Multiple-node model of wind turbine generating system for unbalanced distribution system load flow analysis

ABSTRACT


INTRODUCTION
In general, the electric power distribution system is highly unbalanced.The system unbalance is mainly caused by: i) uneven loads on each phase; and/or ii) untransposed distribution lines.Due to the unbalance, the single-phase approach can no longer be used to analyze such a system, and a three-phase method should be used instead [1], [2].Moreover, the integration of distributed generations with renewable energy sources in the electric power distribution system has also increased recently.It has been acknowledged that primary energy sources for distributed renewable energy generation include: wind power, solar photovoltaic, and hydropower.However, wind-driven electric power generation systems are more established in technology development among the three energy sources and have broader applications [3]- [5].Since the penetration of wind turbine generating system (WTGS) in electric power distribution systems has been increasing significantly, the assessment of the system's steady-state performance will be more difficult.Generally, the system steady-state performance assessment is carried out based on the results of load flow analysis.The first and probably most critical step in the analysis is to model all system components.Several attractive techniques for integrating WTGS in steady-state load flow analysis have been proposed in [6]- [23].
An exciting method to incorporate the WTGS model into a standard load flow program has been proposed in [6]- [8].The inclusion of the WTGS adds two buses (nodes), two series elements, one shunt element, and one load on the existing power system network.A mathematical model of WTGS has been developed in [9]- [11].This mathematical equation (together with the existing load flow equation) is then solved iteratively.Various steady-state load flow models of fixed-speed WTGS have been proposed in [12], [13].The models are developed based on the equivalent circuits of the induction generator.These mathematical models are combined with the steady-state models of the system without WTGS and then solved simultaneously.Some methods for integrating variable speed WTGS have been proposed in [14]- [20].The WTGS models in [14]- [20], are also derived based on the steady-state equivalent circuits of the generator used by the WTGS.Steady-state three-phase models of WTGS have been developed in [21]- [23].The models in [21]- [23] can be incorporated and applied in the load flow analysis of unbalanced electric power systems.
In the methods proposed in [16]- [20] the power system has been assumed to be balanced, and the single-phase load flow has been used in the analysis.Since, as previously mentioned, the electric power distribution system is generally unbalanced, and the single-phase load flow approach is no longer adequate to analyze such a system.Although the proposed methods in [21]- [23] can be used to integrate the WTGS into an unbalanced system's load flow analysis, a standard three-phase load flow program can not be employed to obtain the solution.The program has to be modified to include the WTGS mathematical model in the calculation.
Therefore, against the above background, the objective of the present paper is to develop the WTGS model that can facilitate the load flow analysis in a three-phase unbalanced power system network without the need to modify the standard load flow program.The present work proposes the extension of the single-phase multiple-node model [6]- [8] to a three-phase multiple-node model.The model is incorporated into the load flow analysis of a three-phase unbalanced distribution network.A standard three-phase load flow program can then be employed to compute the unknown quantities in the distribution system load flow (DSLF) problem formulation.The rest of the paper is organized as follows: section 2 addresses the singlephase multiple-node model of WTGS.The extension of the single-phase multiple-node model to the threephase multiple-node model is given in section 3. Section 4 discusses study cases where validation of the proposed method is presented.Finally, some important conclusions of the paper are pointed out in section 5.

MULTIPLE-NODE MODEL OF WTGS
Figures 1 and 2 show induction generator equivalent circuits of WTGS connected to an electric power system at bus k [6]- [10].It is to be noted that both of the equivalent circuits in Figures 1 and 2 are valid and can be used to represent the WTGS induction generator.In Figure 1, Pm is turbine mechanical power input, Sg is WTGS electric power output, VS and VR are stator and rotor voltages, IS and IR are stator and rotor currents, and s is induction generator slip.Also, in Figure 2, ZS and ZR are stator and rotor circuit impedances, and YM is magnetic core circuit admittance.These impedances and admittance are determined based on the induction generator resistances/reactances and have the following forms: = (  +   )/ where RS/XS is resistance/reactance of stator circuit, RR/XR is resistance/reactance of rotor circuit, and Rc/Xm is resistance/reactance of magnetic core circuit.In Figure 1, the turbine mechanical power input is represented by the active power consumed by the variable resistance (RR(1-s)/s).By looking at Figure 1, this mechanical power can be expressed as (4): Based on (4), an equivalent constant power source can therefore be used to represent the variable resistance, as shown in Figure 2. Thus, (4) can be eliminated from the load flow equations, and slip s can also be excluded from the load flow calculations.It should be noted that the value of turbine mechanical power is usually available or known since the turbine manufacturer generally provides the turbine mechanical power curve.Based on the power curve, the turbine mechanical powers, for any wind speed values, can then be determined.
Based on the above discussion, the WTGS induction generator model can be converted into a three-node model in the load flow analysis [6]- [8]. Figure 3 shows the three-node model of the WTGS connected to bus k of an electric power system.In Figure 3, it has been assumed that the power system has n buses and m branches.The three-node model application will modify the load flow analysis by adding two lines and two load buses to the original system network where the WTGS is installed.Thus, a standard load flow program can be employed to compute the unknown quantities in the DSLF problem formulation.Modification to the source code program does not need to be carried out.What needs to be done is to change only the program data input due to the additional lines and buses.  1 and 2. The parameters in Tables 1 and 2 are the additional data input to the load flow program due to the WTGS installation at bus k.It can be seen from Table 1 that the turbine mechanical power is treated as a load with negative power (-Pm).The value of Pm, as mentioned earlier, can be determined based on the power curve provided by the turbine manufacturer.It should also be noted that ZS, ZR, and YM are calculated using (1).

MULTIPLE-NODE MODEL OF WTGS FOR THREE-PHASE DSLF ANALYSIS
Figure 4 shows the application of the three-node model in a three-phase electrical power system network.Figure 4 is obtained based on Figure 3, where the impedances of the induction generator (i.e., ZS, ZR, and YM) have been represented by 3×3 matrices to facilitate the analysis in a three-phase network.Detail of the branch and bus parameters added to the power system due to WTGS installation are presented in Tables 3 and 4. In Tables 3 and 4, the elements of 3×3 series impedance and shunt admittance matrices are calculated as ( 5)- (7): = (   +    )/      (7) where u=a, b, c and v=a, b, c.Also, the elements of turbine mechanical power vector can be determined using: The first case study is based on 19-bus network.A single-line diagram of the network is shown in Figure 5.It is an unbalanced network with a system voltage of 11 kV [23].The system has a total three-phase load of 515.94 kW and 177.27 kVAR (phase-a: 176.33 kW and 61.23 kVAR; phase-b: 166.34 kW and Multiple-node model of wind turbine generating system for unbalanced distribution system … (Rudy Gianto) 697 56.34 kVAR; phase-c: 173.27 kW and 59.70 kVAR).Detail of the system data including the WTGS data can be found in [23].Results of the load flow analysis for the system are shown in Tables 5-7.In Tables 5-7, the values in pu are on a 1 MVA base.It is to be noted that the results in Tables 5-7 are in excellent agreement with the results in [23], which confirm the correctness of the proposed method.

Case study 2
The second case study is based on 25-bus network.A single-line diagram of the network is given in Figure 6.It is also an unbalanced network with a system voltage of 4.16 kV [24], [25].The system has a total three-phase load of 11,145 kW and 2,884 kVAR (phase-a: 1,298.3kW and 957 kVAR; phase-b: 3.919,9 kW and 967 kVAR; phase-c: 1,303.3kW and 960 kVAR).All of the system data can be found in [24], [25].A WTGS with a power rating of 3 MW is assumed to be connected to bus 25.Data of the WTGS (i.e., induction generator impedances) are shown in Table 8. show the load flow analysis results for the unbalanced 25-bus distribution system.In Tables 9-12, the values in pu are also on a 1 MVA base.Since the system is unbalanced, the electrical quantities of the three phases are not identical.The results in Tables 9-12 are also given in the form of graphics as shown in Figures 7-9. Figure 7 indicates that the system voltage profile improves as the amount of turbine mechanical power is raised.This improvement is due to increased WTGS or wind power plant (WPP) output.This WTGS output increment implies that the power injection at the WTGS bus also increases, reducing the line losses and improving the system voltage profile.

Parameter
Resistance/reactance value (Ohm) Stator circuit Self: RS aa =RS bb =RS cc =0.057685; XS aa =XS bb =XS cc =0.288427 Mutual: RS ab =RS ac =RS bc =0; XS ab =XS ac =XS bc =0 Rotor circuit Self: RR aa =RR bb =RR cc =0.057685; XR aa =XR bb =XR cc =0.288427 Mutual: RR ab =RR ac =RR bc =0; XR ab =XR ac =XR bc =0 Core circuit Self: Rc aa =Rc bb =Rc cc =576.85;Xm aa =Xm bb =Xm cc =28.84 Mutual: (Rc ab ) -1 =(Rc ac ) -1 =(Rc bc ) -1 = 0; (Xm ab ) -1 =(Xm ac ) -1 =(Xm bc ) -1 =0  show the variations of WTGS power outputs against turbine mechanical power inputs.Figure 8(a) show that with the increase in turbine power, the WTGS active power output also linearly increases.However, the WTGS active power is slightly smaller than turbine power due to the power loss in the induction generator.Figure 8(b) shows that with the increase in turbine power, the rise in WTGS reactive power demand is not linear but more rapid or almost exponential.This higher demand for reactive power is because more reactive power is needed to magnetize the induction generator as the WTGS active power increases.Since the WTGS can fulfill some load demands, the power supply (active power) from the distribution substation can significantly be reduced as the WTGS active power output increases as shown in Figure 9(a).On the other hand, the substation reactive power will increase as the turbine mechanical power (i.e., the WTGS active power output) is raised as shown in Figure 9(b).This increase in reactive power due to more reactive power is needed for the induction generator magnetization as the WTGS active power increases.

CONCLUSION
A method to integrate WTGS into a three-phase unbalanced DSLF analysis has been proposed in this paper.The present work extends the single-phase multiple-node model to a three-phase multiple-node model.The model is then incorporated into the load flow analysis of a three-phase power distribution network.Application of the multiple-node model will only modify the load flow analysis by adding two lines and two load buses to the distribution system network where the WTGS is installed.Thus, a standard load flow program can be employed to compute the unknown quantities in the DSLF problem formulation.Modification to the source code program does not need to be carried out.What needs to be done is to change only the program data input due to the additional lines and buses.This paper has used two representative three-phase distribution networks (i.e., 19-bus and 25-bus networks) to confirm and validate the proposed method.

Figure 8 .
Figure 8. Variation of WPP outputs; (a) active power and (b) reactive power

Figure 9 .
Figure 9. Variation of substation outputs (a) active power and (b) reactive power

Table 1 .
Addition of bus data

Table 10 .
25-bus network WTGS power outputs (in pu) Multiple-node model of wind turbine generating system for unbalanced distribution system … (Rudy Gianto) 699

Table 12 .
25-bus network WTGS/substation total outputs and line losses (in pu)