Analysis and optimization of frequency control in isolated microgrid with double-fed induction-generators based wind turbine

ABSTRACT

In this paper the role of wind energy conversion systems (WECS) was investigated, In particular, variable speed wind turbines (VSWT) based on double-fed induction-generator (DFIG) in control and the optimization frequency with different wind penetration in the isolated system including Traditional Thermal and Non-thermal units have been investigated too. DFIG is capable of providing power at different mechanical speeds and reducing the Instantaneous speed, thus the release of stored mechanical energy; it is able to support traditional units of frequency tuning system. By achieving this through setting the desired speed, controlling DFIG at different levels of wind penetration is possible. This technique utilizes the particle swarm optimization (PSO) algorithm. The simulation results have been compared to the integral of squared error (ISE). The optimal penetration of WECSs by considering changing parameters in the microgrid (MG) frequency is investigated. The presence of wind turbines has been shown to improve the oscillation frequency and In particular the penetration rate of the wind turbine in the MG. The best frequency control will be achieved. To achieve the computing purposes, use of intelligent algorithms is much better than the methods trial and error methods.

KEYWORDS:

• Control frequency
• wind energy conversion systems
• micro grid
• integral of squared error
• particle swarm optimization

1. Introduction

Nowadays reduced economic dependency on fossil fuels due to ever-increasing energy demands, limitation of fossil fuel resources, environmental pollution caused by fossil fuels, global warming, greenhouse effects, and many other factors have led the world to focus on renewable energies [1,2]. Wind power, among wide variety of renewable energies, is considered as one of the optimistic technologies [3,4]. Using wind energy for electric power production is growing because of robust infrastructures, technological advancement, and low operating cost [5,6]. With the increased wind energy penetration in MGs, new challenges have been appeared with regard to the MG performance such as stability, balance, security, commercial programming and design of MG. Wind power has an intermittent nature, thus, large accumulation of wind power in a MG can significantly influence the design, performance and control of MG. This, in turn, leads to reduced effective frequency drop when DFIG controller is optimally tuned by ISE method [7]. Several efforts have been reported on DFIG-based wind turbines in order to demonstrate independent control of active and reactive power [8,9]. Accordingly, the use of DFIG based wind turbines are of great advantage for utilities compared to the fixed speed turbines [10,11]. A detail dynamic model and a control of a DFIG-based variable-speed wind-turbine grid-connected system in the dq-synchronous reference frame is presented in [12]. A detailed algorithm for the effect of wind farm connection to a certain power system on the system frequency response is presented in [13], which detailed analysis for the system frequency response in case of normal and fault operations were conducted. Authors of [14] presented the concept of kinetic energy release of DFIG-based wind turbines while power system frequency is reduced in order to prevent system inertia reduction. A control scheme of a grid-connected DFIG wind turbine with series grid-side converter to improve the control and operation performance of DFIG system during network unbalance is proposed in [15]. In [16], it was revealed that if wind turbines do not reduce the inertia at the time of light-load, system robustness will be greatly endangered. In other words, frequency drop of system can be remarkably improved if wind turbines contribute in system inertia support. In [17], schematic control for effective participation of DFIG-based wind turbines in adjustment of system frequency was proposed. Many researchers concluded that VSWTs have the capability of controlling initial frequency and inertia by employing supplemental control loops. To do this, the kinetic energy stored in hidden inertia of turbine blades is utilized [18]. In [19,20], frequency control of one and/or two-area of the system was examined with a combination of wind turbines, thermal and non-thermal turbines as well as hydrothermal turbines by employing ISE method, genetic algorithm (GA), fuzzy control, and frequency drop characteristic. DFIG based wind turbine with separate electrical power systems and mechanical rotor frequency, capable to produce power with various mechanical speeds. There is also the rotational inertia of the turbine blades and ability to reduce the instantaneous speed and release of stored mechanical energy. By this system supporting the conventional generators for frequency adjustment is possible. Most articles focus on the wind turbine on MG and the impact of increased penetration of wind energy in conversion systems in small networks has not been studied [21,22].

In this paper, the role of DFIG based wind turbines, in control and tune of frequency were considered and various wind power penetration in a MG compromising of conventional generators also were studied. Setting the desired DFIGs speed controllers by using PSO algorithm for various wind power penetration levels has been done and the results were compared to the ISE in references [23]. Furthermore, the impact of increasing the wind power penetration level on frequency variation caused by load changes in the studied MG also is investigated. Simulation results revealed that the proposed technique could improve the quality of frequency variation and conventional generators power variation imposed by overload and perturbations into MG. This improvement was obtained in any penetration level of wind power. In addition, despite of differences in penetration level coefficients of wind power in a MG, the quality of frequency variations was not the same. The best quality of frequency variation in a MG was recorded roughly at 15–20% penetration level.

2. Wind energy conversion system

Wind power generation system is mainly composed of mechanical, electromagnetic, and electrical components. In addition, other components including generator, electric power converter, and power transformers are among the other components of this system. Generally, the configuration of these systems depends upon type of electric machine and their common aspect of power network. From the structural viewpoint, WECS can be either of fixed-speed or variable-speed type. Each of these types, having their own advantages and disadvantages, and each one is used in various applications. One of the important and common components in all WECSs is gearbox located between main shaft of wind turbine and the generator. The essential role of gearbox is to speed up of blades up to the speed of rotor of the generator, i.e. 1000 or 1500 rpm [24,25].

2.1. DFIG-based wind turbine

Figure 1 shows a DFIG-based wind turbine of WECS and two back to back pulse wide modulation (PWM) converters connected to the generator. In this system, wind turbine system is connected to the DFIG through a mechanical shaft system, including a low speed turbine shaft and high-speed generator shaft and an interfaced gearbox. Back to back converter consists of a rotor side convertor and a grid-side one [26,27]. These two converters are connected via a capacitor. Since only part of total power, approximately 25%, is flowing through power electronic converter, thus the size and cost of the converter are reduced meaningfully [28,29]. The need for sliding ring and brush are among the drawbacks of this system, increasing construction and maintenance cost [30]. This type of WECS can potentially reduce the oscillations introduced by wind speed variations. In addition, PWM back to back power electronic converter controls generated power and reaching maximum power point tracking (MPPT) is likely [31,32]. Despite increase in cost as well as power conversion loss, penetration of these types of WECS is constantly growing [33,34].

Figure 1. Double-fed induction-generator based wind turbine.

When speed decreases, the amount of released kinetic energy from wind turbine shafts is ΔF_k which is obtained by Equations (1) and (2).

(1) ${\mathrm{F}}_{\mathrm{k}}=\frac{1}{2}{\mathrm{J}\omega }_{\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{h}}^2$(1)

(2) $\mathrm{\Delta }{\mathrm{F}}_{\mathrm{k}}={\mathrm{F}}_{\mathrm{k}0}\left(1-\frac{{\omega }_{\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{h}1}^2}{{\omega }_{\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{h}0}^2}\right)$(2)

F_K depends on wind speed varying in the range of zero and unity per unit, (0≤ E_ko≤1.0pu = f(wind speed)). In addition, ω_mech1 should not below minimum of circular mechanical speed of a DFIG-based wind turbine (ω_mech-min≤ω_mech1). Moreover, instantaneous power obtained from WT should not exceed maximum allowable power according to the machine data provided by the manufacturer, (F_ko+ΔF_k≤F_k,max).

Figure 2(a) shows DFIG-based wind turbines controllers trying to maintain turbine in an optimum speed in order to produce maximum power. Operating point power controller obtains ΔP_ω* which is based on the measured speed and electrical power. Operating point power is an input to the converter produces torque and power by controlling the generator’s rotor currents. Supplemental control signal (ΔP_f*) adopt operating point power in terms of a function of deviation rate of change of network frequency. Supplemental control signal of inertia control ring is proportional to controller parameters (K_pf, K_df). Initial frequency control occurs when network frequency violates specified limits, activating the added ring. Inserting this signal (ΔP_f*) into torque relation, the torque is adjusted. Once the system frequency drops, operating point torque increases and the speed of rotor is reduced, releasing kinetic energy. The reference point power (ΔP_fω*) consists of two components: (ΔP_f*) which is based on frequency variation, and (ΔP_ω*) which is based on the optimum speed if turbine in terms of a function of wind speeds, expressed by Equations (3)–(5) [35]:

(3) ${\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}}^{\ast }=-\mathrm{\Delta }\mathrm{f}{\mathrm{K}}_{\mathrm{p}\mathrm{f}}-\frac{\mathrm{d}\mathrm{f}}{\mathrm{d}\mathrm{t}}{\mathrm{K}}_{\mathrm{d}\mathrm{f}}$(3)

(4) ${\mathrm{\Delta }\mathrm{P}}_{\omega }^{\ast }={\mathrm{K}}_{\omega \mathrm{i}}\int \left({\omega }^{\ast }-\omega \right)\mathrm{d}\mathrm{t}-{\mathrm{K}}_{\omega \mathrm{p}}\left({\omega }^{\ast }-\omega \right)$(4)

(5) ${\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}\omega }^{\ast }={\mathrm{\Delta }\mathrm{P}}_{\omega }^{\ast }+{\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}}^{\ast }$(5)

Figure 2. Double-fed induction-generator based wind turbines controllers [23]. (a) Inertial emulation control. (b) Control based on frequency change.

K_df and K_pf are derivative and proportionality gains of controller, respectively. Considering two terms of DFIG’s operating point power, ΔP_ω* varies steadily compared to deviation rate of change of operating point power, ΔP_f*. Thus, when a perturbation is applied at the instant t = 0, ΔP_ω* is considered to be zero. Considering instantaneous variation of operating point power by the converter, it is assumed that ΔP_W = ΔP_fω*, and Equations (6) and (7) are obtained [18].

(6) ${\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}\omega }^{\ast }=0+{\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}}^{\ast }$(6)

(7) $\mathrm{\Delta }{\mathrm{P}}_{\mathrm{W}}={\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}\omega }^{\ast }={\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}}^{\ast }=-\mathrm{\Delta }\mathrm{f}{\mathrm{K}}_{\mathrm{p}\mathrm{f}}-\frac{\mathrm{d}\mathrm{f}}{\mathrm{d}\mathrm{t}}{\mathrm{K}}_{\mathrm{d}\mathrm{f}}$(7)

2.2. DFIG-based WT’S control system model

Figure 2(b) shows, the dynamic model of DFIG against frequency control. The differences between the models given in Figure 2(a,b) is the added reference power based on the frequency variation using wash-out filter with the time constant of Tw. This indicates initial frequency tuning of conventional power production in transient state.

(8) ${\mathrm{\Delta }\mathrm{P}}_{\mathrm{f}}^{\ast }=\frac{1}{\mathrm{R}}\mathrm{\Delta }{\mathrm{X}}^{\prime \prime }$(8)

In Equation (8), R is the governor droop when wind turbine is used, and $\mathrm{\Delta }{\mathrm{X}}^{\prime \prime }$ is measured frequency variation when wind turbine is connected to the network.

3. Thermal and non-thermal turbines control system model

Dynamic performance of small perturbation of a thermal turbine and a non-thermal are shown in Figure 3. These models consist of parameters such as time constant wind turbine (T_t), constant time without reheat (T_h), and constant time with reheat (T_r) [36,37].

Figure 3. Dynamic model of wind turbine. (a) With reheat. (b) Without reheat.

4. Dynamic model of frequency control of a MG with constant of DFIG-base wind turbine

Figure 4(a) depicts power system diagram, while Figure 4(b) illustrates block diagram of transfer function of a MG compromising of conventional generators and DFIG-based generators for frequency tuning. Equation (9) is obtained by subtraction of load change, ΔP_D, from overall conventional power injections, ΔP_G1 and ΔP_G2, as well as from wind power, ΔP_W, by considering Equation (8).

(9) $\mathrm{\Delta }{\mathrm{P}}_{\mathrm{G}1}+\mathrm{\Delta }{\mathrm{P}}_{\mathrm{G}2}+\mathrm{\Delta }{\mathrm{P}}_{\mathrm{W}}-\mathrm{\Delta }{\mathrm{P}}_{\mathrm{D}}=\mathrm{\Delta }{\mathrm{P}}_{\mathrm{f}}$(9)

Figure 4. Dynamic model of frequency control. (a) Transmission power grid. (b) Dynamic configuration of microgrid.

Coefficients T_p and K_p can be seen in Equations (10) and (11) in terms of frequency, damping ratio, and inertia.

(10) ${\mathrm{T}}_{\mathrm{p}}=\frac{2\mathrm{H}}{\mathrm{f}\mathrm{D}}$(10)

(11) ${\mathrm{K}}_{\mathrm{p}}=\frac{1}{\mathrm{D}}$(11)

Based on the model given in Figure 4(b) and considering transfer function of network, load, and generator as K_P/(1 + T_Ps) and Equations (7) and (9)–(11), we have:

(12) $\stackrel{2{\mathrm{H}}^{\ast }}{\overbrace{\left(\frac{2\mathrm{H}}{\mathrm{f}}+{\mathrm{K}}_{\mathrm{d}\mathrm{f}}\right)}}\frac{\mathrm{d}\mathrm{\Delta }\mathrm{f}}{\mathrm{d}\mathrm{t}}=\mathrm{\Delta }{\mathrm{P}}_{\mathrm{G}}+\mathrm{\Delta }{\mathrm{P}}_{\mathrm{G}1}-\stackrel{{\mathrm{D}}^{\ast }}{\overbrace{\left({\mathrm{K}}_{\mathrm{p}\mathrm{f}}+\mathrm{D}\right)}}\mathrm{\Delta }\mathrm{f}-\mathrm{\Delta }{\mathrm{P}}_{\mathrm{D}}$(12)

Figure 5 shows the dynamic model of a small perturbation imposed on a MG consisting of the model of thermal turbine, non-thermal turbine and a turbine based on DFIG. This model simulates frequency control model after perturbation and consists of conventional system parameters such as load damping ratio (D), droop (R), inertia (H), and time constants T_t, T_h, and T_r. System behavior depends on the parameters of MG, particularly controller coefficients of WT speed, K_wi and K_wp. Dynamic model is represented in the steady-state form extended from transfer function of Equation (13).

(13) $\frac{\mathrm{d}\underset{\_}{\mathrm{X}}}{\mathrm{d}\mathrm{t}}=\mathrm{A}\underset{\_}{\mathrm{X}}+\mathrm{\Gamma }\underset{\_}{\mathrm{P}}$(13)

Figure 5. Microgrid dynamic configuration for frequency control.

In Equation (13), $\underset{\_}{\mathrm{X}}$ denotes state vector, $\underset{\_}{\mathrm{P}}$ denotes perturbation vector, A and Γ denote state and perturbation matrix, respectively. State Equation (13) can be extended to Equations (14)–(16).

(14) $\underset{\_}{\mathrm{X}}=\left[\mathrm{\Delta }{\mathrm{P}}_{\mathrm{h}1}\mathrm{\Delta }{\mathrm{P}}_{\mathrm{r}\mathrm{e}\mathrm{f}1}\mathrm{\Delta }{\mathrm{P}}_{\mathrm{G}1}\mathrm{\Delta }{\mathrm{P}}_{\mathrm{h}2}\mathrm{\Delta }{\mathrm{P}}_{\mathrm{r}\mathrm{e}\mathrm{f}2}\mathrm{\Delta }{\mathrm{P}}_{\mathrm{r}}\right.{\left.\mathrm{\Delta }{\mathrm{P}}_{\mathrm{G}2}\mathrm{\Delta }\mathrm{f}\mathrm{\Delta }{\mathrm{X}}^{\prime }\mathrm{\Delta }{\mathrm{X}}^{\prime \prime }\mathrm{\Delta }{\mathrm{X}}^{\prime \prime \prime }\mathrm{\Delta }\omega \mathrm{\Delta }{\mathrm{P}}_{\mathrm{W}}\right]}^T$(14)

(15) $\underset{\_}{\mathrm{P}}={\left[0000000\mathrm{\Delta }{\mathrm{P}}_{\mathrm{D}}00000\right]}^{\mathrm{T}}$(15)

(16) $\mathrm{\Gamma }={\left[0000000\frac{-{\mathrm{K}}_{\mathrm{p}}}{{\mathrm{T}}_{\mathrm{p}}}00000\right]}^{\mathrm{T}}$(16)

Dynamic simulations are performed while considering various penetration coefficients with/without DFIG in MG and with regard to the load.

5. Optimum tuning of DFIG-based WTS speed controller parameters

PSO is one of the most important swarm-based techniques among the intelligent optimization algorithms. PSO which is also known as bird algorithm is one of the strongest algorithms for optimization of continuous and discrete problems. This algorithm is mostly used for high convergence speed. PSO can be expressed by Newton’s mechanical laws. In this algorithm, each particle i with mass of m move throughout D-dimension search space. In search for food by birds, it was seen that total data of swarm is used by particles to specify their movements. Thus, the best swarm and individual positions are obtained at any time. New search direction is a combination of these two positions and particle’s prior position. In D-dimension search space, the best individual position of particle I and the best swarm position are expressed by: ${\vec{p}}_i=({\mathrm{p}}_{\mathrm{i}1},{\mathrm{p}}_{\mathrm{i}2},...,{\mathrm{p}}_{\mathrm{i}\mathrm{D}})$ and $\vec{g}=({\mathrm{g}}_1,{\mathrm{g}}_2,...,{\mathrm{g}}_{\mathrm{D}})$. The position and velocity of each particle i are updated in any iteration by Equations (17) and (18) [38,39].

(17) ${\mathrm{V}}_{\mathrm{i}}(\mathrm{t}+1)=\omega {\mathrm{V}}_{\mathrm{i}}\left(\mathrm{t}\right)+{\mathrm{r}}_1{\mathrm{c}}_1({\mathrm{p}}_{\mathrm{i}}\left(\mathrm{t}\right)-{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{t}\right))+{\mathrm{r}}_2{\mathrm{c}}_2({\mathrm{g}}_{\mathrm{i}}\left(\mathrm{t}\right)-{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{t}\right))$(17)

(18) ${\mathrm{x}}_{\mathrm{i}}(\mathrm{t}+1)={\mathrm{x}}_{\mathrm{i}}(\mathrm{t})+{\mathrm{V}}_{\mathrm{i}}(\mathrm{t}+1)$(18)

where ω is inertia coefficient, c1 and c2 are individual and swarm learning coefficients, r1 and r2 are random numbers in [0, 1].

For the simplicity of computation, cost function (Z) is introduced by Equation (19).

(19) $\mathrm{z}={\omega }_1\ast \mathrm{S}\mathrm{e}\mathrm{t}\mathrm{t}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}+{\omega }_2\ast \mathrm{O}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{t}$(19)

where, ω₁ and ω₂ are weighting factors of settling time and maximum overshoot of output frequency in MG, respectively. Both of the weighting factors in cost function are 1. PSO algorithm adjustment for this problem is given in Table 1. Inertia coefficients (ω), individual learning (c₁), and swarm learning (c₂) are available in [40]. Population coefficients and iteration number are obtained empirically by considering problem nature. Figure 6 shows convergence curve of cost function of Equation (20) considering 5% wind power penetration in MG. Table 2 presents optimum values of WIND TURBINE’s speed controller using PSO and by considering various wind power penetration. In order to evaluate wind power effect on total power supply, penetration index, α_w, is obtained using Equation (20) [18].

(20) ${\alpha }_{\mathrm{w}}=\frac{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{W}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}}{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{V}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{u}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}}\ast 100$(20)

Table 1. PSO parameters tuning.

PSO	Population	Iteration	$\omega$	${\mathrm{c}}_1$	${\mathrm{c}}_2$
Parameters	50	20	0.7298	1.4962	1.4962

Table 2. Optimum DFIG speed controller in different wind penetration.

Wind penetration	%5	%15	%25	%50
Best Cost	6.3693	2.9165	5.8219	13.9137
Settling Time	6.3517	2.9153	5.8181	13.8912
Overshoot	0.0176	0.0012	0.0039	0.0224
${\mathrm{K}}_{\mathrm{w}\mathrm{p}}$	6.5632	7.1054	9.0979	61.3507
${\mathrm{K}}_{\mathrm{w}\mathrm{i}}$	5.2677	0.8851	0.01	0.01

Figure 6. Convergence curve with %5 DFIG penetration (PSO).

6. Simulation results

Simulations were carried out by considering dynamic model for load increase of 0.02 per unit with and without various penetration coefficients of DFIG-based WTs for the studied MG. In addition, optimal parameters for DFIG-WT’s controllers are presented considering results given in Table 2. It should be noted that, supplying extra loads in steady-state are done using conventional generators. Instantaneous load variations and generating power of DFIG are illustrated in Figures 7 and 8. Generating power changes in conventional generating units in response to the step compensation of load are shown in Figure 9.

Figure 7. Speed and power variation with %15 DFIG penetration. (a) Speed variation with %5, %10, %15 and %20 DFIG penetration. (b) Power variation with %5, %10, %15 and %20 DFIG penetration.

Figure 8. Speed and power variation of double-fed induction-generator.

Figure 9. Non-reheat and rehear turbine power generation with %15 DFIG penetration (0.02 Pu disturbance).

In addition, frequency variation of MG in various wind penetration levels is depicted in Figures 10 and 11. It presents a comparison between the proposed method and the ISE method. Figure 7 shows speed change and DFIG generating power at the time of perturbation until reaching stability in wind power penetration level of 15%. According to the figures, once overload is appeared at the instant of 2 sec, DFIG immediately releases kinetic energy by decreasing mechanical energy. Thus, DFIG’s output power increases to participate I frequency control. Afterwards, DFIG’s output power decreases to fix WT speed at the optimal value. Based on the figure, DFIG’s speed controller could retrieve the speed to the appropriate value, and in turn, DFIG’s output power returns to the nominal initial value.

Figure 10. Frequency variation with %5, %10, %15 and %20 DFIG penetration (0.02 Pu disturbance). (a) Frequency variation with %5 DFIG penetration (PSO and ISE) and without DFIG (0.02 Pu disturbance). (b) Frequency variation with %15 DFIG penetration and without DFIG (0.02 Pu disturbance).

Figure 11. Frequency variation with 15% and 5% DFIG penetration and without DFIG (0.02 Pu disturbance).

Figure 8 show DFIG’s speed and output power variations in different wind power penetration levels in MG. Obviously, with the increase of wind power penetration level, the possibility of utilizing released energy by WT blades is also raised. Figure 9 depicts variation of generating units, including thermal, non-thermal, and wind units, in MG. As it is clear, DFIG participates in automatic control of power at the time of perturbation, introduced by overload in transient state in MG, resulting in reduced oscillations of output power of conventional units.

Figures 12 and 13 show the impact of DFIG with various penetration level of wind power in MG on frequency variation. As seen, DFIG could contribute to the improvement of frequency oscillations due to automatic control of power generation. The impact of wind power penetration, in MG, is not the same of all frequency oscillation parameters. Consequently, overshoot and settling time improvements are observed with the steady increase of wind power penetration level up to 15–20%. By contrast, settling time as well as overshoot of frequency variation, in MG, gets raised with penetration level larger than 20%. This, in turn, affects frequency quality. These changes are shown in Figure 1. Also the results of the proposed method is shown in reference [5,19]. It was observed that in the presented method due to the optimal settings for controlling the speed of the wind turbine, the desired computing goals, against Cited references were improved.

Figure 12. Settling time and overshot variation in various double-fed induction-generator penetration (0.02 Pu disturbance).

Figure 13. Frequency variation with %15 DFIG penetration (0.01, 0.02, 0.03 and 0.04 Pu disturbance).

Figure 14 shows system response to load variations from 0.01 to 0.04 per unit with penetration coefficient of 15%. It can be seen that the performance of tuning control is effective and the settling time and overshoot amount are greatly improved. The mentioned tuning, therefore, performs appropriately in the small-signal range of load variation, up to 5% variations of total load. Figure 15 shows the effect of wind speed increase on the performance of wind turbine controllers while the turbulence is 0.02 per unit.

Figure 14. Speed and DFIG power variation with %20 DFIG penetration simultaneous with increase wind speed (0.02 Pu disturbance).

Figure 15. Non reheat and rehear turbine power generation with %20 DFIG penetration simultaneous with increase wind speed (0.02 Pu disturbance).

7. Conclusion

DFIGs with the capability of power production is produced in different mechanical speeds, By releasing stored mechanical energy in their blades, DFIGs are also able to quickly reduce the speed when the frequency drop occurs, supporting conventional generators in tuning frequency. And this capability is obvious in different penetration level of WTs. The frequency tuning is performed by PSO. It was proved that PSO reach better results in determining optimum values for WT’s speed controllers in order to improve important indices of frequency variation compared to the other methods in a MG with conventional generating units. Based on the obtained results, obtaining the best characteristics of frequency variation in a particular penetration level of wind power is feasible in MG. This means less and or more production of energy from WT in a studied MG, can affect frequency response parameters of MG. Essentially, the increased wind energy will not be advantageous in the MG.

Disclosure statement

No potential conflict of interest was reported by the authors.