Fast Decoupled Power Flow for Power System with High Voltage Direct Current Transmission Line System

Problem statement: High voltage direct current transmission line syst em has been widely applied for control power flow in power system. The power flow analysis was the one of powerful tools by which the power system equipped was analyz ed both for planning and operation strategies. Approach: This study presented the method to analyze power f low of power system consisted of HVDC system. HVDC was modeled as the complex power inj ctions. The presented complex power injected was incorporated into the existing power f low program based on fast decoupled method. The presented method was tested on the multimachine pow r system. Results: The transmission line loss of the system with and without HVDC was compared. Conclusion: From the simulation results, the HVDC can reduce transmission line loss of power sys tem.


INTRODUCTION
High Voltage Direct Current (HVDC) transmission line system is getting more and more popular because of lower investment cost in long distance, lower losses, asynchronous interconnection between power systems, better controllable power flow compared with Alternating Current (AC) system (Al-Abdulaziz at al., 2006;Lu et al., 2006;Sun et al., 2008). The great important role of power flow analysis is to determine the operating point of the existing, study in planning the future expansion and evaluate the best operating point of power system (Ahmed at al., 2008;Al-Rawi at al., 2007;Augusto at al., 2008;Noor at al., 2008).
The objective of power flow analysis of the system equipped with HVDC system is to solve operating point both AC and HVDC system. In the performing power flow calculation of AC system on the nodal iterative method, two AC variables are specified while the remaining two AC variables are solved iteratively. There are many methods of power flow analysis (Parry and Gangatharan, 2005;Federico, 2009). The fast decoupled power flow provides rapid solution for power system with low resistance and susceptance ratio (Avakian at al., 2006). HVDC transmission line system is based on advanced power electronic technology. The parameter in HVDC side is the DC quantities. It is simultaneously solved the AC and DC parameters.
This study presents the power flow analysis of power system equipped with HVDC system. The presented mathematical model of HVDC system is incorporated into AC power flow analysis based on fast decoupled method. The simulation results are tested on multimachine system and compared with various cases.

MATERIALS AND METHODS
AC fast decoupled power flow: The fast decoupled power flow equations of solving unknown parameters of Voltage magnitude (V) and angle (δ) are given by: Here B' and B" are the imaginary part of bus admittance. P and Q are the active and reactive power injection at AC system.
HVDC model: Figure 1a shows the schematic diagram of HVDC system. The equivalent circuit of Fig. 1a is shown in Fig. 1b. The subscripts represent the sending quantities end and the subscripts 'r' represents the receiving end parameters. The converter can be represented by the variable DC voltage source (V d ) and constant resistance (R C ). The DC transmission line is represented by constant resistance R L . The ideal no load direct voltage is given by: Here α and γ are the ignition angle of converter I and converter II, respectively.
The average DC output voltage is given by: Here, I d is the DC line current. The power factorφ, fundamental line current lags the line voltage is written by: AC-HVDC fast decoupled power flow: The voltage magnitude, voltage angle and power flow of the AC-HVDC interconnecting equations must be coincident at the interconnecting point of the AC-HVDC systems. The active and reactive power and the bus voltages to be supplied from the AC system are calculated using the specified initial value of DC system. The derived active and reactive power are incorporate into AC fast decoupled power to evaluate the unknown parameter at sending and receiving end bus as shown in Fig. 1c and given by: The procedure is repeated until all the relations interconnecting the AC-HVDC quantities are satisfied with sufficiently small errors.

RESULTS
The proposed method of fast decoupled power flow of power system with HVDC system is tested on the multimachine system as shown in Fig. 2. The HVDC system is equipped between bus 10 and bus 12. The power system consists of 5 generators 18 buses. The proposed method achieved the output of power flow analysis. Table 1 shows the transmission line losses of the power system without HVDC system and with HVDC system.

DISCUSSION
It can be seen from the simulation results that active and reactive power loss of power system without HVDC are around 1.02 and 14.80 p.u., respectively. However, with HVDC system, the active and reactive power loss is decreased to 0.918 and 13.22 p.u., respectively.

CONCLUSION
This study proposed the fast decoupled power flow analysis of power system with HVDC system. The HVDC power flow is specified and then the derived active and reactive power are incorporate into AC fast decoupled power to evaluate the unknown parameter at sending and receiving end.
The proposed method was tested on the multimachine system. It was found that the proposed method achieved the output of power flow analysis. It is shown from simulation results that HVDC not only can control power flow through the transmission line but also can decrease the transmission line loss.