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This study presents the auxiliary damping control with the reactive power loop on the rotor-side converter of doubly-fed induction generator (DFIG)-based wind farms to depress the sub-synchronous resonance oscillations in nearby turbogenerators. These generators are connected to a series capacitive compensation transmission system. First, the damping effect of the reactive power control of the DFIG-based wind farms was theoretically analyzed, and a transfer function between turbogenerator speed and the output reactive power of the wind farms was introduced to derive the analytical expression of the damping coefficient. The phase range to obtain positive damping was determined. Second, the PID phase compensation parameters of the auxiliary damping controller were optimized by a genetic algorithm to obtain the optimum damping in the entire subsynchronous frequency band. Finally, the validity and effectiveness of the proposed auxiliary damping control were demonstrated on a modified version of the IEEE first benchmark model by time domain simulation analysis with the use of DigSILENT/PowerFactory. Theoretical analysis and simulation results show that this derived damping factor expression and the condition of the positive damping can effectively analyze their impact on the system sub-synchronous oscillations, the proposed wind farms reactive power additional damping control strategy can provide the optimal damping effect over the whole sub-synchronous frequency band, and the control effect is better than the active power additional damping control strategy based on the power system stabilizator.

Series capacitive compensation is an important approach to improve the transfer capability and transient stability of existing transmission systems. However, the extensive use of series compensation can cause subsynchronous resonance (SSR), in which electrical networks exchange energy with the generator shaft system at frequencies less than the nominal frequency of the transmission line; this phenomenon results in turbogenerator shaft failure and instability of the power system [

To prevent the turbogenerator shaft from failing and to depress SSR oscillations, flexible AC transmission system (FACTS) devices (e.g., SVC, TCSC, STATCOM) [

Wind energy is the fastest-growing form of renewable energy in the world because it is clean, non-polluting, and abundant. Wind farms with a scale of hundreds of MW level are increasingly being developed and connected to power systems. Doubly fed induction generators (DFIGs) are widely used in wind power plants because of their capability to decouple control of real and reactive power. With the integration of large-scale wind farms into power systems, some researchers have used the control capability of DFIG to damp power system oscillations; however, most studies have focused on damping inter-area low-frequency oscillations [

This study presents the application of auxiliary damping control to the rotor-side converter (RSC) of a DFIG to damp SSR. A transfer function between turbogenerator speed and the output reactive power of wind farms was introduced to derive the analytical expression of damping. The effect of the reactive power of the DFIG-based wind farms on system damping was analyzed, and the phase range to obtain positive damping was determined. Then, a new auxiliary damping control strategy was proposed. The PID phase compensation parameters of the auxiliary damping controller were optimized by a genetic algorithm to obtain optimum damping in the entire sub-synchronous frequency band. Finally, the IEEE first benchmark model, modified by the inclusion of the DFIG-based wind farms, is used to demonstrate the performance of the proposed auxiliary damping control to suppress SSR oscillations by time domain simulation analysis with the use of DigSILENT/PowerFactory.

To evaluate the effectiveness of the proposed strategy on auxiliary damping control, the well-known IEEE first benchmark model, modified by the inclusion of DFIG-based wind farms, is used (_{L}_{L}_{c}_{sys}

The turbogenerator shaft system consists of six shaft segments, namely, a high-pressure turbine (HP), an intermediate-pressure turbine (IP), a low-pressure turbine (LPA), a low-pressure turbine (LPB), the generator (GEN), and the exciter (EXC). All masses are mechanically connected to one another by elastic shafts. The shaft system motion equation is described as follows:
_{i}_{i}_{Ji}_{i}_{e}_{i}_{,} _{i}_{+1} is the rigidity coefficient between the _{ii}_{i}_{,} _{i}_{+1} is the mutual damping ratio between the _{J}

The typical DFIG configuration consists of a wound rotor induction generator, with the stator directly connected to the grid and the rotor interfaced through a back-to-back partial scale power converter, as shown in

To analyze the mechanism of influence of the DFIG-based wind farms on system SSR damping, the system model in _{A}_{B}_{A}_{A}_{B}_{e}_{e}_{g}_{g}_{L}_{L}_{1}, _{2} are the reactance parameters.

The output active/reactive power _{e}_{e}

In the following small signal analysis derivation, the variation of the reactive power from DFIG based wind farm is assumed to only led to minor amplitude changes of the bus voltage _{A}_{0} = δ_{0}− γ_{A}_{0}. The subscript 0 represents an initial value.

Considering the minor amplitude changes of the bus voltage _{A}_{A}

Then, according to the active power balance of the transmission line, the next linearization equation can be obtained:

Substitute

Next, _{e}

The above equation indicates that the Δ_{e}_{g}_{g}_{g}_{ωq}(_{g}

Also, to analyze the damping effects of active power Δ_{g}

Given the sinusoidal microvariation of turbo-generators Δω with amplitude _{0} (Δω = _{0}_{g}

To analyze the damping effects of the last item of _{ωq}.:

When the phase angle between the range
_{ωq} > 0 and _{ωq} were proportional to |_{ωq}(_{g}_{ωq}(s) in the subsynchronous frequency band (62.8 rad/s to 314 rad/s) should be satisfied as follows:

The diagram of the auxiliary damping control system is shown in _{g}_{g}_{g}_{g}_{g}_{dr}_{qr}_{ds}_{qs}_{dr}_{qr}_{r}_{m}_{s}

For an improved approximate time delay effect in the entire sub-synchronous frequency band, we use Pade approximation for the time delay:

After time delay processing, the signal of turbo-generator speed deviation Δω was processed by the Butterworth filter to obtain the SSR modal component.

To efficiently compensate for the phase in the entire subsynchronous frequency band to satisfy the phase-frequency characteristics of damping SSR from _{P}_{I}_{D}_{i}_{i}_{= ∠}_{GC}_{(}_{j}_{i}_{)} and

To ensure that auxiliary damping controllers can provide effective positive damping in subsynchronous frequency bands, the proper phase compensation angle must be selected. Before calculating the phase compensation angle range, we must first determine the initial damping ratio and the initial phase angle range without auxiliary damping control. The amplitude-frequency and phase-frequency characteristic curve of _{ωq}(_{ωq} were obtained, as shown in

Also, for comparision with active power addition damping control, the amplitude-frequency and phase-frequency characteristic curve of _{ωp}(_{ωp}(_{ωq}(_{ωp}(_{ωq}(

Next, based on the condition of the phase compensation angle range for positive damping from _{1} is the set of parameters of the PID controller (_{P}_{I}_{D}_{2} is the set of compensation level, which means the proportion of the series capacitive reactance to the line reactance(_{C}_{L}_{2}.

In the figure, N_{1} is the total number of iterations in the optimization. The value range of PID parameters and compensation level are set as: _{P}_{I}_{D}_{C}/X_{L}∈(0.2,0.8). According to the above calculation process for the optimization of the phase compensation parameters of the PID controller, the changes in best fitness and mean fitness are shown in

After the PID parameters optimization, the _{P}_{D}_{I}_{ωq}(_{ωq} with the auxiliary damping control strategy were obtained, as shown in _{ωp}(

Comparison of _{ωq}(s) was also between −π/2∼−π/2, which ensures that the positive damping can be provided in the whole sub-synchronous frequency band. Furthermore, the damping ratio curve shows that the damping ratio significantly increased compared with that without auxiliary damping control.

Meanwhile, from _{ωp}(_{ωq}(_{ωp}(_{ωq}(

To evaluate the effectiveness of the proposed auxiliary damping control to mitigate SSR, the IEEE first benchmark model, modified by the inclusion of DFIG-based wind farms, was simulated with the use of the simulation program DIgSILENT/PowerFactory (DIgSILENT GmbH, Gomaringen, Germany). The compensation level _{C}_{L}

The time responses of the turbo-generator torques and the angular acceleration during and after clearing fault with auxiliary damping control are shown in _{g}

A novel auxiliary damping control strategy to depress SSR with the use of the reactive power control of DFIG-based wind farms has been presented in this study. Modulating the reactive power of the rotor-side converter of the DFIG to provide a positive damping component to facilitates SSR damping.

First, through a theroetical analysis, a transfer function between turbogenerator speed and the output reactive power of wind farms was introduced to derive the analytical expression of the damping ratio. Next, the effect of the reactive power of the DFIG-based wind farms on SSR damping was analyzed, and the phase range to obtain positive damping was determined. Then, using genetic algorithm, the optimum PID phase compensation parameters of the auxiliary damping controller were optimized to obtain the optimum damping in the entire sub-synchronous frequency band. Finally, the effectiveness of the proposed auxiliary damping control in suppressing SSR oscillations is demonstrated through time domain simulation of the modified IEEE first benchmark model. Results show that compare with no damp control and active power addition damping control based with PSS, the proposed auxiliary damping control can effectively damp SSR oscillations.

This study was supported by the National Natural Science Foundation of China (51377184), the International Science and Technology Cooperation Program of China (2013DFG61520), the Fundamental Research Funds for the Central Universities (CDJXS10151152), the Fundamental Research Funds for the Central Universities (CDJZR12150074), and the integration and demonstration program of Chongqing (CSTC2013JCSF70003). The authors are grateful for the supports.

The authors declare no conflict of interest.

Network parameters:

_{L}_{T}_{L}_{sys}

Turbo-generator parameters:

_{aσ}_{d}_{q}

Shaft parameters:

_{HP}_{IP}_{LPA}_{LPB}_{GEN}_{EXC}_{HP-IP}_{IP-LPA}_{LPA-LPB}_{LPB-GEN}_{GEN-EXC}

DFIG parameters:

Rated power: 2 MW, Rated voltage: 690 V, Rated frequency: 60 Hz, wind speed: 11 m/s, _{s}_{ls}_{r}_{lr}_{m}_{g}_{w}_{s}

The derived expressions of _{ωq}(s) and _{ωp}(s) are given by:

Schematic of a DFIG-based wind farm connected to the IEEE first benchmark model.

Schematic of the DFIG wind turbine.

Schematic of the simplified system model.

Diagram of the auxiliary damping control system.

Characteristics of the transfer function without auxiliary damping control, (

Flowchart of the optimization of the PID controller parameters.

Best fitness and mean fitness

Characteristics of the transfer function with auxiliary damping control, (

Dynamic performance of the turbo-generator during and after clearing fault, (

Dynamic performance of the turbo-generator during and after clearing fault, (