Research and application of a power-flow-calculation method in multiterminal VSC-HVDC power grid

1 Introduction

The VSC-HVDC power transmission is regarded as the third-generation power transmission technology following AC and the conventional DC power transmission [1-7].Compared with the previous two generations of power transmission technologies,the VSC-HVDC has many types of operation modes and can regulate DC voltage flexibly while ensuring transmission capacity [8-14].The Zhangbei VSC-HVDC project is the first VSC-HVDC power grid with a system voltage of ±500 kV.It collects and transmits multiple forms of large-scale energy resources including wind power,PV energy,electrochemical energy storage,and pumped storage.The project includes Zhangbei and Kangbao as the sending converter stations,Beijing as the receiving converter station,and Fengning as the regulating converter station,and uses overhead transmission lines with a total length of 648 km.The project is the first DC power-grid-demonstration project with network features,the highest voltage class,and the largest transmission capacity in the world.In addition,it is the first demonstration project to apply the VSC-HVDC technology to a largescale grid connection with land renewable-energy sources worldwide.Therefore,it has a great significance in innovation leading and technology demonstration.The power-flow-calculation method for a VSC-HVDC power grid plays a critical role in engineering applications.Research and analysis on the power-flow calculation of Zhangbei VSC-HVDC power grid should be performed to provide technical support for the implementation and operation of the project [15-20].

2 Power-flow calculation method for a VSCHVDC power grid

2.1 Technical route for power flow calculation

The structure of an AC-DC hybrid power grid is shown in Fig.1.The interface between the VSC-HVDC and AC power grids involves the active/reactive or voltage/phase angle of the busbar controlled by the VSC-HVDC power grid,and it is related to the control mode used by the VSC-HVDC power grid.The difference between the DC and AC power grids is the number of their physical quantities.The DC power grid only has two physical quantities,namely active power and DC busbar voltage,both of which are coupled.However,the AC power grid has four physical quantities:active power,reactive power,voltage,and phase angle.Among them,active power is coupled with the phase angle,and the reactive power is coupled with the voltage.

Fig.1 Schematic for connecting VSC-HVDC and AC power grids

The power-flow-calculation method for the AC power grid can be used as reference to solve the power flow of a DC power grid by reducing the number of equations.However,the control mode of VSC-HVDC converter station should be considered when calculating the power flow of the VSC-HVDC power grid.If the VSC-HVDC power grid adopts a master-slave control mode,a constant DC voltage node is set as a balance node and the other nodes are the P nodes.If a droop control mode is used,there will be no constant DC voltage node; however,several equations should be added for the relations between DC voltage and active power.

2.2 Power-flow-calculation method for the VSCHVDC power grid

The injection of the current is chosen as the positive direction,and denoted by Pc,dc in Fig.1.Assuming that the DC power grid contains n nodes,the current and active power of any node i are calculated using equations(1)and(2),respectively,and the active power of node i can be calculated using equation(3).

Then,the power error of node i can be determined as follows:

Where,Gdcij is the conductivity of the line between nodes i and j; p is the number of poles of the VSC-HVDC power grid; Pgi is the active power of node i of the power supply injection; and Pdi is the active power of the DC load on node i.

Therefore,the steady-state power-flow model for the VSC-HVDC power grid can be expressed using equation(4)for each of the n nodes.The power flow was calculated to solve this nonlinear system of equations with a given DC voltage and node active power.An iterative solution can be obtained by adopting the Newton-Raphson method.Further,equation(4)can be expanded according to Taylor series to obtain the Jacobian matrix for calculating the DC power flow as

Here,all elements can be determined according to

2.3 Effect of true bipolar VSC-HVDC power grid operation on power-flow calculation

A true bipolar VSC-HVDC power grid can be calculated by considering it as a two parallel unipolar power grids and following the same principle as used for such unipolar grids.However,unlike an AC power grid,the transfer logic between positive and negative poles of the VSC-HVDC power grid should be considered during N-1 calculation,and the input and output power of some poles will be changed.Therefore,when calculating the power flow of the true bipolar power grid under Mode N-1,the power flow should not be broken simply and mechanically.

3 Effect of control mode on VSC-HVDC power-flow calculation

3.1 Control mode of VSC

VSC can realize independent control of active and reactive variables,where the active variables are the main influencers of the power flow of a VSC-HVDC power grid.The control of active variables is generally divided into constant DC voltage control,constant active power control,and active power-voltage droop control.Generally,the active power injected by each VSC into the VSC-HVDC power grid can be expressed as

Where,Psl is the active power injected by VSC of constant DC voltage control and the subscript denotes the number of converter stations.Pdp is the active power injected by the VSCs of a droop control,where k-1 VSCs are set.Ppr denotes the active power injected by the VSCs of constant active power control,where m-k VSCs are set.The remaining m-k nodes are not connected to a VSC or the VSC to which they are connected withdraws from operation.Here,the active power injected by the VSC of droop control is determined as

Where,Pdp0,i and Udc0i are the original operation points set for the VSCs of the droop control at node i and kpi is the corresponding droop coefficient.

According to equation(5),the error of active power of the node expressed by equation(7)can be transformed into equation(9),and does not include the slack node,which is the busbar of the VSC,i.e.,the active power-balance node under constant DC voltage control.For the VSC under droop control,the corresponding known quantities for power-flow calculation are the original operation points Pdp0,i and Udc0i set by the VSC.Therefore,the error in the expression of active power of the node van be corrected as follows:

Where,Pdc,i(Udc)is the active power injected to node i and determined using equation(3),and Pdp0,i can be determined as follows:

After the derivation of node voltage according to equation(11),we obtained the elements of the Jacobian matrix corresponding to the VSC of droop control as

3.2 Control strategy of the VSC-HVDC power grid

The stability of DC voltage is a key precondition for the steady operation of a DC power grid,similar to the necessity of frequency stability in an AC system.At present,the control strategy for a DC power grid is mainly divided into the master-slave control,voltage slope control,and voltage deviation control.In terms of the master-slave control,a converter station is selected as a master converter station,which is controlled by constant DC voltage,while other converter stations are used as the slave converter stations,which are controlled by constant active power.The active power vector injected by VSC is denoted by equation(13).In terms of voltage slope control,multiple converter stations are selected and use active power-voltage droop control,while other converter stations use constant active power control,which can be expressed via equation(13).To ensure the steady control of DC voltage,the master-slave control is usually combined with the voltage slope control,i.e.,the master converter station uses constant DC voltage control,some slave converter stations use droop control,and the remaining converter stations use constant active power control.The corresponding active power injected by each VSC is denoted through equation(14).

In terms of voltage deviation control,a backup master converter station is additionally installed on the foundation of the master-slave control,as represented by equation(15).When the master converter station is under normal operation,the backup converter station adopts constant active power control.When the master converter station loses the capacity of DC voltage control,the backup converter station switches to constant DC voltage control after detecting an exceeded voltage limit and keeps the DC voltage at a new operation point.At this time,the active power error equation of the node corresponding to the backup master converter station,as displayed in equation(9),is replaced by the active power error equation of the node corresponding to the original master converter station.In addition,the known variables of the node corresponding to the backup master converter station are replaced by the DC voltage values,and the known variables of the original master converter station are replaced by the active power injected by VSC.

4 Simplification of power-flow model for VSC-HVDC power grid

The power-flow calculation model for a VSCHVDC power grid can be simplified by referring to the PQ decomposition method used for calculating the power flow of an AC power grid.For example,consider the master-slave control mode; the diagonal elements in the Jacobian matrix are is equivalent to the injection power of node i when applying voltage Udci on node i,and all the other nodes are grounded.Then,we have Therefore,Pdci can be omitted,and the diagonal elements in the Jacobian matrix are the product of the square of the DC voltage and self-conductance at this node.

Therefore,the Jacobian matrix can be transformed into

By substituting this into the VSC-HVDC power-flow equation,we have

By multiplying both sides of equation(17)with

we have

5 Power-flow calculation of the Zhangbei VSC-HVDC power-grid project

5.1 VSC-HVDC power-grid model in a BPA program

At present,the BPA program is used to simulate a VSCHVDC power grid model but fails to distinguish a monopolar model from a bipolar model.A bipolar power grid can only be simulated by building a double-layer parallel power grid of the monopolar model,as shown in Fig.2.

The BPA program simulates a VSC-HVDC power grid converter station by using BZ and BZ+ cards.A converter station model is known to be established as a whole in the BPA,and the AC busbar,converter transformer,and DC busbar are set up into the model,which considers the DC and AC side control under the master-slave control mode.In addition,for the integrated model including AC busbar,converter transformer,and DC busbar,only the voltage at the AC side of the VSC-HVDC power grid converter station can be output in a geographical wiring diagram.Moreover,outputting the DC busbar voltage is difficult.

Fig.2 Bipolar simulation model for a VSC-HVDC power grid

5.2 Power-flow model for Zhangbei VSC-HVDC power grid

Based on the aforementioned illustration,a simulation model was set up for Zhangbei VSC-HVDC power grid project,as is shown in Fig.3.The master-slave control mode was adopted for the grid,with Fengning station as the regulating end under constant DC voltage mode.If an island control mode is set for Kangbao and Zhangbei stations,a VF control method will be used for these stations.In contrast,for the AC-DC hybrid operation mode,the PQ control mode will be adopted for Kangbao and Zhangbei stations.Both of the operation modes are set as node P in the power-flow calculation.The PQ control mode is used at the Beijing station and set as node P in calculating the power flow of a DC power grid.

The Jacobian matrix for the power grid is represented as follows:

Fengning station,as a balance end,can be omitted in the equation.Then,the simulation model for the VSC-HVDC power grid can be shown as follows:

5.3 Power-flow distribution in operation mode 1

With the injection of power in the positive direction,the maximum power of 3750 MW is set for the DC power grid when the Kangbao and Zhangbei stations deliver 1500 and 2250 MW,respectively,and Beijing station receives 3000 MW.The initial conditions are as follows:

Fig.3 Equivalent schematic of the Zhangbei VSC-HVDC power grid

Equation(22)can be solved using the Newton-Raphson method in MATLAB with the maximum power derivation of 1 MW taken as the convergence condition.Then,the result of the power flow of VSC-HVDC power grid in Operation Mode 1 is shown in Fig.4,where Figs.4(a)and 4(b)show the results obtained using MATLAB and BPA simulation.

Table 1 shows the simulation results of MATLAB and BPA in the operation mode 1 of the Zhangbei VSC-HVDC power grid project.As shown,the sending and receiving converter stations show minimal deviation characteristics and the consumptions calculated using the two methods are relatively similar.This result can validate the proposed power-flow calculating method.

Table 1 Comparison of simulation results in operation mode 1

BPA result/MW Line MATLAB result/MW Deviation/MW Zhangbei-Kangbao 98.5 98.3 -0.2 Kangbao-Fengning 1598.5 1598.1 -0.4 Fengning-Beijing 878.8 879.0 0.2 Zhangbei-Beijing 2151.5 2151.5 0 Consumption 41.9 42.4 0.5

Table 2 comparison of simulation results in operation mode 2

Line MATLAB result/MW BPA result/MW Deviation/MW Zhangbei-Kangbao 799.6 799.4 -0.2 Kangbao-Fengning 1549.0 1548.7 -0.3 Fengning-Beijing 830.7 830.9 0.2 Zhangbei-Beijing 2200.4 2200.4 0 Consumption 42.5 43.1 0.6

Fig.4 Result of power flow in mode 1

5.4 Power-flow distribution in operation mode 2

The maximum power of 3750 MW is set for the DC power grid when the Kangbao and Zhangbei stations deliver 750 and 3000 MW,respectively,and Beijing station receives 3000 MW.The initial conditions are as follows:

Equation(23)is solved using the Newton-Raphson method in MATLAB Program with the maximum power derivation of 1 MW taken as the convergence condition.Then,the result of the power flow of the VSC-HVDC power grid in operation mode 1 is as shown in Fig.5.

Fig.5 Result of power flow in mode 2

Table 2 shows the line load flow deviation in Mode 2; it basically resembles the result in Mode 1.This shows that our method can obtain a similar calculation result as that using BPA.

6 Conclusion

This paper focused on power-flow calculation for VSCHVDC power grid and proposed a power-flow model by referring to the power-flow calculation of an AC power grid.The composition of the Jacobian matrix elements for VSC-HVDC power grid was deduced and the influence of different VSC-HVDC power-grid control modes on the power flow calculation was studied.

The proposed power-flow calculation method for VSCHVDC power grid was performed in MATLAB and used to solve the Zhangbei VSC-HVDC power grid system.The results showed a slight difference in the load-flow distribution from the result calculated through BPA,thus confirming that our method can give a reliable solution to power-flow calculation for VSC-HVDC power grid and provide more parameter outputs than those obtained through BPA.This is convenient for the following research on VSCHVDC power grid,e.g.,active/reactive power control and grid protection scheme.

Acknowledgements

This work was supported by the State Grid Corporation of China Headquarter technology project(52010118000K).