PCHD-Based Passivity Control of VSC-HVDC Connected Large Wind Farm

Concentrated integration of large scale wind power demands stronger robustness of VSC-HVDC transmission. Based on PCHD (Port Controled Hamiltonian with Dissipation) equation, the PCHD model of voltage source converter (VSC) in abc frame and d-q rotating frame are built and the strict passivity of VSC is proved. Desired energy function is constructed and used as Lyapunov function by assigning link matrix and damping matrix. Impact from VSC equivalent dc resistance is eliminated by additional damping matrix. The IDA-PB (Interconnection and Damping Assignment Passivity-based) controller is designed based on desired equilibrium point and state variable. With different operation conditions, VSC-HVDC and its control system are simulated by software PSCAD/EMTDC, the results show the proposed control strategy has good performance and strong robustness.


Introduction
The use of wind power is a keystone in the policy of every country for its renewable energy development goals.Meanwhile wind farm is large-scalely developed and the capacity of a single wind farm increases to hundreds or thousands of MW [1].HVDC with voltage source converter (VSC-HVDC) has fine dynamic characteristic and transmission flexibility, furthermore it improves the stability of power system [2,3].In addition, VSC-HVDC is more economical for hundred megawatts wind farm connection [4].Therefore, VSC-HVDC has obvious techno-economic advantages for the connection of large scale wind farm.The VSC-HVDC system can be operated in three modes: 1) constant dc voltage control mode; 2) constant active and reactive power control mode; and 3) constant ac voltage control mode [5].And one of converters has to control the dc voltage to make power balanced and the dc voltage stable [6].However four control inputs of the VSC-HVDC and their interaction make it a truly nonlinear multiple-input and multiple-output system.Furthermore the fluctuation of wind power will cause deviation of the electric variable in connection point.So VSC-HVDC need strong robustness to deliver power.
At present, voltage vector oriented double closed loop PID control [7] based on synchronously rotating frame and direct power control are commonly used.But they both have weak robustness and it is difficult to tune PID parameters.To eliminate the impacts of nonlinearity of VSC-HVDC and improve its robustness, many research works have been carried out, including feedback linearization and sliding mode control [5], adaptive back-stepping control in Ref. [8], fuzzy PI control in Ref. [9] and neural network PID in Ref. [10].But it is still difficult to achieve ideal effects because of the multivariable structure and highly coupled nonlinearity of the VSC-HVDC system.
Passivity control is an emerging nonlinear control theory based on the energy dissipation of system [11,12].Its profound physics meaning has significant relation with Lyapunov function.IDA-PB control is a passivity control based on PCHD.This paper, IDA-PB control strategy is proposed based on the PCHD model of VSC-HVDC.The control decreases dependence of system parameters and makes VSC-HVDC connected large wind power has smaller static error and stronger robustness.The simulation results show its advantages.

Topology and Model of the VSC-HVDC
The single line diagram of the VSC-HVDC connected a wind farm is shown in Figure 1.
The detailed structure of VSC is shown in Figure 2, the transformer reactance and power loss are equivalent to L and R, and the parameters of the three phase circuits are assumed to be identical.
where (j=a,b,c) is the logic switch function, when the upper bridge arm is conductive and lower bridge arm is turn-off, when the contrary is the case.By Park transformation matrix and its inverse matrix, Equation (1) can be transformed to Equation (2) in d-q rotating frame j s where and represent the d and q components of the switch function,   ( ) When d axis is oriented at the vector of the voltage at PCC, then 0 sq u  , and s s dd i , so controlling the and respectively can realize the decoupled control of and .

PCHD Model of VSC-HVDC Converter
Port-controlled Hamiltonian with Dissipation(PCHD) model [13,14] is the form where are the state variables are input variables and y are outp variables.Evaluating the rate of change of the system total energy, we obtain the sy ut Therefore energy input from external is always greater than stored in the system, this makes the system passive.
Make the switch control variable , , where , , i a b c  , according to Equations ( 1) and ( 4), we obtain the PCHD model of VSC in abc frame where , T [ ] and dc dc dc / R u i  i.e. the equivilent resistor at the dc side of VSC.By Park transformation, Equation ( 7) can be transformed to PCHD model in d-q synchronously rotating frame as Equation ( 9) where , T [ ] The energy function of the system is defined as

IDA-PB Controller Design of Converter
According to IDA-PB control theory [14][15], it need to find out functions ( ) x  , a( ) J x , a( ) x  and vector function ( ) K x n R for the desired stable equilibrium points by assigning interconnection and damping marix and make they meet the Equation ( 11 They meets conditions as follows The dc voltage is expect to be the reference value of , and are determined by the requirements of decoupled control of active power and reactive power.Therefore, the anticipated stable equilibrium points are x Cu  . The PCHD model Equation ( 9) can be written as the Equation ( 15 where So dc equivalent resistor exist in converter dissipation matrix.Its impacts are to be eliminated by assigning damping matrix.Make that a( ) 0 J x , According to Equations ( 11), ( 12) and ( 13), we obtain Equation ( 16) Then the expasion of Equation ( 16) is Equation ( 17)  , according to Equation ( 14), we obtain Based on above conditions, a set of solution for where  ,  , 0   .
Substituting Eqation (19) to Eqation (17) and considering that the dc voltage of VSC is equal to desired stable equilibrium voltage i.e. at steady state, then the VSC control laws can be obtained and simplified as where and can be obtained by outer-loop control.
In order to facilitate active power setting and voltage control for wind farm, active power and constant voltage control are used at the outer-loop controller of sending end, and constant dc voltage and constant voltage controls are used at receiving end, Figure 3 shows the control diagram.

Simulation and Analysis
The VSC-HVDC linked wind farm and its control strategy are modeled and simulated by software PSCAD/ EMTDC.The rated dc voltage of the VSC-HVDC is ±160kV and the base capacity is 100 MVA.The power production of the wind farm is 180 MW, the PCC voltage of both ends is 110kV.The simulation time span is 20 s.Comparison is made between PI double closed-loop control and IDA-PB control, and the outer-loop PI parameters of both are identical so as to ensure comparison valid.Figure 4 to Figure 7 show the steady simulation results.In order to compare dynamic response performan ake the wind speed have a step change at 10 s and 15 s under both control modes, as shown in Figure 8. Figure 9 shows the simulation results of each variable.Figure 11 shows the tter steady and dynamic performance under IDA-PB control when the voltage at PCC of receiving end changes.And dc voltage at receiving end has smaller static error, it recover to set value quickly after disturbance under IDA-PB control, as shown in Figure 12.

Conclusions
The robustness of t large wind power is discussed, a IDA-PB control strategy is proposed for converter in this paper.The proposed    1) The system energy function has pa tic.It is accord with Lyaapunov stability theory and has clear physical meaning, and ideal controller can be obtained by making best of it.
2) PCHD function has ge re.Its essence is a nonlinear control strategy and it is apt to nonlinear characteristic of VSC-HVDC.
3) IDA-PB control simplified controller d HD model.Damping assignment decrease the impact from system parameter deviation and make the energy function non-growth and minimum value at equilibrium point.
4) T four inputs.And the control law is easy and of practical value for engineering application.

Figure 3 .
Figure 3. IDA-PB control strategy for both ends VSC.

Figure 9 (
a) shows the dc voltage at sending e le fluctuation and smaller flutter under IDA-PB control.The receiving end dc voltage is stabilized on set value and error is ±0.05 kV under IDA-PB control, but it fluctuates greatly and need much time to reach stability under PI double closed-loop control, as shown in Figure 9(b).
Fig wo ure 5. Wind power and transmited power under t control strategies.

Figure 6 .
Figure 6.Direct voltage of receiving end under tw control o strategies.

Figure 10 .
Figure 10.Voltage step change at PCC of receiving end.Setting the voltage amplitude step change at the PCC of

Figure 11
and Figure 12 show the results.
(a) Voltage pu value in PCC under PI double closed-loop control (b) Voltage pu value in PCC under IDA-PB control

Figure voltage 11 .
Figure voltage 11.Voltage value in PCC under step disturbance at PCC of receiving end.

Figure 12 .
Figure 12.Direct voltage of receiving end under step c