Coordinated control system and method of wind turbine and STATCOM for suppressing unbalanced voltage in dispersed wind farm

Abstract

The disclosure discloses a system and method for suppressing unbalanced voltage at the Point of Common Coupling (PCC) of dispersed wind farm. According to the disclosure, the wind farm comprising a STATCOM and plurality of wind turbines, dispersed wind farm controller, STATCOM controller, wind turbine controller. The dispersed wind farm controller decides that whether the STATCOM or the wind turbines inject negative-sequence current or not. Adaptive virtual negative-sequence output admittance controller is incorporated into the STATCOM controller and wind turbine controller, which can provide the negative-sequence current reference according to their participation factor. The compensation efforts of STATCOM and wind turbines can be flexibly controlled by changing their participation factor, which is related to the voltage unbalance voltage reference and the remaining capacity. The disclosure has significant advantages in cost and effectiveness to suppress the unbalanced voltage of PCC and improve the wind farm Low voltage fault recovery capability.

Claims

1. A system for suppressing unbalanced voltage at a Point of Common Coupling being located between a dispersed wind farm and a grid, the dispersed wind farm comprising a plurality of wind turbines, the system comprising: a measurement device for measuring unbalanced voltage and current at the Point of Common Coupling; a dispersed wind farm controller for controlling the plurality of wind turbines and a STATCOM; a voltage unbalance factor calculating block; wherein the voltage unbalance factor calculating block is coupled to the measurement device; wherein the dispersed wind farm controller is coupled to the voltage unbalance factor calculating block; wherein the voltage unbalance factor is calculated by ratio between an amplitude of negative-sequence and an amplitude of positive-sequence of the voltage at the Point of Common Point; a STATCOM controller; wherein the STATCOM controller is coupled to the dispersed wind farm controller; a plurality of wind turbine controllers; wherein the plurality of wind turbines controllers are coupled to the dispersed wind farm controller; a grid-connected transformer; an adaptive virtual negative-sequence output admittance controller; wherein the STATCOM controller is coupled to the adaptive virtual negative-sequence output admittance controller, and wherein the wind turbine controllers are coupled to the adaptive virtual negative-sequence output admittance controller; wherein a negative-sequence current injected ability of STATCOM is determined by two limitations, and they are a maximum amplitude of output phase voltage V.sub.stmax and the maximum amplitude of output phase current I.sub.stmax,
V.sub.st max≤N.Math.M.sub.dc.Math.V.sub.dc
I.sub.st max≤1.25 wherein M.sub.dc is a modulation index; N is a numbers of cells per phase; M.sub.dc=1; V.sub.dc is the dc voltage of CHB-STATCOM; And wherein the maximum amplitude of output phase voltage V.sub.stmax can be calculated by, $V_{\mathrm{st}\max }=\max \left(\sqrt{V_{\mathrm{stmp}}^2+V_{\mathrm{stmn}}^2+V_{\mathrm{st}0}^2}\right),m=a,b,c$ wherein V.sub.stmp, V.sub.stmn are the amplitude of the positive-sequence and negative-sequence in three-phase, respectively; V.sub.st0 is the amplitude of the zero-sequence voltage, V.sub.stmp, V.sub.stmn and V.sub.st0 can be calculated by a d-q transformation; wherein V.sub.std0 and V.sub.stq0 can be calculated as, $\left[\begin{array}{c}{V}_{\mathrm{std}0}\\ V_{\mathrm{stq}0}\end{array}\right]=\frac{1}{\left(I_{\mathrm{stdp}}^2+I_{\mathrm{stqp}}^2\right)-\left(I_{\mathrm{stdn}}^2+I_{\mathrm{stqn}}^2\right)}.Math.\left[\begin{array}{cc}{I}_{\mathrm{stdp}}-I_{\mathrm{stdn}}& I_{\mathrm{stqp}}-I_{\mathrm{stqn}}\\ I_{\mathrm{stqp}}+I_{\mathrm{stqn}}& -I_{\mathrm{stdn}}-I_{\mathrm{stdp}}\end{array}\right].Math.(\left[\frac{\begin{array}{c}2P_{a\_\mathrm{fb}}\\ 2\sqrt{3}{P}_{a\_\mathrm{fb}}+4\sqrt{3}{P}_{b\_\mathrm{fb}}\end{array}}{3}\right]+\left[\begin{array}{cccc}-I_{\mathrm{stdn}}& I_{\mathrm{stqn}}& -I_{\mathrm{stdp}}& I_{\mathrm{stqp}}\\ I_{\mathrm{stqn}}& I_{\mathrm{stdn}}& I_{\mathrm{stqp}}& I_{\mathrm{stdp}}\end{array}\right].Math.\hspace{1em}\hspace{1em}\left[\begin{array}{c}{V}_{\mathrm{stdp}}\\ V_{\mathrm{stqp}}\\ V_{\mathrm{stdn}}\\ V_{\mathrm{stdn}}\end{array}\right])$ wherein V.sub.stdp, V.sub.stqp, V.sub.stdn, V.sub.stqn, I.sub.stdp, I.sub.stqp, I.sub.stdn, I.sub.stqn are the d-q components of positive-sequence and negative-sequence output voltage and current of CHB-STATCOM; P.sub.a_fb and P.sub.b_fb can be obtained by a proportional integral controller to derive de voltage of phase-A and -B clusters, respectively; wherein a maximum amplitude of output phase current I.sub.stmax can be obtained by,
I.sub.st max=I.sub.stp+I.sub.stn wherein I.sub.stp, I.sub.stn are the magnitude of positive-sequence and negative-sequence current of CHB-STATCOM.

2. The system of claim 1, wherein the wind turbines are permanent magnet synchronous generators.

3. The system of claim 1, where the STATCOM is a cascade H-bridge STATCOM (CHB-STATCOM).

4. The system of claim 1, wherein the grid-connected transformer is a three-winding transformer.

5. The system of claim 3, wherein the CHB-STATCOM is connected to a tertiary-winding of the grid-connected transformer.

6. The system of claim 3, wherein the CHB-STATCOM can inject inductive and capacitive reactive power from the wind farm to the grid.

7. A method for suppressing unbalanced voltage at a Point of Common Coupling being located between a dispersed wind farm and a grid, the dispersed wind farm comprising a plurality of wind turbines, the method comprising: measuring unbalanced voltage and current at the Point of Common Coupling; calculating a voltage unbalance factor which is calculated by ratio between an amplitude of negative-sequence and an amplitude of positive-sequence of the voltage at the Point of Common Point; controlling the plurality of wind turbines and a STATCOM by a dispersed wind farm controller, which can provide a control signal for suppressing the unbalanced voltage at the Point of Common Coupling; wherein the control signal is that whether the STATCOM or wind turbines should share the unbalanced voltage or not; wherein the STATCOM can inject negative-sequence current to the grid to suppress the unbalanced voltage at the Point of Common Coupling; the wind turbines can inject negative-sequence current to the grid to suppress the unbalanced voltage at the Point of Common Coupling; providing a negative-sequence current reference for the STATCOM and the wind turbines by an adaptive virtual negative-sequence output admittance controller, and wherein the wind turbines and the STATCOM can be used to suppress the unbalanced voltage at the Point of Common Coupling by changing their corresponding negative-sequence output admittance; wherein a negative-sequence current injected ability of STATCOM is determined by two limitations, and they are a maximum amplitude of output phase voltage V.sub.stmax and the maximum amplitude of output phase current I.sub.stmax,
V.sub.st max≤N.Math.M.sub.dc.Math.V.sub.dc
I.sub.st max≤1.25 wherein M.sub.dc is a modulation index; N is a numbers of cells per phase; M.sub.dc=1; V.sub.dc is the dc voltage of CHB-STATCOM; And wherein the maximum amplitude of output phase voltage V.sub.stmax can be calculated by, $V_{\mathrm{st}\max }=\max \left(\sqrt{V_{\mathrm{stmp}}^2+V_{\mathrm{stmn}}^2+V_{\mathrm{st}0}^2}\right),m=a,b,c$ wherein V.sub.stmp, V.sub.stmn are the amplitude of the positive-sequence and negative-sequence in three-phase, respectively; V.sub.st0 is the amplitude of the zero-sequence voltage, V.sub.stmp, V.sub.stmn and V.sub.st0 can be calculated by a d-q transformation; wherein V.sub.std0 and V.sub.stq0 can be calculated as, $\left[\begin{array}{c}{V}_{\mathrm{std}0}\\ V_{\mathrm{stq}0}\end{array}\right]=\frac{1}{\left(I_{\mathrm{stdp}}^2+I_{\mathrm{stqp}}^2\right)-\left(I_{\mathrm{stdn}}^2+I_{\mathrm{stqn}}^2\right)}.\left[\begin{array}{cc}{I}_{\mathrm{stdp}}-I_{\mathrm{stdn}}& I_{\mathrm{stqp}}-I_{\mathrm{stqn}}\\ I_{\mathrm{stqp}}+I_{\mathrm{stqn}}& -I_{\mathrm{stdn}}-I_{\mathrm{stdp}}\end{array}\right].Math.(\left[\frac{\begin{array}{c}2P_{\mathrm{a\_fb}}\\ 2\sqrt{3}{P}_{a\_\mathrm{fb}}+4\sqrt{3}{P}_{\mathrm{b\_fb}}\end{array}}{3}\right]+\hspace{1em}\left[\begin{array}{cccc}-I_{\mathrm{stdn}}& I_{\mathrm{stqn}}& -I_{\mathrm{stdp}}& I_{\mathrm{stqp}}\\ I_{\mathrm{stqn}}& I_{\mathrm{stdn}}& I_{\mathrm{stqp}}& I_{\mathrm{stdp}}\end{array}\right].Math.\left[\begin{array}{c}{V}_{\mathrm{stdp}}\\ V_{\mathrm{stqp}}\\ V_{\mathrm{stdn}}\\ V_{\mathrm{stdn}}\end{array}\right])$ wherein V.sub.stdp, V.sub.stqp, V.sub.stdn, V.sub.stqn, I.sub.stdp, I.sub.stqp, I.sub.stdn, I.sub.stqn are the d-q components of positive-sequence and negative-sequence output voltage and current of CHB-STATCOM; P.sub.a_fb and P.sub.b_fb can be obtained by a proportional integral controller to derive dc voltage of phase-A and -B clusters, respectively; wherein a maximum amplitude of output phase current I.sub.stmax can be obtained by,
I.sub.st max=I.sub.sp+I.sub.stn wherein I.sub.stp, I.sub.stn are the magnitude of positive-sequence and negative-sequence current of CHB-STATCOM.

8. The method of claim 7, wherein a relationship between the unbalanced voltage at the Point of Common Coupling and the unbalance voltage at the grid is defined, $v_{pccdqn}=\frac{Y_{sn}}{Y_{eqn}+Y_{sn}}{V}_{sdqn}$ $Y_{\mathrm{eqn}}=\frac{1}{\frac{1}{Y_{t1n}}+\frac{1}{\frac{1}{\frac{1}{\underset{x=1}{\overset{m}{.Math.}}{Y}_{gxn}}+\frac{1}{Y_{t2n}}}+\frac{1}{\frac{1}{Y_{t3n}}+\frac{1}{Y_{\mathrm{stn}}}}}}$ wherein the unbalanced grid is modeled as an unbalanced voltage v.sub.sdqn and a negative-sequence admittance Y.sub.sn, a PMSG and the STATCOM are modeled as negative-sequence admittance Y.sub.gxn (x=1, 2, 3 . . . m) and Y.sub.stn, respectively, a grid-connected three-winding transformer is also modeled as negative-sequence admittance, specifically, Y.sub.t1n, Y.sub.t2n, Y.sub.t3n are the equivalent negative-sequence admittance of the primary-winding, the secondary winding, and the tertiary winding, respectively, Y.sub.eqn is the equivalent negative-sequence admittance seen from Point of Common Coupling.

9. The method of claim 7, the negative-sequence reference can be calculated as,
I.sub.dqrefxn=(I.sub.dqxn+V.sub.gdqnY.sub.bn)k.sub.x wherein Y.sub.bn is a known constant, here Y.sub.bn=8, k.sub.x is a participation factor of the wind turbines (e.g., x=1, 2, . . . m) or the STATCOM (e.g., x=st), I.sub.dqxn and I.sub.dqrefxn are the measured and the reference negative-sequence current, respectively; V.sub.gdqn is the d-q components of negative-sequence voltage at the Point of Common Coupling.

10. The method of claim 9, the k.sub.x should be limited within 0˜1.

11. The method of claim 7, further comprising participation factor calculation for wind turbines, wherein a voltage unbalance factor controller and a remaining capacity calculation block are required; wherein the voltage unbalance factor reference is set to 2%; and wherein a low pass filter is chosen to remove a double-frequency components of an output power in the remaining capacity calculation block.

12. The method of claim 11, further comprising a coordinated control strategy of the CHB-STATCOM and the wind turbines, and which comprising, Step 1: If the voltage unbalance factor at Point of Common Coupling is larger than 2%, then CHB-STATCOM will inject negative-sequence current to suppress the unbalanced voltage at the Point of Common Coupling as much as it can; Step 2: If voltage unbalance factor at Point of Common Coupling is still larger than 2%, and then the participation factor of CHB-STATCOM is equal to 1; Step 3: According to the voltage unbalance factor, and the output power of all wind turbines, calculating the participation factors for all wind turbines; Step 4: Calculating the negative-sequence current reference for all wind turbines.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a dispersed wind farm, which contains m PMSGs and a STATCOM in accordance to an embodiment of the present invention.

(2) FIG. 2 shows the electrical schematic of the PMSG inverter with an LCL filter.

(3) FIG. 3 shows the equivalent circuit of the STATCOM.

(4) FIG. 4 shows the equivalent negative-sequence model of investigated dispersed wind farm.

(5) FIG. 5 shows the equivalent negative-sequence model of FIG. 4.

(6) FIG. 6 shows the overall control structure of the CHB-STATCOM.

(7) FIG. 7 show the compensation region of negative-sequence of CHB-STATCOM under different output reactive power. (a) Q=1 p.u.; (b) Q=0.8 p.u.; (c) Q=0.5 p.u.; (d) Q=0.2 p.u.

(8) FIG. 8 shows the calculation method of negative-sequence current reference for CHB-STATCOM.

(9) FIG. 9 shows the proposed virtual NSOA calculation method.

(10) FIG. 10 shows the control structure for PMSG with the proposed virtual NSOA method.

(11) FIG. 11 shows the participation factor calculation method of PMSG.

(12) FIG. 12 shows the coordinated control for sharing unbalanced grid voltage of CHB-STATCOM and PMSG.

(13) FIG. 13 show the results of CHB-STATCOM operating under unbalanced grid voltage when only CHB-STATCOM participates in compensating unbalanced grid voltage. (a) Output current; (b) d-q components of output negative-sequence current; (c) VUF at PCC; (d) DC voltage in each phase.

(14) FIG. 14 show output current of the CHB-STATCOM when CHB-STATCOM and PMSGs all participate in compensating unbalanced grid voltage. (a) d-q components of negative-sequence current. (b) Three-phase current.

(15) FIG. 15 show the simulation results about PCC and PMSG. (a) Active power; (b) VUF at PCC; (c) Participation factors; (d) Grid voltage without compensation; (e) Grid voltage after compensation.

(16) FIG. 16 show the negative-sequence currents in d-q frame of three investigated PMSGs.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(17) In the following description, the control method of STATCOM and PMSGs thereof and the likes are set forth as preferred examples. It will be apparent to those skilled in the art that modifications, including additions and/or substitutions may be made without departing from the scope and spirit of the invention. Specific details may be omitted so as not to obscure the invention; however, the disclosure is written to enable one skilled in the art to practice the teachings herein without under undue experimentation.

(18) Topology of a Dispersed Wind Farm

(19) FIG. 1 shows a dispersed wind farm, which contains m wind turbines and a STATCOM. Generally, a dispersed wind farm is composed of 25 wind turbines with a rating of 2.0 MW each, with the total installed capacity of 50 MW, so in FIG. 1, m=25. Here, the capacity of STATCOM is ±5 MVar. Referring now to FIG. 1, a DWF controller is required to control the characteristic of the negative-sequence at the PCC. Therefore, a centralized dispersed wind farm controller (DWF Ctrl.) is need to supervise the negative-sequence voltage and current injected at the PCC. The DWF controller is formed by the measurement device (Meas.), which contains the voltage and current sense at the PCC, a dispatcher and a communication hub (COM.). The communication hub will exchange control reference and other signals with all the wind turbines (Wind turbine Ctrl.) and STATCOM (STATCOM Ctrl.).

(20) Still referring to FIG. 1, the dispatcher of DWF controller has the functionality of calculating the participation factors of STATCOM and wind turbines. The way of calculating the participation factor can be done by the following strategies, e.g. minimization of VUF at the PCC. The strategy suggested in view of the present invention is based on using STATCOM and wind turbine as the back-up for the wind farm in case there exist unbalanced grid that exceeds the limit value at the PCC. The strategy also suggested in view of the present invention is based on the STATCOM should inject negative-sequence current immediately if there exist unbalanced grid at the PCC.

(21) Still referring to FIG. 1, wind turbines are connected in parallel to the 35 kV bus via a box-type transformer and then connected to the public network through a grid-connected transformer with three windings. For the three-windings grid-connected transformer, literature proposes an inductive method for suppressing the harmonic in photovoltaic station. Specifically, the STATCOM and passive filter are connected to the tertiary winding of the three-winding transformer, owing to the impendences of tertiary winding and passive filter are equal to zero, the harmonics can be eliminated between the secondary winding and the tertiary winding. In this way, there are no or few harmonic currents at the grid winding of the transformer. Moreover, the traditional coupling transformer can be saved because the STATCOM can be connected to the tertiary winding of the three-winding transformer. In this invention, the passive filter is omitted because the STATCOM has a better dynamic reactive power compensation.

(22) Still referring to FIG. 1, permanent magnetic synchronous generator (PMSG) is adopted in this invention.

(23) Still referring to FIG. 1, cascaded H-bridges STATCOM (CHB-STATCOM) is adopted in this invention.

(24) Modeling of PMSG's Grid-Side Inverter in Negative-Sequence Synchronous Reference Frame (NS-SRF)

(25) FIG. 2 shows a grid-side inverter of PMSG with an LCL filter. According to the Kirchhoff's current law (KCL) and the Kirchhoff's voltage law (KVL), the dynamics of grid-side inverter of PMSG with LCL filter in NS-SRF is obtained as,

(26) $\begin{array}{cc}{L}_f\frac{d{i}_{fdqn}}{dt}=-\left(R_f-j{\omega }_g{L}_f\right)i_{fdqn}-v_{\mathrm{cdqn}}+v_{\mathrm{invdqn}}& \left(1\right)\\ L_g\frac{d{i}_{\mathrm{gdqn}}}{dt}=-\left(R_g-j{\omega }_g{L}_g\right)i_{gdqn}+v_{cdqn}-v_{gdqn}& \left(2\right)\\ C\frac{d{v}_{cdqn}}{dt}=i_{fdqn}-i_{gdqn}+j{\omega }_{g}C{v}_{cdqn}& \left(3\right)\end{array}$
where ω.sub.g is angular frequency of the grid; R.sub.f, L.sub.f, R.sub.g, L.sub.g and C constitute of LCL filter; i.sub.fdqn, i.sub.gdqn are the negative-sequence components of the grid current and the inverter output current, respectively; v.sub.gdqn, v.sub.invdqn, v.sub.cdqn, are the negative-sequence components of grid voltage, inverter output voltage and capacitor voltage, respectively; In the steady state, the dx/dt=0, where x=i.sub.fdqn, i.sub.gdqn, v.sub.cdqn. Therefore, the (1), (2) and (3) can be rewritten as,
v.sub.cdqn=(R.sub.f−jω.sub.gL.sub.f)i.sub.fdqn+v.sub.invdqn  (4)
−(R.sub.g−jω.sub.gL.sub.g)i.sub.gdqn+v.sub.cdqn−v.sub.gdqn=0  (5)
i.sub.fdqn=i.sub.gdqn−jω.sub.gCv.sub.cdqn  (6)

(27) Substituting (4) and (6) into (5), the negative-sequence current of PMSG can be expressed with negative-sequence output voltage of inverter and negative-sequence grid voltage as,
Mi.sub.gdqn=−v.sub.invdqn+NV.sub.gdqn  (7)
where,
M=−(R.sub.g−jωL.sub.g)−(R.sub.f−jω.sub.gL.sub.f)+(R.sub.g−jωL.sub.g)(R.sub.f−jω.sub.gL.sub.f)jω.sub.gC  (8)
N=1−(R.sub.f−jω.sub.gL.sub.f)jω.sub.gC  (9)

(28) Thus, the NSOA of the PMSG can be obtained as

(29) $\begin{array}{cc}{Y}_{\mathrm{gn}}=\frac{i_{{}^{\mathrm{gdqn}}}}{v_{{}^{\mathrm{gdqn}}}}=\frac{N}{M}-\frac{1}{M}\frac{v_{\mathrm{invdqn}}}{v_{\mathrm{gdqn}}}& \left(10\right)\end{array}$

(30) Therefore, we can see from (10) that the NSOA of PMSG can be controlled by changing the negative-sequence components of the grid-side inverter's output voltage.

(31) Equivalent Model of CHB-STATCOM in NS-SRF

(32) FIG. 3 shows an equivalent circuit of CHB-STATCOM, where the CHB-STATCOM is represented by a common converter. The negative-sequence components of CHB-STATCOM in the NS-SRF can be expressed as,

(33) $\begin{array}{cc}{L}_{\mathrm{st}}\frac{d{i}_{\mathrm{stdqn}}}{dt}=-\left(R_{\mathrm{st}}-j{\omega }_g{L}_{st}\right)i_{\mathrm{stdqn}}+v_{\mathrm{stinvdqn}}-v_{{}^{g1\mathrm{dqn}}}& \left(11\right)\end{array}$
where R.sub.st and L.sub.st are the resistance and inductance of the filter. i.sub.stdqn is the negative-sequence current, v.sub.stinvdqn is the negative-sequence component output voltage, v.sub.g1dqn is the voltage of the terminal connected with the CHB-STATCOM.

(34) In the steady state, the left side of (11) is equal to 0. So, the NSOA of CHB-STATCOM can be obtained as

(35) $\begin{array}{cc}{Y}_{\mathrm{stn}}=\frac{i_{\mathrm{stdq}n}}{v_{g1\mathrm{dqn}}}=\frac{1}{\left(R_{\mathrm{st}}-j{\omega }_g{L}_{\mathrm{st}}\right)}-\frac{1}{\left(R_{\mathrm{st}}-j{\omega }_g{L}_{\mathrm{st}}\right)}\frac{v_{\mathrm{invdqn}}}{v_{g1\mathrm{dqn}}}& \left(12\right)\end{array}$

(36) Similarly, we can see from (12) that the NSOA of the CHB-STATCOM can be controlled by changing its output voltage.

(37) Modeling of Overall Wind Power Integration System

(38) The negative-sequence model of overall wind power integration is established to analyze the coordinated mechanism for compensating unbalanced voltage of PCC, as shown in FIG. 4, in which the unbalanced grid is modeled as an unbalanced voltage v.sub.sdqn and a negative-sequence admittance Y.sub.sn. The PMSG and the CHB-STATCOM are modeled as negative-sequence admittance Y.sub.gxn (x=1, 2, 3 . . . m) and Y.sub.stn, respectively. The grid-connected three-winding transformer is also modeled as negative-sequence admittance, specifically, Y.sub.t1n, Y.sub.t2n, Y.sub.t3n are the equivalent negative-sequence admittance of the primary-winding, the secondary winding, and the tertiary winding, respectively. Noting that the positive- and negative-sequence impedances of transformer are same. Furthermore, a simplified negative-sequence model of wind power integration system is obtained, as shown in FIG. 5, in which Y.sub.eqn is the equivalent negative-sequence admittance seen from PCC. According to the FIG. 4, Y.sub.eqn can be calculated as,

(39) $\begin{array}{cc}{Y}_{\mathrm{eqn}}=\frac{1}{\frac{1}{Y_{t1n}}+\frac{1}{\frac{1}{\frac{1}{\underset{x=1}{\overset{m}{.Math.}}{Y}_{\mathrm{gxn}}}+\frac{1}{Y_{t2n}}}+\frac{1}{\frac{1}{Y_{t3n}}+\frac{1}{Y_{\mathrm{stn}}}}}}& \left(13\right)\end{array}$

(40) According to FIG. 5 and KCL, the negative-sequence voltage at PCC can be obtained as,

(41) $\begin{array}{cc}{v}_{pccdqn}=\frac{Y_{sn}}{Y_{eqn}+Y_{sn}}{V}_{sdqn}& \left(14\right)\end{array}$

(42) The negative-sequence admittance of transformer can be obtained after by commissioning tests, in other word, Y.sub.t1n, Y.sub.t2n, Y.sub.t3n cannot be changed. Therefore, from (13) and (14), we can see that as long as the NSOA of PMSGs or CHB-STATCOM is large enough, the NSOA see from the PCC (see FIG. 5) Y.sub.eqn is also large enough, thus, the negative-sequence voltage at PCC is equal or approximately equal to zero, which means that the unbalanced grid voltage can be suppressed. Besides, the coordinated compensation for unbalanced voltage among multiple PMSGs and CHB-STATCOM can be implemented by changing their corresponding NSOA. Specifically, the PMSGs or CHB-STATCOM with large NSOA will inject more negative-sequence current than them with small NSOA.

(43) Operation Characteristic of CHB-STATCOM Under Unbalanced Grid Condition

(44) System Configuration and Controller

(45) The operating principle of CHB-STATCOM under unbalanced grid condition can be found in [8], [12]. FIG. 6 shows the overall control structure of the CHB-STATCOM under unbalanced grid condition. The overall dc voltage control generates the positive-sequence active current (I.sub.dp*) to the positive-sequence current controller, and keeps the average value of the dc bus voltages of all cells at the dc voltage reference (V.sub.dcref). The individual balancing voltage control mainly keeps the dc voltage of each cell at the predefine value.

(46) In this invention, CHB-STATCOM provides negative-sequence currents to suppress the unbalanced voltage, which inevitably result in uneven active powers among three clusters. Thus, the balanced phenomenon of dc voltage of three clusters of CHB-STATCOM will be broken. Here, cluster voltage balancing control is used to generate a suitable zero-sequence command (M.sub.0) to redistribute the active power of three clusters, and make the dc voltage of three-cluster balanced. The M.sub.0 can be calculated as [12],

(47) $\begin{array}{cc}{M}_0=\frac{V_{std0}\cos \left(\omega t\right)+V_{stq0}\sin \left(\omega t\right)}{V_{\mathrm{dc\_ave}}}& \left(15\right)\end{array}$ V.sub.std0 and V.sub.stq0 can be calculated as [16],

(48) $\begin{array}{cc}\left[\begin{array}{c}{V}_{\mathrm{std}0}\\ V_{\mathrm{stq}0}\end{array}\right]=\frac{1}{\left(I_{\mathrm{stdp}}^2+I_{\mathrm{stqp}}^2\right)-\left(I_{\mathrm{stdn}}^2+I_{\mathrm{stqn}}^2\right)}.\left[\begin{array}{cc}{I}_{\mathrm{stdp}}-I_{\mathrm{stdn}}& I_{\mathrm{stqp}}-I_{\mathrm{stqn}}\\ I_{\mathrm{stqp}}+I_{\mathrm{stqn}}& -I_{\mathrm{stdn}}-I_{\mathrm{stdp}}\end{array}\right].Math.(\left[\frac{\begin{array}{c}2P_{\mathrm{a\_fb}}\\ 2\sqrt{3}{P}_{a\_\mathrm{fb}}+4\sqrt{3}{P}_{\mathrm{b\_fb}}\end{array}}{3}\right]+\hspace{1em}\left[\begin{array}{cccc}-I_{\mathrm{stdn}}& I_{\mathrm{stqn}}& -I_{\mathrm{stdp}}& I_{\mathrm{stqp}}\\ I_{\mathrm{stqn}}& I_{\mathrm{stdn}}& I_{\mathrm{stqp}}& I_{\mathrm{stdp}}\end{array}\right].Math.\left[\begin{array}{c}{V}_{\mathrm{stdp}}\\ V_{\mathrm{stqp}}\\ V_{\mathrm{stdn}}\\ V_{\mathrm{stdn}}\end{array}\right])& \left(16\right)\end{array}$
where V.sub.stdp, V.sub.stqp, V.sub.stdn, V.sub.stqn, I.sub.stdp, I.sub.stqp, I.sub.stdn, I.sub.stqn are the d-q components of positive-sequence and negative-sequence output voltage and current of CHB-STATCOM; P.sub.a_fb and P.sub.b_fb can be obtained by a proportional integral (PI) controller to derive dc voltage of phase-A and phase-B clusters, respectively. Here, the voltage drop of inductance is neglected.

(49) The maximum amplitude of output phase voltage of CHB-STATCOM can be calculated as,

(50) $\begin{array}{cc}{V}_{\mathrm{st}\max }=\max \left(\sqrt{V_{\mathrm{stmp}}^2+V_{\mathrm{stmn}}^2+V_{\mathrm{st}0}^2}\right),m=a,b,c& \left(17\right)\end{array}$
where V.sub.stmp, V.sub.stmn are the amplitude of the positive-sequence and negative-sequence in three-phase, respectively; V.sub.0 is the amplitude of the zero-sequence voltage. V.sub.stmp, V.sub.stmn and V.sub.0 can be calculated by the dq transformation. To prevent the over-modulation, V.sub.stmax must be lower than the maximum permit output voltage, that is,
V.sub.st max≤N.Math.M.sub.dc.Math.V.sub.dc  (18)
where M.sub.dc is the modulation index; N is the numbers of cells per phase. In this paper, the PSC-PWM scheme is used, hence, M.sub.dc=1. Except for the limitation of the maximum amplitude of output voltage, the limitation of the peak current should be considered. The instantaneous current of the CHB-STATCOM can be expressed as,

(51) 0$\begin{array}{cc}{I}_{\mathrm{stm}}=\sqrt{{\left(I_{\mathrm{stp}}\right)}^2+{\left(I_{\mathrm{stpn}}\right)}^2+2I_{\mathrm{stp}}{I}_{\mathrm{stn}}\cos \left({\phi }_i-d.Math.2\pi /3\right)}& \left(19\right)\end{array}$
where m=a, b, c, and d=0, 1, −1; pi is the angle difference between the positive-sequence and negative-sequence current. I.sub.stp, I.sub.stn can be calculated as,

(52) $\begin{array}{cc}{I}_{\mathrm{stp}}=\sqrt{{\left(I_{\mathrm{stdp}}\right)}^2+{\left(I_{\mathrm{stqp}}\right)}^2}& \left(20\right)\\ I_{\mathrm{stn}}=\sqrt{{\left(I_{\mathrm{stdn}}\right)}^2+{\left(I_{\mathrm{stqn}}\right)}^2}& \left(21\right)\end{array}$

(53) From (19), we can know that the instantaneous peak current can reach the maximum value when the trigonometric is equal to 1, thus, the peak value of phase current is expressed by,
I.sub.st max=I.sub.stp+I.sub.stn  (22)

(54) It can be found in IEEE Std1517 that the fault current is usually limited to be less than 1.25 times the rated value. Here, the maximum allowable value of phase current is set as 1.25 p.u., therefore, the limitation of phase current can be expressed as,
I.sub.st max≤1.25  (23)

(55) The negative-sequence current injected by CHB-STATCOM is depend on (18) and (23), according to these two limitations, the negative-sequence current injection region of a 10 kV, ±5 MVar CHB-STATCOM can be obtained at the different reactive output power, as shown in FIG. 7.

(56) FIG. 7 clearly shows that when the output reactive power is equal to 1.0 p.u., the compensation range of negative is a circle, which means that the limitation is just depended on (23). When the CHB-STATCOM not working at the rated condition, although the lower output reactive power means the more remaining capacity to be used, the boundary of compensation region is not a positive correlation with remaining capacity, because there is no risk of over-current and it is depend on (18), Therefore, the boundary of compensation region is not an irregular shape. Thus, it is necessary to make sure the negative-sequence current injected by the CHB-STATCOM should be within the safe compensation range.

(57) Negative-Sequence Current References Calculation for CHB-STATCOM

(58) FIG. 8 shows the calculation method for negative-sequence current reference. Here, the two attenuation coefficients d.sub.1, d.sub.2 are introduced to reduce the desired negative-sequence to satisfy the respective inequalities (23) and (18). The expression for reducing negative-sequence current references can be presented as,
I.sub.dnref1=d.sub.1×I.sub.dnc, I.sub.qnref1=d.sub.1×I.sub.qnc  (24)
I.sub.dnref=d.sub.2×I.sub.dnref1, I.sub.qnref=d.sub.2×I.sub.qnref1,  (25)
where I.sub.dnc, I.sub.qnc can be obtained from FIG. 9, which will be discussed in the next section.

(59) The desired negative-sequence current should satisfy (23), otherwise, d.sub.1 uses 0.95 as a step to reduce the negative-sequence reference until (23) is satisfied, we remark the negative-sequence references from the first iteration method are I.sub.dnref1 and I.sub.qnref1. The V.sub.std0 and V.sub.stq0 can be calculated by using the I.sub.dnref1 and I.sub.qnref1 to replace I.sub.stdn and I.sub.stqn in (16), then the maximum amplitude of output phase voltage of CHB-STATCOM can be calculated by using (17), which can be used to judge the (18) is satisfied or not. If the limitation of (18) is satisfied, the I.sub.dnref1 and I.sub.qnref1 will be transmitted to the negative-sequence current controller of CHB-STATCOM, otherwise, d.sub.2 also uses 0.95 as a step to reduce the negative-sequence references until (18) is satisfied. In this way, the desired negative-sequence current can be limited within the safe operation area, in other word, the over-modulation and over-current phenomenon cannot occur, which can make sure the CHB-STATCOM operates stably.

(60) Coordinated Control Strategy of CHB-STATCOM and PMSG for Suppressing Unbalanced Voltage at the PCC

(61) To address the over-modulation problem that the conventional virtual admittance method may bring, a virtual NSOA method based on a negative-sequence current reference for CHB-STATCOM and PMSGs is proposed. The participation factors of them based on a secondary control strategy are designed, thus their NSOA can be changed by controlling the participation factor. Besides, a coordinated control strategy of CHB-STATCOM and PMSGs for suppressing unbalanced voltage is discussed.

(62) Adaptive Virtual NSOA Method

(63) FIG. 9 shows the proposed virtual NSOA method, the negative-sequence reference can be calculated as,
I.sub.dqrfxn(I.sub.dqxn+V.sub.gdqnY.sub.bn)k.sub.x  (26)
where Y.sub.bn is a known constant, here Y.sub.bn=8. k.sub.x is the participation factor of the PMSGs (e.g., x=1, 2, . . . m) or the CHB-STATCOM (e.g., x=st). I.sub.dqxn and I.sub.dqrefxn are the measured and the reference negative-sequence current, respectively; V.sub.gdqn is the d-q components of negative-sequence voltage at the PCC.

(64) Assuming that the PI parameters are perfectly designed, the negative-sequence control loop can track negative-sequence current reference well, as follows,
I.sub.dqrefxn=I.sub.dqn  (27)

(65) Substituting (27) into (26), the NOSA of PMSGs or CHB-STATCOM can be expressed as,

(66) $\begin{array}{cc}{Y}_{\mathrm{eqxn}}=\frac{I_{\mathrm{dqxn}}}{V_{{}^{\mathrm{gdqn}}}}=\frac{k_x}{1-k_x}{Y}_{bn}& \left(28\right)\end{array}$

(67) Equation (28) clearly show that the NSOA of PMSGs or CHB-STATCOM is equal to 0 if k.sub.x=0, while it can reach infinity if k.sub.x=1. Therefore, k.sub.x should be limited to be within 0-1, to control the NSOA of PMSGs or CHB-STATCOM from 0 to infinity.

(68) FIG. 10 shows the control structure of PMSG with NSOA method. In FIG. 10, the angle θ.sub.g of the grid voltage is obtained by a phase-locked loop (PLL) to implement the Park's transformation, then, the positive and negative component of voltage and current in dq frame can be obtained by a dual-second-order-generalized integrator (DSOGI) [30]. Moreover, the positive-sequence control block can track the positive-sequence current reference and generate the active power to the grid. While the negative-sequence control block ensures the PMSGs can inject the negative-sequence current calculated by NSOA method to compensate unbalanced grid voltage.

(69) Participation Factor Calculation for PMSG

(70) FIG. 11 shows the participation factor calculation method for PMSGs. In this paper, a VUF controller is proposed to keep the VUF of PCC equal to the predefined value VUF*, which is equal to 2%. Because the International Electrotechnical Commission recommends that voltage unbalance in power grids should be limited to 2%. The VUF is the ratio between the negative- and positive-sequence components of grid voltage. First, the deviation between the measured VUF and the reference is transmitted to a PI controller, the abs function block ensures the value comes from the PI controller is a positive. Moreover, the double-frequency fluctuation of power will be excited because of the interaction between the positive-sequence voltage and the negative-sequence current, and between the negative-sequence voltage and the positive-sequence current. Therefore, the low pass filter (LPF) is chosen to remove the double-frequency components of the output power.

(71) As mentioned above, the final participation factor k.sub.x should be limited to within 0-1, thus, a 0-1 limiter should be used. In order to ensure that the controller does not work when the VUF is lower than 2%, a selector with dead-band is added in the participation factor calculation block. Specifically, if ΔVUF>e.sub.1, the final participation factor k.sub.x will be equal to k.sub.cx, otherwise, the k.sub.x=0. Here, the e.sub.1 is the threshold of the dead-band, which can be predefined. In this paper, e.sub.1 is set to 0.05. It is worth noting that if the e.sub.1 is too small (e.g., almost 0), the k.sub.x will switch from 0 to k.sub.cx too frequently, which makes the system unstable, while the bigger e.sub.1 makes the compensation accuracy decrease.

(72) Coordination of PMSGs and CHB-STATCOM

(73) FIG. 12 shows the flowchart of coordinated control strategy for unbalanced voltage suppression of CHB-STATCOM and PMSGs. FIG. 12 clearly show that the CHB-STATCOM will inject the suitable negative-sequence currents to compensate for the unbalanced grid voltage first if the VUF of PCC exceeds 2%. Once the VUF exceeds the maximum value that the CHB-STATCOM can compensate for, the PMSGs will participate in sharing the remaining unbalanced grid voltage. Therefore, the participation factor of the CHB-STATCOM k.sub.st is set to 1, and the participation factor of PMSGs k.sub.x can be calculated by the proposed method (see FIG. 11). Note that the participation factors and the remaining capacity of PMSGs are positively related.

(74) Case Study

(75) A typical 50 MW DWF with 25 PMSGs and a ±5 Mvar CHB-STATCOM, as shown in FIG. 1, is simulated in PSCAD/EMTDC to verify the proposed coordinated control strategy. The parameters of CHB-STATCOM are listed in Table I. Three aggregated PMSGs are established to represent the three groups PMSGs, which can be represented by G.sub.1, G.sub.2 and G.sub.3. Here, SCR is equal to 2. Two typical cases are considered. Case I: Only CHB STATCOM injects the negative-sequence current. Case II: CHB STATCOM injects the maximum negative-sequence current and PMSGs participate in sharing the unbalanced grid voltage.

(76) TABLE-US-00001 TABLE I PARAMETERS OF CHB-STATCOM Parameters Value Numbers of cells per 12 phase Rated voltage 10 kV (line-line) Rated capacity 5 MVar Rated current 288 A DC bus voltage 900 V Filter inductance 5 mH Switching frequency 400 Hz
Case I: Only CHB-STATCOM Participates in Compensating Unbalanced Grid Voltage

(77) To test the negative-sequence current injection capability of CHB-STATCOM, the following circumstances are considered in this case: before t=0.9 s, the CHB-STATCOM injects the rated positive-sequence reactive current; at t=0.9 s, it is required to inject the negative-sequence current to track the VUF reference as much as possible; at t=1.78 s, t=2.2 s, t=3.2 s, the reactive power references are changed to 0.8 p.u., 0.5 p.u., and 1.0 p.u., respectively.

(78) FIG. 13 show the results of CHB-STATCOM operating under unbalanced grid voltage when only CHB-STATCOM participates in compensating unbalanced grid voltage. It is found that from FIG. 13a that without the negative-sequence voltage compensation, the VUF at PCC is 2.4%. The VUF can be controlled to 2.0% in the T.sub.2 time interval because the CHB-STATCOM injects the enough negative-sequence currents without over modulation and over current phenomenon. However, the VUF at PCC just can be controlled to 2.05% and 2.15% in T.sub.1 and T.sub.3 time interval, respectively. In T.sub.1 time interval, the CHB-STATCOM has not sufficient capacity to use because it operates at the rated condition, which means that there are no sufficient negative-sequence currents to make the VUF decreasing to 2.0%. In T.sub.2 time interval, although the CHB-STATCOM has enough remaining capacity, the boundary of compensation region depends on the limitation of (18), as shown in FIG. 7c. The negative-sequence compensation capability is less than T.sub.1 time interval, which result that the VUF in the T.sub.3 time interval is larger than T.sub.1 time interval. It can be seen from FIG. 13 b and FIG. 13c that the negative-sequence currents injection capability is strongest than other two time intervals. This phenomenon is in accordance with FIG. 7. FIG. 13d clearly show that the dc voltage of three phase clusters becomes unbalanced when it injects the three-phase unbalanced currents. However, it still operates well even under the unbalanced dc power because of over modulation problem cannot be excited.

(79) Case II: Coordinated Control of CHB-STATCOM and PMSGs

(80) In this case, the simulation considers the following circumstance: at t=0.9 s, the CHB-STATCOM and PMSGs starts to inject negative-sequence according to the algorithm; at t=8.1 s, the active power of G.sub.1 is changed from 11.2 MW to 12.8 MW. At the beginning, we assume that the voltage of Phase-B drops from 1.0 p.u. to 0.85 p.u, which excites the voltage unbalance phenomenon occur. According to the calculation result, the VUF at PCC is 6.8%. Meanwhile, the CHB-STATCOM will inject the maximum negative-sequence to decrease the value VUF as much as possible. Here, the reactive power reference is set to 0.8 p.u.

(81) FIG. 14 shows the output current of CHB-STATCOM. Owing to the VUF at PCC exceeding the compensation capability of CHB-STATCOM, PMSGs are required to share the unbalanced voltage by injecting the negative-sequence current.

(82) FIG. 15 show the simulation results about PCC and PMSG. It can be seen from FIG. 15b that the VUF at PCC can be controlled from 6.8% to 2% in spite of a small fluctuation when the active power of group 1 PMSGs changes as shown in FIG. 15a. FIG. 15d and FIG. 15e are the grid voltage with and without unbalanced voltage compensation, respectively. The grid voltage is close to sinusoidal when CHB-STATCOM and PMSGs inject the desired negative-sequence current at the same time. In FIG. 15c, it can be found that, as the remaining capacity of G.sub.1 decreases, the participation factor k.sub.1 decreases from 0.62 to 0.50, to keep the VUF at PCC at the desired value, and the participation factor of G.sub.2 and G.sub.3, k.sub.2 and k.sub.3, increase from 0.56 and 0.70 to 0.6 and 0.73, respectively.

(83) FIG. 16 shows the d-q components of negative-sequence for three groups PMSG. It can be seen from FIG. 16a that when the participation factor changes, the d-q negative-sequence currents of G.sub.1 change from −0.19 p.u. and 0.2 p.u. to −0.1 p.u. and 0.1 p.u., respectively. Similarly, from FIG. 16b and FIG. 16c, the d-q negative-sequence currents of G.sub.2 and G.sub.3 change from −0.13 p.u. and 0.15 p.u. and −0.15 p.u. and 0.27 p.u. to −0.15 p.u. and 0.18 p.u., and to −0.25 p.u. and 0.31 p.u., respectively. Therefore, the output negative-sequence current of PMSGs are in accordance with the participation factor, which is proportional to their remaining capacity.

(84) Based on the simulation results, it is demonstrated that the CHB-STATCOM will inject negative-sequence current to decrease the VUF at the PCC, it the CHB-STATCOM injects the maximum negative-sequence currents and the VUF cannot be decrease to 2%, the PMSGs will participate in sharing the unbalanced grid voltage according to their participate factor. The coordinate control strategy can suppress the unbalanced grid voltage for a dispersed wind farm without any additional cost but changing the corresponding controller for CHB-STATCOM and PMSGs.

(85) The foregoing description of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to the practitioner skilled in the art.

(86) The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications that are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalence.