Wind Power Fluctuation Compensation by Variable-Speed Pumped Storage Plant in a Grid Integrated System

Abstract

Wind power technology is the fastest-growing technology for electrical energy production due to its potential characteristics. However, due to its randomness, it has an unnecessary impact on the operation and stability of the grid system. For example, the problem of power grid frequency fluctuation is more obvious. Fluctuations in frequency, in turn, can even affect the breakdown of power systems. To minimize these problems, a droop vector control strategy applied to variable-speed pumped storage (VSPS) systems can be implemented. This method should be used as a wind power fluctuation compensation solution in the wind farm grid-connected system. This chapter introduces the droop-fed direct power control strategy in a VSPS-wind farm-grid-connected system. The modeling of the system is based on the phasor model technique. The spectrum analysis method is used in the VSPS system to determine the dynamic performance of the power grid under wind power fluctuation compensation and emergencies and is verified on the MATLAB/Simulink platform. The results show that the spectrum analysis method is effective for determining the fluctuation and stability requirements of wind power in large power grids. The VSPS control strategy in the wind farm grid-connected integrated system achieves good power flow regulation and stable grid frequency, and the deviation is within an acceptable range.

1. Introduction

Due to increasing environmental concerns, wind power generation has undergone rapid growth [1]. In 2013, the world wind power production capacity was 318GW, and it is forecasted to reach 712 GW, 1480GW, 2089GW, and 2672GW by 2020, 2030, 2040, and 2050, respectively, in moderate scenario [2].

In China, the figure is 123GW, 216GW, 414GW, 680GW, and 1000GW in 2015, 2020, 2030, 2040, and 2050, respectively [2, 3].

Wind energy production brings immense advantages such as sustainable, incredible domestic potential, eco-friendly, revitalizing to rural economies, low operational cost, space efficient, etc. Nevertheless, its main drawback is its stochastic over time in nature; hence, significant power fluctuations are observed in the wind farm. For a power system even with moderate wind power penetration, the fluctuations should be mitigated; otherwise, this may lead to substantial deviations in the grid frequency [1], voltage sag and flicker at the grid busses [4], steady-state voltage deviation, even equipment damage, and system collapse at large. A study in busses [4] asserts that the variable-speed pumped storage (VSPS) system is able to improve the dynamic stability and steady-state operations of the power system. Having dependable features and performances, the VSPS can play a crucial role in stability control and frequency regulator and AC voltage control during contingencies.

Previous works have focused on converter topology development [5, 6, 7, 8, 9, 10, 11], which has led to improvements in VSPS system performance and penetration of renewable energy development level [12]. Furthermore, control strategies have been intensively studied in doubly fed induction machine (DFIM)-based VSPS applications. These works mainly relate to the vector control category, including Field-Oriented Control (FOC) [9, 13, 14] and Direct Torque Control (DTC) [5, 8, 11, 13, 14]. As a result, the system performance improvement has achieved remarkable results.

In Ref. [8], a direct power control (DPC)-based frequency regulator is implemented in a full-scale converter-fed synchronous machine. DPC is also used in the application of DFIM-based VSPS systems in [11], with a focus on converter topology studies. A grid-integrated VSPS system was proposed in [5] to study the impact of faults on grid frequency stability and VSPS active power flow. In [9], a VSPS-based H-bridge cascaded multilevel converter with a stator voltage FOC strategy was proposed to suppress the effects of wind farm power fluctuations. On the other hand, the work in [1] proposed a power filter algorithm to solve the control method to adjust the frequency deviation of the power grid caused by wind power fluctuations. However, the above work does not consider the phasor model simulation technique because it is very important in the stability and control analysis of large power systems where simulation time and computational storage are critical. Since sinusoidal voltages and currents are replaced by phasors in polar form in the phasor model technique; and where electromagnetic transients are not important, dynamic simulation time is greatly reduced. Implementing a phasor model in any linear system is also an advantage, since the study of small-signal stability is based on the eigenvalue analysis of linearized power systems, which complements the dynamic simulation of nonlinear systems [15]. However, implementing phasor modeling techniques in DFIM applications, grid frequency control has always been a challenge. In the phasor model technique, the grid frequency is assumed to be a constant fundamental frequency. It is impossible to develop a phasor locked loop for synthesizing frequencies. Therefore, grid frequency control is performed through an active power control strategy, which is an open-loop control scheme for frequency, as shown in Figure 1. Therefore, the response of grid frequency and AC voltage lacks good dynamic performance, especially during emergencies [16].

Figure 1.

Open-loop frequency and AC-bus voltage control through the power control strategy.

On the other hand, grid frequency is very sensitive to load/source changes. If the load/power connected to the AC grid system is suddenly turned on/off, the grid frequency will decrease/increase, causing the power plant to generate more power or stop it. Furthermore, due to the applied frequency drop, the converter will respond to the decrease in frequency by increasing the inverter power or decreasing the rectifier power. Therefore, the frequency drop is estimated per unit increment of rectified power fed to the closed control system. Since a change in the converter power results in a change in the DC voltage level, the frequency drop will appear as a drop in the DC voltage level in the AC/DC interface system, which in turn results in the need for power flow compensation [17]. Therefore, the way to solve this problem is that adding a synchronous machine to the grid system helps to obtain the measured and estimated frequency, because the rotor speed of the synchronous machine is absolutely the same as the scale factor of the grid frequency.

However, this chapter aims to propose a frequency droop feeding DPC for VSPS systems to accommodate grid frequency deviations due to wind power fluctuation effects. Spectral analysis is newly used to tune the stability balance and verify the dynamic performance of the proposed control system. The converter used is a three-level back-to-back neutral-point clamped voltage source converter (NPC-VSC).

2. Basic description of frequency control

The replacement system frequency is a measure of the effective power balance in the system. It is a feedback signal that allows the operator to monitor the balance of energy produced and consumed. It is a common characteristic of all location voltages, but varies over time, while system conditions change within an AC power system. Any change in power generation or load will result in a frequency deviation that can lead to system instability and minimal operation of generators and consumers. In extreme cases, system equipment may be damaged.

The concept of power system frequency stability is defined as the requirement to ensure that the system frequency remains within a given safe range during normal operation and emergency situations [1]. This is ensured by using two mechanisms, frequency control and active power balance control [18]. Frequency control is a crucial control problem in system design and operation. This is even more important today due to the complexity of modern power systems driven by ever-increasing scale, environmental constraints, emerging renewable energy sources, and uncertainty.

Based on the dynamic model of generator load based on the correlation between mismatched power (ΔP_m - ΔP_L) and grid frequency deviation, a simplified frequency response model can be defined for an interconnected multigenerator power system. (Δf) and can be expressed by the oscillatory differential equation [19] as

$$\Delta P_m\left(t\right)-\Delta P_L\left(t\right)=2H\frac{\mathit{d\Delta f}\left(t\right)}{\mathit{dt}}+\mathit{D\Delta f}\left(t\right)$$E1

where ∆P_m, ∆P_L, D, and H are respectively change of the mechanical power, change of the load, the load damping coefficient, and the inertia constant.

In terms of Laplace transformation function, the expression of the change of frequency in (1) is denoted by

$$\mathit{\Delta f}\left(s\right)=\frac{\Delta P_m\left(s\right)-\Delta P_L\left(s\right)}{2\mathit{Hs}+D}$$E2

It can be seen from Eq. (2) that the frequency deviation is inversely proportional to the load damping coefficient and inertia constant.

To keep the power system frequency at the nominal value, different mechanisms can be used depending on the magnitude of the frequency deviation faced. Small frequency deviations can be adjusted by primary control and load frequency control systems. When the situation is complex and the deviation is large, emergency control schemes such as low-frequency load shedding should be used to restore the system frequency.

Frequency stability studies can range in time from seconds to minutes as both fast and slow dynamics affect it. For high-power fluctuating systems, the long-term stability issue [19] is considered so in this chapter.

3. The wind power

Wind speed is random in nature and varies erratically over time. As a result, significant wind fluctuations can be observed.

For a given power factor C_p, the mechanical power (P_m) and torque (T_m) produced by the wind turbine rotor can be defined as

$$P_m=0.5\mathit{\rho A}{C}_p\left(\lambda ,\beta \right){v_w}^3$$E3

$$T_m=\frac{P_m}{{\omega }_r}$$E4

where ρ, v_w, A, and ω_r are respectively the air density, wind speed, swept area, and angular speed of the generator rotor. Maximum mechanical power extraction is possibly made at maximum value C_p and is a function of the pitch angle (β) and tip-speed ratio (λ), which are related as

$$\lambda =\frac{{\omega }_{\mathit{rot}}{R}_T}{v_w}$$E5

The angular speed of the wind turbine ω_rot is related to the generator rotor angular speed ω_r and as a function of gear ratio Ng and given by

$${\omega }_r=N_g{\omega }_{\mathit{rot}}$$E6

The power coefficient expression Cp has been shown to have a unique maximum, C_p-max, for λ_opt = 8.1 and β_opt = 0 [20].

The maximum coefficient of Cp, i.e., the Betz limit is 16/27. But maximum value of C_p is determined in this chapter. Based on the modeling turbine characteristics of [21], a generic Eq. (7) is used to model C_p(λ,β).

$$C_p\left(\lambda ,\beta \right)=C_1\left(C_2/{\lambda }_i-C_3\beta -C_4\right)e^{-C_5/{\lambda }_i}+C_6\lambda$$

$$⟹\frac{1}{{\lambda }_i}=\frac{1}{\lambda +0.08\beta }-\frac{0.035}{{\beta }^3+1}$$E7

Particular optimal value of λ is defined (λ_opt = 8.1). Thus, for β = 0⁰ and the coefficients of C₁ = 0.5176, C₂ = 116, C₃ = 0.4, C₄ = 5, C₅ = 21, and C₆ = 0.0068, the maximum value of C_p, which is C_pmax = 0.48, is achieved.

Normalizing Eq. (3) in the pu system, we get

$$P_{m-\mathit{pu}}=C_{p-\mathit{pu}}\left(\lambda ,\beta \right)v_{w-\mathit{pu}}^3$$E8

Thus, implementing the above equations, the turbine power is determined and the result is shown in Figure 2 as power versus speed of the wind turbine.

Figure 2.

Wind turbine power versus speed characteristics.

The electromagnetic torque (T_em) is expressed as

$$T_{\mathit{em}}=p\left({\Psi }_{\mathit{ds}}{i}_{\mathit{qs}}-{\Psi }_{\mathit{qs}}{i}_{\mathit{ds}}\right)$$E9

The output active (P_g) and reactive power (Q_g) of a wind turbine supplied to the grid are computed by.

$$\begin{array}{c}{P}_g=1.5\left(-v_{\mathit{ds}}{i}_{\mathit{ds}}+v_{\mathit{qs}}{i}_{\mathit{qs}}-v_{\mathit{qr}}{i}_{\mathit{qr}}-v_{\mathit{dr}}{i}_{\mathit{dr}}\right)\\ Q_g=1.5\left(v_{\mathit{qs}}{i}_{\mathit{ds}}+v_{\mathit{ds}}{i}_{\mathit{qs}}-v_{\mathit{dr}}{i}_{\mathit{qr}}-v_{\mathit{qr}}{i}_{\mathit{dr}}\right)\end{array}$$E10

4. Modeling of the system

4.1 System description

The structure of the proposed system is shown in Figure 3. The grid contains conventional synchronous generator-based thermoelectricity, represented by SG1, SG2, and SG3, and loads. VSPS stands for variable-speed pumped storage powered by a doubly fed induction machine. As shown in Figure 3, the VSPS induction motor is configured with the rotor connected to the rotor-side voltage source converter (VSC) and the stator connected to the grid. The grid-side VSC NPCg is connected to the grid through a coupling inductor. Details are explained in [22]. IG stands for induction generator-based wind farm.

Figure 3.

Overview of a proposed VSPS system based on doubly fed induction machine and VSC converter topology.

4.2 The VSPS machine modeling

As shown in Figure 3, the doubly fed induction machine (DFIM)-fed VSPS unit is based on the VSC NPC converter topology. The dynamics model of the three-phase induction machine is expressed in Eqs. (11)–(15) including electrical and mechanical systems. Further details are explained in [22].

$$\begin{array}{c}\frac{d{\Psi }_{\mathit{ds}}}{\mathit{dt}}=V_{\mathit{ds}}-R_s{i}_{\mathit{ds}}-{\omega }_s{\Psi }_{\mathit{qs}}\\ \frac{d{\Psi }_{\mathit{qs}}}{\mathit{dt}}=V_{\mathit{qs}}-R_s{i}_{\mathit{qs}}+{\omega }_s{\Psi }_{\mathit{ds}}\end{array}$$E11

$$\begin{array}{c}\frac{d{\Psi }_{\mathit{dr}}}{\mathit{dt}}=V_{\mathit{dr}}-R_r{i}_{\mathit{dr}}+\left({\omega }_s-{\omega }_r\right){\Psi }_{\mathit{qr}}\\ \frac{d{\Psi }_{\mathit{qr}}}{\mathit{dt}}=V_{\mathit{qr}}-R_r{i}_{\mathit{qr}}-\left({\omega }_s-{\omega }_r\right){\Psi }_{\mathit{dr}}\end{array}$$E12

$$T_{\mathit{em}}=1.5p\left({\Psi }_{\mathit{ds}}{i}_{\mathit{qs}}-{\Psi }_{\mathit{qs}}{i}_{\mathit{ds}}\right)$$E13

$${\Psi }_{\mathit{ds}}=L_s{i}_{\mathit{ds}}+L_m{i}_{\mathit{dr}}$$

$${\Psi }_{\mathit{qs}}=L_s{i}_{\mathit{qs}}+L_m{i}_{\mathit{qr}}$$

$${\Psi }_{\mathit{dr}}=L_r{i}_{\mathit{dr}}+L_m{i}_{\mathit{ds}}$$

$${\Psi }_{\mathit{qr}}=L_r{i}_{\mathit{qr}}+L_m{i}_{\mathit{qs}}$$

$$L_s=L_{\mathit{ls}}+L_m$$

$$L_r=L_{\mathit{lr}}+L_m$$E14

$$\begin{array}{c}\frac{d{\omega }_m}{\mathit{dt}}=\frac{1}{2H}\left(T_{\mathit{em}}-F{\omega }_m-T_m\right)\\ \frac{d{\theta }_m}{\mathit{dt}}={\omega }_m\end{array}$$E15

where, ${\Psi }_{\mathit{dqs}}{\Psi }_{\mathit{dqr}}$, $V_{\mathit{qds}}{i}_{\mathit{dqs}}$, $L_{\mathit{ls}}{L}_{\mathit{lr}}$, $V_{\mathit{qdr}}{i}_{\mathit{dqr}}$, $L_m$, $R_s{R}_r$, $\omega {\omega }_r$, $T_m{T}_{\mathit{em}}$, $H$,$F$, $s$, and $P$ are respectively dq-axis stator and rotor fluxes, dq-axis stator voltage and current, stator and rotor leakage reactance, dq-axis rotor voltage and current, magnetizing reactance, stator and rotor resistance, synchronous and rotor angular speeds, turbine shaft and electromagnetic torque, combined inertia constant, combined viscous friction coefficient, slip ratio of the induction machine, and number of pole pairs.

4.3 The VSC-NPC converter modeling for deploying VSPS

The VSC is a self-commutating converter that is fast and controllable for AC/DC interface applications. One type of VSC converter is a three-level NPC power converter. The tertiary block contains three arms, each with its own four switch assemblies with antiparallel diodes and two NPCs.

The VSC self-commutated converter is a fast and controllable converter for AC/DC interface applications. One type of VSC converter is a three-level NPC power converter. The three-level block contains three arms with their own four switch assemblies with antiparallel diodes and two NPCs. Nonetheless, since this chapter is devoted to verifying the performance of the proposed system according to the phasor model technique, since the proposed system is large and should exhibit wind energy compensation and frequency stability not possible to see in the detailed model technique, assumptions are adopted. It is assumed that power losses in the converter are ignored. The switching dynamics can also be ignored because the PWM frequency in the three-level VSC NPC is much larger than the system frequency [23]. Therefore, the model of VSC NPC was developed based on (16).

$$u_{\mathit{dqr}}=\frac{m_{\mathit{dqr}}{V}_{\mathit{dc}}}{2}$$E16

where u_dqr, u_dqg and m_dqr, m_dqg are converter-injected voltages and modulated signals respectively in the rotor and grid-side converters.

The converter dynamics can be given by.

$$\frac{d{V}_{\mathit{dc}}}{\mathit{dt}}=\frac{1}{C_{\mathit{eq}}}{i}_c=\frac{1}{C_{\mathit{eq}}{V}_{\mathit{dc}}}\left(P_g-P_r\right)$$E17

Or in Laplace transform function

$${\mathit{V}}_{\mathit{dc}}\left(\mathit{s}\right)=\frac{\mathrm{1}}{\mathit{s}{\mathit{C}}_{\mathit{eq}}}{\mathit{I}}_{\mathit{c}}\left(\mathit{s}\right)=\frac{\mathrm{1}}{\mathit{s}{\mathit{C}}_{\mathit{eq}}{\mathit{V}}_{\mathit{dc}}\left(\mathit{s}\right)}\left[{\mathit{P}}_{\mathit{g}}\left(\mathit{s}\right)-{\mathit{P}}_{\mathit{r}}\left(\mathit{s}\right)\right]$$E18

where C_eq and V_dc are the equivalent capacitance and DC voltage, respectively, and i_c is the DC link capacitor charging current. P_g and P_r are active power flow in the grid and rotor side of the converters, respectively. Hence, Eq. (18) can be illustrated by Figure 4 [22].

Figure 4.

DC-link phasor model.

4.4 Control strategies for the VSC NPC system

4.4.1 Active power control

Using the DPC strategy, the response speed is fast, and the control system directly and effectively compensates for wind power fluctuations. Even if this is a local control scheme placed in the VSPS unit, as long as the VSPS operates within specified limits, an important output of an adjustable and almost constant power flow can be seen from the network of the power system. The power command P_opt of the VSPS is determined by the capacity of the VSPS and its efficiency.

In this regard, an external setpoint P_set should be assumed for the VSPS, which is the input to the power control system. The set point depends on the VSPS capacity and grid conditions. The value of this setpoint is specifically used to optimize the system energy balance and is updated at a slower rate. However, the main focus is on controlling wind power fluctuations and regulating VSPS power to mitigate the impact on the grid.

The active power P_s and reactive power Q_s equations provide the basis for the control strategy modeling, and given as.

$$\begin{array}{c}{P}_s=1.5\left(v_{\mathit{qs}}{i}_{\mathit{qs}}+v_{\mathit{ds}}{i}_{\mathit{ds}}\right)\\ Q_s=1.5\left(v_{\mathit{qs}}{i}_{\mathit{ds}}-v_{\mathit{ds}}{i}_{\mathit{qs}}\right)\end{array}$$E19

Based on the detail works in [22], we have.

$$\begin{array}{c}{P}_s=1.5V_s\left(L_m/L_s\right)i_{\mathit{qr}}\\ Q_s=1.5V_s\left\{\left({\Psi }_s/L_s\right)-\left(L_m/L_s\right)i_{\mathit{dr}}\right\}\end{array}$$E20

which implies the independent control of the real power and reactive power in the application of DFIM in VSPS.

Starting from the voltage equations of (11)–(14), assuming that the voltage drop across the stator resistance is very small compared with the grid voltage, and that the magnitude of the stator flux is fairly constant, we have the mathematical equation of (21).

$$V_{\mathit{qr}}=R_r{i}_{\mathit{qr}}+L_r^{\ast }\frac{d{i}_{\mathit{qr}}}{\mathit{dt}}+\left({\omega }_s-{\omega }_r\right)\left(L_r{i}_{\mathit{dr}}+L_m{i}_{\mathit{ds}}\right)$$

$$V_{\mathit{dr}}=R_r{i}_{\mathit{dr}}+L_r^{\ast }\frac{d{i}_{\mathit{dr}}}{\mathit{dt}}-\left({\omega }_s-{\omega }_r\right)\left(L_r{i}_{\mathit{qr}}+L_m{i}_{\mathit{qs}}\right)$$

$$\text{where}$$

$$L_r^{\ast }=L_r-\left(L_m^2/L_s\right)$$E21

From (21), the rotor dynamics model is determined and defined as

$$\frac{I_{\mathit{dqr}}\left(s\right)}{I_{\mathit{dqr}-\mathit{ref}}\left(s\right)}=G_i\left(s\right)=\frac{1}{\frac{L^{\ast }}{R_r}s+1}$$E22

Thus, the current control (inner loops) structure of Figure 5 is supposed to be developed. The PI control of K_i(s) is defined by

Figure 5.

The current control structure of the VSC NPC1.

$$K_i\left(s\right)=\frac{P_{i}s+I_i}{s}$$E23

where P_i and I_i are proportional and integral gains. P_i and I_i are determined and tuned based on the control stability theory.

From Eq. (23), we obtain

$$I_{\mathit{qr}}\left(s\right)=G_i\left(s\right)I_{\mathit{qr}-\mathit{ref}}\left(s\right)$$E24

Multiplying both sides of (24) by 1.5V_sL_m/L_s, we get

$$1.5V_s{L}_m/L_s{I}_{\mathit{qr}}\left(s\right)=G_i\left(s\right)1.5V_s{L}_m/L_s{I}_{\mathit{qr}-\mathit{ref}}\left(s\right)$$E25

Therefore, based on Eq. (20), from (25), we can deduce (26).

$$P_s\left(s\right)=G_i\left(s\right)P_{s-\mathit{ref}}\left(s\right)$$E26

That is the dynamic model for active power control of rotor-side converter VSC NPCr is the same as the current control dynamic model. The PI control of K_p(s) of Figure 6 is defined in (30)

Figure 6.

The active power control structure of the VSC NPC1.

$$K_p\left(s\right)=\frac{P_{p}s+I_p}{s}$$E27

Considering the power command ΔP_wind to the VSPS power control unit, it is computed by

$$\Delta P_{\mathit{\text{wind}}}=P_{\mathit{\text{wind}}}-P_{\mathit{set}}$$E28

where P_wind is the wind farm power measured, and P_set an assumed forecasted power output. This P_wind is added to the power command P_opt to feed the fluctuated wind power to the control loop for regulating.

4.4.2 Frequency droop control for the improvement of active power control performance

Controlling the VSPS unit in primary frequency control is very important in power systems. By implementing a frequency droop control scheme, the response of the power system to emergencies is improved in the case of fluctuations in the dominant wind farm power generation. Power transfer within the DC link can be modulated by frequency droop control. It is specially designed for converters to provide frequency support to the grid. The control structure shown in Figure 7 provides a governor-like droop behavior through active power flow. Droop-type control is built on the concept of power synchronization control, where grid synchronization is achieved regardless of dedicated synchronization units [24]. This droop control system provides a DC link with frequency droop characteristics. Load sharing is possible for other generator sets in the grid system.

Figure 7.

Typical wind speed characteristics.

The introduction of VSPS can support the improvement of system performance to cope with all emergencies of the power system. Therefore, the additional power command ΔP_f due to the frequency variation of the VSPS active power control system (29) is determined.

$$\Delta P_f=-K_{\mathit{\text{droop}}}(f_{\mathit{ref}}-f_{\mathit{\text{grid}}})$$E29

where K_droop is the droop constant, f_ref is the 50 Hz reference frequency used in this chapter, and f_grid is the grid frequency. Through the active power closed-loop control system, frequency droop control can be used as a support for grid frequency control. Therefore, in order to obtain more possible controllability in the operation of the power system, the frequency droop control of the VSPS system must be introduced significantly. The above strategies are combined for the active power control scheme in the VSPS unit in the proposed system, as shown in Figure 8.

Figure 8.

A frequency droop-fed DPC control strategy for VSPS system.

The models and details of the reactive power control in both rotor-side and grid-side converters and DC voltage control in the grid-side converter are presented in [22].

4.5 The wind power fluctuation and its spectrum characteristics

The distribution of wind speed and direction varies by region and season overtime. The spectral characteristics of wind power fluctuations recorded over time for a typical wind farm can be obtained using the Fast Fourier Transform (FFT) algorithm. Figure 7 shows wind speed fluctuations; the corresponding wind power generation and its spectral characteristics are shown in Figure 9a and b, respectively.

Figure 9.

The wind-turbine output power; (a) in time domain, (b) the frequency spectrum characteristics.

Spectral analysis is the process of estimating the power spectral density (PSD), which characterizes the frequency content or random processes of a signal, from its time domain representation. Spectrum automatically decomposes a signal or random process into different frequencies and identifies periodicity. FFT-based nonparametric methods make no assumptions about the input data, can be used for any type of signal, produce more accurate spectral estimates, and allow us to convert flow time-domain signals to frequency domain and vice versa. The frequency domain representation of a signal reveals important signal characteristics that are difficult to analyze in the time domain.

One of the definitions of power spectral density (PSD) function [25] is given by

$$\varphi \left(\omega \right)=\underset{N\to \infty }{\mathit{lim}}E\left\{\frac{1}{N}{\left|\sum _{t=1}^{N}y\left(t\right)e^{-\mathit{i\omega t}}\right|}^2\right\}$$E30

Certainly, the PSD ϕ(ω) measures the power at frequency ω in the signal’s auto-covariance sequence r(k), i.e., r(k) = r*(−k). Since ϕ(ω) is a power density, it should be real valued and nonnegative, i.e., ϕ(ω) ≥ 0 for all ω. Thus, according to [25], the other equivalent definition of the PSD is given by

$$\varphi \left(\omega \right)=r\left(0\right)+2\sum _{k=1}^{\infty }r\left(k\right)\mathit{cos}\left(\mathit{\omega k}\right)$$E31

where r(0) is the averaging value of the function over the sampled time, and its inverse transformation is

$$r\left(k\right)=\frac{1}{2\pi }{\int }_{-\pi }^{\pi }\varphi \left(\omega \right)e^{\mathit{i\omega k}}\mathit{d\omega }$$E32

Therefore, the spectral characteristic of the wind power fluctuation is well described and analyzed by the above PSD equations, and the simulating result of Figure 9a is shown in Figure 9b.

As shown in Figure 9b, the wind power fluctuation is insignificant for the spectral frequency greater than about 1.2 Hz. Hence, the VSPS is engaged to compensate the significant wind power fluctuation components and the spectrum of the VSPS control response is determined accordingly.

According to statistics, the typical frequency of wind power fluctuations is recorded from a few minutes to a few days [9]. For slow fluctuations that are not an obvious problem, such as daily, the grid has adequate means of control. However, it is difficult to adjust minute-to-minute fluctuations only by traditional means such as thermal power. Therefore, to solve such problems caused by the randomness of wind power, VSPS is a possible option for stabilizing and smoothing grid frequency changes.

4.6 The VSPS system spectrum analysis and its implication for wind power fluctuation compensation

The power control in the DFIM-based wind farm VSPS system is essentially the control of the VSC-fed VSPS system. As shown in Figure 10, the frequency-droop-fed DPC-controlled VSPS system integrated in the grid tracks the power fluctuation command well. Small distortions are observed when the command signal changes from one state to another.

Figure 10.

The tracking of active power instruction in the droop fed DPC-driven VSPS system.

We know that the dynamic characteristics of the generator set and pump set of VSPS are closely related to the control method and system structure, but it is difficult to obtain a specific value by using the analytical method. Therefore, this chapter uses the spectral analysis method to verify the results obtained by the time domain analysis, as shown in Figure 11. The spectral characteristics are determined using the driving mathematically equivalent total active power control system equation of (33). Therefore, the simulation results of the spectral characteristics of the controlled active power response of the VSPS are shown in Figure 12. It is observed that the bandwidth of the response of the VSPS control system is large enough to cover the bandwidth power fluctuation of the spectral results of the wind as shown in Figure 10b. This means that the frequency-fed DPC control strategy of the VSPS system can use the derivation function of (33) to quickly and flexibly adjust the power fluctuations caused by the wind farm energy in the grid integrated system.

Figure 11.

The frequency spectrum characteristics of the VSPS control system simulated in time response of Figure 10.

Figure 12.

Single-line diagram of the VSPS-wind farm-grid integrated system simulating setup.

$$G\left(s\right)\approx \frac{\frac{P_p}{I_p}s+1}{\frac{\left(\frac{1+P_i}{I_i}\right)k_{\mathit{\text{droop}}}}{I_p}{s}^2+\frac{\left(P_p+1\right)}{I_p}s+1}$$E33

5. Simulation of models

In this chapter, a case study is presented involving a 300 MW DFIM-based VSPS and a grid system integrated with a wind farm consisting of seven identical 15 MW wind turbine induction generators. To study the effect of wind fluctuations on grid frequency, a model of a medium-sized power system consisting of two 200MVA hydropower plants and one 15MVA diesel generator set and conventional synchronous generators was established. Phasor modeling techniques in MATLAB/Simulink are applied. For conventional synchronous machines, the primary voltage regulation method in automatic voltage regulators based on the standard IEEE type I and the primary frequency regulation method in turbine speed governors are used. The simulation setup is shown in Figure 12.

6. Results and discussion

Figure 13 shows the active power generation characteristics of the VSPS unit. Its power generation trends vary according to the characteristics of wind power fluctuations. Figure 14 shows a comparison of VSPS active power compensation with wind power fluctuations. The comparison takes into account the power fluctuations of the wind farm from its mean value (40.74 MW) and the difference in VSPS production from its mean value (247.1 MW). The error between the wind farm power fluctuation and the power produced by the VSPS is small. Therefore, VSPS can effectively and quickly compensate for large fluctuations in wind energy. This verifies the ability of VSPS to meet wind power fluctuation compensation requirements. Therefore, as shown in Figure 15, a very small deviation in grid frequency is observed, less than 0.002%.

Figure 13.

The active power characteristics of the VSPS.

Figure 14.

The fluctuation compensation characteristics. a) the wind farm power fluctuation from its average value and the compensation power generated and regulated by VSPS system. b) the active power difference between the wind fluctuation and the VSPS compensation.

Figure 15.

The grid frequency response associated with the wind power fluctuation.

Figure 16 shows the evolution of the grid frequency response by comparing VSPS active power control with and without droop control during emergency. Compared with the vector control strategy without droop feed control, the deviation of frequency from the nominal value is greatly reduced in the droop feed vector control strategy. The grid frequency response deviation was observed to be ±0.04 Hz, while active power was regulated to track wind power fluctuations, start-up transients, and three-phase faults. Importantly, the settling time of the droop control scheme is very short. Therefore, the grid frequency dynamics and steady-state response in the droop-fed vector control strategy are quite stable, and the deviation is within an acceptable range.

Figure 16.

Evolution of the network in grid frequency response comparing the VSPS active power control with and without droop control during the start-up transient and three-phase faults imposed.

7. Conclusion

This chapter discusses VSPS systems in wind farm grid-connected systems, which play a vital role in the context of increasing penetration of renewable energy. It also has an important function in real-time applications for balancing generation and demand as it provides fast-response generation. VSPS active power generation can quickly adjust wind power fluctuations, so that the power flow on the grid bus is stable. This chapter proposes a VSPS system based on a droop-fed DPC strategy as a solution. Spectral analysis is used to verify the performance of the proposed control system as well.

The results show that VSPS has important stability control characteristics to respond to different contingencies, such as generator losses, large load changes, faults, and start-up transient disturbances. The proposed control strategy can also well regulate grid frequency and AC bus voltage. Spectral analysis method implemented in this chapter is also effective for determining the requirements of wind power fluctuations and stability in large power systems.