Dynamic performance improvement of a hybrid multimachine system using a flywheel energy storage system

Abstract

This article presents a detailed, yet simple control scheme based on a flywheel energy storage system for dynamic performance enhancement. A permanent magnet machine-based 70 MW flywheel energy storage system is incorporated in a wind-integrated Western System Coordinating Council multimachine system. An elaborate mathematical modelling of the flywheel energy storage system as an effective current source is provided along with the wind-embedded multimachine system to investigate the transient stability profile of the said system. Generator speed and voltage are continuously monitored by the flywheel energy storage system plant controllers, and subsequent real and reactive reference power commands are generated. Two first-order lag blocks are employed to emulate the grid side and machine side converters’ dynamics. The developed non-linear model is tested against three-phase faults in a variable wind condition, and the effectiveness of the control scheme is confirmed by the enormous damping and extension in the stability margin of the system.

Keywords

Multimachine power system hybrid system Western System Coordinating Council flywheel energy storage system wind energy squirrel cage induction generator dynamic performance transient stability modelling simulation DC link voltage controller faults

Introduction

There has been a spectacular growth and development in harnessing wind energy in the last few decades. This is primarily because of the promising role which the wind energy conversion systems play in terms of their large-scale potential fulfilment. The inclusion of wind energy systems in an otherwise conventional power system undoubtedly results in better reliability in terms of power production. But the very integration also results in system variable fluctuations due to the inherent random nature of the wind (Wang et al., 2009; Xu et al., 2013). Under normal conditions, a wind farm (WF) calls for a power control scheme to facilitate control over active power output of the farm. However, in events of grid disturbances, such as short circuits and intense load changes, an energy storage system (ESS) appears to be the most ideal option to compensate for the fluctuating components of the WF.

Dynamic stability study plays a vital role in power system stability investigations. It is a common practice to operate power systems within the ambit of their steady-state operating points. Whenever a system is hit by an intense disturbance, it is prone to lose synchronism in the very first swing, if a proper transient support strategy is not provided. At this end, an energy storage can rescue the troubled power system.

An ESS selection can be made from multifarious options, such as battery energy storage system (BESS), superconducting magnetic energy storage (SMES), flywheel energy storage system (FESS) and supercapacitor energy storage system (SCESS), depending upon the requirements. The slow action in terms of charging–discharging and dead band blocks of BESS, high cost of SMES and a thorough energy depletion along with lesser storage capacity of a supercapacitor are some of the loopholes of these very storage options (Taj et al., 2015). An FESS on the contrary, even though prone to power losses, survives on essential merits such as clean energy, longer life, least maintenance charges, high power density and no chemical interference. Just to state a few FESS features, it has a calendar life of 15–20 years, an efficiency of 80%–96%, an energy density of around 0.24–424 kWh/m³, a power density of 40–2000 kW/m³, a cycle life of 10,000–100,000 cycles and so on (Eckroad and Gyuk, 2003; Guerrero et al., 2009; Inage, 2009; Lazarewicz and Rojas, 2004). The energy-storing ability of FESS has increased manifold and is nowadays around 1–500 MJ with peak power around gigawatts (Hebner et al., 2002). Because of the advances in power electronic interface and control systems, the response time of FESS is very quick, in the range of milliseconds (<1/4 cycle). This property of FESS has been manoeuvred to serve as a transient support and impart oscillation damping and a low voltage ride over in the case of intense system trouble.

The application of FESS in power quality improvement due to its fast response characteristic has been reported in the studies by Lazarewicz and Rojas (2004) and Zhang et al. (2014). Frequency regulation of wind-based systems has been supported by FESS incorporation in various studies, such as Yao et al. (2016) and Suvire et al. (2012). Transient stability improvement of conventional multimachine systems and grid-connected WFs has been explored in the studies by Wang and Chen (2005) and Feng et al. (2011), respectively. The investigations in isolated microgrids using flywheel energy injection have been reported in the studies by Nair and Senroy (2016) and Jin et al. (2017). Adaptive neuro fuzzy-controlled FESS has been analysed in the study by Taj et al. (2015). The eigenvalue loci of a wind generation system with flywheel storage have been detailed in the study by Yao et al. (2016). The high efficiency and fitness of FESS to work in a large range of temperatures have been explored in the study by Gurumurthy et al. (2013).

Despite the availability of a voluminous literature on FESS control strategies, there lies a consistency in active power control, and the aspect of voltage seems neglected, altogether. In this article, both generator rotor speed and bus voltage are anticipated in FESS control. The respective active and reactive power references are drawn on the lines of generator speed and bus voltage deviations. In addition, the flywheel rotor speed is also brought into account by controlling the state of charge (SOC) of the storage, and a final active power reference is generated. The Q–V coupling is also adhered to, and the reactive power compensation at the bus is subject to the variation in the bus voltage. This provides an effective voltage smoothing when the system is hit by a disturbance.

Various machine configurations have been taken up in FESS incorporation, with most prominent being permanent magnet DC machines, induction machines and synchronous machines (Gurumurthy et al., 2013; Lee et al., 2009; Suvire and Mercado, 2012). In this article, a wound rotor machine configuration has been avoided due to higher speed concerns, and a simple permanent magnet machine has been endorsed.

In this article, the dynamic performance assessment of an FESS-based Western System Coordinating Council (WSCC) 9-bus system is considered, with a 60 MVA squirrel cage induction generator (SCIG) installed at bus 4. A power system base of 100 MVA is assumed, with 60 Hz as the nominal frequency. The FESS location has been randomly chosen as a generator node (bus 3), as against the common placement of the storage along the wind generator bus. The resultant hybrid study system is shown in Figure 1.

Figure 1.

Modified wind-integrated WSCC system for simulation studies.

A three-phase fault, though a rare occurrence in any power system, but an objective tool of ascertaining the transient stability profile of the system, is considered in this study. The hybrid system is subjected to faults with different clearing times. The efficacy of the FESS-based system in improving the overall dynamic stability profile of the system is justified. The damping enhancement is quite visible, and the stability margin is also expanded.

Mathematical modelling of the hybrid system

The mathematical model of the hybrid power system comprises three synchronous generators, a wind generator as an SCIG and an FESS unit at the third generator bus (bus 3). All the synchronous machines as well as the asynchronous machines are mathematically modelled in terms of the stator algebraic equations and the differential rotor circuit equations. A current source methodology has been proposed in FESS modelling and incorporation. The differential equations corresponding to machines and exciter kinetics and algebraic equations pertaining to stator and network equations are combined in a single robust mathematical model.

The stator equations defining the synchronous generators can be interpreted in matrix form for ‘i’ machines as in the study by Ahsan et al. (2017)

[\begin{matrix} V_{i} s i n (δ_{i} - θ_{i}) \\ V_{i} c o s (δ_{i} - θ_{i}) \end{matrix}] = [\begin{matrix} {E^{'}}_{d i} \\ {E^{'}}_{q i} \end{matrix}] + [\begin{matrix} - r_{s i} & {X^{'}}_{q i} \\ - {X^{'}}_{d i} & - r_{s i} \end{matrix}] [\begin{matrix} I_{d i} \\ I_{q i} \end{matrix}]

(1)

Differential equations describing the rotor dynamics of the ith synchronous generator in the system are given by the equation set (Ahsan et al., 2017)

{\dot{E}}^{'}_{q i} = - \frac{1}{{T^{'}}_{d o i}} [{E^{'}}_{q i} + (X_{d i} - {X^{'}}_{d i}) I_{d i} - E_{f d i}]

(2)

{\dot{E}}^{'}_{d i} = - \frac{1}{{T^{'}}_{q o i}} [{E^{'}}_{d i} - (X_{q i} - {X^{'}}_{q i}) I_{q i}]

(3)

The stator algebraic equations pertaining to the induction generator (wind generator) at bus 4 are as follows

[\begin{matrix} V_{d w g} \\ V_{q w g} \end{matrix}] = [\begin{matrix} {E^{'}}_{d w g} \\ {E^{'}}_{q w g} \end{matrix}] + [\begin{matrix} r_{s w g} & - {X^{'}}_{w g} \\ {X^{'}}_{w g} & r_{s w g} \end{matrix}] [\begin{matrix} I_{d w g} \\ I_{q w g} \end{matrix}]

(4)

The SCIG rotor winding dynamics can be explained using

[\begin{matrix} {\dot{E}}_{d w g} \\ {\dot{E}}_{q w g} \end{matrix}] = \frac{1}{T_{o}} {[\begin{matrix} - {E^{'}}_{d w g} \\ - {E^{'}}_{q w g} \end{matrix}] - [\begin{matrix} 0 & X_{w g} - {X^{'}}_{w g} \\ X_{w g} - X'_{w g} & 0 \end{matrix}] [\begin{matrix} I_{d w g} \\ I_{q w g} \end{matrix}]} + [\begin{matrix} s {E^{'}}_{q w g} \\ - s {E^{'}}_{d w g} \end{matrix}] ω_{o}

(5)

All induction generator details are provided in detail in the study by Sauer et al. (2017). The wind turbine aerodynamic characteristics are defined in terms of the mechanical power extraction by the wind turbine generator (Manwell et al., 2010) and given as

P_{m e c h} = \frac{1}{2} ρ A {v_{w i n d}}^{3} C_{p}

(6)

where $ρ$ is the wind air density, A is the area swept by the turbine rotor, $v_{w i n d}$ is the wind speed and $C_{p}$ is the power coefficient.

The modelling equations from the dq frame (rotor reference frame) can be transformed into DQ frame of reference (synchronously rotating frame) using the equations given below, which can be inferred from Figure 2 (Anderson and Fouad, 2008; Kundur et al., 1994; Sauer and Pai, 1998)

[\begin{matrix} A_{d} \\ A_{q} \end{matrix}] = [\begin{matrix} s i n δ & - c o s δ \\ c o s δ & s i n δ \end{matrix}] [\begin{matrix} A_{D} \\ A_{Q} \end{matrix}]

(7)

Figure 2.

Rotor reference frame (dq) to synchronous reference frame (DQ) transformation.

Steady-state analysis of the system is performed to obtain the pre-fault (or pre-disturbance) states of the system. The load flow results of the hybrid system are mentioned in Table 1.

Table 1.

Load flow results.

Bus no.	Voltage magnitude	Angle degrees	Generation		Load
Bus no.	Voltage magnitude	Angle degrees	MW	MVAr	MW	MVAr
1	1.040	0.000	0.000	0.000	0.216	0.416
2	1.025	10.791	0.000	0.000	1.630	0.098
3	1.025	6.157	0.000	0.000	0.850	−0.078
4	1.017	−0.676	0.000	0.000	0.500	−0.215	Slip = 0.0074
5	0.989	−2.495	1.250	0.500	0.000	0.000
6	1.006	−2.190	0.900	0.300	0.000	0.000
7	1.024	5.220	0.000	0.000	0.000	0.000
8	1.014	2.214	1.000	0.350	0.000	0.000
9	1.031	3.454	0.000	0.000	0.000	0.000

A basic prototype system can simply be modelled in terms of a reduced bus admittance matrix by using the Kron reduction technique. By virtue of this method, our test system reduces to a four-machine system, consisting of three alternators and a single induction generator. The network for the four-machine system can be denoted mathematically as

[\begin{matrix} V_{s g 1} \\ V_{s g 2} \\ V_{s g 3} \\ V_{w g} \end{matrix}] = [\begin{matrix} R_{11} + j X_{11} & R_{12} + j X_{12} & R_{13} + j X_{13} & R_{14} + j X_{14} \\ R_{21} + j X_{21} & R_{22} + j X_{22} & R_{23} + j X_{23} & R_{24} + j X_{24} \\ R_{31} + j X_{31} & R_{32} + j X_{32} & R_{33} + j X_{33} & R_{34} + j X_{34} \\ R_{41} + j X_{41} & R_{42} + j X_{42} & R_{43} + j X_{43} & R_{44} + j X_{44} \end{matrix}] [\begin{matrix} I_{s g 1} \\ I_{s g 2} \\ I_{s g 3} \\ I_{w g} \end{matrix}]

(8)

A multi input–multi output MATLAB function interface is created for realizing the multimachine network equations. The four-machine power system is designated in terms of four-generator terminal voltages and currents they inject at their respective buses. This can be effectively put in DQ axis terminology by simplifying all stator equations applicable to the machines as

V_{D Q a l l} = E_{D Q a l l} - [\begin{matrix} M_{m a i n} \end{matrix}] I_{D Q a l l}

(9)

Here, the matrix $M_{m a i n}$ is obtained by making transformations in the frame of reference (dq–DQ) in all the machine stator equations. The power system vectors can be defined as

V_{D Q a l l} = {[\begin{matrix} V_{D_{s g 1}} & V_{Q_{s g 1}} & V_{D_{s g 2}} & V_{Q_{s g 2}} & V_{D_{s g 3}} & V_{Q_{s g 3}} & V_{D_{w g}} & V_{Q_{w g}} \end{matrix}]}^{T}

(10)

E_{D Q a l l} = {[\begin{matrix} {E^{'}}_{D_{s g 1}} & {E^{'}}_{Q_{s g 1}} & {E^{'}}_{D_{s g 2}} & {E^{'}}_{Q_{s g 2}} & {E^{'}}_{D_{s g 3}} & E_{Q_{s g 3}} & {E^{'}}_{D_{w g}} & {E^{'}}_{Q_{w g}} \end{matrix}]}^{T}

(11)

I_{D Q a l l} = {[\begin{matrix} I_{D_{s g 1}} & I_{Q_{s g 1}} & I_{D_{s g 2}} & I_{Q_{s g 2}} & I_{D_{s g 3}} & I_{Q_{s g 3}} & I_{D_{w g}} & V_{Q_{w g}} \end{matrix}]}^{T}

(12)

The incorporation of an FESS in the system at bus 3 as an effective current source can be mathematically shown as

V_{D Q a l l} = [R X] {I_{D Q a l l} + I_{D Q f e s s}}

(13)

where

I_{D Q f e s s} = {[\begin{array}{l} 0 & 0 & 0 & 0 & I_{D f e s s} & I_{Q f e s s} & 0 & 0 \end{array}]}^{T}

(14)

Upon comparing equations (9) and (13), the hybrid system mathematics resolves to

I_{D Q a l l} = {(M_{m a i n} + [R X])}^{- 1} {E_{D Q a l l} - [R X] I_{D Q f e s s}}

(15)

The details of the abovementioned matrices are provided in Appendix 2.

FESS dynamic modelling and control

The following three components primarily constitute an FESS: (1) a rotating mass that stores kinetic energy, (2) a machine that is responsible for energy conversion and (3) power electronic converters that control the machine and regulate power flow between the grid and the flywheel storage system. A detailed mathematical modelling pertaining to all these flywheel components is addressed in this article. The equations governing the flywheel dynamics are as follows (Silva-Saravia et al., 2017)

T_{e f e s s} = 2 H \frac{d w_{r f e s s}}{d t}

(16)

P_{g r i d_{f e s s}}^{o u t} = V_{t}^{b u s} I_{g r i d}^{o u t}

(17)

I_{g r i d}^{o u t} - \frac{w_{r f e s s} T_{e}}{V_{d c}} = I_{c}

(18)

The DQ current components contributed by FESS at its bus location, as shown in equation (15), are obtained from the FESS power outputs and corresponding bus voltage as follows (Ahsan et al., 2017)

[\begin{matrix} {I_{D f e s s}}^{o u t} \\ {I_{Q f e s s}}^{o u t} \end{matrix}] = \frac{1}{{V_{D}}^{2} + V_{Q}^{2}} [\begin{matrix} V_{D 3} & V_{Q 3} \\ V_{Q 3} & - V_{D 3} \end{matrix}] [\begin{matrix} {P_{g r i d f e s s}}^{o u t} \\ {Q_{g r i d f e s s}}^{o u t} \end{matrix}]

(19)

Figure 3 depicts the FESS incorporation and control in the multibus system. At the plant level, a washout filter is used to curb rotor speed excursions and enhance transient support. This is further coupled with a moderate gain to impart sufficient oscillation damping to the generator speed deviations. Two active power reference command signals are mixed to realize a final power requirement. A simple gain-based error controller is put to use in SOC control. This helps in limiting the flywheel rotor speed to its nominal pre-disturbance value. The generation of $P_{r e f}$ is shown in Figure 4. Equation (16) is used in modelling the permanent magnet machine dynamics. The machine side converter (MSC) is represented by a first-order delay, with $T_{m s c} = 0.01 s$ . Figure 5 shows the FESS power output alongside the MSC end, given by

P_{f e s}^{o u t} = w_{r f e s s} T_{e f e s s}

(20)

Figure 3.

FESS incorporation and control.

Figure 4.

Reference active power template generation using generator rotor speed deviation and SOC control on flywheel.

Figure 5.

Flywheel power generation control along with MSC dynamics.

The DC link voltage is obtained as shown in Figure 6. Ideal FESS control demands that the capacitor voltage must be maintained constant, as quickly as possible. The $V_{d c}$ controller in this article has been a cascaded gain-PI combination.It is further followed by a first-order grid side converter (GSC). The contribution of FESS, ${P_{g r i d f e s s}}^{o u t}$ , is the result of regulating the DC link voltage around its nominal value, as shown in Figure 7.

Figure 6.

Contribution of grid current injection and FESS output current in DC link voltage.

Figure 7.

Grid current injection following DC link voltage control with GSC dynamics.

Another control loop owes its origin to the deviation in voltage at the FESS bus. This defines the voltage control or reactive power control and is shown in Figure 8. A simple gain is used to induce damping in electromechanical oscillations. A GSC is modelled as a first-order delay with $T_{g s c} = 0.01 s$ . The resultant FESS’ reactive power contribution is given by ${Q_{g r i d f e s s}}^{o u t}$ . Table 2 provides the FESS parameter details.

Figure 8.

FESS Q–V control.

Table 2.

FESS control parameters.

Parameter	Value	Parameter	Value	Parameter	Value
$T_{w 0}$	10	$K_{w r}$	50	$K_{p}$	100
$V_{d c r e f}$	1100 V	$K_{v d c}$	1/1100	$K_{d c}$	100
$T_{p}$	0.1	$T_{d c}$	100	$H$	8 s
$w_{f e s s r e f}$	0.7 p.u.	$w_{r e f}$	$2 f$	$V_{t}^{b u s}$	1.025 p.u.
$C_{e q}$	2.25 mF	$K_{v}$	2.5	$P_{m a x}$	0.7 p.u.
$Q_{m a x}$	0.25 p.u.	$P_{m i n}$	−0.7 p.u.	$Q_{m i n}$	−0.25 p.u.

Results and discussion

A three-phase fault is simulated on the line connecting buses 4 and 6. The fault is cleared by tripping the faulty connection. The location of the fault has intentionally been chosen nearer to the wind generator bus. Two fault scenarios have been considered in the study, namely

F a u l t c a s e_{1} = (\begin{array}{l} N o r m a l s t a t e, & 0 \leq t < 1 s \\ F a u l t - o n, & 1 s \leq t < 1.1 s \\ L i n e t r i p p e d, f a u l t c l e a r e d, & 1.1 s \leq t < 20 s \end{array}

F a u l t c a s e_{2} = (\begin{array}{l} N o r m a l s t a t e, & 0 \leq t < 1 s \\ F a u l t - o n, & 1 s \leq t < 1.25 s \\ L i n e t r i p p e d, f a u l t c l e a r e d, & 1.25 s \leq t < 20 s \end{array}

In the second fault study, the fault-clearing time is increased to 250 ms. The role of FESS in imparting stability to the system can be witnessed in both the studies (Figure 9).

Figures 10 to 13 show the generator rotor speed deviations, rotor angle deviations, bus voltage profile and the FESS power contribution, for the first fault study. Similarly, the second fault study results are shown in Figures 14 to 17.

Figure 9.

Wind speed for all studies.

Figure 10.

Rotor speed deviations with $t_{c l e a r}$ = 0.1 s.

Figure 11.

Rotor angle deviations with $t_{c l e a r}$ = 0.1 s.

Figure 12.

Generator bus voltage profiles with $t_{c l e a r}$ = 0.1 s.

Figure 13.

FESS real and reactive power injection response at bus 3, under first fault study with $t_{c l e a r}$ = 0.1 s.

Figure 14.

Rotor speed deviations with $t_{c l e a r}$ = 0.25 s.

Figure 15.

Rotor angle deviations with $t_{c l e a r}$ = 0.25 s.

Figure 16.

Generator bus voltage profiles with $t_{c l e a r}$ = 0.25 s.

Figure 17.

FESS real and reactive power injection response at bus 3, under second fault study with $t_{c l e a r}$ = 0.25 s.

The DC link voltage and flywheel rotor speed for both the fault studies can be compared in Figure 18. Table 3 gives the reduced bus admittance matrices for all the study stages.

Figure 18.

Flywheel rotor speed and DC link voltage, under both fault studies.

Table 3.

Reduced $Y_{B U S}$ of the system for different scenarios.

Pre-fault	0.0000 – 17.3611i	0.0000 + 0.0000i	0.0000 + 0.0000i	0.0000 + 17.3611i
	0.0000 + 0.0000i	0.7361 – 5.5157i	0.1401 + 2.4218i	−0.1366 + 3.0819i
	0.0000 + 0.0000i	0.1401 + 2.4218i	0.7552 – 5.4288i	−0.2638 + 3.0952i
	0.0000 + 17.3611i	−0.1366 + 3.0819i	−0.2638 + 3.0952i	2.0607 – 23.6179i
Fault-on	0.0000 – 17.3611i	0.0000 + 0.0000i	0.0000 + 0.0000i	0.0000 + 0.0000i
	0.0000 + 0.0000i	0.7629 – 6.3256i	0.1486 + 2.2350i	−0.4332 + 3.6695i
	0.0000 + 0.0000i	0.1486 + 2.2350i	0.7577 – 5.4719i	−0.1104 + 0.8457i
	0.0000 + 0.0000i	−0.4332 + 3.6695i	−0.1104 + 0.8457i	3.3797 – 16.5045i
Post-fault	0.0000 – 17.3611i	0.0000 + 0.0000i	0.0000 + 0.0000i	0.0000 + 17.3611i
	0.0000 + 0.0000i	0.7448 – 5.4338i	0.1844 + 2.8152i	−0.0836 + 2.5813i
	0.0000 + 0.0000i	0.1844 + 2.8152i	0.9814 – 3.5395i	−0.0257 + 0.6874i
	0.0000 + 17.3611i	−0.0836 + 2.5813i	−0.0257 + 0.6874i	1.1035 – 20.6941i

The results in the figures can be summarized as follows:

The rotor speed and rotor angle deviations are reduced by around 70% using the FESS-based system in the first case study. In the increased fault-clearing time scenario without any FESS aid, the generators lose synchronism, as their rotor speed as well as the angles become unbounded and unstable. Zoomed in graphs (Figures 14 to 15) have been used in effectively showing the role of FESS in imparting damping and stability, as against the storage-less system.

Significant voltage smoothing can be seen when the system is hit by a fault. The FESS-based system is capable of providing a low-voltage ride over in both fault studies. The ripple in the voltage is negligible, and the steady-state voltage values are attained in a span of 4–5 s only. On the contrary, oscillations in voltage can be seen in all fault studies, without FESS incorporation. The highly smoothed voltage of all buses in the FESS-based hybrid system can be witnessed in the zoomed voltage graphs in Figure 12. A significantly high-level voltage chattering is also visible in the FESS-deficient system in Figure 16.

The active and reactive powers injected by the FESS at bus 3 act as transient supports. The FESS remains in a floating state under normalcy. It only exchanges power under perturbed conditions. This is facilitated by the power controllers, which generate signals only when the rotor speed and bus voltage fluctuate. The increase in power exchange is visible when the fault intensity increases, due to longer fault-clearing time.

The robustness of the FESS control strategy is evident in Figure 18, because the DC link voltage does not vary beyond ±5 V (first case) and ±11 V (second case). Also, the capacitor voltage returns to its nominal value in a mere 3-s span. The FESS exchanges energy to compensate the power system imbalance, but the flywheel rotor speed remains closer to its steady-state value. Due to the SOC control, once the disturbance vanishes, the rotor speed catches its original speed, as quickly as possible.

The FESS-based hybrid system acts as a robust system, which attains its stability quickly in both the studies performed. Not only is the steady state acquired quickly but also considerable damping of the first swings is evident.

Conclusion

Non-linear dynamic system modelling and an effective FESS control strategy in a wind-integrated multibus system are presented. To validate the proposed control strategy, a simulation platform is developed in MATLAB–Simulink environment. The ability of an FESS to exchange huge amounts of energy in a very limited span of time with the system has been the basis of its adoption as a transient support system. The proposed control strategy is highly robust in dealing with intense fault disturbances. It clearly increases the fault-bearing time margin of the system. FESS weighs in as a promising solution in damping adverse swings in various power system variables. The novelty of the FESS incorporation and control lies in the fact that it uniformly addresses rotor speed, angle and voltage deviations on all the buses. The effect of wind variations is also tackled properly by the storage clad system. Performance investigation of the hybrid system with and without FESS clearly demonstrates the stable dynamic behaviour of former against latter, in all respects.

Footnotes

Appendix 1

Appendix 2

\begin{array}{l} [R X] = [\begin{matrix} R_{11} & - X_{11} & R_{12} & - X_{12} & R_{13} & - X_{13} & R_{14} & - X_{14} \\ X_{11} & R_{11} & X_{12} & R_{12} & X_{13} & R_{13} & X_{14} & R_{14} \\ R_{21} & - X_{21} & R_{22} & - X_{22} & R_{23} & - X_{23} & R_{24} & - X_{24} \\ X_{21} & R_{21} & X_{22} & R_{22} & X_{23} & R_{23} & X_{24} & R_{24} \\ R_{31} & - X_{31} & R_{32} & - X_{32} & R_{33} & - X_{33} & R_{34} & - X_{34} \\ X_{31} & R_{31} & X_{32} & R_{32} & X_{33} & R_{33} & X_{34} & R_{34} \\ R_{41} & - X_{41} & R_{42} & - X_{42} & R_{43} & - X_{43} & R_{44} & - X_{44} \\ X_{41} & R_{41} & X_{42} & R_{42} & X_{43} & R_{43} & X_{44} & R_{44} \end{matrix}] \\ M_{m a i n} = [\begin{matrix} A_{1} & B_{1} & 0 & 0 & 0 & 0 & 0 & 0 \\ C_{1} & D_{1} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & A_{2} & B_{2} & 0 & 0 & 0 & 0 \\ 0 & 0 & C_{2} & D_{2} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & A_{3} & D_{3} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{3} & D_{3} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & A_{4} & B_{4} \\ 0 & 0 & 0 & 0 & 0 & 0 & C_{4} & D_{4} \end{matrix}] \\ \forall i = 1, 2, 3, A_{i} = r_{s i} + (X_{d i}^{'} - X_{q i}^{'}) \sin δ_{i} \cos δ_{i} and B_{i} = - (X_{d i}^{'} \cos^{2} δ_{i} + X_{q i}^{'} \sin^{2} δ_{i}) \\ \forall i = 1, 2, 3, C_{i} = (X_{d i}^{'} \sin^{2} δ_{i} + X_{q i}^{'} \cos^{2} δ_{i}) and D_{i} = r_{s i} - (X_{d i}^{'} - X_{q i}^{'}) \sin δ_{i} \cos δ_{i} \\ A_{4} = r_{s w g}, B_{4} = - X_{w g}^{'}, C_{4} = X_{w g}^{'} and D_{4} = r_{s w g} \end{array}

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

Hailiya Ahsan

References

Ahsan

Salam

Lone

, et al. (2017) Modeling and simulation of an energy storage based multi-machine power system for transient stability study. In: Conference on energy conversion (CENCON), Kuala Lumpur, Malaysia, 30–31 October, pp. 78–83. New York: IEEE.

Anderson

Fouad

(2008) Power System Control and Stability. Hoboken, NJ: John Wiley & Sons.

Eckroad

Gyuk

(2003) EPRI-DOE handbook of energy storage for transmission & distribution applications. Report, Electric Power Research Institute, Palo Alto, CA.

Feng

Gongbao

Lijun

, et al. (2011) Applying flywheel energy storage system to integrated power system for power quality and stability enhancement. In: International conference on electrical machines and systems (ICEMS), Beijing, China, 20–23 August, pp. 1–5. New York: IEEE.

Guerrero

Romero

Barrero

, et al. (2009) Overview of medium scale energy storage systems. In: Compatibility and power electronics (CPE’09), Badajoz, 20–22 May, pp. 93–100. New York: IEEE.

Gurumurthy

Agarwal

Sharma

(2013) Optimal energy harvesting from a high-speed brushless dc generator-based flywheel energy storage system. IET Electric Power Applications 7(9): 693–700.

Hebner

Beno

Walls

(2002) Flywheel batteries come around again. IEEE Spectrum 39(4): 46–51.

Inage S-i (2009) Prospects for large-scale energy storage in decarbonised power grids. International Energy Agency 3(4): 125.

Jin

Jiang

Zhong

, et al. (2017) Research on coordinated control strategy of flywheel energy storage array for island microgrid. In: Conference on energy internet and energy system integration (EI2), Beijing, China, 26–28 November, pp. 1–6. New York: IEEE.

10.

Kundur

Balu

Lauby

(1994) Power System Stability and Control, vol. 7. New York: McGraw Hill.

11.

Lazarewicz

Rojas

(2004) Grid frequency regulation by recycling electrical energy in flywheels. In: Power engineering society general meeting, Denver, CO, 6–10 June, pp. 2038–2042. New York: IEEE.

12.

Lee

H-I

K-h

Yoo

E-J

, et al. (2009) Design of a micro flywheel energy storage system including power converter. In: TENCON2009-2009 IEEE region 10 conference, Singapore, 23–26 January, pp. 1–6. New York: IEEE.

13.

Manwell

McGowan

Rogers

(2010) Wind Energy Explained: Theory, Design and Application. Hoboken, NJ: John Wiley & Sons.

14.

Nair

Senroy

(2016) Dynamics of a flywheel energy storage system supporting a wind turbine generator in a microgrid. International Journal of Emerging Electric Power Systems 17(1): 15–26.

15.

Sauer

Pai

(1998) Power system dynamics and stability. Urbana 51: 61801.

16.

Sauer

Pai

Chow

(2017) Power System Dynamics and Stability: With Synchrophasor Measurement and Power System Toolbox. Hoboken, NJ: John Wiley & Sons.

17.

Silva-Saravia

Pulgar-Painemal

Mauricio

(2017) Flywheel energy storage model, control and location for improving stability: The Chilean case. IEEE Transactions on Power Systems 32(4): 3111–3119.

18.

Suvire

Mercado

(2012) Active power control of a flywheel energy storage system for wind energy applications. IET Renewable Power Generation 6(1): 9–16.

19.

Suvire

Molina

Mercado

(2012) Improving the integration of wind power generation into ac microgrids using flywheel energy storage. IEEE Transactions on Smart Grid 3(4): 1945–1954.

20.

Taj

Hasanien

Alolah

, et al. (2015) Transient stability enhancement of a grid-connected wind farm using an adaptive neuro-fuzzy controlled-flywheel energy storage system. IET Renewable Power Generation 9(7): 792–800.

21.

Wang

Chen

Lee

, et al. (2009) Dynamic stability enhancement and power flow control of a hybrid wind and marine-current farm using SMES. IEEE Transactions on Energy Conversion 24(3): 626–639.

22.

Wang

Chen

(2005) Transient stability control of multimachine power systems using flywheel energy injection. IEE Proceedings – Generation, Transmission and Distribution 152(5): 589–596.

23.

Morrow

(2013) Power oscillation damping using wind turbines with energy storage systems. IET Renewable Power Generation 7(5): 449–457.

24.

Yao

Gao

, et al. (2016) Frequency regulation control strategy for PMSG wind-power generation system with flywheel energy storage unit. IET Renewable Power Generation 11(8): 1082–1093.

25.

Zhang

Tokombayev

Song

, et al. (2014) Effective flywheel energy storage (FES) offer strategies for frequency regulation service provision. In: Power systems computation conference (PSCC), Wroclaw, 18–22 August, pp. 1–7. New York: IEEE.