A Nonlinear Coordinated Approach to Enhance the Transient Stability of Wind Energy-Based Power Systems

Mohammad Javad Morshed,

Abstract—This paper proposes a novel framework that enables the simultaneous coordination of the controllers of doubly fed induction generators(DFIGs)and synchronous generators(SGs).The proposed coordination approach is based on the zero dynamics method aims at enhancing the transient stability of multi-machine power systems under a wide range of operating conditions. The proposed approach was implemented to the IEEE 39-bus power systems.Transient stability margin measured in terms of critical clearing time along with eigenvalue analysis and time domain simulations were considered in the performance assessment. The obtained results were also compared to those achieved using a conventional power system stabilizer/power oscillation(PSS/POD) technique and the interconnection and damping assignment passivity-based controller(IDA-PBC). The performance analysis confirmed the ability of the proposed approach to enhance damping and improve system’s transient stability margin under a wide range of operating conditions.

I.Introduction

TRANSIENT stability is one of the most challenging problems in large scale power systems[1].It refers to the power system’s ability to converge to a stable post-fault equilibrium following large disturbances such as faults,overload,or loss of generating units.Random oscillations caused by faults,sudden changes in loads,lightning may lead to transient instability and subsequently voltage collapse and blackouts.The increased penetration of wind energy systems into the grid have led to additional challenges to power system’s stability.This is mainly due to the intermittent power availability of DFIG-based wind turbines along with the differences in the dynamic behavior characteristics of their generators compared with the conventional synchronous generators(SGs)[1]–[4].Power system stabilizers(PSSs)have traditionally been considered to enhance both the transient and dynamic stability of SGs[5],while DFIGs were equipped with power oscillation damping(POD)devices to effectively damp power system oscillations[6],[7].However,because the operating points of power systems change remarkably,linear approaches such as PODs and PSSs lack the necessary robustness under all operating conditions.Further,system nonlinearities can also affect power system characteristics during large disturbances,hence limiting the damping properties of PODs/PSSs.Finally, the interactions between the conventional SGs and DFIGs,which are widely deployed in wind energy systems,may cause dynamic instability in the absence of coordinated control designs.Hence,it is imperative to coordinate the design of the various controllers of the DFIGs and SGs while also taking into consideration power system’s nonlinearities in wind energy based power systems[8],[9].

Nonlinear excitation controllers were recently proposed to overcome the limitations of linear techniques and enhance the transient stability of large scale power systems in a much better way than the conventional techniques. A control structure based on two switching controllers working in a coordinated manner was proposed in[10]to enhance the transient stability of multi-machine power systems.A decentralized adaptive excitation control scheme was proposed in[11]for a three-machine power system.It was shown to enhance transient stability in the event of a large sudden fault. A decentralized multivariable adaptive voltage and speed regulator was proposed in[12] to stabilize power systems with multiple SGs.The approach was based on a nonlinear linearizing part with time varying parameters and an auxiliary stabilizing one and was shown to improve system stability and transient performance when implemented to a four-machine power system.An exact feedback linearizing excitation controller was proposed in to improve the stability margin of power systems under various operating conditions[13].However,the implementation of exact feedback linearizing excitation controllers requires using an observer for rotor angle estimation [14].A nonlinear approach based on the interconnection and damping assignment passivity-based control(IDA-PBC)was proposed in[15].The IDA-PBC control design methodology was used to achieve power angle stability and provide both frequency and voltage regulation for DFIGs,SGs,and STATCOM.Success of the IDA-PBC design,however,relied on the suitable selection of the closedloop interconnection structure and dissipation matrices and no general method currently exists for their selection,thus making its implementation to large scale power systems quite challenging [15].

Partial feedback linearization,or zero dynamics(ZD),approach have recently been considered to design excitation controllers for synchronous generators in multi-machine power systems[16].In[17] the approach was used to allow the decoupling of the multi-machine power system based on the excitation control inputs of the synchronous generators.Among the attractive features of the zero dynamics(ZD)approach are its ability to 1)convert system’s highly nonlinear dynamics into a partial linear one algebraically;2)lead to a transformed system that is of reduced order and independent of the operating point.Further,ZD does not require the full model dynamics of the system [18].

This paper focuses on the design of a coordinated approach based on the ZD technique for large scale power systems.The proposed approach takes into consideration the various interactions between SGs and DFIGs along with system nonlinearities.It aims at enhancing the transient stability of large scale power systems with DFIG-based wind energy systems.The main features of the proposed approach are,its ability to:

1)A framework that enables the simultaneous coordination between SGs and DFIGs controllers.Contrary to existing approaches which either coordinate the design between SGs only[19],[20],or DFIGs only[21].Further, the proposed methodology was developed for large scale power systems withm-SGs andn-DFIGs, making it easily implemented to large scale complex power systems,which is one of the most significant contributions of this manuscript.

2)A design methodology that takes into consideration the interactions between the SGs and DFIGs in multi-machine power systems.Contrary to existing approaches which omitted those interactions and resulted in poor dynamic stability [7],[19]–[23].

3)A coordinated design to handle system nonlinearities,uncertainties and the differences in the dynamic behavior of all the generators.Existing approaches[19],[20],[24]–[26]have either considered an exact linearization or a traditional zero dynamics approach.

The remainder of the paper is organized as follows.The dynamic models of the synchronous generators(SGs)and DFIGs are described in Section II.The proposed coordinated design is detailed in Section III.The performance of the proposed approach is illustrated in Section IV.A comparison analysis with other control approaches is also reported in that section. Some concluding remarks are finally given in Section V.

II.Pow er System’s modelling

Consider amulti-machine power system withm- SGs andn-DFIG-based wind energy systems.The dynamic models of each SG and DFIG can be represented as follows.

III.Zero Dynamics Technique

First order approximation of system’s dynamics around a given operating point is conventionally considered in linearizing nonlinear systems.While this technique yields satisfactory performance for systems with slowly varying equilibrium,it is not suitable for systems with inherently nonlinear dynamics[32]since it neglects high-order dynamics.Zero dynamics approach is a technique that transforms a nonlinear system to a linear one so that linear control methodologies can be used. Unlike conventional linearization,zero dynamics yields an input-output linear behavior that is valid globally,rather than in the vicinity of an equilibrium point [32]–[34].

Consider the following state space model for the nonlinear multi-machine power system:

IV.COMPUTER EXPERIMENTS

To illustrate the performance of the proposed coordinated control(Fig.2),we implemented it to the modified IEEE 39-bus 10-machine New England power system illustrated in Fig.3[9].

The New England power system was modified by adding two 200 MW DFIG-based wind turbines at buses 14 and 17,respectively.The parameters of the DFIGs considered in the simulation are listed in Table III in the Appendix.The data used for the SGs, transmission lines and transformers of the power system can be found in[9].The participation factor method[38]was considered to determine the optimum locations of the excitation controllers of the SGs.The results indicated that the synchronous generators,SG5,SG7,andSG9are the best locations for designing the excitation controller to damp out the local and inter-areas modes of oscillations.Further,in order to simulate the coupled dynamic response of the wind turbine and prevent the negative interaction between the fast and slow controllers, we implemented the fatigue,aerodynamics,structures,and turbulence(FAST) program proposed by the Renewable Energy Laboratory[39].Hence,three SGs(m=3)and two DFIGs(n=2) were considered in designing the nonlinear coordinated controller.The remaining SGs were equipped with PSS and were not considered in the coordination design implemented in this section.Eigenvalue analysis and time domain simulations were carried out to assess the damping performance and dynamic stability of the proposed approach.The control system dynamics were obtained by solving the differential equations(16)in MATLAB/Simulink environment R2011b version 7.13.

Fig.1.Flow chart of the proposed coordinated approach.

Fig.2.Block diagram of the proposed approach.

Fig.3.Single-line diagram of the IEEE 39-bus New England power system.

The performance of the proposed coordinated design was further compared with the following approaches:

1) PSS/POD:the SGs are equipped with power system stabilizers(PSSs),while the DFIGs are equipped with power oscillation dampers(PODs)[9],[40].

2) IDA-PBC:the passivity-based control design method(Interconnection and damping assignment passivity-based control (IDA-PBC))proposed in [15].

A. Eigenvalues Analysis

Eigenvalue analysis was performed to assess the system’s transient performance and damping capabilities.Further,in order to gain insight into the need for a type of control strategy to enhance system’s transient dynamics, the eigenvalues were also computed for the case where SGs and DFIGs were not equipped with any controller.

The dominant eigenvalues of the power system at some normal operating conditions are illustrated in Fig.4 for all the approaches. Note that the minimum damping ratio(ζmin) of the power system with no controller is 0.0130.The system is clearly undamped and installing a controller for the SGs and DFIGs is a must.Equipping SGs with PSS and DFIGs with POD,however,did slightly improve damping and stabilize the power system.The minimum damping ratio in this case was ζmin=0.0423which means that all system eigenvalues are confined to the conic illustrated in Fig.4.Implementing the IDA-PBC approach resulted in even better improvement in dominant eigenvalues compared to the PSS/POD(ζmin=0.0830), but the best results were obtained with the proposed coordinated design (ζmin=0.1137)compared to all considered situations.Thus,clearly confirming the ability of the proposed approach to greatly enhance power system damping and transient behavior.

B.Case I: Three-Phase Fault Scenario at Bus 16

In this section,the performance of the proposed approach is evaluated under a three-phase fault condition.This choice is motivated by the fact that such unavoidable fault often results in one of the most severe disturbances to power systems.Assessment was carried over for two scenarios:one that includes DFIGs and one that does not.This aims at evaluating the effectiveness of approach in mitigating the impact of wind energy stems in the grid.Comparison analysis with PSS/POD and IDA-PBC is also carried over.A symmetrical three-phase fault at bus 16 for 100 ms is considered to evaluate the performance of the proposed controller.The rotor angle responses ofSG5,SG7,andSG9with respect to generatorSG10, rotor speed and term inal voltage ofSG5,SG7,andSG9generators are illustrated in Figs.5–7 while the rotor angle responses ofDFIG1andDFIG2with respect to generatorSG10and rotor speed ofDFIG1andDFIG2are illustrated in Figs.8 and 9.

Fig.4.Dominant eigenvalues for the 39-bus New England system with:(+)no control;(O)PSS/POD;(□)IDA-PBC;(△)the proposed approach.

Fig.5.Rotor angels of SG5, SG7, SG9under a three-phase fault at bus 16(Case I).

Fig.6.Rotor speed of S G5, S G7, andS G9under a three-phase fault at bus 16(Case I).

Fig.7.Terminal voltage of S G5, S G7, S G9under a three-phase fault at bus16(Case I).

Fig.8.Rotor angels of DFIG1 and DFIG2under a three-phase fault at bus 16(Case I).

Fig.9.Rotor speed of DFIG1and DFIG2under a three-phase fault at bus 16(Case I).

Figs.5–9 show that the post-fault responses of the rotor angles,rotor speed and terminal voltage with PSS/POD and IDA-PBC are quite oscillatory.The time histories of the control signals,EfdiandVrkare depicted in Fig.10.The range ofEfdiandVrkare? 2 pu and ?1.5 pu.Those results confirm that the proposed coordinated approach has significantly improved the power system transient and voltage regulation.

Fig.10.Control signals of SGs and DFIGs under a three-phase fault at bus 16(Case I).

The oscillations in the rotor angles were slowly damped however but the rotor took a relatively long time to settle back to their post-fault steady state behavior. Note that,it took the proposed coordinated design less than 2 s from the fault occurrence to damp the oscillations in the rotor angles.Hence,we can conclude that the proposed coordinated approach improves the post-fault transient dynamic response of the system and enables it to regain its steady-state behavior faster than the IDA-PBC method.

C.Case II:Three-Phase Fault Scenario at Bus34

System performance is assessed in the presence of a symmetrical three-phase fault at the terminal ofSG5(bus34).In this case,since the SG will not supply any power when subjected to a three-phase fault at its terminal,the power system may become unstable after the fault is cleared because of the improper damping generated by the excitation system.Further,in order to assess the effectiveness of the proposed approach in dealing with the variability introduced by DFIGbased wind energy systems, the rotor angle of each SG was assessed in the presence and absence of DFIG.The rotor angle responses ofSG5,SG7,andSG9in this case are illustrated in Fig.11.

D.Critical Clearing Time(CCT)and Computational Burden analysis

Transient stability refers to the power system’s ability to converge to a stable post-fault equilibrium following large disturbances.It is often assessed by how quickly the power system is able to clear a fault so as to maintain the faulttriggered transients inside the stability boundary[32].Critical clearing time(CCT)is a well-established metric that measures the upper bound of such clearing time.Exceeding this maximum value results in the loss of stability and synchronism by the generators.

In this section, we assess system’s transient stability by measuring the CCT following a critical fault such as a threephase fault occurring at various locations in the power network.The obtained results are illustrated in Table I for the proposed approach,PSS/POD,and IDA-PBC approach.

TABLE I Critical Clearing Time (CCT) of the Different Approaches

Table I shows that the proposed coordinated control approach resulted in an improvement of critical clearing time and subsequently transient stability by up to 23.33%for the considered fault.

Further,the three approaches were qualitatively compared in terms of mathematical complexity,computational cost,reliability and robustness.The comparison analysis is illustrated in Table II.

TABLE II Computational Burden and Various Parameters of the Different Approaches

Note that,though the mathematical complexity and computational cost of the proposed approach is higher than that of the traditional PSS/POD,it outperforms this latter in terms of stability,robustness,transient performance,and application to large scale power systems.The computational burden and mathematical complexity of the proposed approach is lower than that of the IDA-PBC approach however.

Based on the above results and discussions, we can conclude that the proposed coordinated design enhances the transient stability and performance of large scale power systems with SGs and DFIG-based wind energy systems,while keeping a reasonable computational cost.

V.Conclusion

This paper proposed a coordinated framework for large scale power systems with DFIG-based wind turbines and synchronous generators(SGs).The design is based on the multi input-multi output(M IMO)zero dynamics(ZD)approach and aims at enhancing power system’s transient stability.It captures system’s nonlinearities and considers the dynamic interactions among the various generators.The proposed framework resulted in faster post-fault recovery time and better transient stability compared to other approaches such as PSS/POD and IDA-PBC.One of the main features of the proposed approach is its ability to reduce the order of the feedback linearized power system,thus making the coordinated control design simple and cost effective.Further,the proposed approach can easily be implemented,in practice,using synchronized phasor measurement units(PMUs).These latter can be installed on the bus of each generator to estimate all the parameters of the network and generators needed for small signal stability analysis.

In closing,we recognize that the multi-machine power system results presented in this paper are preliminary and that there is considerable work that needs to be done to extend this approach to large-scale power systems with different types of renewable energy sources such as PV systems,and/or considering delay time of the controllers[41].However,we have clearly shown that integrating a DFIG into power systems using a nonlinear coordinated control design methodology has the potential to improve power system performance.We are currently working to demonstrate these results on the laboratory scale power system.

APPENDIX

TABLE III DFIG Parameters