Adaptive fractional integral terminal sliding mode power control of UPFC in DFIG wind farm penetrated multimachine power system
- P. K. Dash^{1}Email author,
- R. K. Patnaik^{2} and
- S. P. Mishra^{1}
https://doi.org/10.1186/s41601-018-0079-z
© The Author(s) 2018
Received: 22 August 2017
Accepted: 31 January 2018
Published: 30 March 2018
Abstract
With an aim to improve the transient stability of a DFIG wind farm penetrated multimachine power system (MPN), an adaptive fractional integral terminal sliding mode power control (AFITSMPC) strategy has been proposed for the unified power flow controller (UPFC), which is compensating the MPN. The proposed AFITSMPC controls the dq- axis series injected voltage, which controls the admittance model (AM) of the UPFC. As a result the power output of the DFIG stabilizes which helps in maintaining the equilibrium between the electrical and mechanical power of the nearby generators. Subsequently the rotor angular deviation of the respective generators gets recovered, which significantly stabilizes the MPN. The proposed AFITSMPC for the admittance model of the UPFC has been validated in a DFIG wind farm penetrated 2 area 4 machine power system in the MATLAB environment. The robustness and efficacy of the proposed control strategy of the UPFC, in contrast to the conventional PI control is vindicated under a number of intrinsic operating conditions, and the results analyzed are satisfactory.
Keywords
1 Introduction
The increase in the penetration of wind power, especially from doubly fed induction generator based wind farms into the existing power grids, is although beneficial, but has significant pessimistic impacts [1] such as voltage and frequency control, power transfer capability, transient stability, etc. The employment of the power system stabilizers (PSS) is helpful in stabilizing such power systems, but they demonstrate an unreliable performance for the interarea oscillations between the generators of the multimachine power systems [2]. In the process, the application of the Flexible AC Transmission System (FACTS) devices, such as Unified Power Flow Controllers (UPFC) along with the PSS has illustrated excellent results, especially for improving the oscillations exhibited by the power system components [3]. Adding to it, they also control both the active and reactive power flows across the ac transmission lines [4, 5]. A number of configurations of the UPFC used for the ac transmission lines in the last few decades have been reviewed in [6]. Most of the models constitute a large number of parameters involved and hence are computationally more complex. On the contrary, a simple model which is easier for deriving the controls has been proposed in [7], where the voltage injected in the series portion of the UPFC is resolved into quadrature and phase components, with respect to the current flowing along the line. These components are further used to effectively control the reactive and active power flow through the transmission line, respectively.
A review on some of the control systems for the UPFC as well as their drawbacks has been discussed in [8]. The proportional-integral (PI) control is one of the effective conventional controller for the UPFC [9], but its performance is unreliable under some of the intermittent operating conditions (DFIG based wind farms) [10]. In the due course of time some of the non-linear controls such as sliding mode control [10] (SMC), Neuro-SMC techniques [11] etc., have been proposed for the control of the UPFC. The choice of an ideal hyper plane that assures the asymptotic stability of the non- linear systems is very much important for the controller design of the SMC. Adding to it, SMC is endowed with the well-known chattering phenomenon which makes it unreliable under certain operating conditions. Thus in order to overcome the above mentioned problems, a fractional integral terminal sliding mode power control (FITSMPC) has been investigated for the nonlinear and dynamic systems [12] that shows a very much promising result in terms of guaranteed finite time chatter free error convergence.
- (a)
A FITSMPC is proposed to control the dq- axis series injected voltage of the UPFC that subsequently controls the proposed admittance model of the UPFC.
- (b)
The controller gains of the proposed FITSMPC for the admittance model of the UPFC are made dynamic [13], such that they adjust with the intermittent operating conditions.
- (c)
This subsequently controls the active power injection at the DFIG wind farm terminal, which maintains the power balance of the nearby generators. As a result, the rotor angular oscillations between the generators in the multimachine system gets recovered, which will help in improving the power transfer capability of the associated transmission lines (though this later portion has not been investigated in the current paper, but is considered for future work).
The proposed controllers for the admittance model of the UPFC is installed in a standard 2-area 4-machine system [7], which has been penetrated by a DFIG based wind farm [14]. The overall model with their controllers have been simulated in the MATLAB/Editor environment following the necessary requirements for multimachine simulation [15]. The size and location for installation of the UPFC and DFIG based wind farm in the multimachine power system has been followed as per the references [7, 16], respectively. Critical Clearing Time (T_{ CCL }) [1], one of the key indicators of the transient stability index, has been taken as the basis for comparison of the performance of the proposed controller with the conventional PI control of the admittance model of the UPFC installed in the DFIG wind farm penetrated multimachine power system, and which is subjected to three phase fault and the DFIG wind farm experiences a realistic wind profile [17]. It is observed that as compared to the conventional PI control, the proposed control strategy for the admittance model of the UPFC is very much significant and robust in improving the transient stability of the DFIG penetrated multimachine power system and exhibits the largest T_{ CCL } for all most all the cases simulated in this paper. These outputs as illustrated in the simulation and results section are satisfactory and vindicate the real time application of the proposed technique.
2 Proposed admittance model of UPFC
2.1 Basic model of the UPFC
2.2 Admittance model of the UPFC
2.3 Design of μ_{α} and υ
Where i_{ ζD } and i_{ ζQ } re the dq- axis component of the series injected current I_{ ζ }.
Thus UPFC has been modeled as controllable admittance loads as specified in Eqs. (6) and (7), respectively. It is to be noted that the admittance across the loads Y_{ m } and Y_{ n }, can be controlled by μ_{ α } and υ which are again controlled by ϑ_{ ζP } and ϑ_{ ζQ }, respectively, which depends upon δ_{ξ}, ϑ_{ ζD } and ϑ_{ ζD }, respectively. Thus the control of the UPFC as controllable loads is achieved by controlling the series injected voltage, as shown in Eq. (22), which is the main contribution of this manuscript. Modelling of the dc link voltage is referred to [7].
3 Methods
3.1 The non- linear dynamic model of the UPFC
Thus γ_{ Q } and γ_{ P } are the target control terms which are used to control the final dq- axis series injected voltages (Eq. (34)), which subsequently control the proposed AM of the UPFC, respectively.
3.2 Proposed adaptive fractional integral terminal sliding mode power control (AFITSMPC) of UPFC
Where \( {p}_n^{\ast } \) and \( {q}_n^{\ast } \) are the reference value of the active and reactive powers, which are evaluated in the initial solution.
With α_{ 1 }, α_{ 2 } > 0, β_{1}, β_{2} are fractional numbers satisfying the relation 0 < [β_{1}, β_{2}] < 1.
In the above Eqs. (34)–(37), {β_{ ProbV }, β_{ QrobV }, β_{ ProbA }, β_{ QrobA }} > 0, are the gains of the controller, whose initial values are mentioned in the Appendix. Eq. (37), which makes the controller adaptive i.e., adjusts the controller gains according to the varying operating conditions, is defined as the fractional integral terminal sliding mode adaptive law for the admittance model of the UPFC.
Equation (39) guarantees a finite time convergence of the tracking error functions [12] as defined in Eq. (25).
From Eq. (43), it is proved that as the value of \( {\dot{V}}_L\le 0 \) for all σ_{ r1 } ≠ 0 and σ_{ r2 } ≠ 0, which guarantees the system stability. This completes the proof.
4 DFIG wind farm model
The GSC operation has been restricted to unity power factor and hence, results in zero reactive power at the GSC terminal.
5 Results
A three phase short-circuit fault is considered as the disturbance which has been simulated on one of the load bus (bus ‘7’ in Fig. 5) for certain duration of time ‘t_{ f }’ in sec. The highest value of t_{ f } in the post fault region within which synchronism between the relative rotor angles of the generators in a power system is maintained is defined as the critical clearing time denoted as T_{ CCL } [1]. Thus it is very much significant that, for a given operating condition, the T_{ CCL } provides an exact clue of the transient stability margin of the power system.
5.1 Performance of the control strategies of the UPFC in the DFIG wind farm penetrated two area four machine system (Fig. 5) with the DFIG wind farm subjected to fixed wind speed
In this particular case, a three phase fault is initiated on bus 7 of the test system (Fig. 5) at the timing instant t_{ s } = 2.11 s, where the DFIG wind farm is subjected to fixed wind speed of 6.29 m/s. The performance of the controllers has been tested for both the lower as well as higher level of penetration of the DFIG wind farm, which are illustrated in Figs. 7 and 8, respectively. In order to evaluate the T_{ CCL }, the performance of the proposed as well as conventional controls of the AM of the UPFC is observed by repetitive simulations by increasing the duration of fault ‘t_{ f }’. It is observed that, the T_{ CCL } for the conventional PI control for this particular case is 249 ms and 161 ms for lower and higher penetration of DFIG wind farm, respectively, at which the generators in the system losses synchronism (subplots (d)). On the contrary, for the same duration of fault (T_{ CCL } for PI control), the proposed control of the AM of the UPFC is very much significant in improving the ‘Y_{ m }’ and ‘Y_{ n }’ placed between the buses ‘m’ and ‘n’ as shown in subfigures (a) and (b), respectively. Subsequently, the power at the DFIG wind farm terminal (P_{ dg }) is improved (subplot (c)), which is responsible for restraining the electrical and mechanical power equilibrium of the nearby generators. This minimizes the rotor angular deviation of the generators and hence stabilizes the MPN, which is reflected in the improvement on the interarea oscillation between generators 1 and 4, (DW 1–4 (Rad/s)) as illustrated in subplot (d), in these figures, respectively. Further, the T_{ CCL } for the proposed control strategies is found out to be 266 ms and 181 ms, for lower and higher penetration of DFIG wind farm, which illustrates a 17 ms and 20 ms improvement in CCL, respectively, for the proposed controller (STRATEGY B) in the fixed wind speed operation of the DFIG wind farm.
5.2 Performance of the control strategies of the UPFC in the DFIG wind farm penetrated two area four machine system (Fig. 5) with the DFIG wind farm subjected to variable wind speed
Critical Clearing time for the conventional and proposed controllers subjected to Lower penetration of DFIG Power
Operating Points | T _{ CCL } for STRATEGY A in ms | T _{ CCL } for STRATEGY B in ms | Improvement in T_{CCL}for STRATEGY B in ms |
---|---|---|---|
A | 498 | 514 | 16 |
B | 514 | 523 | 09 |
C | 485 | 504 | 19 |
D | 507 | 521 | 14 |
Critical Clearing time for the conventional and proposed controllers subjected to Higher penetration of DFIG Power
Operating Points | T _{ CCL } for STRATEGY A in ms | T _{ CCL } for STRATEGY B in ms | Improvement in T_{CCL}for STRATEGY B in ms |
---|---|---|---|
A | 391 | 414 | 23 |
B | 411 | 426 | 15 |
C | 387 | 392 | 05 |
D | 355 | 371 | 16 |
The improvement in T_{ CCL } ranges between 9 ms − 19 ms in the lower DFIG wind power penetration case, where as it lies between 5 ms − 23 ms for the higher DFIG wind power penetration case. Thus as the proposed AFITSMPC for the AM of the UPFC illustrates an improved result in terms of damping out the oscillations between the generators of the multimachine power system for a number of intrinsic operating conditions, hence it guarantees the robustness of the method and also the applicability of the method in real time applications (which is considered as a future work in this paper).
6 Discussion
It is observed that from previous two subsections and Figs. 7, 8, 9, 10, 11 and 12, that after the initiation of disturbance, the simulation of the overall model (Fig. 5), illustrates some low frequency oscillations (as in case of the interarea oscillation between the generators 1 and 4) which is uncontrollable. On the contrary, the above simulation with the proposed AFITSMPC for the AM of the UPFC, i.e., STRATEGY B, also exhibits some low frequency oscillation (as in case of the interarea oscillation between the generators 1 and 4), which deviates approximately between − 2 and 2 Rad/S. But in spite of it, the active power or the reactive power based AFITSMPC control of an AM of the UPFC considerably damps out the respective inter-area low-frequency oscillations exhibited by the network. In addition, the DFIG wind farm is also equipped with the PI control mechanism on active and reactive powers for both the rotor side as well as grid side converters [21], which also boosts up in damping the above low frequency interarea oscillations [22]. It is also observed that, [22] illustrates a method by which the low-frequency oscillation modes of the presented power system can be calculated through a low- frequency oscillation modal analysis combined with the dynamic small signal mathematical models of DFIG wind turbines and synchronous generators, including their eigenvalues, oscillation frequencies, and damping ratios. This is an important and interesting topic which will be given full consideration as a future work.
In addition, the adaptive nature of the controller gains of the proposed AFITSMPC for the AM of the UPFC, is very much significant in quickly stabilizing the admittance model of the UPFC where the DFIG wind farm in the multimachine power system has been subjected to fixed as well as sporadic wind profile. In all the cases, there has been a significant improvement in the interarea oscillations exhibited by the MPN by the strategy B, which is justified in subfigure (d) of the Figs. 6, 7, 8, 9, 10 and 11, respectively. The T_{ CCL } for both the strategy A and B have been tabulated which justifies its improvement for proposed STRATEGY B for almost all the cases illustrated in this section. Further it is observed that, with the increase in penetration level of the DFIG wind farm, there is a significant increase in the maximum overshoots of the P_{ dg }. In spite of this, the proposed AFITSMPC for the AM of the UPFC, in comparison to the conventional PI controller, is very much significant and robust to enhance the stability of the MPN, subjected to both the higher and lower level DFIG wind farm penetration with fixed as well as sporadic wind profiles subjected to different intrinsic operating conditions.
7 Conclusion
An adaptive fractional integral terminal sliding mode power control strategy of the admittance model (AM) of the UPFC, in order to damp out the oscillation between the generators in a DFIG wind farm penetrated multimachine power system is proposed in this paper. Taking the critical clearance time (T_{ CCL }) as the basis, the performance of the conventional PI is compared with the proposed AFITSMPC for the AM of the UPFC. It is observed that the adaptive nature of the proposed strategy B is very much significant in maintaining the synchronism between the generators in the multimachine system for a larger period of time (T_{ CCL }), which is evident by improvement in TCCL for the proposed strategy for almost all the case studies illustrated in the paper. It is also observed that the proposed AFITSMPC for the AM of the UPFC significantly stabilizes the active power output of the DFIG wind farm. This improves the electric power of the nearby generators, which subsequently improves (diminish) the irrespective rotor angle deviations and hence leads to the stability enhancement of the multimachine power system. The proposed controllers for the UPFC has been tested for the stability enhancement of the MPN for higher and lower penetrations of the DFIG power, at various operating points, where the DFIG wind farm has been subjected to a fixed as well as a sporadic wind profile, respectively. It is observed that, with an increase in penetration level of the DFIG, the oscillations shown by its active power in the post fault region increases. In spite of this, the proposed controller for the AM of the UPFC has outperformed the conventional one, by inheriting larger T_{ CCL }, for the DFIG penetrated multimachine system, under a number of intrinsic operating conditions. This has been analyzed in the simulation and result section, where the outputs shown are satisfactory and vindicates the superiority of the proposed controller.
Declarations
Authors’ contributions
Author RKP designed the Adaptive fractional sliding mode algorithm for the DFIG wind farm with UPFC along with some simulations. Author P.K.Dash conceived the original problem for detailed study along with results verification and coordition of the various sections of the manuscript.. Author S.P.Mishra did some simulations and provided data and took part in revising the paper.. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.” Also no fund is received from any financial or non-financial organization.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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