An optimization methodology of susceptance variation using lead-lag controller for grid connected FSIG based wind generator system
Introduction
Since efforts are being made to generate electricity from clean, green, and environment friendly energy sources; renewable sources such as wind, small hydro, solar, tidal, geothermal, and waste are gaining more popularity with time [1], [2]. Among these clean energy sources, wind seems to be more prominent technology considering following facts: its development in last decade [3], available abundantly all the time (unlike solar, tidal, geothermal and waste) [1], zero carbon emission [4], and also zero fuel cost [5]. Now, this wind energy is first converted to mechanical energy by a wind turbine, and then to electrical energy by a suitable generator (such as synchronous, induction) [6]. However, wind power is unpredictable, means its speed varies with time, and hence, due to the imbalance between mechanical input and electrical output, low frequency oscillations may occur and hinder stability of the power grid [7] if not properly damped.
To mitigate these oscillations, several types of control mechanisms are adopted such as proportional integral derivative (PID), fuzzy based controller/neural network based controller, robust controller, predictive controller, and lead-lag based controller. PID controller, reported in [8], has only one optimization algorithm to tune its parameters without presenting any comparative study with other optimization algorithms. Also in reference [9], application of PSO technique for wide-area oscillation control using proportional integral (PI) controller is shown, however, results are not compared with any other standard optimization techniques. In case of fuzzy based [10] and neural network based [11] controllers, actual dynamic model is not considered. Rather, a data-driven model is generated, which may degrade controller performance due to lack of accurate training. Hence, even with the slightest variation in the data, controller does not show acceptable response. Advanced control techniques, such as robust control and predictive control are much more mathematically involved and their implementation in practical field are cumbersome [12]. On the other hand, lead-lag controller is comparatively simpler in structure and unlike neural network based controller, it can deal with actual dynamic model [13].
Although lead-lag controller is effectively employed in many control applications, its usage is hardly found in susceptance variation for mitigation of oscillations in wind power generation system. Variation of susceptance at machine terminal modulates the flow of power balance between electrical and mechanical subsystems [14]. Moreover, improper modulation resulting from inappropriate tuning of controller parameters also leads to unstable system dynamics [15], [16]. Hence, a methodology is proposed to optimize controller parameters to ensure system stability through proper modulation of susceptance. The contribution of this paper can be summarized as follows:
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To start our methodology, we need to derive a dynamic algebraic equation (DAE) model of wind energy system. We build our system matrix using fourth order dynamic model of generator, lumped-mass drive train model, and algebraic model for mechanical input power to turbine, electrical output power of generator, and transmission system. Then, we analyze system stability without controller through eigenvalue and participation factor analyses.
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We use a lead-lag type controller for varying susceptance at generator terminal. Parameters of this lead-lag controller are tuned using three different optimization algorithms: namely, PSO, GA, and FPA. The optimization of controller is performed based on minimization of an eigenvalue based objective function. Later, quantitative comparison is conducted based on iteration number, fitness value, and elapsed time between these three optimization algorithms. Moreover, statistical tools such as one sample Kolmogorov–Smirnov test and Wilcoxon signed-rank test are used to discover statistical significance among the optimizers.
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We visualize our proposed methodology on a FSIG based wind energy system. Here, we compare stability scenario of the study system before and after incorporating lead-lag type variable susceptance controller using three optimization algorithms. However, our proposed methodology is applicable for controlling any other types of energy conversion system, different sorts of generating plants such as Doubly Fed Induction Generator (DFIG), Permanent Magnet Synchronous Generator (PMSG), etc [17], [18] and as well as, for various optimization algorithms.
Our analysis shows that damping ratio associated with rotor electro-mechanical oscillation without any controller (i.e. open loop system) is 0.1458 and with incorporation of lead-lag controller (i.e. close loop system) through optimization of its parameters by three different optimization algorithms PSO, GA, and FPA are 0.2387, 0.2962, and 0.2662 respectively. Hence, all three optimization algorithms effectively suppress the oscillation originating due to power imbalance. Although damping ratio achieved by GA is better than FPA, average fitness value achieved by GA and FPA are 2.3725e6 and 2.3813e6 with standard deviations for 30 independent runs 8.6e3 and 2.8e respectively. The remainder of this paper is organized as follows. Section 2 discusses the overview of our proposed methodology. Then, we discuss the first step of our proposed methodology in Section 3, where we develop a nonlinear DAE model of our FSIG based wind power generating system. Section 4 explains linearization of DAE model and formation of system matrix. Later, Section 5 discusses eigenvalue and participation factor analysis along with effect of susceptance variation on system stability. Section 6 presents implementation of a lead-lag controller, whose parameters are tuned based on three optimization scenarios—FPA, GA and PSO. And later, we discuss trade-off among these algorithms in terms of stability, quantitative study, and nonparametric statistical analysis in Section 7. Finally, Section 8 concludes our paper.
Section snippets
The overview of our methodology
Fig. 1 shows the overview of our proposed methodology. At the first step, we develop a nonlinear DAE model of FSIG based wind energy conversion system under this study. However, our proposed methodology is applicable for any other kinds of energy conversion system having low frequency oscillation problems as mentioned in Section 1. Here, we consider complex fourth order dynamic model of FSIG, since stator dynamics are neglected in simplified second order model. However, a simplified version of
Step 1: formulation of DAE model
Fig. 2 shows an overview of FSIG based wind energy conversion system as mentioned in Section 2. Here, wind power is extracted using wind turbine, which is later converted to electrical energy by a FSIG based generation system and then supplied to infinite bus through a double circuit transmission line. Y11 in Fig. 2 is denoted as a complex load comprising of susceptance and conductance, whereas Y12 is admittance of transmission line. Dynamic and algebraic models of our study system are as
Truncation of higher order term
Since DAE model formulated in step I is non-linear in nature, we need to employ some linearization algorithm to obtain linearized form of the nonlinear DAE model. To obtain linearization, we resort Taylor series expansion first. However, conventional Taylor series includes infinite number of terms including nonlinear higher order terms, and hence, truncation of non-linear higher order terms is employed to obtain corresponding linearized form with moderately sacrificing accuracy [30]. Moreover,
Eigenvalue and participation factor analysis
Eigenvalues resulting from system matrix A formulated at Section 4 are presented in Table 1. These eigenvalues are calculated using control system toolbox of Matlab ver 2014b. The numerical data-sets used for our study system are listed in Table 2. Here, for calculating eigenvalues, we consider a negative value for slip, as the rotor of an induction machine should operate at a speed higher than the synchronous while working as a generator [33]. Moreover, we also consider a small value for slip,
Step 4: controller parameter optimization for susceptance variation
Fig. 6 shows a turbine-generator system along with a controller connected at generator terminal. The variation of susceptance at this terminal modulates voltage profile, which enhances the system stability. The block diagram of a lead-lag controller is shown in Fig. 7. The controller first takes Δω (i.e. change in rotor angular speed) as input and then, passes it through wash-out filter block. This wash-out block helps controller output to be gradually drawn towards zero in steady state
Parameters selection
Parameters, such as population size (), maximum number of iterations (), and maximum number of run () are kept equal for each algorithm to have a fair comparative judgment among these algorithms. As it is mentioned earlier, we perform statistical analysis on the data obtained by these algorithms, therefore, we consider the maximum number of 30 runs to have enough data as sample, since probability and randomness are part of these algorithm.
Now, in case of FPA, probability switch
Conclusion
We present an optimization methodology for mitigating low frequency oscillations in wind power generation system. Then, we visualize our methodology using a lead-lag type variable susceptance controller for FSIG based wind generation system. The gain and time constants of this particular controller are optimized using three different optimization algorithms: PSO, GA, and FPA. However, our proposed methodology is easily applicable to any other generation system, controller type, and also for
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