the controllers under different loading conditions and fault scenarios is studied in order to illustrate the effectiveness of the IWO based design approach.
Keywords
- Invasive weed optimization
- Static synchronous series compensator
- Single machine infinite bus power system
- Power oscillation damping (POD)
- Integral of time absolute error
Introduction
Power oscillation is a familiar dynamic fact that arises in power system when subjected to disturbance. If adequate damping is not provided, these unwanted oscillations may survive and cause system separation (Kundur 1994). Power system stabilizers (PSS) came into forth with the idea of damping these oscillations by injecting supplementary excitation control signal and increase the stability of the power system. However, PSS were found responsible for causing significant variations in voltage level which may lead to power system instability during the time of three phase faults.
Flexible ac transmission systems (FACTS) utilize power electronic based fast switching devices which can control power flow in the lines and improve stability (Padiyar 2007). FACTS devices are considered as the prominent ones among many effective means to improve operation of power system, increase power transfer capacity etc. Series capacitive compensation method has been employed to remove significant portion of the reactive line impedance and hence improve the amount of transmittable power under dynamic conditions. Static Synchronous Series Compensator is a voltage source converter based FACTS device which is connected in series with the transmission line (Gyugi et al. 1997).
SSSC injects a controllable and almost sinusoidal voltage which remains in series with the transmission network (Hingorani & Gyugi 2000). The injected voltage source imposes virtual reactance in the line which in turn controls the power flow of the transmission line. This control of line power flow is independent of the magnitude of the line current (Hingorani & Gyugi 2000). The ability of SSSC to operate in both inductive and capacitive mode makes it very efficient in controlling the power flow in the system. In either case the injected voltage remains in quadrature with the line current and therefore acts as capacitive or inductive reactance in series with the transmission line. Besides controlling line power flow, SSSC offers good response time with perfectly smooth transition from (+ve) positive to (−ve) negative power through zero voltage injection. Unlike other series compensating devices, SSSC does not run the risk of getting into classical resonance issues at fundamental frequency operation because of the fact that for every practical scenarios line inductance (L) is essentially regulated by injected compensating voltage produced (Acha et al. 2004). Aside from controlling the power flow of the line, SSSC can be utilized as a Power Oscillation damping (POD) device through modulation of series reactive power compensation (Zhang et al. 2006). The energy storage ability of SSSC can enhance the effectiveness of POD by absorbing or injecting real power into the transmission line.
The attractive features and effectiveness of SSSC has made its use widespread in very short period. The SSSC based damping controller design has been handled differently in recent literatures. Time optimal control theory has been employed to design a SSSC based damping controller in (Pandey & Singh 2008). A simplified two area system is considered and the linearized power system model is used. The drawback of this work is that the solution of the Riccati equation is time consuming and large matrix manipulations are required to obtain the desired result. Three different operating modes of SSSC are identified in (David & Venkataramanan 2007) and the controller design problem is handled by frequency domain based loop shaping technique. The results presented shows that the response time taken by the proposed controllers is quite large. Tuning of the SSSC damping controller is performed by real coded genetic algorithm (RCGA) in (Swain et al. 2011). An integral time absolute error based objective function is selected and deviation in the rotor speed from the synchronous speed is referred as the error. Like genetic algorithm, RCGA, too, has a tendency to get stuck at a local minimum of the solution space. A differential evolution (DE) based approach is proposed in (Swain et al. 2013). Built-in Simulink blocks are used for the analysis which may not allow much freedom for the user to work with. No information is provided regarding the convergence scenario of the proposed algorithm which is one of the major criteria to evaluate an optimization algorithm. Similar drawbacks are observed in (Swain et al. 2012). Adaptive Neuro-fuzzy inference system (ANFIS) is employed to design the damping controller of SSSC in a multi-machine power system network (Murali & Rajaram 2010). The deviation in line power is taken as the error signal for the controller and the output is the SSSC injected voltage magnitude. Self- tuning PID controller is utilized in (Therattil & Panda 2011) to damp out electromechanical oscillations. The responses show that it takes around 5 seconds to completely suppress the oscillations. Nonlinear adaptive control technique is proposed for the SSSC damping controller design (Gu et al. 2010). Like any adaptive control algorithm, it takes a healthy computation time to get the required control effort. Design of SSSC damping controller is modeled as a multi-objective optimization problem and solved using Particle Swarm Optimization (PSO) algorithm in (Ajami & Armaghan 2010). Different loading scenarios are considered to show the effectiveness of the proposed method. Nonlinear feedback linearization control technique is employed in (Ghaisari & Bakhshai 2005) where the study system dynamic model is represented as a multi-input multi-output system. Although the paper describes the need of zero-dynamic study for the stability of overall system, it is not explained for the study system.
Invasive Weed Optimization (IWO) is a recent meta-heuristic search algorithm which is inspired from the weed colonizing technique (Mehrabian & Lucas 2006). IWO was tested for different multi-dimensional benchmark systems and the performance is compared with other efficient search algorithms. Performance of IWO was found superior to Genetic Algorithm, Simulated Annealing, Particle Swarm Optimization, Memetic Algorithm and Shuffled Frog Leaping algorithm. From then on IWO has found numerous applications in diversified field of engineering and science. IWO is efficiently applied for optimizing and tuning of a robust controller (Mehrabian & Lucas 2006), designing an E-shaped MIMO antenna (Mallahzadeh et al. 2009), optimal positioning of piezoelectric actuators (Mehrabian & Yousefi-Koma 2007), studying the electricity market dynamics (Ardakani et al. 2008), designing the encoding sequences for DNA computing (Zhang et al. 2009), and developing a recommender system (Rad & Lucas 2007).
This paper utilizes the superior performance of IWO to find out the optimal parameter of SSSC damping controller in an SMIB system. A time-domain based objective function is chosen which considers deviation in the rotor speed as error signal and the job of the optimizer is to minimize the error in the quickest possible time. The performance of IWO is then compared to that of PSO based controller.
The paper is organized as follows: Mathematical model discusses the system investigated and SSSC structure, Invasive weed optimization discusses Invasive Weed Optimization Algorithm. The simulation results are presented and discussed in Simulation results. Finally, the conclusions are given in Conclusion.
Mathematical model
System model and SSSC structure
The SSSC comprising of a voltage source converter, a series injection transformer and a dc-storage capacitor is indicated in a dotted block. The SSSC injects ${\overline{V}}_{\mathit{Bt}}$ into the transmission line which can be modulated for control of power flow in the line. The control variables are the modulation index m_{b} and phase angle δ_{b} of the voltage source converter.
SSSC damping control
The rotor speed deviation Δω is achieved by introducing different dynamic scenarios for different loading conditions. The system is initialized each time there is any change in operating condition. The rotor speed deviation is taken as the input to the PI controller through a wash-out block. The same speed deviation signal is passed to the IWO optimizer which calculates an objective function and tries to obtain an optimal solution to the problem at hand by minimizing the deviation in the speed signal. The IWO optimizer then sends the optimized parameter set (in this case K_{p} and K_{i}) to the controller block and the controller output gives the desired magnitude of modulation index (m_{b}) in order to improve the system damping. The optimizer is applied for a certain fault case and loading condition.
Objective function
Invasive weed optimization
Invasive Weed Optimization is a bio-inspired numerical stochastic optimization algorithm that simply simulates natural behavior of weeds in colonizing and finding suitable place for growth and reproduction. Some of the distinctive properties of IWO in comparison with other evolutionary algorithms are the way of reproduction, spatial dispersal, and competitive exclusion (Mehrabian & Lucas 2006).
The IWO process is summarized as follows
Initialize a random population
To start with, a random population set is defined over the allocated search space. The allocated search space is generally confined to the constrained boundaries.
Reproduction
Each randomly produced seeds are tested on the objective function to find out their individual fitness to achieve a certain target. These seeds are now allowed to reproduce depending on their own fitness in a linear fashion, i.e., none of the seeds are excluded from the regeneration phase. Each seed has a chance to reproduce and the reproduction rate varies from the maximum to the minimum for the best to the worst fit seed, respectively.
Spatial dispersal
where, it_{max} is the maximum number of iterations, S_{it} is the SD at the present time step, m is the nonlinear modulation index, S_{i} is the initial SD and S_{f} is the final SD. The produced seeds are then evaluated and allowed to go forward for further production if they provide better solutions than the parent weeds with lower fitness in a colony.
Competitive exclusion
The dispersed plants should go under competition so that only the best fit plants are kept for further generation. So, after some iteration, whenever the number of plants in a colony reaches the maximum, some of the unfit or less fit plants should be replaced by better fit plants. For this purpose, the parents and the offspring are ranked together and according to the fitness value some of the unfit candidates are excluded from the colony and thus keeping the final set of population equal to the maximum number of plants.
Simulation results
The expectation from IWO tuned SSSC damping controller is to provide faster solution to power oscillation damping, quick settling time for the states and the overshoot/undershoot within acceptable limit. This will require some control effort. Again, as there is a hardware limit of designed controller system, for the case of SSSC, the control input parameter m_{b} should be within its limit. In this work, the boundaries for the modulation index are set between m_{bmin} and m_{bmax}. The values of m_{bmin} and m_{bmax} are given in the Appendix.
Various loading conditions
Loading condition | P_{e}(p.u) | V_{t}(p.u) | Q_{e}(p.u) |
---|---|---|---|
Light | 0.8 | 1.0 | 0.0808 |
Nominal | 1.0 | 1.0 | 0.127 |
Heavy | 1.2 | 1.1 | 0.6068 |
The effectiveness of the optimization algorithm can be interpreted as i) the number of iterations taken by the optimizer to reach at the optimal solution, ii) the level of objective achieved in the form of minimization/maximization and iii) ability to search for an optimal result within the given constraints. The constraints are interpreted as the boundary values of the PI controller gains and the values are provided in the Appendix. In view of the above, the performance of IWO is compared with that of the Particle Swarm optimization (PSO) for the designing of the controller. Detail discussion on PSO can be found in (Kennedy & Eberhart 1995).
IWO and PSO parameters
IWO | PSO | ||
---|---|---|---|
Parameter | Value | Parameter | Value |
Population | 30 | Population | 30 |
Number of generation | 500 | Number of generation | 500 |
m | 3 | weight | 0.9 |
S_{i} | 1 | alpha | 0.99 |
S_{f} | 0.0001 |
- i)
A mechanical torque pulse having a magnitude of 0.2 p.u. is applied at 1.0 sec and removed at 1.083 sec.
ii) A three phase short circuit fault is applied at the middle of one of the transmission line at 1.0 sec and the fault is cleared at 1.083 sec. So, the post fault and the pre fault transmission line reactance remain same.
iii) A three phase short circuit fault is applied at the middle of one of the transmission line at 1.0 sec and the faulted line is removed at 1.083 sec. So, the transmission line reactance gets doubled in the post fault period.
All of the above cases are simulated for the three different operating conditions provided in Table 1.
Results and discussion
Figures 4, 5 and 6 presents the results of case (i) for light load conditions. It is seen that under no control the system experiences oscillatory instability as the rotor angle and active power oscillations are increasing with time. The introduction of optimized control action stabilizes the system for both PSO and IWO algorithms. But the damping action achieved is lot better for IWO than that of PSO. PSO optimized control action dampens the oscillation at a slow rate and even after the 5 sec simulation it requires some more time to reach to a steady value. On the other hand the IWO optimized control action can damp out the system oscillation within 1 sec of the introduction of the dynamics. Figure 6 shows that the control effort required by both algorithms are within the limit but the one with IWO settles to a steady value of 0.01 p.u. whereas the PSO control action keeps oscillating around 0.005 p.u.
Figures 7, 8 and 9 presents the results of case (i) under nominal load condition. With increase in loading level the first swing of the rotor speed goes a little higher but the controller successfully damps out the subsequent oscillations. Here, too, the performance of the IWO optimizer is found superior than the PSO optimizer. Figure 9 ensures the fact that a little more control effort is required for the nominal load condition compared to the light load condition as the IWO optimized control signal settles at around 0.0125 p.u.
Optimized parameters of IWO and PSO for different case studies
Optimizer | Case | Loading | K_{p} | K_{i} |
---|---|---|---|---|
PSO | I | Light | 1 | 28 |
Nominal | 1 | 28 | ||
Heavy | 1 | 12.5119 | ||
II | Light | 1 | 17.9417 | |
Nominal | 1 | 14.5325 | ||
Heavy | 1 | 25.4302 | ||
III | Light | 1 | 6.2319 | |
Nominal | 1 | 6.6266 | ||
Heavy | 1 | 21.9208 | ||
IWO | I | Light | 17.760 | 28 |
Nominal | 20.454 | 27.3489 | ||
Heavy | 9.8019 | 21.9525 | ||
II | Light | 4.3441 | 11.4455 | |
Nominal | 4.3441 | 11.4455 | ||
Heavy | 11.4738 | 15 | ||
III | Light | 4.3441 | 11.4455 | |
Nominal | 4.3441 | 11.4455 | ||
Heavy | 15 | 0.8943 |
The incidents where the optimizer hits the limit are shown in bolded form. It is found that the PSO optimizer reaches the lower limit of K_{p} in each case and the higher limit of K_{i} for the first two scenarios. On the other hand, the IWO optimizer hits the upper limit of K_{i} only in one scenario. This gives an indication of the better performance of IWO in finding an optimal solution within a confined search space.
Conclusion
Power system stability enhancement using SSSC based damping controller is studied in this paper. A PI controller based design is considered where the optimal parameters of the controller are found by minimizing a time integral of absolute error based objective function. Different fault scenarios and loading conditions are studied for an SMIB system and IWO technique is employed to search for the optimal controller parameters. The performance of IWO optimizer is compared to that of PSO optimizer in a constrained search space. The simulation results show the superiority of IWO over PSO in tuning SSSC controller for the damping of power oscillations of a single machine power system.
Appendix
Synchronous Generator: (2100 MVA, 13.8 kV).
f_{b} = 60 Hz, ω_{0} = 377 rad/sec, D = 0, M = 8.0 MJ/MVA, x_{ d }=1.0 p.u., ${x}_{d}^{\prime}=0.3\phantom{\rule{0.25em}{0ex}}\mathrm{p}.\mathrm{u}.$, x_{ q }=0.6 p.u., ${T}_{d0}^{\prime}=5.044\phantom{\rule{0.25em}{0ex}}sec$.
Exciter: K_{A} = 10.0, T_{A} = 0.01 sec.
SSSC: S_{nom} = 100 MVA, V_{noms} = 500 kV (AC side), V_{nomp} = 5 kV (DC side), V_{dcrated} =2*V_{nomp}, C_{dc} = 2.0 p.u., V_{dc0} = 10.0 p.u., m_{b0} = 0, δ_{ b }= − 30.88°, m_{bmax} = 1.0, m_{bmin} = 0.
Transformer: (2100 MVA, 13.8/500 kV).
X_{t} = 0.1 p.u.,
Transmission Line: X_{L1} = X_{L2} = 0.3 p.u.
Infinite Bus: V_{b} = 1.0 p.u.
PI Controller gain Limits: K_{pmin} = K_{imin} = 1, K_{pmax} = K_{imax} = 28.
Declarations
Authors’ Affiliations
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