Voltage and frequency control of wind–diesel power system through adaptive sliding mode control of superconducting magnetic energy storage

Abstract

The random nature of wind power along with active and reactive load changes results in both frequency and voltage fluctuations in a wind–diesel power system. In order to improve the dynamic performance by regulating the frequency as well as voltage of the system, an adaptive sliding mode control strategy is proposed on superconducting magnetic energy storage unit interfaced with a wind–diesel power system. Sliding mode control strategy developed with the superconducting magnetic energy storage unit achieves fast and effective exchange of real and reactive power via firing angle control of the converter. With the help of suitable switching surface design and use of adaptive control law, chattering elimination and controller robustness is achieved. This work is carried out in MATLAB/Simulink, and simulation results presented shows a positive impact of proposed scheme.

Keywords

Wind–diesel power system wind power superconducting magnetic energy storage sliding mode controller adaptive sliding mode controller

Introduction

Exploitation of renewable energy sources to generate the electrical power is the need of hour. Wind power along with diesel system as backup supply offers an enticing and reliable source of power supply. However, due to random and fluctuating nature of wind power and sudden changes in load, the operating point of the system gets disturbed frequently and with the result fluctuations in both the voltage and frequency of the system is observed because of mismatch in the active and reactive power generation and demand. Any large disturbance in the system load or wind power supply may lead the system to the state of unstability. Therefore, it becomes important to control the active and reactive power flow in the wind–diesel system so as to reduce the system voltage and frequency deviations whenever the system operating point is set to a disturbance (Amirthalingam, 2010; Sharma et al., 2013; Wang and Truong, 2013).

Superconducting magnetic energy storage (SMES) unit possess the phenomenal ability to exchange both active as well as reactive power with very high speed of operation. Installation of SMES unit with the wind–diesel system can reduce the mismatch in active and reactive power by supplying the deficit power to and absorbing excess power from the system, whenever the system is subjected to disturbances in load or wind power. Thus, deviations occurring in the system frequency and voltage are reduced to a large extent (Salama et al., 2019; Vulusala and Sreedhar, 2017; Yunus et al., 2012). However, with the use of robust and intelligent control techniques, SMES unit could help to further bring down these deviations and ensure the system robustness. Frequency control of wind–diesel system through active power control using robust and predictively controlled SMES unit is reported in Ngamroo (2009); Zargar et al. (2017a); Magdy et al. (2018), but voltage control of the system is not included. Voltage control of wind–diesel system through reactive power control using intelligent control strategies like fuzzy control, sliding mode control (SMC), and predictive control is reported in Bansal (2006); Kassem and Abdelaziz (2014); Mohanty and Viswavandya (2016), but frequency control is not carried out. Control of frequency and voltage deviations in wind–diesel system under load and wind power disturbances using SMES as storage unit is done in Zargar et al. (2018), but no control strategy is applied over SMES unit to achieve system robustness and improvement in system performance.

Simultaneous frequency and voltage control of wind–diesel system is done in Zargar et al. (2017b), but two devices that is energy storage unit and SVC are used that can lead to increase in cost as well as complexity of the system. Genetic algorithm is applied to SMES unit for simultaneous voltage and frequency control in Abass and Mufti (2019), but such a control technique becomes cumbersome for practical implications. In Mi et al. (2019), voltage as well as frequency control is done based on robust sliding mode controller design; however, SMES unit is not incorporated instead STATCOM is used for reactive power control. Robust controller design for SMES unit is reported in Khosraviani et al. (2017); Li et al. (2019), but either only the frequency control is carried out or else wind power is not taken into account.

In this article, control of voltage as well as frequency deviations that occurs in a wind–diesel power system due to various disturbances like sudden load changes, wind power disconnection, and random nature of wind power is reported by interfacing SMES unit with the system. SMC strategy is employed over the SMES unit to ensure the fast and effective active and reactive exchange of the unit with system by controlling the firing angle of the converter. Moreover, to eliminate the drawback of chattering phenomenon in the system response, an adaptive control law is incorporated with the designed sliding mode controller. Finally, comparison of system voltage and frequency deviations under different case studies is presented to highlight the impact of interfacing the SMES unit and the proposed controller-based SMES unit with the system.

Mathematical modeling of wind diesel power system

The wind–diesel hybrid system consists of a diesel engine synchronous generator (SG) equipped with IEEE type-I excitation system, induction generator (IG) along with wind energy conversion system (WECS), supermagnetic energy storage (SMES) unit, and load model. Block diagram of the power system model is shown in Figure 1, where $V$ is the bus voltage; $f$ is the system frequency; $P_{SG}$ and $Q_{SG}$ are the active and reactive components of the power generated by the SG; $P_{IG}$ and $Q_{IG}$ , respectively, are the IG active power output and required reactive power; $P_{smes}$ and $Q_{smes}$ are the active and reactive power components exchanged by the SMES unit with the system; $P_{L}$ and $Q_{L}$ are the active and reactive components of the load, respectively.

Figure 1.

Block diagram of wind–diesel power system.

The variation in wind power due to wind gusts and load changes may cause the deviation in the frequency and voltage of the hybrid system (Liao and Xu, 2018), then the active and reactive power balance equations of the system may be given as

\begin{matrix} Δ f (s) = \frac{K_{fs}}{1 + s T_{fs}} [Δ P_{SG} (s) + Δ P_{IG} (s) + Δ P_{smes} (s) - Δ P_{L} (s)] \end{matrix}

(1)

\begin{matrix} Δ V (s) = \frac{K_{vs}}{1 + s T_{vs}} [Δ Q_{SG} (s) - Δ Q_{IG} (s) + Δ Q_{smes} (s) - Δ Q_{L} (s)] \end{matrix}

(2)

where $K_{fs}$ , $K_{vs}$ and $T_{fs}$ , $T_{vs}$ represent the gains and time constants of the system.

Modeling of SG and excitation system

SG is considered to be the primary source of both active and reactive power in the system. Deviation in the active power of the SG considering Figure 2 is given as

Δ P_{SG} (s) = \frac{1}{1 + s T_{t}} Δ P_{cv} (s)

(3)

Δ P_{cv} (s) = \frac{1}{1 + s T_{g}} (\frac{1}{R} + \frac{K_{I}}{s}) Δ f

(4)

where $Δ P_{cv} (s)$ is the increment in the position of control valve, $R$ is the rate adjustment of governor action, $K_{I}$ is the integral control gain, $T_{g}$ and $T_{t}$ are the governor and turbine time constants.

Figure 2.

Simulink-based modeling diagram of the system.

Deviation in the reactive power of the SG (Elgerd, 1982) is given as

Δ Q_{SG} (s) = K_{1 a} Δ E'_{q} (s) + K_{2 a} Δ V (s)

(5)

K_{1 a} = \frac{Vcos δ}{{X'}_{d}}, K_{2 a} = \frac{{E'}_{q} \cos δ - 2 V}{{X'}_{d}}

(6)

where $X'_{d}$ is the direct axis transient reactance, $X_{d}$ is the direct axis steady state reactance. $δ$ is the power angle, $E'_{q}$ represents the voltage at armature terminals. The equation of flux linkage in the SG is given as

Δ E'_{q} (s) = \frac{1}{1 + s T_{g}} (K_{3 a} Δ E_{fd} (s) + K_{4 a} Δ V (s))

(7)

T_{g} = \frac{{X'}_{d} {T'}_{d 0}}{X_{d}}

(8)

K_{3 a} = \frac{{X'}_{d}}{X_{d}}, K_{4 a} = \frac{(X_{d} - {X'}_{d}) \cos δ}{X_{d}}

(9)

where $Δ E_{fd}$ represents the deviation in voltage of excitation system.

Excitation system modeled as IEEE type-I (Bansal, 2006) is considered for the SG.

Modeling of wind power and IG system

Wind power drives the wind turbine/mill which in turn acts as a prime mover to the IG. The IGs act as source of active power while absorbing the reactive power from the system.

The mechanical power output of windmill (Mi et al., 2017) can be given as

P_{wm} = \frac{1}{2} ρ {Av}_{w}^{3} C_{p} (λ, β)

(10)

where $ρ$ is the air density, $A = π R^{2}$ is the rotor cross section, $v_{w}$ is the wind speed, $C_{p} (λ, β)$ is the wind power coefficient, $λ = ω R / v_{w}$ is the tip-speed ratio, $β$ is the pitch angle of the rotor blade, $ω$ is the rotor angular speed and can be defined as

ω^{2} = \int \frac{2}{J} (P_{wm} - P_{IG}) dt

(11)

where $J$ is the inertia of the windmill and $P_{IG}$ is the output power of IG which can be given as

P_{IG} = \frac{- 3 V (1 + \frac{1}{s_{1}}) R_{2}}{{(\frac{R_{2}}{s_{1}} - R_{1})}^{2} + {(X_{1} + X_{2})}^{2}}

(12)

where $V$ is the phase voltage; $R_{1}$ and $R_{2}$ are the stator and rotor resistances, respectively; $X_{1}$ and $X_{2}$ are the respective stator and rotor reactances; $s_{1} = ((ω_{0} - ω) / ω_{0})$ is the rotor slip; and $ω_{0}$ is the synchronous angular speed.

The deviation in the reactive power absorbed by the IG depends on the voltage and generator parameters (Bansal and Bhatti, 2007) can be given as

Δ Q_{IG} (s) = K_{5 a} Δ V (s) + K_{6 a} Δ P_{wm} (s)

(13)

K_{5 a} = \frac{2 V X_{e}}{R_{v}^{2} + X_{e}^{2}}, K_{6 a} = \frac{2 R_{v} X_{e}}{2 R_{v} R_{p} - (R_{v}^{2} + X_{e}^{2})}

(14)

R_{v} = R_{p} - R_{e}, R_{p} = \frac{{R'}_{2} (1 - s_{1})}{s_{1}}

(15)

R_{e} = R_{1} + R_{2}, X_{e} = X_{1} + X_{2}

(16)

Modeling of SMES unit

The schematic configuration of the supermagnetic energy storage (SMES) unit is shown in Figure 3, with $Y - Δ / Y$ step down transformer connected to AC bus, a set of two six-pulse converters and supermagnetic coil. The independent operation of SMES to exchange active and reactive powers is achieved via the control of firing angles $α_{1}$ and $α_{2}$ of the converters.

Figure 3.

Schematic diagram of SMES.

The output voltage of the 12 pulse converter can be varied over the wide range of positive and negative values by controlling the converter firing angles $α_{1}$ and $α_{2}$ . Gate turn off thyristors (GTOs) are used to achieve this feature of the converter and therefore leads to three different modes of operations of the SMES unit (Mitani et al., 1988; Rabbani et al., 1999) as follows:

Charging mode when $α_{1} > 0 °$ and $α_{2} > 0 °$ , the power flow occurs from the AC bus to SMES unit.

Standby mode when $α_{1} = α_{2} = 90 °$ , the voltage across the SMES coil is zero and hence no power flow occurs through the converter.

Discharging mode when $α_{1} > 90 °$ and $α_{2} > 90 °$ , the power flow occurs from SMES unit to AC bus.

Charging and discharging of the SMES coil depends on the amount and nature of disturbances and can be varied through proper adjustments of the firing angles $α_{1}$ and $α_{2}$ of the converter. The firing angles of the converter for exploring the four quadrant operation can calculated as (Abu-Siada et al., 2002; Mitani et al., 1988)

α_{1} = co s^{- 1} (\frac{P_{smes}}{\sqrt{P_{smes}^{2} + Q_{smes}^{2}}}) + co s^{- 1} (\frac{\sqrt{P_{smes}^{2} + Q_{smes}^{2}}}{2 V_{sm 0} I_{sm}})

(17)

α_{2} = co s^{- 1} (\frac{P_{smes}}{\sqrt{P_{smes}^{2} + Q_{smes}^{2}}}) - co s^{- 1} (\frac{\sqrt{P_{smes}^{2} + Q_{smes}^{2}}}{2 V_{sm 0} I_{sm}})

(18)

Neglecting the switching losses and assuming that $α_{1} = α_{2} = α$ , the voltage on the DC side of whole converter is given as

V_{sm} = E_{d 1} + E_{d 2} = 2 V_{sm 0} \cos (α)

(19)

where $E_{d 1}$ and $E_{d 2}$ are the DC voltage at each converter terminals and $V_{sm 0}$ is the no-load maximum value of DC voltage.

The active and reactive power transferred through 12-pulse converter is given as

P_{smes} = 2 V_{sm 0} I_{sm} \cos (α)

(20)

Q_{smes} = 2 V_{sm 0} I_{sm} \sin (α)

(21)

The current and voltage relationship in the SMES coil is given as

L_{sm} \frac{d I_{sm}}{dt} = V_{sm} - R I_{sm}

(22)

where $L_{sm}$ and $R$ are the inductance and resistance of the SMES coil, $I_{sm}$ is the current flow via SMES coil.

The active power transfer from/to SMES via converter is controlled based on the continuously varying frequency of the system (Khosraviani et al., 2017; Wu and Lee, 1993) and is given as

Δ P_{sm} (s) = \frac{K_{fc}}{1 + s T_{fc}} Δ f (s)

(23)

where $K_{fc}$ and $T_{fc}$ are the closed loop gain and time constant of the frequency controller.

The reactive power transfer from/to SMES via converter is dependent on the continuously varying system voltage (Wu et al., 2012; Wu and Lee, 1993) and is given as

Δ Q_{sm} (s) = \frac{K_{vc}}{1 + s T_{vc}} Δ V (s)

(24)

where $K_{vc}$ and $T_{vc}$ are the closed loop gain and time constant of the voltage controller.

Design of control strategy for SMES

To develop the control strategy for the effective and fast exchange of active and reactive power via SMES unit with the wind–diesel system by controlling the firing angle of the converter so as to reduce the voltage and frequency deviation, whenever the system is set to disturbances consider the modeling diagrams shown in Figures 2 and 4.

Figure 4.

Modeling diagram of SMES unit.

For the purpose of design of proposed control strategy, the dynamics of the system can be expressed as

\overset{\cdot\cdot}{x} (t) = f (x (t)) + bu (t) + f_{d} (t)

(25)

where $x (t) \in R^{n}$ is the state vector, $u (t) \in R^{m}$ is the control input vector, $f_{d} (t) \in R^{n}$ is the lumped representation of model uncertainty and external disturbances, $b \in R^{n}$ is the input matrix, $f (x (t))$ is a map of $x (t) \in R^{n} \to f (x (t)) \in R^{n}$ . The objective of controller is to generate a control law so that the error in the state $x$ is tracking the reference error $x_{ref}$ .

Assumption: The lumped representation of model uncertainty and external disturbances is bounded that is $| f_{d} (t) | ⩽ \bar{ρ}$ , where $\bar{ρ}$ is a positive constant.

Sliding mode controller

The design of sliding mode controller is a two-step process, the design of equivalent control law with suitable sliding manifold/surface and the design of switching control law that keeps the system dynamics onto the designed sliding manifold (Itkis, 1976; Nouri et al., 2017; Utkin et al., 1970).

Sliding surface design

Defining a suitable sliding manifold/surface as follows

\begin{matrix} σ_{i} (t) = (\frac{d}{dt} + λ_{i}) e_{i} (t) \\ = {\overset{\cdot}{e}}_{i} (t) + λ_{i} e_{i} (t) \end{matrix}

(26)

where $λ_{i}$ is the matrix of sliding coefficients, $e_{i}$ and ${\overset{\cdot}{e}}_{i}$ are the vector of state errors and the vector of derivative of state errors, respectively, and are defined as

λ_{i} = [\begin{matrix} λ_{1} 0 \\ 0 λ_{2} \end{matrix}]

(27)

\begin{matrix} e_{i} = x - x_{ref} \\ = [Δ f - Δ f_{ref}, Δ V - Δ V_{ref}]^{T} \end{matrix}

(28)

\begin{matrix} {\overset{\cdot}{e}}_{i} = \overset{\cdot}{x} - {\overset{\cdot}{x}}_{ref} \\ = [Δ \overset{\cdot}{f} - \overset{\cdot}{Δ} f_{ref}, Δ \overset{\cdot}{V} - \overset{\cdot}{Δ} V_{ref}]^{T} \end{matrix}

(29)

where $Δ f$ and $Δ V$ are the actual deviations in system frequency and voltage; $Δ f_{ref}$ and $Δ V_{ref}$ are the reference/desired deviations in system frequency and voltage (see Figure 5).

Figure 5.

Control structure of SMES unit.

Sliding mode controller law design

The SMC law can be given as

u (t) = u_{eq} (t) + u_{sw} (t)

(30)

The equivalent control law $u_{eq} (t)$ possesses a control action to achieve ideal sliding motion that is to hold the control variable onto the sliding manifold when model uncertainty and external disturbances are no taken into account. The switching control law $u_{sw} (t)$ possesses the control action to ensure system robustness and chattering free property with the inclusion of system uncertainty and external disturbances. In order to derive the $u_{eq} (t)$ , we have

\begin{matrix} {\overset{\cdot}{σ}}_{i} (t) = {\overset{\cdot\cdot}{e}}_{i} (t) + λ_{i} {\overset{\cdot}{e}}_{i} (t) \\ = (\overset{\cdot\cdot}{x} - {\overset{\cdot\cdot}{x}}_{ref}) + λ_{i} {\overset{\cdot}{e}}_{i} (t) \end{matrix}

(31)

Using equation (25) in equation (31) and omitting $f_{d} (t)$ , we get

{\overset{\cdot}{σ}}_{i} (t) = f (x (t)) + bu (t) - {\overset{\cdot\cdot}{x}}_{ref} + λ_{i} {\overset{\cdot}{e}}_{i} (t)

(32)

To obtain the equivalent control law, set ${\overset{\cdot}{σ}}_{i} (t) = 0$ in equation (32), we get

u_{eq} (t) = \frac{1}{b} (- λ_{i} {\overset{\cdot}{e}}_{i} (t) - f (x (t)) + {\overset{\cdot\cdot}{x}}_{ref})

(33)

The switching control law based on traditional SMC approach with constant reaching rate (Itkis, 1976) is given as

u_{sw} (t) = - ksgn (σ_{i} (t))

(34)

where $k$ is a positive constant known as controller switching gain and $sgn ()$ is defined as

sgn (σ_{i}) = {\begin{matrix} + 1 if σ_{i} > 0 \\ 0 if σ_{i} = 0 \\ - 1 if σ_{i} < 0 \end{matrix}

using equation (34) in equation (30), we get

u (t) = u_{eq} (t) - ksgn (σ_{i} (t))

(35)

Stability analysis

To determine the stability of traditional sliding mode controller while taking the disturbance $f_{d} (t)$ into account and using $‖ b ‖ \neq 0$ , construct the Lyapunov function as

V (t) = \frac{1}{2} σ_{i}^{2} (t)

(36)

Taking the derivative of equation (36) and using equations (32), (33), and (35) along with assumption, we get

\begin{matrix} \overset{\cdot}{V} (t) = σ_{i} (t) {\overset{\cdot}{σ}}_{i} (t) \\ = σ_{i} (t) (f (x (t)) + bu (t) + f_{d} (t) - {\overset{\cdot\cdot}{x}}_{ref} + λ_{i} {\overset{\cdot}{e}}_{i} (t)) \\ = σ_{i} (t) (- ksgn (σ_{i} (t)) + f_{d} (t)) \\ = - k σ_{i} (t) sgn (σ_{i} (t)) + σ_{i} (t) f_{d} (t) \\ ⩽ - k | σ_{i} (t) | + | σ_{i} (t) | \bar{ρ} \\ ⩽ - (k - \bar{ρ}) | σ_{i} (t) | \end{matrix}

(37)

Therefore, choosing the proper switching gain $k ⩾ \bar{ρ}$ , the derivative of Lyapunov function becomes negative semi-definite that is $\overset{\cdot}{V} (t) ⩽ 0$ , and thus ensures that system is asymptotically stable with $lim_{t \to \infty} σ_{i} (t) = 0$ , that is, $σ_{i} (t)$ and $e_{i} (t)$ asymptotically converges to zero in finite time.

Adaptive sliding mode controller

To achieve the chattering free response of the system and ensure that system possess the robustness against the disturbances, the switching control law used in the traditional sliding mode controller above is modified. The switching control law is designed based on the reaching law (Gao et al., 1995) is given as

u_{s w} (t) = - \hat{ϵ} s g n (σ_{i} (t)) - k σ_{i} (t)

(38)

where $k > 0$ , $sgn ()$ is a sign function, and $\hat{ϵ}$ is parameter and is designed based on the adaptive law given as

\dot{\hat{ϵ}} = a | σ_{i} (t) |

(39)

where $a$ is a small positive constant.

Using equation (38) in equation (30), the adaptive controller law obtained is given as

u (t) = u_{e q} (t) - ϵ s g n (σ_{i} (t)) - k σ_{i} (t)

(40)

Stability analysis

To determine the stability of adaptive sliding mode controller (ASMC) with system uncertainty and external disturbances $f_{d} (t)$ and using $| | b | | \neq 0$ , taking the Lyapunov function as

V (t) = \frac{1}{2} σ_{i}^{2} (t) + \frac{1}{2 a} {\tilde{ϵ}}^{2}

(41)

where $\tilde{ϵ} = \hat{ϵ} - ϵ$ is defined as estimation in error variable and $ϵ$ is a positive constant. The derivative of Lyapunov function given in equation (41) is given as

\dot{V} (t) = σ_{i} (t) {\dot{σ}}_{i} (t) + \frac{1}{a} \tilde{ϵ} \dot{\tilde{ϵ}}

(42)

Using equations (32), (33), and (40) in equation (42) and the assumption, we get

\begin{array}{l} \dot{V} (t) = σ_{i} (t) (f (x (t)) + b u (t) + f_{d} (t) - {\overset{\cdot\cdot}{x}}_{r e f} + λ {\dot{e}}_{i} (t)) \\ + \frac{1}{a} \tilde{ϵ} \dot{\hat{ϵ}} \\ = σ_{i} (t) (- \hat{ϵ} s g n (σ_{i} (t)) - k σ_{i} (t) + f_{d} (t)) + \frac{1}{a} (\hat{ϵ} - ϵ) \dot{\hat{ϵ}} \\ ⩽ - k | σ_{i} (t) |^{2} + \bar{ρ} | σ_{i} (t) | - \frac{1}{a} ϵ \dot{\hat{ϵ}} + \hat{ϵ} (\frac{1}{a} \dot{\hat{ϵ}} - | σ_{i} (t) |) \\ ⩽ - k | σ_{i} (t) |^{2} + \bar{ρ} | σ_{i} (t) | - ϵ | σ_{i} (t) | \\ ⩽ - (k + \frac{ϵ}{| σ_{i} (t) |} - \frac{\bar{ρ}}{| σ_{i} (t) |}) | σ_{i} (t) |^{2} \end{array}

(43)

Therefore, for a bounded disturbance $| f_{d} (t) | ⩽ \bar{ρ}$ and with the choice of proper value of gain $k$ and constant $ϵ$ , the derivative of Lyapunov function becomes negative semi-definite that is $\overset{\cdot}{V} (t) ⩽ 0$ . Hence, the system is asymptotically stable with $lim_{t \to \infty} σ_{i} (t) = 0$ , that is, $σ_{i} (t)$ and $e_{i} (t)$ asymptotically converges to zero in finite time.

Simulation studies

In order to study the impact of using SMES unit on the system performance like voltage and frequency deviations and proposed control strategy employed on the SMES unit, the system under consideration with parameters shown in Appendix I, is subjected to three different types of disturbances, step change in load, wind power disconnection, and the fluctuating wind power generated from continuously varying wind gusts illustrated in case studies below. Finally, comparison between the deviations in system parameters of interest are made with system not using SMES, system with traditionally PI (proportional–integral) controller–based SMES, SMC-based SMES, and ASMC-based SMES.

Case 1: step change in load

In this case, the system is subjected to a step change in load $Δ Q_{L} = 0.01 pu$ at $t = 0.02 s$ and $Δ P_{IG} = 0.1 pu$ at time $t = 1 s$ . Deviation in the system bus voltage and frequency is observed and comparison of results is shown between the system without SMES, PI controller–based SMES, SMC-based SMES, and ASMC-based SMES.

From Figures 6 and 7, it can be seen that with the use of PI controller–based SMES, the deviations in system bus voltage and frequency are reduced in comparison to system without SMES, then with use of SMC-based SMES further reduction in the amount of deviations and improvement in the settling time response is achieved; however, the chattering phenomenon that is minute but continuous oscillations are observed and finally the use of ASMC-based SMES provides the chattering free response as observed in the SMC-based SMES. Therefore, with the system subjected to step change in load, it is clear that voltage and frequency deviations occurring in the system are reduced with the use of SMES unit and proposed controller-based SMES ensures system robustness while constraining amount of deviations and reducing settling the time post disturbance instant.

Figure 6.

Deviation in system voltage.

Figure 7.

Deviation in system frequency.

In Figure 8, peak-to-peak values of frequency and voltage deviations are shown that occurs in the system due to step load change with system without SMES, system with PI controller–based SMES, SMC-based SMES, and ASMC-based SMES.

Figure 8.

Peak-to-peak deviations in system frequency and voltage under step disturbance.

Case 2: wind power disconnection

In this case, the performance of system is observed in the event of wind power disconnection and impact of installation of SMES unit along with proposed control strategy is shown. At time $t = 0.01 s$ , the wind power is disconnected leading to active and reactive power mismatch in demand and generation and thus results in deviations in both the voltage and frequency of the system.

From Figures 9 and 10, it can be seen that in the event of wind power disconnection the voltage and frequency response shown in terms of deviations is improved by reducing the settling time and eliminating the steady state error through fast and effective exchange of active and reactive power by SMES with the system through SMC-based SMES and chattering phenomenon that occurs in it is eliminated through ASMC-based SMES.

Figure 9.

Deviation in system voltage.

Figure 10.

Deviation in system frequency.

Case 3: operation under wind gusts

In this case, to check the robustness of proposed control strategy–based SMES, system under consideration is subjected to the time varying continuous wind gusts. Under such wind gusts, windmill output power variation occurs as shown in Figure 11 that leads to IG reactive power deviations and hence voltage deviation occurs. Wind speed variations shown in Figure 12 cause IG active power deviations and consequently the frequency deviations in the system.

Figure 11.

Windmill output power deviation under wind gust.

Figure 12.

Wind speed variation.

From Figures 13 and 14, it can be observed that continuously varying voltage and frequency deviations occurs in the system. These deviations are reduced with the use of PI controller–based SMES in comparison to those occurring in the same system without SMES. The deviations are further more reduced with the use of proposed control strategy that is SMC-based SMES; however, chattering phenomenon is associated with it. With ASMC-based SMES, the chattering drawback is eliminated and also the deviations occurring in the system voltage and frequency are reduced.

Figure 13.

Deviation in system voltage.

Figure 14.

Deviation in system frequency.

Conclusion

In this article, control of voltage and frequency deviations that occurs in a wind–diesel power system is done through active and reactive power flow control whenever the system is subjected to disturbances like step change in load, wind power disconnection, or wind power variations. To exchange both the active and reactive power with the system, a fast acting energy storage device known as SMES system is interfaced with the system and reduced deviations are observed. Sliding mode controller is designed for SMES unit ensuring system robustness as well as reduced deviations in the system frequency and voltage. ASMC is designed to avoid chattering drawback occurring in sliding mode controller–based SMES. MATLAB-based simulation results are presented to show the impact on the system performance with the use of SMES unit and the proposed controller–based SMES unit.

Footnotes

Appendix 1

Table 4.

SMES data.

$P_{sm 0} = 0.9 pu$	$V_{0} = 1.05 pu$	$pf = 0.9 lag$	$α_{0} = 0.02 rad$
$I_{sm 0} = 0.202 pu$	$V_{sm 0} = 0.253 pu$	$T_{sm} = 0.001 s$	$L_{sm} = 0.5 H$
$K_{fc} = 1$	$T_{fc} = 0.025 s$	$K_{vc} = 1$	$T_{vc} = 0.025 s$

SMES: superconducting magnetic energy storage.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Zahid Afzal Thoker

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