香京julia种子在线播放

The mechanical power produced from the wind by the PMSG-WT is expressed as (Okedu, 2022): P w = 1 2 ρ A V W 3 C p λ , β (1)

In Eq. 1, P w represents the wind power harnessed, measured in watts (W). The parameter C P denotes the power coefficient, while ρ denotes the air density in kilograms per cubic meter ( Kg / m 3 ). A represents the swept area in square meters ( m 2 ), and V w stands for the wind velocity without any rotor interference, expressed in meters per second (m/s). The power coefficient C P of the wind generator is determined by the ratio of the tip speed (λ) to the pitch angle (β), and this relationship is expressed in Eq. 2 (Okedu, 2022). C p λ , β = c 1 c 2 λ i − c 3 β − c 4 e − c 5 λ i + c 6 λ (2) Where 1 λ i = 1 λ − 0.08 β − 0.035 β 3 + 1 (3)

Eq. 2 incorporates coefficients c 1 to  c 6 , which represent the characteristics of the wind turbine (WT). In the context of Permanent Magnet Synchronous Generator (PMSG) wind turbines, the maximum power point tracking (MPPT) relies on the rotor speed, enabling the attainment of maximum power output (Wang et al., 2018). P MAX = 1 2 ρ A ω r R λ opt 3 c popt (4)

The variables in question are as follows: λ opt represents the optimal tip speed, c popt denotes the optimal power coefficient, and ω r indicates the rotor speed of the wind generator.

The dynamic model of the PMSG wind turbine in the d-q reference rotating frame is presented as shown in reference (Wang et al., 2018). d ψ sd dt = − V sd − R s I sd − ω e ψ sq (5) d ψ sq dt = − V sq − R s I sq − ω e ψ sd (6)

From Eqs 5, 6 ψ sd = L sd + L md I sd + ψ m (7) ψ sq = L sq + L mq I sq (8)

In the dynamic model of the PMSG wind turbine, the following variables are involved: V sd and V sq represent the stator circuit’s voltage, R s denotes the stator winding resistance, and I sd and I sq are the currents in the d and q reference frames, respectively. Furthermore, ω e signifies the rotational speed of the wind generator, while ψ sd and ψ sq stand for the flux linkages of the stator circuit. Additionally, L sd and L sq represent the stator winding leakage inductances, and L md and L mq denote the magnetizing inductances. Finally, ψ m signifies the flux linkage of the machine’s permanent magnet. By substituting Eqs 7, 8 into Eqs 5, 6, the resulting differential equation can be obtained. L d d I sd dt = − V sd − R s I sd − ω e I q I sq (9) L q d I sq dt = − V sq − R s I sq + ω e L d I sd + ω e ψ m (10) L d = L sd + L md (11) L q = L sq + L mq (12)

The active and reactive power of the Permanent Magnet Synchronous Generator (PMSG) are expressed as follows: P g = 3 2 V sd I sd + V sq I sq (13) Q g = 3 2 V sq I sd − V sd I sq (14)

The electro-torque of the wind generator with pole pairs (p) is represented as follows: T e = 0.5 p   ψ m I sq + L d − L q I sd I sq (15)

In the case of a surface-seated Permanent Magnet Synchronous Generator (PMSG), it is reasonable to assume that L d = L q . Consequently, the expression for T e can be formulated as follows: T e = 0.5 p   ψ m i sq (16)

Among the various commercial energy storage devices (ESD) available, superconducting magnetic energy storage (SMES) stands out due to its rapid response speed, high power density, and extended lifespan (Gouda et al., 2020). In this study, SMES is emulated as an inductor with negligible resistance. The DC-DC side of the converter comprises two Insulated Gate Bipolar Transistors (IGBT) and two diodes, enabling a bidirectional, two-quadrant operation of the SMES magnet. This allows the SMES to charge, store, and discharge energy while the current is positive. The switching pattern of the transistors is adjusted to produce either positive or negative voltage at the magnet’s terminals, turning it into an intrinsic zero-voltage device. The fundamental electrical circuit for the SMES chopper is depicted in Figure 3.

In the charging mode, when the controller commands the SMES to absorb energy, the current path is illustrated in Figure 3A. During this mode, IGBT G1 and IGBT G2 are activated to charge the SMES from the DC bus. The voltage V(t) across the inductor can be expressed as follows: V t = L s di t dt (17)

The expression for the energy stored in the SMES can be obtained as follows, taking into account the DC bus voltage (V), the coil inductance ( L s ), and the charging current (i(t)) as a function of time (t). The DC current flowing in the coil is represented by I s , while R 1 denotes the coil resistance, with the inner resistance considered negligible ( R 1 ≈ 0). Therefore, the energy stored in the SMES can be calculated using the given parameters: E t = 1 2 L s I s 2 t (18)

In the discharge mode, IGBT G1 and G2 are turned off, and the controller manages the duty cycle of IGBT G2 to achieve the desired output current I ref . For the discharge process, assuming the initial current in the SMES is I 0 , and the duty ratio for IGBT G2 is denoted by D, the current in the SMES at time t can be expressed as follows: I t = I 0 ⁡ exp ⁡ − R * t * D L s (19)

When the SMES does not require power exchange with the power grid, the chopper operates in standby mode to maintain the stored energy in the SMES. In this standby state, the current path is depicted in Figure 3C, where IGBT G1 remains continuously turned on, and IGBT G2 remains continuously turned off. The current flowing in the superconductor during the storage process can be represented as follows: I t = I 0 ⁡ exp − R 1 * t L s (20)

If the superconductor material exhibits zero resistance ( R 1 ≈ 0), both the storing current and the stored energy remain constant. The control diagram of the chopper will be discussed in the subsequent section. For a summary of the essential characteristics of the SMES device, please refer to Table 2.

Eq. 21 illustrates the behavior of the DC link, where C and V c represent the capacitance and voltage of the dc-link, respectively. P f and P r correspond to the grid filter and rotor power, respectively. To maintain dc-link voltage stability, it is necessary for the power transferred from the generator side ( P r ) to equal the power transferred from the dc-link capacitor to the grid filter ( P f ) (Xu et al., 2019). However, during voltage dips or spikes, a power imbalance occurs, leading to variations in the values of P r and P f Consequently, a rise in voltage occurs across the dc-link capacitor.

During High Voltage Ride-Through (HVRT), if the grid voltage increases, the output of the MSC ( P f ) will not change significantly. Nevertheless, an overvoltage condition may cause energy to flow back toward the WTG, resulting in an unexpected spike in the capacitor voltage. Such an occurrence poses a threat to the normal operation of the WTG (De Siqueira and Peng, 2021).

To address this issue, the excess energy received by the dc-link capacitor during voltage fluctuations needs to be dissipated, or alternatively, the total capacitance of the DC-link (C_Total) should be increased, as depicted in Eq. 22, to maintain the dc-link voltage within a safe range (De Siqueira and Peng, 2021). CV C dV c dt = P f − P r (21) V c = 2 E c C Total (22)

The primary aim of this study is to enhance the Fault Ride-Through (FRT) capability in the PMSG-based Wind Turbine Generator (WTG). To achieve this objective, the methods presented in Nielsen et al. (2010), which pertain to Machine and Grid Side Converter control, are adopted. Consequently, these methods will not be reiterated in this work. Instead, this section focuses on a modified control strategy for the grid-side converter that incorporates SMES to address the FRT issue, as illustrated in Figure 4.

The dc-dc chopper operates with binary on and off settings. Consequently, it has a set of switching states that encompass all possible permutations. However, certain combinations leading to short-circuits in the DC link are avoided. To determine the optimal switching state of the dc-dc chopper corresponding to the dc-link voltage, an optimization process is carried out. Subsequently, the optimal switching states are applied. Unlike traditional PID control, where pulse width modulation (PWM) is used to generate switching signals for the converters, the MPC-based SMES system directly produces the required switching signals for the chopper. Figure 5 illustrates the predictive control method for the dc-dc chopper. For calculating the expected voltage across the dc link, the predicted current flowing through the SMES coil at the sampling time T s is utilized. Below is a discrete-time model representing the dynamic current in the SMES coil at the sampling time T s .

The expected SMES current at time k is given by: i L p k + 1 = i L k T s + T s L s V d c k (23) Where, L s represents the inductance of the SMES coil, i L k represents the current of the SMES coil at time k, Dc link Voltage at time k is denoted by, V d c k .

With its accompanying switching function as: s = 0 , while = G 1 is off and  G 2 is on 1 , while = G 1 is on and  G 2 is of (24)

Table 3 illustrates the complete switching sequence for the DC-DC chopper. Where G 1 and G 2 represents the dc-dc chopper’s switches.

At time k, the capacitor’s expected current is: i c k = i s k − i l k − i g k (25)

But since the SMES coil is considered already charged, the next available state is the discharge state, hence i c k is represented as; i c k = i s k + i l k − i g k (26)

The relationship between voltage and capacitor current is as follows: i C = CdV dc dt (27) i c k + 1 = C V d C K + 1 − V d C K T s (28)

The derivative capacitor voltage dVC dt , is also replaced by the forward Euler approximation. Thus, the capacitor’s predicted dc voltage at time k+1 can be derived as follows: V dc p k + 1 = i c k * T S c + V dc k (29) where, V dc p (k + 1) represents the capacitor’s predicted voltage at time k + 1.

The cost functions g 1 , thus the difference between the reference and forecast signal levels is defined as Eq. 30. g 1 = V dc p k + 1 − V dc * K (30)

Where V dc * represents the reference value of the dc-link voltage.

Figure 6 depicts the control algorithm used by the MPC-based SMES system. The dc voltage forecast relies on Eq. 29.

For grid voltage angle detection, a phase-locked loop (PLL) is utilized (Yuan et al., 2020). During regular operation, iqref is set to 0, enabling the Grid-Side Converter (GSC) to operate in unity power factor mode. However, when the WTG is in Fault Ride-Through (FRT) mode, the dynamic reactive current reference is determined based on the magnitude of the voltage dips, as expressed in Eq. 31. i gqref = k × I N × V N − V (31)

In Eq. 32, K represents the coefficient, i_gqref denotes the reactive current reference, and V refers to the instantaneous terminal voltage. V N and I N represent the nominal voltage and current of the WTG, respectively. During operation, if the terminal voltage is below the nominal voltage, a capacitive current reference will be transmitted to the converter. Conversely, if the terminal voltage exceeds the nominal voltage, an inductive current reference will be sent to the converter. It is essential to ensure that the active current reference is governed by Eq. 32 to restrict its value within the IGBT’s current threshold during Fault Ride-Through (FRT) mode. i gdref ≤ I max 2 − I gqref 2 (32)

The threshold current of the IGBT is denoted as I max , and i gqref represents the active current reference. For the purpose of this study, the maximum allowable current is set to 1.8 pu. As depicted in Figure 4, the active and reactive references remain the same as in conventional vector control during normal operating conditions. However, when the Fault Ride-Through (FRT) mode is activated, the i_gqref changes to Eq. 31 to provide reactive power assistance either in a capacitive or inductive manner, while ensuring that the i gqref stays within the safe operating current limit of the IGBT.

During High Voltage Ride-Through (HVRT) and Low Voltage Ride-Through (LVRT) events, the Grid-Side Converter (GSC) is configured to operate in the Q-priority mode. This means that the converter prioritizes the contribution of reactive current over the contribution of active current.

In this experimental study, a balanced voltage drop of 0.80 pu is applied to the grid at t = 3s and persists for 150 m. Figure 6A illustrates the 0.80 pu voltage drop at the grid-connected point during the fault. The root mean square value of the voltage drop at the grid-connected point is depicted in Figure 6B. Without any Q support, the voltage at the grid-connected point peaks at 0.2 pu and gradually increases to 0.25 pu when the SMES is controlled by MPC (Model Predictive Control).

Figure 6C presents the behavior of the DC-link voltage. Without Q support, the DC-link voltage exhibits uncontrolled growth, exceeding the fault period, resulting in a 5,450 V increase over a time period of 3.5s, surpassing the fault duration. However, when MPC-controlled SMES is activated, the DC-link voltage is effectively regulated to 1,200 V, enabling the wind turbine to ride through the fault within the fault period.

Figure 6D depicts the active power management profile under two scenarios: without Q support and with SMES + MPC schemes. Without Q support, the grid’s active power decreases from its nominal value of 1.5 MW to approximately 0.365 MW until t = 3.47s, before returning to its nominal value. When SMES regulated by MPC is engaged, the grid-side active power is cushioned at around 0.736 MW until t = 3.15s, before returning to its nominal value.

Similarly, Figure 6E shows the behavior of the grid’s reactive power. Without any Q support mechanism, there is no grid reactive power support during the fault. However, with the MPC + SMES technique, the reactive power reaches 0.35 MVar to facilitate PCC (Point of Common Coupling) voltage recovery. As depicted in Figure 6F, the SMES’s active current is injected into the grid during this recovery period. Following the elimination of the grid fault, the SMES current, controlled by MPC, is increased to 1,750 A, ensuring that these operations remain below the SMES critical current threshold.

Table 4 provides a summary of the advantages of MPC in the proposed technique, as detailed in reference (Aimene et al., 2022). The comparison includes the percentage change in the DC-link voltage (Δ V_dc) and the control settling time (s). Table 4 demonstrates that the MPC + SMES technique, owing to its capability to handle control uncertainties, facilitates a reasonable system recovery.

In this experimental study, a balanced voltage swell of 0.20 pu is applied to the grid at t = 3s and lasts for 150 m. Figure 7A illustrates the 0.20 pu voltage swell at the grid-connected point during the fault. The root mean square value of the voltage swell at the grid-connected point is depicted in Figure 7B.

Without any Q support, the voltage at the grid-connected point peaks at 1.2 pu and gradually decreases to 1.16 pu when the SMES is controlled by MPC (Model Predictive Control). The DC-link behavior is shown in Figure 7C. If no Q support mechanism is introduced, the DC-link voltage would increase uncontrollably, resulting in a 1,600 V rise in the DC-link voltage. However, when MPC-controlled SMES is activated, the DC-link voltage decreases to about 1,250 V, enabling the wind turbine to ride through the fault within the fault period.

Figure 7D depicts the active power management profile under two scenarios: without Q support and with MPC + SMES schemes. Without Q support, the grid’s active power decreases from its nominal value of 1.5 MW to around 1 MW until t = 3.2s, before returning to its nominal value. When SMES regulated by MPC is engaged, the grid-side active power is cushioned at about 1.3 MW for a duration of t = 3.15s before returning to its nominal value.

Similarly, Figure 7E shows the behavior of the grid’s reactive power. Without any Q support mechanism, there is no grid reactive power support during faults. However, with the MPC-SMES technique, the reactive power reaches a noticeable rise of −0.4 MVar to facilitate PCC (Point of Common Coupling) voltage recovery.

As shown in Figure 7F, during the voltage swell at t = 3s, the SMES coil increases, leading to a positive slope with MPC. Energy is transferred from the grid to the SMES coil during this recovery period. Following the elimination of the grid fault, the SMES current returns steadily to 1,500 A, which is well below its critical current threshold.

Table 5 provides a summary of MPC’s advantages over other techniques proposed in the literature. The comparison includes the percentage change in the DC-link voltage ( Δ   V dc ) and the control settling time (s). From Table 5, it can be seen that the MPC-SMES technique, due to its capability to handle control uncertainties, facilitates a reasonable system recovery.