Mitigation of Sub Synchronous Resonance in DFIG Based Windgeneration Using Fuzzy Logic Controller

Mitigation of Sub Synchronous Resonance in DFIG Based Windgeneration Using Fuzzy Logic Controller

Anjaneyulu Atkuri, M.Tech.,

PVP Siddhartha Institute of Technology, Vijayawada, India.

A. PurnaChandrarao. ,

PVP Siddhartha Institute of Technology, Vijayawada, India.

AbstractThe rapid growth of wind power systems worldwide will likely see the integration of large wind farms with electrical networks that are series compensated for ensuring stable transmission of bulk power. This may potentially lead to sub synchronous resonance (SSR) issues. Although SSR is a well- understood phenomenon that can be mitigated with flexible ac transmission system (FACTS) devices, scant information is available on the SSR problem in a series- compensated wind farm. This paper reports the potential occurrence and mitigation of SSR caused by an induction- generator (IG) effect as well as torsional interactions, in a series-compensated wind farm. In this study, a wind farm employing a self-excited induction generator is connected to the grid through a series-compensated line. The DFIG converters will be explored for SSR mitigation. The major contributions of the paper are 1) investigation of the potential of wind farm converters for SSR mitigation and

1. identification of an effective control signal for mitigating SSR using fuzzy logic controllers to simultaneously enhance both sub synchronous and super synchronous resonance modes .Extensive simulations have been carried out using Matlab/Simulink.

   Keywords Doubly-Fed induction generator (DFIG), sub synchronous resonance (SSR), Fuzzy logic controller.

   1. INTRODUCTION

      Sub synchronous resonance (SSR) phenomenon in wind farms connected with series compensated transmission network has been researched in recent literature [2][4]. It is well known that series compensation is an effective means of increasing power transfer capability of an existing transmission network. However, series compensation is shown to cause a highly detrimental phenomenon called sub synchronous resonance in electrical networks.

      A grid side converter (GSC) of a DFIG has a similar topology of a STATCOM yet exchanges both active and reactive power in fast speed. Hence, the objective of this paper is to explore the control capability of DFIG-based wind farms in mitigating SSR using SSR damping controller at the GSC.

      In order to have torsional interaction, the network mode should have a frequency of 5759 Hz. This requires a very high level of series compensation which rarely happens. The rotor speed has been used in SSR mitigation control [2]-[4]. A preliminary study exploring the capability of the grid-side converters (GSCs) of a DFIG in mitigating SSR is presented in [11]. The control scheme is demonstrated to enhance the SSR damping. The line current and the voltage across the series compensation are chosen and their effectiveness will be discussed in the paper.

      Therefore, the objective of the paper is twofold:

      1. To investigate the potential of SSR mitigation in DFIG converters;

      2. To identify a control signal for SSR mitigation and for overall system stabilization enhancement.

      The paper is organized as follows. Section II presents the study system, the DFIG converter controls, and the auxiliary damping control for SSR mitigation. Section III presents Comparison of control input signals Section IV presents Fuzzy logic controller Section V presents the simulation results to demonstrate the effectiveness of the SSR damping controllers. Section VI concludes the paper.

   2. STUDY SYSTEM AND SYSTEM MODEL

      The study system based on the IEEE first benchmark model for SSR studies [12] is shown in Fig. 1, where a DFIG- based wind farm (100 MVA from the aggregation of 2-MW units) is connected to a 161-kV series-compensated line. The collective behavior of a group of wind turbines is represented by an equivalent lumped machine. This assumption is supported by several recent studies [13][16] that suggest that wind farm aggregation provides a reasonable approximation for system interconnection studies. In this paper, an aggregated DFIG model is used and the voltage level of the transmission network is chosen to be 161 kV. The machine and the network parameters are listed in the Appendix. The length of the transmission line is approximately 154 miles for which it is reasonable to install series compensation.

      The unique feature of SSR phenomena in wind farms inter faced with series compensated network is that induction generator effect (IGE) due to the network resonant oscillatory model is the major cause of SSR. The frequency of torsional modes in wind turbines can be as low as 13 Hz.

      In the GSC control loops, the q-axis loop is to regulate the dc-link voltage and the d-axis loop is to regulate the terminal voltage, as shown in Fig. 3.

      V dc

      –

      K P3 +

      V * +

      iqg

      SSR damping

      K p4 +

      +i

      * –

      qg

      vqg

      K p3 +

      dc

      V

      * t

      Fig.1 The study system. The rated power of the wind farm is 100 MVA. The +

      nominal voltage of the wind farm terminal bus is 690 V and the nominal

      voltage of the network is 161 kV. –

      Vt

      When individual wind turbines are aggregated, the aggregated inertia is scaled up. However, the base power is

      K p4 +

      i

      +

      *

      dg

      –

      SSR damping

      idg

      vdg

      also scaled up; therefore, the per unit value of the inertia does not change. The same also happens to other machine parameters such as impedances. Therefore, the parameters of A 2-MW DFIG in per unit values can continue to be used for the equivalent wind generator.

      As a summary, the complete dynamic system model includes the series compensated network model, the wind turbine aerodynamic model, the torsional dynamics model, the induction generator model, the dc-link model, and the DFIGs converter controls. The auxiliary SSR damping control will be designed and added in for SSR mitigation study.

      1. DFIG Converter Controls:

         Both rotor-side converter (RSC) and grid-side converter (GSC) controls are modeled in this study. Cascaded control loops similar to the ones in [17] are adopted in this paper. The control loops are shown in Figs. 2 and 3.

         In the RSC control loops, the reference torque is obtained through the lookup table. When wind speed is greater than the rated speed, it is a constant value and is the optimal torque corresponding to the measured rotating speed. Through this lookup table, the wind turbine is able to extract the maximum wind power. The q -axis loop is to regulate the active power and the d-axis loop is to regulate the reactive power.

         Fig.3 Supplementary control schemes in the GSC control loop for SSR mitigation through either the terminal voltage modulation or dc-link voltage modulation.

      2. Auxiliary SSR Damping Control

      It has been identified in [3] and [9] that the RSC control loop gains negatively impact the SSR network mode and these gains have to be limited. It is, therefore, not suitable to explore SSR mitigation through RSCs. Instead, the focus is on GSC. The GSC is similar to a STATCOM in terms of the topology. The difference between STATCOM and GSC SSR mitigation is the consequent impact. For example, a GSC is connected to an RSC through a dc-link. Hence, SSR mitigation in GSC may cause impact on both GSC and RSC outputs. In Option1 the supplementary control is added in the GSC reactive power/voltage cotrol loop for the d-axis to modulate the terminal voltage demand as shown in Fig. 3.

      Similarly in Option 2 modulation is through the dc- link voltage reference modulation. The dotted box and line show the SSR damping controller and the injection point. Modulation of the dc-link voltage reference is expected to cause more oscillations on the real power exchange through the dc-link and the electromagnetic torque.

      m

      lookup

      Te

      K Te +

      + iqr*

      T

      *

      e

      K id +

      K Qs +

      +

      iqr

      + –

      +

      q + d

      vqr

      K iq +

      ia i a

      A

      B

      ib i b C/

      D

      ic i c Q

      i q

      i d

      ( i2 i2 )1/2

      to SSR damping controlle r

      Q

      * Three-Phase

      *

      s

      PLL

      idr

      – –

      vdr

      Voltage

      measurement

      s

      Qs idr

      Fig 2. RSC control loops

      Fig. 4 Estimation of capacitor voltage Vc through three phase current measurement

      Therefore, the capacitor voltage can be estimated through the local current measurements. The relationship between the instantaneous current through the line and the instantaneous voltage across the capacitor is given by

      C (dVC,P/dt)=ip, where = a ,b ,c

      The following Fig. 4 presents the estimation diagram of obtaining the estimated voltage magnitude from the a,b,c instantaneous current measurements. Three integral units will be used to obtain another set of signals ia, ib and ic,. These signals are proportional to the instantaneous capacitor voltage. Through a,b,c to dq reference frame transformation, three-phase balanced variables can be transformed into two dc variables. The fundamental component phasor magnitude can then be computed from the two dc variables.

   3. COMPARISON OF CONTROL INPUT SIGNALS The unique feature of SSR phenomena in wind

      farms interfaced series compensated network is that induction

      generator effect due to the network resonant oscillatory mode is the major cause of SSR. Torsional interactions in wind farms are rare because the torsional modes have a low frequency due to the low shaft stiffness of wind turbine drive trains [10].

      The rotor speed is used in SSR mitigation control [2], [4].Since it is the network mode that is of the utmost concern, measurements closely related to such mode should

      function can have different shapes; the simplest and most commonly used MF is the triangular-type, which can be symmetrical or asymmetrical in shape. A trapezoidal MF has the shape of a truncated triangle.

      The basic properties of Boolean logic are also valid for Fuzzy logic. Once the inputs have been fuzzified, we know the degree to which each part of the antecedent of a rule has been satisfied. Based on the rule, OR or AND operation on the fuzzy variables is done. The implication step helps to evaluate the consequent part of a rule. There are a number of implication methods in the literature, out of which Mamdani and TS types are frequently used. Mamdani proposed this method which is the most commonly used implication method. In this, the output is truncated at the value based on degree of membership to give the fuzzy output. Takagai-Sugeno-Kang method of implication is different from Mamdani in a way that, the output MFs is only constants or have linear relations with the inputs.

      The result of the implication and aggregation steps is the fuzzy output which is the union of all the outputs of individual rules that are validated or fired. Conversion of this fuzzy output to crisp output is defines as defuzzification. There are many methods of defuzzification out of which Center of Area (COA) and Height method are frequently used. In the COA method (often called the center of gravity method) of defuzzification, the crisp output of particular variable Z is taken to be the geometric center of the output

      be chosen as control signals. Both the line current magnitude

      fuzzy value

      1. area, where this area is formed by taking

         out

         and the voltage across the series compensation are chosen.

   4. FUZZY LOGIC CONTROLLER

      In a fuzzy logic controller, the control action is determined from the evaluation of a set of simple linguistic rules. The development of the rules requires a thorough understanding of the process to be controlled, but it does not require a mathematical model of the system.

      A fuzzy inference system (or fuzzy system) basically consists of a formulation of the mapping from a given input set to an output set using fuzzy logic. This mapping process provides the basis from which the inference or conclusion can be made. A fuzzy inference process consists of the following steps:

      • Step 1: Fuzzification of input variables

      • Step 2: Application of fuzzy operator (AND, OR, NOT) in the IF (antecedent) part of the rule

      • Step 3: Implication from the antecedent to the consequent (THEN part of the rules)

      • Step 4: Aggregation of the consequents across the rules

      • Step 5: Defuzzification

      The crisp inputs are converted to linguistic variables in fuzzification based on membership function (MF). An MF is a curve that defines how the values of a fuzzy variable in a certain domain are mapped to a membership value (or degree of membership) between 0 and 1. A membership

      the union of all contributions of rules whose degree of fulfillment is greater than zero. In height method of defuzzification, the COA method is simplified to consider the height of the each contributing MF at the mid-point of the base.

      Here in this scheme, the error e and change of error Ce are used as numerical variables from the real system. To convert these numerical variables into linguistic variables, the following seven fuzzy levels or sets are chosen as: NB (negative big), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), and PB (positive big).

      The fuzzy controller is characterized as follows:

      • Seven fuzzy sets for each input and output.

      • Triangular membership functions for simplicity.

      • Fuzzification using continuous universe of discourse.

      • Implication using Mamdani's 'min' operator.

      • Defuzzification using the 'height' method.

      Fig.5 Simulink block diagram for Fuzzy logic Controller

      Table1 The rule bases used for the Fuzzy logic controller.

      	PL	PM	PS	ZE	NS	NM	NL
      PL	PL	PL	PL	PL	PM	PS	ZE
      PM	PL	PL	PL	PM	PS	ZE	NS
      PS	PL	PL	PM	PS	ZE	NS	NM
      ZE	PL	PM	PS	ZE	NS	NM	NL
      NS	PM	PS	ZE	NS	NM	NL	NL
      NM	PS	ZE	NS	NM	NL	NL	NL
      NL	ZE	NS	NM	NL	NL	NL	NL

   5. SIMULATION

      The study system based on the IEEE first benchmark model for SSR studies are shown in Fig. 1 is simulated using MATLAB/SIMULINK. The dynamic responses of the ystem without SSR damping controller and with SSR damping controller based on PI and fuzzy logic controller based are plotted. The major contributions of the paper are 1) investigation of the potential of wind farm converters for SSR mitigation and 2) identification of an effective control signal for mitigating SSR using fuzzy logic controllers.

      Case 1) Without SSR damping controller

      (a)

      (b)

      (c)

      (d)

      Fig.6 Dynamic responses (a) line current Iline , (b) DFIG output power P (c) DFIG exporting reactive power Q , (d) rotor speed Wr .

      (a)

      (b)

      (c)

      (d)

      Fig. 7 Dynamic response (a)electromagnetic torque Te ,(b) capacitor voltage Vc, (c) dclink voltge Vdc (d) terminal voltage Vt .

      The increase of power transfer capability of long transmission lines can be achieved by increasing Series compensation level. However, series-compensated transmission lines connected to turbogenerators can result in subsynchronous resonance (SSR), leading to adverse torsional interactions.

      In this study shows that when wind speed is 7 m/s, the system can suffer SSR instability when the compensation level reaches 75% due to IGE. In the simulation study, initially, the compensation level is set at 50%. At t = 1 s, the compensation level changes to 75%.

      Figs.6 and 7 shows that the dynamic responses line current Iline , DFIG output power P, DFIG exporting reactive power Q, rotor speed Wr, electromagnetic torque Te , capacitor voltage Vc, dclink voltge Vdc, terminal voltage Vt of the system without SSR damping controller. From these Figs. it can be observed that the system without damping control becomes unstable when the series compensation level increases to 75%. In rotor speed Wr there exist high oscillations in the waveform because of more torsional interactions.

      The dynamic responses of line current Iline , DFIG output power P, DFIG exporting reactive power Q , rotor speed Wr, electromagnetic torque Te,dclink voltge Vdcc that there exist oscillations in the waveforms are high due to induction generator effect(IGE). In dclink voltgeVdc there exist high oscillation peak value 2.2KV in the waveform because of induction generator effect (IGE).

      Case 2) PI controller vs. fuzzy controller

      1. A damping controller is implemented with Iline as the input signal and Vt as the output signal. The gain of the controller is 10.

         (a)

         (b)

         (c)

         (d)

         (e)

         (f)

         (g)

         (h)

         (i)

         Fig.8 Dynamic responses (a) rotor speed r ,(b) terminal voltage Vt ,(c) electromagnetic torque Te , (d) DFIG output power P , (e) DFIG exporting reactive power Q,(f) capacitor voltage Vc , (g) line current Iline , (h) dc link voltage Vdc , (i) the output of the SSR damping controller Vssr .

         In case2 the SSR damping controller is implemented with PI and fuzzy logic controllers with the gains of 10, 30 and 46. The control signals line current magnitude and voltage across the series compensation are chosen. Fig.8 shows that the dynamic responses of rotor speed r , terminal voltage Vt , electromagnetic torque Te , DFIG output power P, DFIG exporting reactive power Q, capacitor voltage Vc , line current Iline , dclink voltage Vdc and the output of the SSR damping controller Vssr of the system with PI and fuzzy based SSR damping controller when line current magnitude Iline as input control signal and Vt as output control signal. In these waveforms the blue line denotes the system with the SSR damping controller using PI controller while the red line denotes the system with fuzzy logic controller.

         Fig.8 shows that the dynamic responses of electromagnetic torque Te , DFIG output power P, DFIG exporting reactive power Q, capacitor voltage Vc , line current Iline , dclink voltage Vdc and the output of the SSR damping controller Vssr when gain is 10 respectively slightly reduces SSR damping oscillations except that dc link voltage when the proposed Fuzzy based controller is used. It is observed that the terminal voltage Vt and rotor speed r are having less oscillations compared to without SSR damping controller. In case of without SSR damping controller the output power P the oscillation peak value is 1.75pu, but in PI based SSR damping controller it is reduced to 0.52pu. In Fuzzy controller based SSR damping controller the oscillation peak value further reduced to 0.48pu. Simulation results show that Fuzzy logic controller based decreases the amplitude of SSR damping oscillations.

      2. A damping controller is implemented with Vc as the input signal and Vt as the output signal, gain is chosen as 30.

         (a)

         (b)

         (c)

         (d)

         Fig.9 Dynamic responses (a) line current Iline , (b) capacitor voltage Vc ,

         (c) the output of the SSR damping controller Vssr . (d) DFIG output powerP, (d) DFIG exporting reactive power Q,

         (a)

         (b)

         (c)

         (d)

         (e)

         Fig.10 Dynamic responses (a) DFIG exporting reactive power Q,

         (b) rotor speed r , (c) electromagnetic torque Te , (d) Vdc ,(e) terminal Voltage Vt .

         Figs. 9 and 10 shows that the dynamic responses of line current Iline , capacitor voltage Vc , DFIG output power P, DFIG exporting reactive power Q, rotor speed, electromagnetic torque Te , dc link voltage Vdc , terminal voltage Vt and the output of the SSR damping controller

         Vssr of the system with PI vs fuzzy based SSRdamping controller when capacitor voltage Vc as control signal, with gain of 30. In these waveforms the blue line denotes the system with the SSR damping controller using PI controller while the red line denotes the system with fuzzy logic controller.

         It is observed that the dynamic responses of terminal voltage Vt and rotor speed r are having less oscillations compared to Iline as control signal but these dynamic responses approximately equal when PI and fuzzy based SSR damping controllers are used. In case of PI and fuzzy based SSR damping controller when Iline as control signal with gain 10 the output power P oscillation peak values 0.52pu and 0.48pu and these values further reduced to

         0.495 and 0.45 when Vc as control signal with gain 30.

         Fig.11 shows that the dynamic responses of DFIG output power P, line current Iline , DFIG exporting reactive power Q , electromagnetic torque Te , capacitor voltage Vc , dc link voltage Vdc , terminal voltage Vt , wind speed r and the output of the SSR damping controller Vssr of the

         system with PI and fuzzy based SSRdamping controller when capacitor voltage Vc as input control signal and Vdc as output control signal with gain 46.

      3. A damping controller is implemented with Vc as the input signal and Vdc as the output signal, gain is chosen as 46.

      (a)

      (b)

      (c)

      (d)

      (e)

      (f)

      (g)

      (h)

      (i)

      Fig. 11 Dynamic response(a) DFIGoutput powerP , (b) the output of the

      SSR damping controller V ssr , (c) line current Iline , (d) DFIG exporting reactive power Q , (e)electromagnetic torque Te , (f) capacitor voltage Vc ,

      (g) Vdc , (h) terminal voltage Vt , (i) wind speed .

      The waveforms in fig.11shows that the blue line denotes the system with the SSR damping controller using PI

      controller while the red line denotes the system with fuzzy logic controller. It can be observed that the dynamic responses of terminal voltage Vt and rotor speed r are having less oscillations compared to Iline as control signal but these dynamic responses approximately equal when PI and fuzzy based SSR damping controllers are used.

      In case of PI and fuzzy based SSR damping controller when Vc as control signal with gain 30 the output power P the oscillation peak values 0.495pu and 0.45pu and these values further reduced to 0.395 and 0.351 when Vc as control signal with gain 46. Simulation results show that Fuzzy controller based slightly decreases the amplitude of SSR damping oscillations.

      Table2. SSR oscillation (peak) values for Iline as control signal with gain 10

      Dynamic Response

      Without SSR Damping controller	SSR Damping controller with PI	SSR Damping controller with Fuzzy
      Te	1.5	-0.3	-0.36
      Pe	1.75	0.52	0.48
      Qe	1	0.08	0.03
      Vc	0.6	0.175	0.16
      Iline	1.8	0.7	0.64
      Vdc	2200	1201	1201.7
      Speed	10	0.7505	0.7503
      Vt	12	1.0008	1.0005

      Table3. SSR oscillation (peak) values for Vc as control signal with gain 30

      Dynamic Response	SSR Damping controller with PI	SSR Damping controller with Fuzzy
      Te	-0.302	-0.362
      Pe	0.495	0.45
      Qe	0.05	0.02
      Vc	0.174	0.158
      Iline	0.496	0.45
      Vdc	1205.3	1202.5
      Vssr	2	0.75

      Table4. SSR oscillation (peak) values for Vc as control signal with gain 46

      Dynamic Response	SSR Damping controller with PI	SSR Damping controller with Fuzzy
      Te	-0.301	-0.363
      Pe	0.395	0.351
      Qe	0.049	0.018
      Vc	0.173	0.158
      Iline	0.48	0.439
      Vdc	1205.2	1202.4
      Vssr	1.95	0.74

      The table2 shows that the comparison between without SSR damping controller and PI and fuzzy based SSR damping controller when Iline as control signal with gain of 10. From table2 it is observed that the negative peak in the dynamic response of the torque is 1.5pu without SSR damping controller and it is reduced to -0.3pu when PI based SSRdamping controller is implemented. The negative peak in the dynamic response of the torque is further reduced to

      -0.36pu when fuzzy based SSRdamping controller is used.

      The table3 shows that the comparison between PI and fuzzy based SSR damping controller when Vc as control signal with gain of 30. From the table3 it is observed that the negative peak in the dynamic response of the torque is – 0.302pu when PI based SSRdamping controller is implemented. The negative peak in the dynamic response of the torque is further reduced to -0.362pu when fuzzy based SSRdamping controller is used.

      The table4 shows that the comparison between PI and fuzzy based SSR damping controller when Vc as control signal with gain of 46.From the table4 it is observed that the negative peak in the dynamic response of the torque is – 0.301pu when PI based SSRdamping controller is implemented. The negative peak in the dynamic response of the torque is further reduced to -0.363pu when fuzzy based SSRdamping controller is used.

      Simulation results show that Fuzzy controller based slightly decreases the amplitude of SSR damping oscillations. Results comparison between conventional PI Controller and the proposed Fuzzy based controller for DFIG indicates that the proposed Fuzzy based controller has less settling time and less overshoot when compared with the conventional PI Controller.

      The following observations can also be made from Figs.

      1. Both the transmission line current and the voltage across the series capacitor reflect the SSR oscillation well.

      2. Though the electromagnetic torque reflects the SSR oscillation, the rotor speed reflects mainly the torsional mode.

      3. The terminal voltage shows SSR oscillation due to the damping controller.

      Overall, the control signal Vc can effectively damp SSR oscillations. In this paper observed that the capacitor voltage is an effective control signal for SSR mitigation when Vdc as output control signal with fuzzy logic controller.

   6. CONCLUSION

In this paper an effective control signal for SSR damping controller is implemented which mitigate both sub synchronous and super synchronous resonance in DFIG. Various simulations are carried out to analyze the performance of the system. Both Proportional Integral (PI) controller based and fuzzy logic controller based are implemented for mitigating SSR in wind farms connected with series compensated transmission network. Auxiliary damping control schemes to modulate either the terminal voltage or the dc-link voltage references of the grid side converter controls are proposed for SSR mitigation. Capacitor voltage is demonstrated to be an effective signal to enhance damping for both SSR and supersynchronous modes. Though it is a remote signal, it can be estimated through local current measurements. The performance of both the controllers has been studied and compared. A model has been developed in MATLAB /SIMULINK and simulated to verify the results. The fuzzy logic controller based SSR damping controller has a better performance compared with PI controller in steady state response and less settling time.

APPENDIX

The parameters of the DFIG and study system are shown in Tables 5 to 7

TABLE 5

Parameters of a Single 2-Mw DFIG and the Aggregated DFIG in network system

TABLE 6

Parameters of the network system

TABLE 7

Parameters of the Control Loops in A DFIG

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