Power System Stabilizer for Voltage Source Converters

Abstract

Devices and methods for mechanism-based feedback controller employed in a wind powered power system are provided. A controller can include a vector control-based voltage source converter with feedback control circuitry. The feedback control circuitry is configured to modulate either a power order or a dc-link voltage order to control coupling between voltage and power. The controller can be connected to a wind-based turbine generator of a wind farm and regulate power deployed to a power grid.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application Ser. No. 62/701,029, filed Jul. 20, 2018, the disclosure of which is hereby incorporated by reference in its entirety, including all figures, tables, and drawings.

BACKGROUND

4 Hz oscillations and 30 Hz oscillations have been observed in real world wind farms connected to weak grid power systems. Stability issues caused by these occurrences can limit the efficiency of the delivery of wind-based energy to a power grid.

Weak grid stability of power systems can be due to the coupling of the power delivery and the voltage at the point of common coupling (PCC). Increasing the power delivery can lead to a reduction in the PCC voltage and lead to instability in weak grid power systems. By reducing the instability in a weak grid power system, the delivery efficiency to a power grid can be enhanced.

BRIEF SUMMARY

Embodiments of the subject invention provide methods and devices for mechanism-based feedback control for vector control-based voltage source converters (VSCs) employed in wind-based power systems.

Embodiments of the subject invention provide methods and devices that reduce the coupling between power and voltage. Feedback control strategies are provided that can modulate either the power order or the dc-link voltage order with either the d-axis current or the PCC voltage as an input signal. Experiments of the PCC voltage feedback control have demonstrated the capability of the devices and methods for enhancing the stability of a power system and improved delivery of wind-based energy to a power grid.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a wind farm grid integration system.

FIG. 2 is a block diagram of a linear system.

FIG. 3(a) is plot of root loci for a set of voltage control parameters (case 1). FIG. 3(b) is plot of root loci for a set of voltage control parameters (case 2).

FIG. 4(a) is block diagram of a linear system (system 1). FIG. 4(b) is a block diagram of a linear system (system 2).

FIG. 5 is a plot of root loci for the systems described in FIGS. 4(a) and 4(b).

FIG. 6(a) is a block diagram of a linear system with feedback controls, in which Δi_d is an input signal. FIG. 6(b) is a block diagram of a linear system with feedback controls, in which ΔV_PCC is an input signal.

FIG. 7 is a circuit diagram for an analytical model.

FIG. 8(a) is a block diagram illustrating a control method implementation (Model 1). FIG. 8(b) is a block diagram illustrating a control method implementation (Model 2).

FIG. 9(a) is a plot of Eigenvalue loci for a system, wherein P=0.9, V_PCC=1, K_id increases from 0 to 10 with X_g=0.88 pu. FIG. 9(b) is a plot of Eigenvalue loci for a system, wherein P=0.9, V_PCC=1, K_vpll increases from 0 to 2 with X_g=0.88 pu. FIG. 9(c) is a plot of Eigenvalue loci for a system, wherein P=0.9, V_PCC=1, X_g increases with K_vpll=10. FIG. 9(d) is a plot of Eigenvalue loci for a system, wherein P=0.9, V_PCC=1, X_g increases with K_vpll=0.9.

FIG. 10(a) shows plots of time-domain results wherein K_vpll=0.9, X_g=1.1 pu, P=0.9 pu. FIG. 10(b) shows plots of time-domain results wherein K_vpll=0.9, X_g=1.0 pu and P=1.0 pu.

FIG. 11 shows plots illustrating a comparison of dynamic responses with and without the high pass filter (HPF), wherein X_g: 0.5→0.61.

FIG. 12(a) is a plot of Eigenvalue loci for a system with dc-link voltage control, wherein K_id increases from 0 to 5000 with X_g=0.61 pu. FIG. 12(b) is a plot of Eigenvalue loci for a system with dc-link voltage control, wherein K_vpll increases from 0 to 5 with X_g=0.61 pu. FIG. 12(c) is a plot of Eigenvalue loci for a system with dc-link voltage control, wherein X_g increases with K_id=4000. FIG. 12(d) is a plot of Eigenvalue loci for a system with dc-link voltage control, wherein X_g increases with K_vpll=2.

FIG. 13(a) is a plot of time-domain results, wherein K_vpll=2, X_g=1.01 pu, P=0.9 pu; FIG. 13(b) is a plot of time-domain results, wherein K_vpll=2, X_g=1 pu and P=0.97 pu.

FIG. 14(a) is a diagram illustrating a MATLAB/SimPowerSystems testbed showing a 90 MW Type-3 wind farm connected to a grid through a long transmission line. FIG. 14(b) is a diagram illustrating a MATLAB/SimPowerSystems testbed showing a 100 MW Type-4 wind farm connected to a grid through a long transmission line.

FIG. 15 shows plots of Type-3 wind testbed simulation results: X_g: 0.5→0.88 at 2 sec. Red line: no control; Blue line: voltage-based control (K_id=0, K_vpll=0.9); Green line: current-based control (K_id=10, K_vpll=0).

FIG. 16 shows plots of Type-3 wind testbed results: with K_vpll=0.9, X_g: 0.5→1.0 (blue line) and X_g: 0.5→1.01 (green line).

FIG. 17 shows plots of Type-4 testbed results: X_g: 0.5→0.61 at 2 sec. Red line: no control; Blue line: voltage-based control (K_id=0, K_vpll=2); Green line: current-based control (K_id=4000, K_vpll=0).

FIG. 18 shows plots of Type-4 wind testbed results: with K_id=4000, X_g: 0.5→0.63 (blue line), X_g: 0.5→0.64 (green line).

FIG. 19 shows plots of Type-4 wind testbed results: with K_vpll32 2, X_g: 0.5→0.91 (blue line), X_g: 0.5→0.92 (green line).

DETAILED DISCLOSURE

The following disclosure and exemplary embodiments are presented to enable one of ordinary skill in the art to make and use controller system comprising a vector-based voltage source converter according to the subject invention. Various modifications to the embodiments will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments. Thus, the devices and methods related to the controller system comprising the vector-based voltage source converter are not intended to be limited to the embodiments shown, but are to be accorded the widest scope consistent with the principles and features described herein.

A “weak grid” power system comprises a grid in which voltage level does not remain as constant as in a “strong grid” power system, such that the voltage level and fluctuations need to be taken into account. Weak grid power systems can also be characterized by low short circuit capacity, low inertia, and low fault currents.

FIG. 1 is a diagram illustrating a wind farm 100 connected to a grid through a transmission line 110, which can be represented as reactance, X_g, in a circuit diagram. A Type-3 or a Type-4 wind farm can be represented as a controllable current source in a circuit diagram. Both Type 3 and Type 4 wind farms employ voltage source converters (VSCs). A vector control method can be employed for a VSC.

Vector control can be based on the PCC voltage, (i.e., the dq-frame's d-axis is aligned with the PCC voltage space vector). Hence P=V_PCCi_d and Q=−V_PCCi_q. For a given PCC voltage, adjusting the d-axis current can adjust the active power P and not influence the reactive power Q at the steady state. Similarly, adjusting the q-axis current can adjust the reactive power Q and not influence the active power P. The converter's outer control loops can generate dq-axis current orders and a current control effect can be represented by a first order delay.

The relationship between the wind farm currents, PCC voltage, and the grid voltage is as follows:

v_PCC,d+jv_PCC,q=jX_g(i_d+ji_q)+V_g   (1)

It is assumed that V_PCC is aligned with the d-axis so (1) can be rewritten as the following:

V_PCC'v_PCC,d=−X_gi_q+V_g cos δ

0=v_pCC,q=X_gi_d−V_g sin δ  (2)

wherein δ is the angle by which V_PCC is leading V_g and δ has a range of

$\left[-\frac{\pi }{2},\frac{\pi }{2}\right].$

Combining the two equations in (2) leads to the following:

V_PCC=−X_gi_q+√{square root over (V_g²−(X_gi_d)² )}  (3)

ΔV_PCC=−X_gΔi_q-−cΔi_d   (4)

wherein

$c=X_g/\sqrt{{\left(\frac{V_g}{X_gi_d}\right)}^2-1}.c>0$

and c→∞ if i_d is close to the short circuit current, V_g/X_g.

Equation 4 indicates that an increase in the d-axis current leads to a reduction in the PCC voltage. Further, the linear expression of P versus V_PCC and i_d can be found as follows:

P=V_PCCi_d→ΔP=i_dΔV_PCC+V_PCCΔi_d   (5)

The entire system's linear model including the circuit and vector control can be seen in FIG. 2. When the grid is strong and the impact of Δi_d to ΔV_PCC can be ignored (c=0), the system is stable. The circuit path from Δi_d to ΔV_PCC and further to ΔP₂ can introduce a destabilizing mechanism. If there is no voltage control, (block G(s)=1), when ci_d>V_PCC, the system will be unstable. With voltage control employed, block G(s), as seen in FIG. 2, can be described as:

$\begin{array}{cc}\begin{array}{c}G\left(s\right)=\frac{1}{1+X_g\left(K_{\mathrm{pv}}+\frac{K_{\mathrm{iv}}}{s}\right)\frac{1}{1+{\tau }_is}}\\ =\frac{s\left(1+{\tau }_is\right)}{{\tau }_is^2+\left(1+X_gK_{\mathrm{pv}}\right)s+X_gK_{\mathrm{iv}}}.\end{array}& \left(6\right)\end{array}$

At the steady state, G(s→∞)=0. If the bandwidth of block G(s) is high, in a lower frequency range, then G(s) from equation (6) can be equivalent to 0. Faster voltage control can lead to increased bandwidth and be beneficial for stability. Additionally, slower power control is also beneficial for stability. The root locus method can verify that both faster voltage control and slower power control are beneficial to the stability of a power system.

The system in FIG. 2 is decoupled at the power measurement. The open loop system from the power order to power measurement can be expressed as follows:

$\begin{array}{cc}{\mathrm{Loop}}_1=\frac{K_{\mathrm{ip}}\left({\tau }_ps+1\right)}{s}\frac{1}{1+{\tau }_is}\left(V_{\mathrm{PCC}}-{\mathrm{ci}}_dG\right)& \left(7\right)\end{array}$

wherein τ_p=K_pp/K_ip.

The root loci based on L₁ for two sets of voltage control parameters are shown in FIGS. 3(a) and 3(b) where X_g=1, i_d=0.9, τⁱ=0.05, K_pp=0.25 and K_ip=25. For case 1, as seen in FIG. 3(a), (K_pv, K_iv)=(0.4, 40) and for case 2, as seen in FIG. 3(b), (K_pv, K_iv)=(1, 100). The root loci plots shown in FIGS. 3(a) and 3(b) show that the system has four loci. FIG. 3(a) shows that for case 1, the system is unstable since the gain is 0.702 when the two loci reach the imaginary axis. When the loop is closed with a unit gain, there can be two closed-loop poles located in the right-half plane (RHP). FIG. 3(b) shows that for case 2, the system is stable due to increased voltage control parameters. From the loci movement trends seen in FIGS. 3(a) and 3(b), it can be found that if the τ_p is kept the same and the gain of the power control K_ip decreases, the closed-loop system can be more stable.

FIGS. 4(a) and (b) show block diagrams of two linear systems (system 1 and system 2). The respective open loop circuits of the two systems are obtained by breaking the points marked by the crosses 200 and 210. System 1, as seen in FIG. 4(a), has an open-loop gain equivalent to the expression Loop₁ in equation 7. The root loci for the respective loop gains of the two systems are plotted in FIG. 5. For both systems, there are two root loci move to the RHP, which causes instability in each respective system.

FIGS. 4(a) and (b) show respective block diagrams of two linear systems. Two feedback control configurations can suppress the effect of ΔV_PCC on real power, ΔP. The first strategy is to modulate the power order using the d-axis current. The effect is the same as increasing V_PCC, which is the gain from Δi_d to ΔP₁. A second strategy is to modulate the power order using the PCC voltage ΔV_PCC. The effect is the same as decreasing i_d, the gain from ΔV_PCC to ΔP₂. FIGS. 6(a) and 6(b) show block diagrams of the two above-referenced feedback control methods.

The coupling between power and voltage can be suppressed by introducing feedback control to modulate the power order or the dc-link voltage order for vector control-based grid-side converters. Input signals can be either the d-axis converter current or the PCC voltage. The feedback control is implemented in both analytical models and detail model-based MATLAB/SimPowerSystems Type-3 and Type-4 wind testbeds. The analytical models verify that the feedback control can improve weak grid power system operation for VSCs in both power control and dc-link voltage control modes. The MATLAB/SimPowerSystems testbeds demonstrate that the PCC voltage-based control can significantly improve operation margins for both Type-3 and Type-4 wind farms.

FIGS. 8(a) and 8(b) show block diagram of a system with a grid-side converter (GSC) in active power mode and ac voltage control mode, respectively. FIG. 8(a) also includes the dynamics of phase-locked-loop (PLL), inner current control, and the grid dynamics. The grid dynamics block uses the grid reference frame, whose d-axis is aligned with the grid voltage; while each of the converter control blocks use the converter reference frame whose d-axis is aligned with the PCC voltage.

Either the PCC voltage measured by PLL ΔV_pll or the converter d-axis current Δi_1d can be used to modulate the real power order. The output of a proportional control method using ΔV_pll as an input signal is added to the real power order. The output of the proportional control method using Δi_1d as an input is subtracted from the real power order.

The performance of the feedback control can be analyzed based on the eigenvalue loci generated from the analytical model (Model 1). Because the analytical model is nonlinear, an initialization procedure is required to perform a flat run. At the steady state, the output from the stability control power is zero. The parameters used in the analytical model are listed in Table I.

TABLE I
Parameters of model I and Type-3 wind testbed
Parameter	Value (SI)	Per-unit (pu)
# of WT	60
Rated Power	1.5 MW	0.9
DC-Link voltage	1150 V
Rated voltage	575 V	1
Nominal freq.	60 Hz	1
Lls(Xls), Rs	94.5 μH, 5.6 mΩ	0.18, 0.023
L′lr(X′lr), R′r	84.0 μH, 3.9 mΩ	0.16, 0.016
Lm(Xm)	1.5 mH	2.9
Inertial, poles	8.03 J, 6
Friction factor	0.01
Cdc	10 mF
Lc(Xc), Rc	0.16 mH, 0.59 mΩ	0.3, 0.03
C1(B1)	2.9 mF	0.267
LT1(XT1), RT1	0.165 mH, 6.25 mΩ	0.02, 0.002
LT2(XT2), RT2	19.25 mH, 725 mΩ	0.03, 0.003
L2(X2)	0.58 → 1.35 H	0.45 → 1.05
R2	21.78 → 50.82 Ω	0.045 → 0.105
Current control	Kpi = 0.6, Kii = 8, pu
Power control	Kpp = 0.4, Kip = 40, pu
Voltage control	Kpv = 0.25, Kiv = 25, pu
PLL	KpPLL = 60,KiPLL = 1400, pu

The system is assumed to operate at 0.9 pu power and the PCC voltage is set at 1 pu. Eigenvalue loci are plotted in FIGS. 9(a)-9(d) show the effect of feedback gains for a VSC in power and ac voltage (PV) control mode. For PV control, the marginal stable condition is X_g=0.86 pu. FIGS. 9(a) and 9(b) show how the different values of K_id or K_vpll affect the system stability wherein X_g=0.88 pu. FIGS. 9(c) and 9(d) show the eigenvalue loci and X_g increasing wherein the control gain K_id or K_vpll is fixed.

In control design, a small gain is preferred to avoid reaching system limits. A current-based stability control requires a larger gain than voltage-based stability control. FIG. 9(d) demonstrates that with the voltage-based stability controller (K_vpll=0.9), the system is stable even when X_g increases to 1.1 pu. FIGS. 10(a) and 10(b) present the time-domain responses from the analytical model (Model 1) with a small disturbance (0.001 pu increment in the power order) at t=2 s. Using a PCC voltage-based control method, a wind farm can transfer 1 pu power to a weak grid power system with a short circuit ratio (SCR) at 1.

Stability control can be implemented to modulate the dc-link voltage reference instead of the power order if the VSC is in dc-link voltage control mode. To have a similar effect as modulating the power order, an integrator can be used. Experiments show that modulating the dc-link voltage reference with the output from an integrator control with PCC voltage input can lead to increase or reduction of the dc-link voltage at the steady state. Therefore, a high pass filter (HPF)

$\left(\frac{s}{0.1s+1}\right)$

can be used after the integrator to filter out the dc component. Combining the integrator 1/s and the HPF can be equivalent to a low pass filter (LPF)

$\left(\frac{1}{0.1s+1}\right).$

This control implementation is presented in FIG. 8(b).

FIG. 11 shows plots of the different dynamic responses of the system (Model 2): (a) without voltage-based stability control, (b) with an integrator-based voltage feedback control, and (c) with an additional HPF. The responses are the output power, dc-link voltage, ΔV_pll, and the output of the stability control or compensation on V_DC. Although the integrator-based feedback control of ΔV_pll can improve the stability of the system, a dc component is added to the dc-link voltage order at the steady state. By adding the HPF, the dc component can be eliminated.

The eigenvalue loci for the system (Model 2), as seen in FIG. 8(b), are plotted in FIGS. 12(a)-12(d). The marginal stable condition for a VSC in dc-link voltage control mode is X_g=0.6 pu. The upper two plots FIGS. 12(a) and FIG. 12(b) show that the effect of the gain of the stability controller K_id or K_vpll wherein X_g=0.61 pu. FIGS. 12(c) and 12(d) show the closed-loop system eigenvalues for a varying X_g with a fixed controller gain (K_id=4000, or K_vpll=2).

It can be seen that the stability control can enhance the system stability. In addition, for VSCs in dc-link voltage control mode, the gain required for the current-based stability control is very large. FIG. 12(b) shows that when the gain of the voltage-based stability control increases, the critical mode can move to the left-half plane (LHP) while another mode can move to the RHP and that K_vpll=2 is a suitable gain. FIG. 12(d) demonstrates that the marginal stable condition can be increased to X_g=1 pu, wherein K_vpll=2.

FIGS. 13(a) and 13(b) present the time-domain responses from the analytical model (Model 2) with a small disturbance (0.01 pu reduction in ac voltage order) at t=2 s. With the

PCC voltage-based stability control, the wind farm can transfer more than 0.9 pu power to a very weak grid power system (SCR=1). It can be seen when P=0.97 and X_g =1, the system has two oscillation frequencies, one at 7 Hz and the other at 2 Hz. The time-domain simulation results corroborate with the eigenvalue analysis in FIG. 12(d) where two modes, one at 7 Hz and the other at 2 Hz, move towards the RHP when the grid becomes weaker.

Final stage validation was carried out in two testbeds in MATLAB/SimPowerSystems. The testbeds aligned with the real-world system with full dynamics and converter limitations. The two testbeds were based on the demo testbeds of Type-3 wind and Type-4 wind in SimPowerSystems. The topologies of Type-3 and Type-4 wind testbeds are shown in FIGS. 14(a) and 14(b). The Type-3 wind rotor-side converter (RSC) was operated in power control mode. As the majority of power was delivered through a RSC, the Type-3 wind testbed was viewed similar to Model 1. The Type 4 wind's GSC was operated in dc-link voltage control mode and viewed similar to Model 2.

Both of wind farms were connected to the grid through respective 220 kV long transmission lines. The respective parameters of the two testbeds are listed in Table I and Table II.

TABLE II
Parameters of Model 2 and Type-4 wind testbed
	Parameter	Value (SI)	Per-unit (pu)
	# of WT	50
	Rated power	2 MW	0.9
	DC-link voltage	1100 V
	Rated voltage	575 V	1
	Nominal freq.	60 Hz	1
	Xd, Xq	313 mΩ, 114 mΩ	1.305, 0.474
	X′d	71.0 mΩ	0.296
	X″d, X″q	60.5 m, 58.3 mΩ	0.252, 0.243
	Rs,Xl	1.44 mΩ, 40.8 mΩ	0.006, 0.18
	T′do, T″do	4.49 s, 0.0681 s
	T″q	0.0513 s
	Inertial, poles	9.69 J, 2
	Friction factor	0.01
	Lboost	1.2 mH
	Cdc, τ	90 mF, 0.0272 s
	L1(X1), R1	0.06 mH, 0.45 mΩ	0.15, 0.003
	C1(B1)	3.6 mF	0.203
	LT1(XT1), RT1	0.15 mH, 5.65 mΩ	0.02, 0.002
	LT2(XT2), RT2	17.35 mH, 655 mΩ	0.03, 0.003
	L2(X2)	0.52 → 1.21 H	0.45 → 1.05
	R2	19.6 → 45.8 Ω	0.045 → 0.105
	Current control	Kpi = 0.48, Kii = 3.28, pu
	dc control	Kpp = 0.4, Kip = 40, pu
	Voltage control	Kpv = 0.25, Kiv = 25, pu
	PLL	KpPLL = 60, KiPLL = 1400, pu

The testbeds imposed limitations on the respective converter currents. In the Type-3 wind testbed, the limitation of the RSC current was [0 0.9] pu. In the Type-4 wind testbed, the limitation was [−1.1 1.1] pu.

In the Type-3 wind farm, the feedback control loop was implemented in a rotor-side converter (RSC) to change the power order. The wind farm power base was 100 MW, while the rated power output of the wind farm was 90 MW or 0.9 pu. At the steady state, the rotating speed of the rotor was 1.25 pu and the slip value was −0.25. With the total d-axis current from wind at 0.90 pu, the RSC d-axis current was 0.72 pu and the GSC d-axis current was 0.18 pu to the grid.

FIG. 15 presents wind output power P, dc-link voltage V_DC, PCC voltage V_PCC, RSC d-axis current order i*_r,d, and the output from the stability control compensation for three scenarios: (a) without control, with either (b) voltage-based control (K_vpll=0.9) or (c) current-based control (K_id=10). At t=2 seconds, X_g changed from 0.5 pu to 0.88 pu to emulate a parallel line tripping event.

Without stability control, the system suffered 3 Hz oscillations. This performance aligns with the eigenvalue analysis presented in FIGS. 9(a) and 9(b). When the gain of the stability controller was 0, the system was at the marginal stability condition and the oscillation frequency was 3 Hz.

The system operating limit increases with voltage-based control. FIG. 16 presents the dynamic responses of the system when X_g=1.0 pu and 1.01 pu. The system was stable when X_g=1 pu and unstable when X_g=1.01.

The power base of the Type-4 wind was 110 MW and the rated power was 100 MW or 0.9 pu. For Type-4 wind, the feedback control was implemented in a GSC to modulate the V_DC order. In the first case study, the system dynamic responses without control, with voltage or current-based control were compared. X_g was increased from 0.5 pu to 0.61 pu at 2 seconds to emulate a parallel transmission line tripping event. FIG. 17 shows plots of the dynamic responses of P, V_DC, V_PCC, i*_1d and the stability controller output compensation for three scenarios: (a) without control, with (b) voltage-based and (c) current-based control.

Without stability control, 3 Hz oscillations appeared after the dynamic event. Both of the voltage-based and current-based control methods made the system stable. The voltage-based control (K_vpll=2) had shorter transients and lower overshoot than the current-based control (K_id=4000).

The system operating limits were examined with stability control equipped. The values of K_id and K_vpll were set to 4000 and 2, respectively. FIG. 18 shows plots of the dynamic responses of the system with current-based control for two large disturbances: X_g: 0.5→0.63 and X_g: 0.5→0.64. Because of the large overshoot, the current-based control (K_id=4000) makes the converter current order reach its limits. The marginal stable condition changed from X_g=0.6 pu to 0.63 pu. FIG. 19 shows plots of the dynamic responses of the system with voltage-based control (K_vpll=2) for two large disturbances: X_g: 0.5→0.91, Xg: 0.5→0.92. It can be observed that the system is stable when X_g reaches 0.91 pu. The marginal stable condition was increased from X_g=0.60 pu to 0.91 pu.

The methods and processes described herein can be embodied as code and/or data. The software code and data described herein can be stored on one or more machine-readable media (e.g., computer-readable media), which may include any device or medium that can store code and/or data for use by a computer system. When a computer system and/or processer reads and executes the code and/or data stored on a computer-readable medium, the computer system and/or processer performs the methods and processes embodied as data structures and code stored within the computer-readable storage medium.

It should be appreciated by those skilled in the art that computer-readable media include removable and non-removable structures/devices that can be used for storage of information, such as computer-readable instructions, data structures, program modules, and other data used by a computing system/environment. A computer-readable medium includes, but is not limited to, volatile memory such as random access memories (RAM, DRAM, SRAM); and non-volatile memory such as flash memory, various read-only-memories (ROM, PROM, EPROM, EEPROM), magnetic and ferromagnetic/ferroelectric memories (MRAM, FeRAM), and magnetic and optical storage devices (hard drives, magnetic tape, CDs, DVDs); network devices; or other media now known or later developed that are capable of storing computer-readable information/data. Computer-readable media should not be construed or interpreted to include any propagating signals. A computer-readable medium of the subject invention can be, for example, a compact disc (CD), digital video disc (DVD), flash memory device, volatile memory, or a hard disk drive (HDD), such as an external HDD or the HDD of a computing device, though embodiments are not limited thereto. A computing device can be, for example, a laptop computer, desktop computer, server, cell phone, or tablet, though embodiments are not limited thereto.

All patents, patent applications, provisional applications, and publications referred to or cited herein are incorporated by reference in their entirety, including all figures and tables, to the extent they are not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof can be suggested to persons skilled in the art and are to be included within the spirit and purview of this application. In addition, any elements or limitations of any invention or embodiment thereof disclosed herein can be combined with any and/or all other elements or limitations (individually or in any combination) or any other invention or embodiment thereof disclosed herein, and all such combinations are contemplated with the scope of the invention without limitation thereto.

REFERENCES

[1] N. P. W. Strachan and D. Jovcic, “Stability of a variable-speed permanent magnet wind generator with weak ac grids,” IEEE Transactions on Power Delivery, vol. 25, no. 4, pp. 2779-2788, Oct 2010.

[2] J. Hu, Y. Huang, D. Wang, H. Yuan, and X. Yuan, “Modeling of grid-connected dfig-based wind turbines for dc-link voltage stability analysis,” IEEE Transactions on Sustainable Energy, vol. 6, no. 4, pp. 1325-1336, Oct 2015.

[3] Y. Zhou, D. D. Nguyen, P. C. Kjr, and S. Saylors, “Connecting wind power plant with weak grid-challenges and solutions,” in 2013 IEEE Power Energy Society General Meeting, July 2013, pp. 1-7.

[4] S. H. Huang, J. Schmall, J. Conto, J. Adams, Y. Zhang, and C. Carter, “Voltage control challenges on weak grids with high penetration of wind generation: Ercot experience,” in 2012 IEEE Power and Energy Society General Meeting, July 2012, pp. 1-7.

[5] H. Liu, X. Xie, J. He, T. Xu, Z. Yu, C. Wang, and C. Zhang, “Subsynchronous interaction between direct-drive pmsg based wind farms and weak ac networks,” IEEE Transactions on Power Systems, vol. 32, no. 6, pp. 4708-4720,2017.

[6] L. Fan and Z. Miao, “An explanation of oscillations due to wind power plants weak grid interconnection,” IEEE trans. Sustainable Energy, vol. 9, no. 1, pp. 488-490, Jan 2018.

[7] L. Fan, “Modeling type-4 wind in weak grids,” accepted, IEEE trans. Sustainable Energy, Jun 2018.

[8] L. Fan and Z. Miao, “Wind in weak grids: 4 hz or 30 hz oscillations,” to appear, IEEE trans. Power Systems.

[9] Y. Li, L. Fan, and Z. Miao, “Low-frequency and subsynchronousfrequency oscillations in type-4 wind with weak grid interconnections,” submitted, IEEE trans. Power Systems.

[10] A. Dissanayaka, J. Wiebe, and A. Isaacs. (2018, March) Panhandle and South Texas Stability and System Strength Assessment. Electranix. [11] B. Wu, Y. Lang, N. Zargari, and S. Kouro, Power conversion and control of wind energy systems. John Wiley & Sons, 2011, vol. 76.

[12] X. Yuan, F. Wang, D. Boroyevich, Y. Li, and R. Burgos, “Dc-link voltage control of a full power converter for wind generator operating in weakgrid systems,” IEEE Transactions on Power Electronics, vol. 24, no. 9, pp. 2178-2192, Sept 2009.

[13] H. T. Ma, P. B. Brogan, K. H. Jensen, and R. J. Nelson, “Subsynchronous control interaction studies between full-converter wind turbines and series-compensated ac transmission lines,” in 2012 IEEE Power and Energy Society General Meeting, July 2012, pp. 1-5.

[14] L. Zhang, L. Harnefors, and H. P. Nee, “Power-synchronization control of grid-connected voltage-source converters,” IEEE Transactions on Power Systems, vol. 25, no. 2, pp. 809-820, May 2010.

[15] J. Alipoor, Y. Miura, and T. Ise, “Power system stabilization using virtual synchronous generator with alternating moment of inertia,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 2, pp. 451-458,2015.

[16] K. Givaki, D. Chen, and L. Xu, “Current error based compensations for vsc current control in weak grid for wind farm applications,” IEEE Transactions on Sustainable Energy, pp. 1-1,2018.

[17] A. Egea-Alvarez, S. Fekriasl, F. Hassan, and 0. Gomis-Bellmunt, “Advanced vector control for voltage source converters connected to weak grids,” IEEE Transactions on Power Systems, vol. 30, no. 6, pp. 3072-3081, Nov 2015.

[18] K. Clark, N. W. Miller, and J. J. Sanchez-Gasca, “Modeling of GE wind turbine-generators for grid studies,” GE Energy, Tech. Rep., April 2010.

Claims

1. A controller system for a wind-based power system, the controller comprising:

a vector control-based voltage source converter configured to have feedback control circuitry;

wherein the feedback control circuitry is configured to modulate either a power order or a dc-link voltage order,

wherein a first input signal into the controller system is an alternating current (AC) voltage, and

wherein the feedback control circuitry is configured such that a change in magnitude of the AC voltage is used as an input into the feedback control circuitry to modulate the power order or the dc-link voltage order.

2. The controller system of claim 1, wherein the feedback control circuity is configured to reduce coupling between an active power and a voltage at a point of common coupling.

3. The controller system of claim 1, wherein a second input signal into the controller system is a d-axis converter current.

4. The controller system of claim 1, wherein the first input signal into the controller system is a voltage at a point of common coupling.

5. The controller system of claim 3, wherein the controller system is configured to modulate either the power order or the dc-link voltage order by using the d-axis converter current.

6. The controller system of claim 4, wherein the controller is configured to modulate either a power order or a dc-link voltage order by using the voltage at a point of common coupling.

7. The controller system of claim 1, further comprising:

an integrator; and

a high pass filter connected to the integrator,

wherein the integrator and the high pass filter are configured to modulate the dc-link voltage order.

8. The controller system of claim 1, wherein the controller system is connected to a wind-powered turbine generator.

9. The controller system of claim 1, wherein the controller system is connected to a power grid system.

10. The controller system of claim 9, where the power grid system is a weak grid power system.

11. The controller system of claim 1, wherein the controller system is configured for Type-3 wind.

12. The controller system of claim 1, wherein the controller system is configured for Type-4 wind.

13. The controller system of claim 1, wherein the first input signal is a phase-locked-loop (PLL) voltage of the controller system.

14. The controller system of claim 4, wherein the voltage at a point of common coupling is a PLL voltage.

15. The controller system of claim 3, wherein the first input signal into the controller system is a voltage at a point of common coupling.

16. The controller system of claim 15, wherein the voltage at a point of common coupling is a PLL voltage.

17. A controller system for a wind-based power system, the controller comprising:

a vector control-based voltage source converter configured to have feedback control circuitry;

wherein the feedback control circuitry is configured to modulate either a power order or a dc-link voltage order,

wherein a first input signal into the controller system is an alternating current (AC) voltage,

wherein the feedback control circuity is configured to reduce coupling between an active power and a voltage at a point of common coupling,

wherein a second input signal into the controller system is a d-axis converter current.

wherein the first input signal into the controller system is a voltage at a point of common coupling,

wherein the controller system is configured to modulate either the power order or the dc-link voltage order by using the d-axis converter current.

wherein the controller is further configured to modulate either a power order or a dc-link voltage order by using the voltage at a point of common coupling,

wherein the controller system further comprises: an integrator; and a high pass filter connected to the integrator,

wherein the integrator and the high pass filter are configured to modulate the dc-link voltage order,

wherein the controller system is connected to a wind-powered turbine generator or a weak grid power system,

wherein the controller system is configured for Type-3 wind or Type-4 wind, and

wherein the first input signal is a phase-locked-loop (PLL) voltage of the controller system.