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International Review on Modelling and Simulations (I.RE.MO.S.), Vol. xx, n. x February 2011

Steady-State Wind Turbine Generation Model for Three-Phase Distribution Load Flow Analysis Syafii1, Khalid Mohamed Nor2, Mamdouh Abdel-Akher3 Abstract – The paper presents Wind Turbine Generation (WTG) models as the three-phase resource and analyses their effect when they are connected in distribution networks using threephase distribution load flow. The WTGs can be modelled as a voltage-controlled node (PV node) or as a complex power injection (PQ node). The three-phase distribution load flow has been developed based on the symmetrical components. Newton Raphson method has been chosen for well known excellent convergence characteristics. The three-phase load flow program has been tested using IEEE 13 node feeder. The solution of the base case is compared with the radial distribution analysis package (RDAP). Then the three-phase load flow method is used to analyze distribution networks with WTGs. The analysis is carried out with various WTG mathematical models. The simulation results show that the integration of WTG into an existing distribution network can improve the voltage profile as well as reduces the total system losses. Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords: Three Phase Load Flow, Wind Turbine Generation (WTG), Sequence Decoupled Newton Raphson Method

I.

Introduction

The distribution network needs to analyse on threephase basis instead to single phase. The unbalanced condition in the distribution network cause of existence two phase and single phase line section with balanced and unbalanced load connected cannot be solved using single phase load flow. Therefore, the three-phase load flow is required when solving the unbalanced systems. The three-phase distribution components such as distributed generations (DG), three-phase transformer, multiphase line and balanced and unbalanced load need to modelled and improved for future complete and accurate analysis. There are some works has been reported for distribution load flow solution such as back/forward sweep analysis method for radial distribution feeder, compensation based balanced power flow and unbalanced power flow analysis [1-6]. The application of Newton-Raphson method based on symmetrical components is proposed in [6]. This method has some advantages such as fast execution time and low memory requirements [6] and have an ability to handle Distributed Generations (DGs) as PV node [7]. Distributed generation using renewable energy sources, such as wind, solar radiation, and hydro has received considerable attention in recent years. Wind power is the world's fastest growing electricity generation technology. Global wind power capacity reached 94,100 megawatts by the end of 2007 and available wind turbine sizes with capacities up to 3500

Manuscript received January 2011, revised January 2011

kW [8]. Therefore, there is a need to improve specific DG model to cover wind turbine generator (WTG). Over recent years, there has been much discussion on wind turbine generation (WTG) models in the load flow analysis. The impact of wind turbine integrated to distribution networks using the simple model for simple network presented in [9,10]. Simulation results in [9] show that WTG can improve voltage profile at the load point. Impact of DG for loss line reduction already simulated in [10] for a simple case of a radial distribution line with one concentrated load at the end and one cogeneration. The results clearly indicate that WTG can reduce the electric line losses. However, the model need to improve specially for unbalanced three-phase distribution network analysis. The objective of this paper are to improve WTG model and study the effect when they are connected in distribution networks. The studies include on both voltage profile and system losses. The paper is organized such that section 2 presents the WTG model, section 3 presents the three-phase load flow method, Section 4 shows the system under study, Section 5 gives comprehensive results and the effect of WTG gridconnected on both the voltage profile as well as system losses, and finally the conclusions are drawn in section 6.

II.

Wind Turbine Generation

The wind turbine generator can be used induction type or synchronous type. Distributed generation of induction type driven by wind power have different characteristics, because power output is not fixed by turbine governor

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

Syafii, K. M. Nor, M. Abdel-Akher

setting, but depend on wind speed which is a variable quantity and they usually draw almost fixed reactive power from the associated network [11]. The wind turbine with asynchronous generation in a load flow analysis modelled as PQ and RX [12, 13] buses are the most commonly used. Typical 0.9 and 1.5 MW Turbine model to find power output related to wind speed provide in [14]. The fixed speed Wind Turbine Generator Unit (WTGU) has been suggested in [12]. Conventional wind turbine models same as its generator type as PV bus model or PQ bus model. For Accurate wind models, the real and reactive power outputs specified depend on wind speed and terminal voltage [15]. So, we need to models some computation first before running power flow with a given wind speed and other parameters. The wind speed cannot he predicted, but the probability of a particular wind speed occurring can be estimated. This can be done if the probability distribution is known by assuming it to be a Weibull distribution or a Rayleigh one [16]. Once the wind speed is known, the power injected into the grid can be calculated by means of the wind turbine (WT) power curve. So, in order to assess the impact of wind energy on the steady state security of electrical networks, the problem can be planned from a probabilistic point of view, by knowing the probability of injecting a determined power, if previously the probability of a given wind speed is known. General wind turbine model using basic speed and power relations presented in [15,16] to calculate the output power as state below: 1 P = ρ. A. V 3 . Cp (1) 2

Where : P is power in watts, ρ is air density in kg/m3, A is the rotor swept area m2, V is the wind speed in m/s, and 𝐶𝑝 is rotor efficiency. The output power of wind turbine varies linearly with the rotor swept area and thirties with wind speed. For horizontal axis turbine the 𝜋 rotor swept area is given by 𝐷2 , where D is the rotor 4

diameter. The value of 𝐶𝑝 depends on ratio of the downstream to upstream wind speed as relation 𝑉0 𝑉

𝑉0 2

1 2

(1 +

Fig. 1. Power curve of typical 900 kW and 1.5 MW wind turbine

Other model using power Curve such as for GE wind energy [14] to find power output related to wind speed as shown in Fig 1. This curve usually provided by companies which produce wind turbine technologies. Different company give the different wind turbine curve, by use this curve wind speed can be plot to find specified power input in power flow calculation. Presently various types of Wind Turbine Generator Unit (WTGU) have been installed can be broadly classified into three categories, namely fixed, semivariable and variable speed types. The fixed speed WTGU has been suggested in [12,13]. The use of probabilistic measures to characterize the impact of WTGU on distribution networks in a steady state context has been suggested in ref [17]. The probabilistic analysis carried out in [17] obtains the probability distribution function (PDF) of node voltages considering a simple Gaussian distribution for the load and wind speed variations. In order to account for the probabilistic variation of load, wind speed as well as other generation, a sequence of steady state load flow solutions (using mean values of the variables) is obtained. From these load flow solution results, the PDF of node voltages are obtained. According to literature review, other types of WTGU (semi-variable speed, doubly fed induction generator and generator with front end converter) and so far no attempt have been made to model them for steady state threephase studies. Using the voltage control technique [18] of grid connected WTG, the synchronous WTG can model as PV node. Probabilistic load flow schemes used in [17] also make use of only simple WTGU models.

) [1 − ( ) ] where V is upstream wind velocity at the 𝑉

entrance of rotor blades and 𝑉0 is downstream wind velocity at exit of rotor blades. Other formulation, the output power for induction wind turbine is obtained as : 1−𝑠 𝑃(𝑉, 𝜔𝑟 ) = |𝐼2 |2 𝑅2 (2) 𝑠

where 𝐼2 is rotor current, the rotor speed is determined by equating the mechanical power input and the developed electrical power. Once the rotor speed is determined, the electrical power output can be computed. Detail explanation provided in [15].


III. Three-Phase Distribution Load Flow Three-phase load flow is required when solving unbalanced system such as in distribution networks. There are many causes of unbalanced condition such as unbalanced loads, long untransposed lines, presence of single-phase lines or two-phase lines, or both type of lines, in a distribution networks. The three-phase load flow algorithms can be categorized into two groups. The first group solves using phase component approach and the second used sequence component approach. However the sequence component have some advantages such as International Review on Modelling and Simulations, Vol. x, N. x


the size of the problem is effectively reduced in comparison to phase components approach [6] and easy to handle unbalanced power system components [7]. In this paper, the sequence components three-phase power flow algorithm and model [6] are used for developing three-phase WTGs model. The new class library to model WTG have been add in object oriented power system model [6,7] using C++ programming. III.1. Symmetrical component based three-phase load flow Algorithm The solution of the symmetrical component based three-phase load flow requires the construction of the three-phase power system models in terms of their sequence components. The three-phase power system models represented by sequence admittance matrices of three sequence network. The sequence admittance matrices comprise of positive-, negative- and zerosequence decoupled bus admittance matrices. Then, these sequence admittance matrices used to solve the three sequence network in the iteration scheme. The state variable of three-phase voltage update using the result of three decomposed sub-problem in an iterative scheme. The positive-sequence network has been solved using the standard Newton-Raphson and fast decoupled balanced three-phase power-flow methods whereas the negative- and zero-sequence are represented by two nodal voltage equations. The three sequence networks are solved in an iterative scheme. The specified values of sequence networks for three decomposed subproblem calculated by combining the current injection due to loads, distributed load, capacitor bank and system unbalanced.

The positive sequence voltage magnitude at the terminal bus is the same as the positive sequence network of the generator, and hence, the positive sequence voltage magnitude of the positive sequence network of the generator is specified. The total power specified at the terminal bus is mainly due to the positive sequence network of the generator since there is no induced EMF in both the negative- and zero-sequence networks. Consequently, the specified power of the positive sequence network of is known. For WTG connected, the specified voltage and power can be calculated using mathematical model as shown in table 1. TABLE 1. WIND TURBINE GENERATION MODEL

Wind Turbine Model Model 1 (PV Bus)

1 1 A  1 a 2 1 a

1 a  a 2 

(3)

where a =1.0 120 The result is sequence component model that can be included in three phase power flow algorithm as new class library. By used sequence component model, balanced wind turbine generator can be modeled in unbalanced system. The sequence component model allows using the balanced three-phase load flow specifications for generators. Normally at a terminal generator bus, both the positive sequence voltage and the total power leaving the terminal of the actual three-phase bus are specified. Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

P Calculate from : P = ½ .A.v3.Cp watts Or P obtain from Power Curve V is specified

Model 2 (PV Bus with Qlimit)

P Calculate from : P = ½ .A.v3.Cp watts Or P obtain from Power Curve V is specified Qlimit specified

Model 3 (PQ bus)

P obtain from Power Curve for wind speed given Q is specified or If pf (cos ) specified Q calculate from : Q= -P tan (cos-1 ) P obtain from Power Curve for given wind speed. Q calculated from induction generation parameters and V as equation (4) and The Q updated in load flow iteration process. P obtain from Power Curve for wind speed given Q is specified or If pf (cos ) specified Q calculate from : Q= -P tan (cos-1 ) And have a compensate capacitor

III.2. Wind Turbine Model In sequence three phase power flow program, every power system component need to convert to sequence components using A matrix (3). The A matrix is defined as the symmetrical components transformation matrix:

Specified Value

Model 4 (PQ Bus)

Model 5 (PQ bus, unity PF)

By knowing of injected power and voltage magnitude at generator bus, the WTG can modeled as voltage controlled device or PV model. If the Q limit is used, the PV model will be automatically converted to a PQ model. The asynchronous generator based wind turbine is modelled as a PQ node.

International Review on Modelling and Simulations, Vol. x, N. x


The consumed reactive power is calculated from induction generator parameters and voltage using the following equation [15]: Q

[ X m X l 2 s 2 ( X m  X l 2 )  X l1s 2 ( X m  X l 2 ) 2  R22 ( X m  X l1 )]V

2

[ R2 R1  s( X  ( X m  X l 2 )( X m  X l1 ))]  [ R2 ( X m  X l1 )  sR1 ( X m  X l 2 )]2 2 m

2

(4)

Where: V is stator terminal voltage, Xl1, Xl2 are the stator and rotor leakage reactance, Rl1, Rl2 are the stator and rotor resistance and Xm is the magnetizing reactance. The slip calculated using: 𝑠 = 𝑚𝑖𝑛 |

−𝑏±√𝑏 2 −4𝑎𝑐 2𝑎

|

(5)

Where:

The voltage is delivered from load flow calculation. Therefore, the reactive power specified is updated in every iteration process of the three-phase load flow calculation. The sequence components three-phase power-flow algorithm and model [6] are extended for modeling threephase synchronous/asynchronous WTG. The WTG class library has been added in exiting power system model [6].

IV. Description of Test System The modified IEEE 13 node test feeder [19] is used for Wind Turbine Generation (WTG) test cases as shown in Fig. 2. The cases presented WTG model as PQ node and PV node. A WTG with five different model as in table 1 connected at new node 672 via step down transformer with connected to node 671 of original node. The specified positive sequence voltage at this node is 1.0 pu when WTG model as PV node. For asynchronous WTG model Q specified calculated using equation in ref [15] with the following parameters given in p.u. values: R1=0.005986, X1=0.08212, R2=0.01690, X2=0.107225, Xm= 2.5561 and Xc=2.5561.

650

645

646

632

633

634

675

671 611

684

652

692

672

~ ~ ~ ~

680

This IEEE 13 node feeder is used to validate the improved algorithm for analyzing grid-connected different WTG models. The solution of the IEEE 13 node is compared with the solution calculated using the radial distribution analysis program (RDAP) [20].

V.

Result

First test is carried out to validate the improved generator model in three-phase distribution load flow with RDAP software. The loads are the same as the original data except that the distributed load is removed. This is for the sake of comparison between proposed method and the RDAP as the distributed load is modeled differently in the two methods. In this test, the IEEE 13 node is solved using sequence three-phase power flow algorithm and the RDAP software. The solution of the IEEE 13 node feeder is given in Table 2. The result from the developed program closely match with RDAP result without WTG connected as shown in table 2 for Colum 2 and 3. The other Colums show that WTG connected have improved voltage profile of IEEE 13 node system. The result with WTG connected as PV node shows that the voltage at WTG connected node 672 exactly 1.0 pu same as specified value as shown in Fig.3. The dummy nodes have the same voltages with upstream nodes voltage since the current flow through the dummy lines is zero for dummy phases. The missing phase in unbalanced lateral showed empty in the result of Table 2 and Fig. 3, because no actual voltage node available here. TABLE 2 THREE PHASE VOLTAGE PROFILE (PHASE A)

650

RDAP Without WTGU 1

1

1

1

1

1

632

0.9559

0.9557

0.9702

0.9613

0.9549

0.9650

633

0.9528

0.9524

0.9670

0.9581

0.9516

0.9618

634

0.9271

0.9267

0.9417

0.9326

0.9259

0.9363

645

-

-

-

-

-

-

646

-

-

-

-

-

-

671

0.9232

0.9226

0.9506

0.9329

0.9210

0.9402

672

0.9232

0.9226

1.0000

0.9548

0.9251

0.9731

680

0.9232

0.9226

0.9506

0.9329

0.9210

0.9402

684

0.9214

0.9209

0.9488

0.9311

0.9192

0.9384

611

-

-

-

-

-

-

652

0.9154

0.9150

0.9427

0.9251

0.9133

0.9324

692

0.9232

0.9226

0.9506

0.9329

0.9210

0.9402

675

0.9161

0.9154

0.9438

0.9258

0.9138

0.9332

Node

Without WTGU

Model 1&2

Model 3

Model 4

Model 5

The system losses are evaluated without and with WTG connected. The voltage-controlled node (PV node) and complex power injection node (PQ node) are used in the models. The system losses are 124.70 MW and 365.11 MVAr before WTG connected. After WTG connected system losses reduced to 99.5 MW and 260.66 MVAr for WTG modeled as PV node model 1 and

Fig. 2. IEEE 13 node test feeder Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved



system losses reduced to 107.86 MW and 296.82 MVAr for WTG modeled as PQ node model 4.

reported in this paper. The Malaysian Ministry of Science, Technology and Innovation contribution in terms of research funding to the project is also gratefully acknowledged.

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

Fig. 3. Three-phase voltage profile for 13 node test feeder

[8]

The simulation results have presented that the integration of WTG into an existing distribution network can improve the voltage profile as well as reduces the total system losses. Among the WTG models, model 1 and 2 which act as PV node have better performance relate to voltage profile and loss reduction.

[9]

VI. Conclusion

[11]

The paper has presented WTG model as three-phase source for three-phase distribution load flow and analyzed their effect when they are connected in distribution networks. In this paper, the WTG was modeled as PV node with have an option to convert to a PQ node when it achieved Q limit and as PV node with have three different type of P calculation. The model was tested and analyzed using a 13 node IEEE distribution feeder. The simulation results show that the integration of WTG into an existing distribution network can improve the voltage profile as well as reduces the total system losses.

[10]

[12] [13] [14]

[15]

[16] [17]

Acknowledgements The authors gratefully acknowledge the assistance rendered by the Centre of Electrical Energy systems (CEES), Universiti Teknologi Malaysia, in the work Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

[18]

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Simulations (IREMOS) Journal,Vol. 3. n. 5 (part A), pp. 864-869, October 2010 [19] W. H. Kersting, “Radial distribution test feeders”, PES winter meeting, vol. 2, no. 28, pp. 908-912, Jan. 28/Feb. 1, 2001: Available:http://ewh.ieee.org/soc/pes/dsacom/test feeders.html. [20] Radial Distribution Analysis Program (RDAP), which can be downloaded from http://www.zianet.com/whpower/

Authors’ information 1

is with the Centre of Electrical Energy systems (CEES), Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Malaysia. Phone: +6-07-5536264 Fax: +6-07-5536267 3

is with the Faculty of Engineering, South Valley University, 81542 Aswan, Egypt.

(Email: [email protected], Phone: +60-166134175) (Email: [email protected], Phone: 002-0120977190) (Email: [email protected], Phone: +603-26154515)

1

Syafii was born in Lhokseumawe, Indonesia. He received B.Eng. degree from North Sumatera University, Medan, Indonesia in 1997 and M.Sc from Institute Technology Bandung in 2002. He is currently working toward the Ph.D. degree in the Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Skudai, Malaysia. Since 1998, he has been associated with the Department of Electrical Engineering, Faculty of Engineering, Andalas University, Padang, Indonesia, as a Lecturer. His current research interest is in power system analysis, parallel programming and distributed generation.

Khalid Mohamed Nor (M’81-SM’92) was born in Sungai Pelong, Selangor, Malaysia. He received B.Eng. degree with a first class honors from the University of Liverpool, U.K. He later received an M.Sc. degree in 1978 and a Ph.D. in 1981, both from the University of Manchester Institute of Science and Technology, U.K. He is currently a Professor in the Faculty of Electrical Engineering, Universiti Teknologi Malaysia. His research interests are in the field of electrical power system simulation and power quality. 2

3

Mamdouh Abdel-Akher was born in Qena, Egypt on October 9, 1974. He received the B.Sc. with a first class honors and M. Sc. degrees from Assiut University, Egypt, in 1997 and 2002 respectively and the Ph. D in 2006 from University of Malaya, Kuala Lumpur, Malaysia. Since 1999, he has been associated with the Department of Electrical Engineering, South Valley University, Egypt as a research engineer, and since 2002, as an Assistant Lecturer, and currently as an assistant professor. His current research interest is in power system analysis and simulation.

