Improved frequency dynamic in isolated hybrid power system using an intelligent method

Electrical Power and Energy Systems 78 (2016) 225–238

Contents lists available at ScienceDirect

Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Improved frequency dynamic in isolated hybrid power system using an intelligent method Amirhossein Modirkhazeni a, Omid Naghash Almasi b, Mohammad Hassan Khooban c,⇑ a

Department of Electrical and Engineering, Islamic Azad University, Science and Research, Tehran Branch, Iran Department of Electrical and Engineering, Islamic Azad University, Gonabad Branch, Iran c Institute of Electrical Engineering, Shahid Bahonar College, Technical and Vocational University, Shiraz, Iran b

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 7 September 2015 Received in revised form 7 October 2015 Accepted 26 November 2015

Keywords: Control load-frequency Variable speed wind turbines Inertia response T–S fuzzy system

The Isolated Hybrid Distributed Generation (IHDG) studied in this paper is consisted of a wind turbine generator and a diesel engine generator. The equivalent inertia of power grid reduces by increasing influence of variable speed wind turbines in power systems. Consequently, when a disturbance occurs in the power system the frequency fluctuations increases. To overcome this problem, a supplementary control loop is added to the converter of the variable speed wind turbine in order to share the inertia of the turbines in the power grid. But the appropriate rate of this contribution depends on the amount of load and must be suitably changed based on the load. In this paper, a Takagi–Sugeno (T–S) fuzzy system is designed to determine the contribution coefficient of variable speed wind turbine in such a way that variable wind turbine shares the maximum value of its inertia to compensate the reduced production in the power grid. However, the turbine does not pass its minimum speed limit while sharing the maximum value of inertia in the grid and prevents the cause of another disturbance in the power grid. In the proposed method, first, by using Particle Swarm Optimization (PSO) algorithm, the optimal values of contribution coefficient of wind turbines are attained proportional to the load in such a way that the minimum speed constraint is not violated. In the next stage, the initial T–S fuzzy system is extracted from the obtanied the optimal values of contribution by using subtractive clustering algorithm. In addition, Recursive Least Square (RLS) algorithm is used to adjust the consequent part of the T–S system. The efficiency of the proposed method is demonstrated through the simulation for different amount of load. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction The frequency stability is one of the most important issues in a power system which is determined by the balance between all production and consumption in the system. When a high power generator is out of the grid or a substantial load of power surges into the circuit, the balance between production and consumption is disturbed and cause changes in power system frequency. Generally, a power system responds to the load in three stages. The first stage is the inertial response of the synchronous generator which improves the dynamic frequency of the system in the first seconds of disturbance occurrence. In the second stage, the governor increases the input power of turbine to prevent the reduction of frequency and finally, a supplementary control loop changes the load reference point to stabilize the frequency at its nominal value [1].

⇑ Corresponding author. E-mail addresses: (M.H. Khooban).

[email protected],

http://dx.doi.org/10.1016/j.ijepes.2015.11.096 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

[email protected]

The recent widespread usage of wind energy has called growing attention to wind turbines connected to Double-Fed Induction Generator (DFIG). These generators have attracted significant attention thanks to their feature in operating with variable speed wind. By increasing usage of this type of turbine-generators in power system, the contribution of synchronous generators reduces in the grid and the control frequency of the power system confronts greater challenges. Synchronous generators are naturally responded to the load fluctuations, but due to the use of electronic power convertors in variable-speed wind turbines, the rotation speed of generator is separated from the grid. Thus, the grid frequency variation is not observable in the generators rotors. Consequently, these power plants do not normally contribute to the frequency control of the grid and the frequency stability of the system is jeopardized [2,3]. Researchers have been done great efforts to resolve the challenges posed by the use of variable-speed wind turbines. In [2] and [3] a comparison is made between the inertia responses of DFIG and fixed-speed wind turbines during the frequency deviation of a

226

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

power system. The results show that similar to the synchronous machines a fixed-speed generator can share its inertia in the grid; however, it is not true for DFIG. Therefore, a supplementary control loop has proposed for DFIG, which can increase the active power output of the system during the frequency disturbance. Furthermore, it is observed that the released kinetic energy from the variable-speed wind turbine is greater than the kinetic energy released through the fixed-speed turbines. However, this method has some limitations such as the approximate value of its derivative function [4]. In [5], a study is carried out on the behavior and capacity of variable-speed wind turbines in generating extra active power immediately after a load disturbance. The results present that variable-speed wind turbines can share their power derived from its inertia for about 10 s in the grid. A supplementary control signal called inertia control was added to the active power control loop of the wind turbines for effective contribution of variable-speed wind turbine in adjusting the grid frequency. This loop is activated during the deviation of the grid frequency and by injecting a power greater than the wind turbine, which is derived from the kinetic energy stored in the rotating mass of its blades, improves the frequency dynamics of the power system in the early seconds after the occurrence of load disturbance. In general, the control inertia of a wind turbine can be categorized into two groups. In the first group, the extra amount of power is proportional to the frequency derivative [2,3]. In the second group, a control strategy is implemented to adjust the initial frequency of wind turbine. In this case, the provided additional power is proportional to the difference between nominal and measured frequency [6]. In [7], a combination of two control strategies proposed for producing the inertial response of wind turbines. In this method, an additional control signal which is proportional to the deviation and frequency deviation is used to increase the power of the wind turbine. Another method used for controlling the frequency of the variable-speed wind turbine is de-loading. In this technique, the frequency adjustment is done by changing the angle of blades in

the wind turbine. In this case, the variable-speed wind turbine operates approximately near to its maximum power. In the first moments after the load disturbance and also drop in system frequency, the wind turbines are able to inject greater power into the grid by altering the angle to absorb the maximum wind power. In this technique, wind turbines have the capability to adjust frequency for long-term condition [8,9]. Takagi–Sugeno and Kang (TSK) fuzzy systems are useful tools for modeling the expert knowledge in order to control and describe the nonlinear systems with unknown dynamics [10]. In TSK system, the antecedent (IF) part of IF-THEN rules is the same as typical fuzzy systems (Mamdani), but the consequent part (THEN) is a linear combination of input variables. As a result of this modification, TSK fuzzy system provides a more detailed description of a complex system in comparison with other learning algorithms [11]. The knowledge base of a fuzzy system can be built based on expert knowledge or even input–output data pairs. However, the former is less accurate than the latter in terms of performance [12]. In order to extract fuzzy rules from input–output data pairs, a variety of techniques such as Kohonen neural networks and fuzzy clustering method proposed [13,14]. In this paper, subtractive clustering algorithm is used to extract fuzzy rules [15]. In this paper to improve the frequency dynamics of the power system, supplementary frequency control loops are added to power electronic converters to share the inertia of these turbines in power grid. In addition, a TSK fuzzy system is designed to absorb the maximum inertia in variable-speed wind turbines and prevent excessive speed reduction of the turbine, which causes turbine exit from the grid. TSK fuzzy system determines the contribution coefficient of wind turbine in a way that after the occurrence of disturbance, wind turbines share the maximum inertia to compensate the reduced generation in the grid meanwhile they do not violate the minimum speed limit. Particle Swarm Optimization (PSO) is used to determine optimal input–output data pairs to generate initial TSK fuzzy system. PSO algorithm searches and specifies the optimal contribution

Fig. 1. A block diagram of a two-area power system with variable speed wind turbines.

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

227

Fig. 2. Block diagram of a wind turbine model (adopted from [20,21]).

coefficient of wind turbines relative to the load in a way that wind turbines can yield its maximum inertia without violating the minimum speed limit. After gathering input-out data pairs using subtractive clustering algorithms, the initial TSK fuzzy system is extracted from the optimized parameters. In the final step, the recursive least squares method is employed to adjust the TSK fuzzy systems. The rest of this paper is organized as follows. In Section ‘Frequ ency control system’, the dynamic models of a two-area power system and a variable-speed wind turbine are reviewed. Inertial control and sharing methods are discussed in Section ‘Inertia control technique’. In Section ‘The proposed method’, after presenting summary of TSK fuzzy system, the proposed method is stated. Some simulations are presented to support the effectiveness of the proposed method in Section ‘Simulation’. Finally, the conclusions are drawn in Section ‘Conclusions’. Frequency control system

The generated mechanical power is a complex function of wind speed, rotor speed and the pitch angle as follow:

Pm ¼

q 2

Ar V 3x C p ðk; hÞ

where q is air density, Vx is the wind speed and Cp is the power coefficient, which is a function of k and h. k is the ratio of rotor tip speed to wind speed and h is the pitch angle. Cp is the characteristic of wind turbines, which is usually determined as a set of Cp curves in terms of k where h acts as a parameter. Cp curves in terms of k for a typical General Electric (GE) wind turbine are shown in Fig. 3 [17]. The curves fitting performed to achieve a mathematical representation of Cp curves as follow [17]:

C p ðk; hÞ ¼

4 X 4 X

ai;j hi k j

ð2Þ

i¼0 j¼0

The curve fitting is a good approximation for 2 < k < 13. The k values outside this range show extremely high and low wind speeds, which are not within the operating range of the turbine.

In this study, the dynamic models of a two-area power system as a power system and a variable-speed wind turbine as a wind turbine are considered. Dynamic model of multi-area power systems Although power system models are generally nonlinear, linearized model is used for load–frequency control studies. Fig. 1 represents the linearized model of a two-area power system for frequency control. In this model, only the slow dynamics of the system like governor and turbine speed are considered and the other electrical dynamics are neglected [1]. The system consists of two similar thermal areas and the wind power is added as a negative load to the first area. Dynamic model of variable-speed wind turbine In this paper, a 1.5 MW variable-speed wind turbine made by General Electric Company is used [16–19]. In frequency control studies, the focus is on the active power control loops. For this aim, the model of wind turbine is simplified as shown in Fig. 2 [20,21].

ð1Þ

Fig. 3. Cp curves of the GE wind turbine.

228

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

where P is the measured electrical power. For power levels greater than the nominal power, the rotor speed is controlled by pitch angle [17].

Inertia control technique

Fig. 4. Supplementary control loop of the wind turbine.

According to Fig. 3, the turbine speed in variable-speed wind turbines is a function of wind speed which is controlled in a way that the maximum reachable power is generated by the turbine. In other words, the maximum turbine power is generated. Since the measuring of electric power is easier and more accurate than measuring wind speed for finding maximum power point tracking (MPPT), the reference turbine speed is calculated according to the measured power. Reference speed is normally 1.2 pu, but it decreases for power levels below 0.75. The reference speed for tracking the maximum power of the wind in the levels below 0.75 of nominal power is calculated according to the following equation:

xref ¼ 0:67P2 þ 1:42P þ 0:51

ð3Þ

The variable-speed wind turbines have a significant amount of kinetic energy stored in their rotating mass, but the grid frequency variations is not seen by the rotor of these turbines because of fixing the slip by power electronics devices. Thus, they are unable to release their inertia and share the resultant energy in the grid. Therefore, with the increased influence of variable-speed wind turbines in the grid, the equivalent inertia of the system is reduced and the adjustability of the grid frequency is undermined, which increases instability possibility and even collapse of the grid after the frequency loss. To solve this problem, the inertia control technique has proposed. In this method, an additional supplementary signal is placed on the wind turbine control to add an extra power as soon as a frequency deviation is detected in the grid. And, this extra power is a function of grid frequency deviation [22,23]. Fig. 4 shows a schematic diagram of this method. In this figure, LP is the amount of penetration of wind turbines powers in the grid. Thus, if Lp is the percentage of generated electricity by wind turbines, a similar reduction is produced in the system inertia with non-contribution of wind power turbines. Also, Kf is the contribution coefficient of wind turbines in the grid frequency control. According to Fig. 4, as the value of Kf increases the turbine output power increases. And subsequently, the frequency dynamics of power system is improved. The increase of

Fig. 5. Frequency dynamics of the two-area system with fuzzy contribution of wind turbines.

229

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Kf, however, reduces the turbine speed significantly, which may increase the possibility of tripping out the turbine after passing the minimum speed limit. This may cause another disturbance in the grid and increases the possibility of failure for other wind turbines. Thus in inertia control method for determining the amount of Kf, there is a compromise between the relative improvement of the frequency and prevention of the system instability. The grid equivalent inertia without the contribution of the variable-speed wind turbine for grid frequency control is as follow:

Heq;Lp ¼ Heq ð1  Lp Þ

Table 1 The optimal values of Kf parameter. Load

Optimal Kf

0.1 0.2 0.3 0.4 0.5

20.0000 11.8112 5.9381 3.9856 3.0021

ð4Þ

Also, the modified equivalent inertia in the presence of % LP of wind power is shown in Eq. (5):

Heq;Lp ¼ Heq ð1  Lp Þ þ Hwt Lp

ð5Þ

The use of PSO algorithm to find optimal K f

The equivalent drop of generation units in both states is calculated according to Eq. (6):

RLp ¼ R=ð1  Lp Þ

ð6Þ

The construction of initial fuzzy system using subtractive clustering

The proposed method In order to improve the performance of wind turbines in controlling the grid frequency and using the maximum kinetic energy stored in the rotating mass, a method based on fuzzy logic is proposed. In this method, first the optimal contribution coefficient of wind turbines is determined proportional to the load by using PSO algorithm. PSO algorithm finds the optimal contribution coefficient such that variable-speed wind turbines can yield the maximum inertial without passing the minimum turbine speed limit. Then, using subtractive clustering algorithms, the initial TSK fuzzy system is extracted from the optimal parameters. Finally, the recursive least squares method is employed to adjust the TSK fuzzy system.

The use of RLS to optimize initial fuzzy system Fig. 6. The process of proposed method.

Particle swarm optimization algorithm 1

v id ¼ wv id þ c1 r1 ðpbid  xid Þ þ c2 r2 ðpgb  xid Þ

ð7Þ

xid ¼ xid þ v id

ð8Þ

where w is called the inertia coefficient with the value range of [0, 1]. To increase the search ability of PSO, the inertial velocity of w is reduced linearly over the iterations of the algorithm.

wðiterÞ ¼ wmax 

wmax  wmin  iter iter max

ð9Þ

where, itermax is the maximum iteration of algorithm. C1 and C2 are non-negative coefficients called acceleration; r1 and r2 are randomly generated in the range of [0,1]. vid e [vmax, vmax] and vmax is the maximum velocity [26].

High

Medium

0.8

Degree of membership

PSO algorithm is an evolutionary computation technique. It uses swarm of particles to find a global optimum solution in search space [24,25]. Each particle represents a candidate solution for the objective function and has its own position and velocity vector. It is assumed that each particle has D-dimension in the search space. The i-th particle in a D-dimensional space which is represented by xi = (xi1, . . ., xid, . . ., xiD). In each iteration, the best position of each particle, obtaining the optimal value of the objective function, is represented by Pbi and stored as pbi = (pbi1, . . ., pbid, . . ., pbiD). The best position of entire data, which is the best position among all the Pbi particles, is notated as Pgb. Each particle has a velocity which is expressed by vi = (vi1, . . ., vid, . . ., viD). In each iterations, the velocity and position of each particle are updated according to Eq. (8) and Eq. (9), respectively.

Low

0.6

0.4

0.2

0 0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Load Fig. 7. Membership functions describing the load.

The evolutionary algorithm is terminated when the maximum number of iterations is reached. In this research, a maximum of 50 iterations is selected. The standard PSO algorithm is shown in Appendix (C). Each PSO particle has a mono-dimensional to find the best contribution rate of wind turbines proportional to the load. After the last iteration, the best position of all particles, i.e. global best, shows the optimal solution which is the optimal Kf.

230

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Each fuzzy rule in the TSK fuzzy system is shown as follows:

20

Ri : IF x is Ai THEN yi ¼ aTi x þ bi ;

18

i ¼ 1; 2; . . . ; M

ð10Þ

where x e R and yi e R are input and output variables of i-th fuzzy rule. M represents the number of rules. Ai is the fuzzy variables of IF part in the interval of [0, 1] e Rn. The IF part in a fuzzy system is summarized as follows. n

16 14

Kf

12

Ai ðxÞ ¼

10

n Y

lij ðxj Þ

ð11Þ

j¼1

8

For k-th input of xk, the overall output of the system, i.e. y(k), is defined by the aggregate contribution of independent rule as follows.

6 4 2 0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Ai ðxk Þ uki ¼ PM 0 0 i ¼1 Ai ðxk Þ

0.5

Load Fig. 8. The relation between the load and optimal contribution coefficient of wind turbines in TSK fuzzy systems.

ð12Þ

where normalized uki is the antecedent of i-th rule and formulated as follows.

yðkÞ ¼

M X uki yi ðkÞ

ð13Þ

i¼1

TSK fuzzy system TSK fuzzy systems are general approximators. They have the ability to approximate any continuous function on a compact set to any degree of accuracy [27,28]. TSK fuzzy systems do not have defuzzification part. In fact, TSK fuzzy system can be described as a weighted average of the values in consequent part.

Knowledge base is the heart of a TSK fuzzy system and the selection of suitable numbers of fuzzy rules and variable perquisites a primary knowledge of the problem. It is usually taken into account by experts in designing the classical knowledge base. A large number of rules complicate the fuzzy system, which may not be necessary for the problem and the resultant model occupies a great deal of the memory with low processing speed. In contrast, a small number of rules weaken the fuzzy system,

Lp = 10% 0.1

0.1

0.05

0.05

0

Frequency of Area 1

Frequency of Area 1

Lp = 0% 0.15

0 -0.05 -0.1

-0.1 -0.15 -0.2

-0.15 -0.2 55

-0.05

60

65

70

75

80

85

90

95

-0.25 55

100

60

65

70

Time (Sec.) Lp = 30%

85

90

95

100

85

90

95

100

Lp = 50%

0.2

Frequency of Area 1

0.1

Frequency of Area 1

80

0.3

0.2

0

-0.1

-0.2

-0.3 55

75

Time (Sec.)

0.1 0 -0.1 -0.2 -0.3

60

65

70

75

80

Time (Sec.)

85

90

95

100

-0.4 55

60

65

70

75

80

Time (Sec.)

Fig. 9. Frequency dynamics of the first area without the contribution of wind turbines.

231

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Lp = 0%

Lp = 10% 0.02

0.15

f1 0.1

f1

f2

f2

0

Frequency

Frequency

0.05 0 -0.05

-0.02

-0.04

-0.1 -0.06 -0.15 -0.2

55

60

65

70

75

80

85

-0.08 55

90

60

65

Time (Sec.)

70

75

80

85

90

Time (Sec.)

Lp = 30% 5

0.005

x 10

Lp = 50%

-3

f1

f1 0

f2

f2

0

Frequency

Frequency

-0.005 -0.01 -0.015

-5

-10

-0.02 -15 -0.025 -0.03

55

60

65

70

75

80

85

90

-20 55

60

65

Time (Sec.)

70

75

80

85

90

Time (Sec.)

Fig. 10. Frequency dynamics of two-area system with contribution of wind turbines and constant inertia control coefficient.

which may not achieve the desired goal [28]. In addition, the knowledge base designed in accordance with the knowledge of experts often displays poor performance in terms of accuracy compared to the knowledge base designed based on input–output data pairs. This poor performance accuracy is rooted in the fact that the expert is able to formulate the conscious knowledge of human by a set of IF-THEN fuzzy rules and unable to formulate his/her unconscious knowledge. Therefore, a variety of methods proposed for formulating the unconscious knowledge by researchers [29–31]. In these methods, the expert is considered as a black box and his/her inputs and outputs are collected, i.e., the conscious and unconscious knowledge is seen as a series of input–output pairs. Thus, by constructing the fuzzy system based on input and output pairs, both conscious and unconscious knowledge is utilized. In this study to use both knowledge, the subtractive clustering technique is use for constructing the fuzzy system. Subtractive clustering is in fact a combination of input– output spaces. More accurately, each data zi = (xi, yi) is a vector containing input- output pairs. The clusters are dispersed proportional to the data mass in input–output spaces. Each cluster center Ci is a basic rule in a form (10) that expresses the input– output behavior of the system. By considering an input vector X, the i-th rule is achieved relative to the cluster center in which it is classified.

li ¼ ea kX  C i k2

ð14Þ

where Ci is the center of i-th cluster and a is a constant number which is calculated according to the neighboring radius of subtractive clustering algorithm.

a ¼ 4=r 2a

ð15Þ

where ra is the neighborhood radius, finally, the output of TSK fuzzy system is calculated according to Eq. (12). The consequent part of a fuzzy system is computed according to the following equation

yi ¼ aTi x þ bi ; i ¼ 1; 2; . . . ; M

ð16Þ aTi

where M is number of rules and and bi are the coefficients that need to be adjusted to achieve the optimal performance in the fuzzy system [32–40]. The initial model is not optimal because the antecedent part of the rule is achieved based on classification of input– output space. Thus, the resulting model is unable to show the input and output relationship properly. In this paper, thanks to higher speed and lower memory size compared to the gradient descent methods and the least-squares method the recursive least squares (RLS) method is used for optimizing TSK fuzzy system [28]. RLS considers Mean Squares Error (MSE) as error criteria. For further information on subtractive clustering method and the construction of fuzzy system based on this method see references [41,42].

232

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Load = 0.2 0.2

0.05

0.1

0

0

Frequency of Area 1

Frequency of Area 1

Load = 0.1 0.1

-0.05 -0.1

-0.1 -0.2

-0.15

-0.3

-0.2

-0.4

-0.25

56

58

60

62

64

66

68

70

72

74

76

-0.5

78

56

58

60

62

64

Time (Sec.)

66

68

70

72

74

76

78

70

72

74

76

78

Time (Sec.) With participation of wind power (Kf=6)

(a)

(b)

Without participation of wind power Load = 0.3

Load = 0.4

0.3

0.4

0.2

0.2 0

0

Frequency of Area 1

Frequency of Area 1

0.1

-0.1 -0.2 -0.3 -0.4

-0.2 -0.4 -0.6

-0.5 -0.8

-0.6 -0.7

56

58

60

62

64

66

68

70

72

74

76

78

-1

56

58

60

62

64

66

68

Time (Sec.)

Time (Sec.)

(c)

(d)

Fig. 11. Frequency dynamic of the first area in different loads, (a) without the contribution of the variable speed wind turbine, (b) with the contribution of the variable speed wind turbine and constant inertia control coefficient.

The parameters required for clustering using subtractive clustering algorithms is shown in Appendix (C). Mean least squares error is defined as follows [43–46].

MSE ¼

K 1X ðy  yd Þ2 K i¼1 i

ð17Þ

where y is the output of TSK fuzzy system, yd is the optimal output and K is the total number of data. Inertia control of variable-speed wind turbine using TSK fuzzy system In this method, to improve the frequency dynamics of the power system and the maximum contribution of variable-speed wind turbine inertia in controlling grid frequency, a supplementary signal is placed on variable speed wind-turbine similar to the

inertia control technique. The only difference is that the contribution coefficient of wind turbines is determined by TSK fuzzy system. Fig. 5 shows a block diagram of this plan in which variablespeed wind turbines are added to the first area of power system as a negative load. While a frequency deviation is detected in the grid, an additional power as a function of frequency deviation of grid and as a ratio of the optimal contribution coefficient of wind turbine is imposed to the power systems. In this case, the wind turbines share their maximum inertia in the grid and improve the frequency dynamics of the system immediately after a load disturbance occurrence. The initial rules of the TSK fuzzy system is derived from input– output data pairs optimizing by PSO. To this end, PSO algorithm determines the contribution coefficient of wind turbines for various loads in a way that variable-speed wind turbines can generate the maximum inertia without violating the minimum turbine

233

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Load = 0.1

Load = 0.2 1

0.98

0.98

Rotor speed of wind turbine

Rotor speed of wind turbine

0.96 0.94

0.92 0.9

0.88 0.86

0.96 0.94 0.92 0.9 0.88

0

10

20

30

40

50

60

70

80

90

0.86

100

0

10

20

30

40

(a)

(b)

Load = 0.3

70

80

90

100

70

80

90

100

Load = 0.4 1

0.98

0.98

0.96

Rotor speed of wind turbine

Rotor speed of wind turbine

60

Time (Sec.)

1

0.94 0.92 0.9 0.88 0.86 0.84 0.82

50

Time (Sec.)

0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82

0

10

20

30

40

50

60

70

80

90

100

0.8

0

10

20

30

40

50

60

Time (Sec.)

Time (Sec.)

(c)

(d)

Fig. 12. Speed dynamics of the wind turbine with constant contribution coefficient of wind turbines for different loads.

speed limit. In this type of wind turbine the minimum speed limit is 0.85 pu. Finding the optimal value of Kf is defined as a minimization problem. The objective function is defined as the weighted sum of mean square error of the wind turbine speed and the settling time of power system frequency.

IF Load is Low THEN y1 = - 9.684  Load + 7.844 IF Load is Medium THEN y2 = 13.5  Load + 10.08 IF Load is High THEN y3 = 0.002  Load + 24.15

ObjFcn ¼ a1 :E1 þ a2 :E2

ð18Þ

E1 ¼ MSEð0:85  wt Þ

ð19Þ

Finally, the optimal Kf is achieved using the above fuzzy rules and Eq. (13). The process of proposed method is shown in Fig. 6. Fig. 7 shows the membership functions extracted by subtractive clustering method. And, the relation between the amount of load and the optimal contribution coefficient of wind turbines achieved by TSK fuzzy system is shown in Fig. 8.

E2 ¼ Settling Time of frequency

ð20Þ

Simulation

where a1 and a2 are the significance coefficients parts of the objective function, which are selected as a1 = 0.8 a2 = 0.2 to maintain the minimum speed of the wind turbine within the permitted limit. The search scope for the optimal parameter of Kf is in the range of [0, 20]. Table 1 shows the optimal values of the contribution coefficients of the wind turbines for different loads obtained by the PSO algorithm. Now, the subtractive clustering algorithm is used to generate the initial TSK fuzzy system based on the optimal data pairs of Table 1. Finally, the RLS method is used to adjust the TSK fuzzy system. The obtained fuzzy rules are as follow:

This section examines the results derived from the simulation of the studies discussed in the previous sections. The system shown in Fig. 1 is the basis of simulation. In this system, wind turbines are in the form of a wind farm added as a negative load to the first area. Fig. 9 shows the frequency diagram of the first area without the contribution of wind turbines for different influence of wind power in the grid. By adding 0.1 pu load disturbance to the first area, the balance between production and consumption is disturbed and causing a frequency decline in both areas. As it can be seen, with increasing

234

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Load = 0.2 0.02

0

0

-0.01

-0.02

Frequency of Area 1

Frequency of Area 1

Load = 0.1 0.01

-0.02 -0.03 -0.04 -0.05 -0.06

-0.04 -0.06 -0.08 -0.1

55

60

65

70

75

80

85

-0.12

90

55

60

65

Time (Sec.)

70

75

80

85

90

80

85

90

Time (Sec.) With the optimal fuzzy Kf

(a)

(b)

With the constant Kf (Kf=6) Load = 0.3

Load = 0.4

0.05

0.1

0

Frequency of Area 1

Frequency of Area 1

0

-0.05

-0.1

-0.2

-0.15

-0.2

-0.1

55

60

65

70

75

80

85

90

-0.3

55

60

65

70

75

Time (Sec.)

Time (Sec.)

(c)

(d)

Fig. 13. Frequency dynamics of the first area with the contribution of variable speed wind turbines for different loads, (a) with optimal fuzzy contribution coefficient, (b) with a constant contribution coefficient.

influence of wind power, the equivalent inertia of grid is reduced caused by non-contribution of wind turbines and frequency dynamics of the power system is aggravated which itself reduces the stability of the system frequency. Fig. 10 shows the frequency diagram for areas 1 and 2 of the power system with the contribution of wind turbines for different influence of wind power in the grid. The inertia control applied to the wind turbine has a constant contribution ratio of Kf = 6, which increases the equivalent inertia of the grid and thus improves the frequency dynamics of power system compared to non-contribution state of wind turbines. Fig. 11 shows the frequency dynamics diagram for the first area in both contribution and non-contribution cases of wind turbines in the grid frequency control for different values of load. The influence of wind power in grid is assumed to be Lp = 0.1 pu. As it can be seen, by increasing the amount of load the frequency reduction, which is resultant of equivalent inertia reduction, increases. By using the inertia control loop with a constant contribution coefficient can improve the dynamic and drop of power system frequency. The injected power into the grid in the early seconds after load disturbance is obtained from the kinetic energy stored

in the rotating mass of wind turbines. The injected power according to Fig. 4 is equivalent to:

DP e ¼ k f Df

ð21Þ

Therefore, it is expected that by increasing load and frequency deviation in the grid, the wind turbine speed bring down from the optimal point and thus it is reduced. It should be noted, however, this amount should not exceed the minimum speed limit of the wind turbine, which in this case may lead to the failure of the wind turbine. If the wind turbine failed, it caused another disturbance in the grid that may put other wind turbines out of service as well. Fig. 12 demonstrates the mentioned issue. As it can be seen, as the load increases, the speed of the wind turbine is reduced due to the releasing inertia and the subsequent power injection into the grid. If the minimum speed of the wind turbine is set at 0.85 pu. For any load increases about 0.3 pu the turbine speed exceeds the minimum limit and leads to the failure of wind turbine. Thus, based on Fig. 11c, and d, the use of inertia control loop with a constant contribution coefficient in wind turbine control

235

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Load = 0.1

Load = 0.2 1

0.98 0.96

0.95

Rotor speed

Rotor speed

0.94 0.92

0.9

0.9 0.88 0.86

0

10

20

30

40

50

60

70

80

90

0.85

100

0

10

20

30

40

Time (Sec.) With the optimal fuzzy Kf

(a) Load = 0.3

70

80

90

100

70

80

90

100

Load = 0.4 1

0.95

0.95

Rotor speed

Rotor speed

60

(b)

With the constant Kf (Kf=6)

1

0.9

0.9

0.85

0.85

0.8

50

Time (Sec.)

0

10

20

30

40

50

60

70

80

90

100

0.8

0

10

20

30

40

50

Time (Sec.)

Time (Sec.)

(c)

(d)

60

Fig. 14. Speed dynamic of variable-speed wind turbines for different loads, (a) with optimal fuzzy contribution coefficient, (b) with constant contribution coefficient.

can actually worsen the frequency dynamics of power system. Also, according to the Fig. 12a and b, variable-speed wind turbine do not use their maximum inertia in presence of disturbance load below 0.2 pu, while by releasing greater inertia and reaching minimum speed, they can involve into larger contribution in the improvement of frequency dynamics of power system. To solve this problem, the contribution coefficient of wind turbines is changed proportional to the load by fuzzy rules in such a way that after the appearance of disturbance, variable-speed wind turbine share their maximum inertia to compensate the decreased production in the grid while keeping to the minimum speed limit. Figs. 13 and 14 illustrate these results. As it can be seen, by increasing load and frequency deviation in the system, the wind turbine speed is reduced to its minimum limit due to the use of optimal contribution coefficient proportional to the load, which it means greater release of inertia and consequently injected power to the grid. Therefore, the drop of the frequency in Fig. 13a and b is decreased compared

to using constant contribution coefficient. Furthermore, the turbine speed in Figs. 14c and d is consolidated in the minimum point, which is prevented the failure of wind turbines in the grid. Due to power electronic converters, variable speed wind turbines have faster dynamics compared to the steam power plant. As a result, in the early seconds after the occurrence of load disturbance, variable speed wind turbines can take a greater share in injecting active power into the grid. This does not increase the active power of synchronous generators significantly compared to the previous state. Fig. 15 shows the active power of the firstarea turbine output for different loads. Based on the result, the output power of steam turbines is increased gradually when wind turbines operate in the grid using optimal contribution coefficient, compared to non-contribution of wind turbines or their contribution with constant coefficient. It should be noted that the support of variable-speed wind turbines is only in transient state and the secondary control of the steam power plant in charge of making zero steady state error.

236

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

Load = 0.1 output power turbine generator of area 1

0.12 0.1 0.08

0.06 0.04

With the optimal fuzzy Kf 0.02

With the constant Kf (Kf=6) Withuot participation wind power

0

55

60

65

70

75

80

70

75

80

Time (Sec.) Load = 0.2 output power turbine generator of area 1

0.25

0.2

0.15

0.1

0.05

0

55

60

65

Time (Sec.) Fig. 15. The comparison of the output power of turbines in the first-area for different loads (a) with contribution of the wind turbine and constant Kf , (b) with contribution of wind turbines and fuzzy Kf, (c) without the contribution of wind turbines.

Conclusions In this paper, the effect of variable-speed wind turbines on controlling power system frequency was discussed. Then, to improve the frequency dynamics of the power system, the supplementary frequency control loops were added to the electronic converters to share the inertia of this type of turbines into the grid. To utilize the maximum capacity of wind turbines in the first seconds after the occurrence of disturbance, the contribution coefficient of variable speed wind turbines designed so that they share their maximum inertia to compensate the reduced generation in the grid while keeping the turbine to their minimum speed limit. As a consequence, another disturbance in the grid was avoided. PSO algorithm was used to determine the optimal contribution coefficient of wind turbines proportional to the load. Then, a TSK fuzzy system was generated based on these optimal coefficients. Some simulations were run to test inertia control loops using a TSK fuzzy system under various load conditions. The results demonstrated the efficiency of TSK fuzzy system in determining the appropriate amount of inertia contribution coefficient. Appendix A see Table 2. Appendix B see Tables 3 and 4.

Table 2 Power system parameters. Area 1

Area 2

Kp1 = 120 Tp1 = 20 Tt1 = 0.2 Tg1 = 0.06 R1 = 2.4 B1 = 0.425 Ttie = 0.04

Kp2 = 120 Tp2 = 25 Tt2 = 0.3 Tg2 = 0.08 R2 = 2.5 B2 = 0.425

Table 3 Wind turbine parameters. 1/2qAr = 0.00159 Kpp = 150 Kpc = 3.0 Kic = 30.0 Kitrq = 0.6

Appendix C see Fig. 16. Appendix D see Table 5.

Kb = 56.6 Tp (s) = 0.01 Tpc = 0.05 Kptrq = 3.0 Kip = 25

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

237

Table 4 Coefficients of matrix Cp.

a00 = –4:1909e1 a10 = –6:7606e2 a20 = 1:5727e2 a30 = –8:6018e4 a40 = 1:4787e5

a01 = 2:1808e1 a11 = 6:0405e2 a21 = –1:0996e2 a31 = 5:7051e4 a41 = –9:4839e6

a02 = –1:2406e2 a12 = –1:3934e2 a22 = 2:1495e3 a32 = –1:0479e4 a42 = 1:6167e6

Initial population generation

Objective function evaluation

Pbest(t)>Pbest(t-1) Update Pbest

Store Pbest

Select Gbest

Update position and velocity

Stop

Gbest Fig. 16. Operating process of PSO algorithm.

Table 5 Subtractive clustering parameters. Range of influence Squash factor Accept ratio Reject ratio

1 2 0.5 0.15

References [1] Kunder P. Power system stability and control. USA: McGraw-Hill; 1994. [2] Ekanayake J, Jenkins N. Comparison of the response of doubly fed and fixedspeed induction generator wind turbines to changes in network frequency. IEEE Trans Energy Convers 2004;19(4):800–2. [3] Lalor G, Mullane A, O’Malley M. Frequency control and wind turbine technologies. IEEE Trans Power Syst 2005;20(4):1905–13. [4] Gautam D, Goel L, Ayyanar R, Vittal V, Harbour T. Control strategy to mitigate the impact of reduced inertia due to doubly fed induction generators on large power systems. IEEE Trans Power Syst 2011;26(1):214–24. [5] Tarnowski GC, Kjar PC, Sorensen PE, Ostergaard J. Variable speed wind turbines capability for temporary over-production. In: IEEE conf power and energy society general meeting; 2009. p. 1–7. [6] Morren J, Haan SWH, Kling WL, Ferreira JA. Wind turbines emulating inertia and supporting primary frequency control. IEEE Trans Power Syst 2006;21 (1):433–4. [7] Mauricio JM, Marano A, Exposito AG, Martinez Ramos JL. Frequency regulation contribution through variable-speed wind energy conversion systems. IEEE Trans Power Syst 2009;24(1):173–80.

a03 = –1:3365e4 a13 = 1:0683e3 a23 = –1:4855e4 a33 = 5:9924e6 a43 = –7:1535e8

a04 = 1:1524e5 a14 = –2:3895e5 a24 = 2:7937e6 a34 = –8:9194e8 a44 = 4:9686e10

[8] Almeida RG, Lopes JAP. Participation of doubly fed induction wind generators in system frequency regulation. IEEE Trans Power Syst 2007;22(3):944–50. [9] Ramtharan G, Ekanayake JB, Jenkins N. Frequency support from doubly fed induction generator wind turbines. IET Renew Power Gener 2007;1(1): 3–9. [10] Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybernet 1985;15:116–32. [11] Qi R, Tao G, Tan C, Yao X. Adaptive control of discrete-time state-space T–S fuzzy systems with general relative degree. Fuzzy Sets Syst 2013;217:22–40. [12] Guillaume S. Designing fuzzy inference systems from data: an interpretabilityoriented review. IEEE Trans Fuzzy Syst 2001;9(3):426–43. [13] Ching-Yi C, Chiang J-S, Chen K-Y, Liu T-K, Wong C-C. An approach for fuzzy modeling based on self-organizing feature maps neural network. Appl Math 2014;8(3):1207–15. [14] Setnes M. Supervised fuzzy clustering for rule extraction. IEEE Trans Fuzz Syst 2000;8(4):416–24. [15] Priyono A, Ridwan M, Alias AJ, Rahmat RA, Hassan A, Mohd Ali MA. Generation of fuzzy rules with subtractive clustering. Jurnal Teknologi 2012;43 (1):143–53. [16] Miller NW, Sanchez-Gasca JJ, Price WW, Delmerico RW. Dynamic modeling of GE1.5 and 3.6 MW wind turbine-generators for stability simulations. In: Proc IEEE power eng soc general meeting; 2003. p. 1977–83. [17] Miller NW, Price WW, Sanchez-Gasca JJ. Dynamic modeling of GE 1.5 and 3.6 wind turbine-generators, GE—Power System Energy Consulting, Tech. Rep. version 4.5; 2010. [18] Zhu C, Hu M, Wu Z. Parameters impact on the performance of a double-fed induction generator-based wind turbine for subsynchronous resonance control. IET Renew Power Gener 2012;6(2):92–8. [19] Sathyanarayanan R, Kumar C. A novel approach For damping subsynchronous resonance oscillations in a series compensated network using wind turbine driven doubly fed induction generator. Int J Sci Eng Res 2014;5(5):222–8. [20] Zeni L, Rudolph AJ, Münster-Swendsen J, Margaris I, Hansen AD, Sørensen P. Virtual inertia for variable speed wind turbines. Wind Energy 2013;16 (8):1225–39. [21] Ullah NR, Thiringer T, Karlsson D. Temporary primary frequency control support by variable speed wind turbines potential and applications. IEEE Trans Power Syst 2008;23(2). [22] Attya AB, Hartkopf T. Wind turbine contribution in frequency drop mitigationmodified operation and estimating released supportive energy. Gener Trans Distrib, IET 2014;8(5):862–72. [23] Bhatt P, Roy R, Ghoshal SP. Dynamic participation of doubly fed induction generator in automatic generation control. Renewable Energy 2011;36:1203–13. [24] Kennedy J, Eberhart RC. Swarm intelligence. USA: Academic Press; 2001. [25] Wang Y, Li B, Weise T, Wang J, Yuan B, Tian Q. Self-adaptive learning based particle swarm optimization. Inf Sci 2011;181(20):4515–38. [26] Moravej Z, Jazaeri M, Gholamzadeh M. Optimal coordination of distance and over-current relays in series compensated systems based on MAPSO. Energy Convers Manage 2012;56:140–51. [27] Bede B, Rudas I.J. Takagi-Sugeno approximation of a Mamdani fuzzy system, In: Advance trends in soft computing. Springer International Publishing; 2014. p. 293–300. [28] Xin WL. A course in fuzzy systems and control. Englewood Cliffs, NJ: PrenticeHall; 1996. [29] Alizadeh M, Jolai F, Aminnayeri M, Rada R. Comparison of different input selection algorithms in neuro-fuzzy modeling. Expert Syst Appl 2012;39 (1):1536–44. [30] Hüllermeier E. Fuzzy sets in machine learning and data mining. Appl Soft Comput 2011;11(2):1493–505. [31] Guillaume S, Charnomordic B. Fuzzy inference systems: an integrated modeling environment for collaboration between expert knowledge and data using FisPro. Expert Syst Appl 2012;39:8744–55. [32] Khooban Mohammad Hassan, Niknam Taher. A new intelligent online fuzzy tuning approach for multi-area load frequency control: self adaptive modified bat algorithm. Int J Electr Power Energy Syst 2015;71:254–61. [33] Khooban Mohammad Hassan, Soltanpour Mohammad Reza, Abadi Davood Nazari Maryam, Esfahani Zahra. Optimal intelligent control for hvac systems. J Power Technol 2012;92(3):192–200. [34] Niknam Taher, Khooban Mohammad Hassan, Kavousifard Abdollah, Soltanpour Mohammad Reza. An optimal type II fuzzy sliding mode control design for a class of nonlinear systems. Nonlinear Dyn 2014;75(1–2):73–83. [35] Niknam Taher, Khooban Mohammad Hassan. Fuzzy sliding mode control scheme for a class of non-linear uncertain chaotic systems. IET Sci Meas Technol 2013;7(5):249–55.

238

A. Modirkhazeni et al. / Electrical Power and Energy Systems 78 (2016) 225–238

[36] Mohammad Hassan Khooban, Abadi Davood Nazari Maryam, Alfi Alireza, Siahi Mehdi. Swarm optimization tuned Mamdani fuzzy controller for diabetes delayed model. Turkish J Electr Eng Comput Sci 2013;21(Suppl. 1):2110–26. [37] Khooban Mohammad Hassan. Design an intelligent proportional-derivative PD feedback linearization control for nonholonomic-wheeled mobile robot. J Intell Fuzzy Syst: Appl Eng Technol 2014;26(4):1833–43. [38] Khalghani Mohammad R, Shamsi-Nejad Mohammad A, Farshad Mohsen, Khooban Mohammad H. Modifying power quality’s indices of load by presenting an adaptive method based on hebb learning algorithm for controlling DVR. AUTOMATIKA: cˇasopis za automatiku, mjerenje, elektroniku, racˇunarstvo i komunikacije 2014;55(2):153–61. [39] Soltanpour Mohammad Reza, Khooban Mohammad Hassan, Soltani Mahmoodreza. Robust fuzzy sliding mode control for tracking the robot manipulator in joint space and in presence of uncertainties. Robotica 2014;32 (03):433–46. [40] Alfi Alireza, Kalat Ali Akbarzadeh, Khooban Mohammad Hassan. Adaptive fuzzy sliding mode control for synchronization of uncertain non-identical chaotic systems using bacterial foraging optimization. J Intell Fuzzy Syst 2014;26(5):2567–76.

[41] Priyono A, Ridwan M, Alias AJ, OK Rahmat RA, Hassan A, Mohd Ali MA. Generation of fuzzy rules with subtractive clustering. J Technol 2012;43(1):143–53. [42] Bataineh KM, Naji M, Saqer M. A comparison study between various fuzzy clustering algorithms. Jordan J Mech Ind Eng 2011;5(4):335–43. [43] Shahsadeghi Mokhtar, Khooban Mohammad Hassan, Niknam Taher. A robust and simple optimal type II fuzzy sliding mode control strategy for a class of nonlinear chaotic systems. J Intell Fuzzy Syst: Appl Eng Technol 2014;27 (4):1849–59. [44] Khalghani Mohammad Reza, Khooban Mohammad Hassan. A novel self-tuning control method based on regulated bi-objective emotional learning controller’s structure with TLBO algorithm to control DVR compensator. Appl Soft Comput 2014;24:912–22. [45] Khooban Mohammad Hassan, Taher Niknam. A new and robust control strategy for a class of nonlinear power systems: adaptive general type-II fuzzy. In: Proceedings of the institution of mechanical engineers, Part I: Journal of systems and control engineering, vol. 229(6); July 2015. p. 517–28. [46] Abadi Davood Nazari Maryam, Khooban Mohammad Hassan. Design of optimal Mamdani-type fuzzy controller for nonholonomic wheeled mobile robots. J King Saud Univ – Eng Sci 2015;27(1):92–100.