An Improved Droop Control Method for Multi-Terminal VSC-HVDC Converter Stations

Abstract

Multi-terminal high voltage direct current transmission based on voltage source converter (VSC-HVDC) grids can connect non-synchronous alternating current (AC) grids to a hybrid alternating current and direct current (AC/DC) power system, which is one of the key technologies in the construction of smart grids. However, it is still a problem to control the converter to achieve the function of each AC system sharing the reserve capacity of the entire network. This paper proposes an improved control strategy based on the slope control of the DC voltage and AC frequency (V–f slope control), in which the virtual inertia is introduced. This method can ensure that each AC sub-system shares the primary frequency control function. Additionally, with the new control method, it is easy to apply the secondary frequency control method of traditional AC systems to AC/DC hybrid systems to achieve the steady control of the DC voltage and AC frequency of the whole system. Most importantly, the new control method is better than the traditional control method in terms of dynamic performance. In this paper, a new control method is proposed, and the simulation model has been established in Matlab/Simulink to verify the effectiveness of the proposed control method.

1. Introduction

In recent years, wind, solar, and other new energy technologies have developed rapidly. However, they have the characteristics of intermittence and randomness, which makes it more and more limiting for the traditional power grid to absorb ultra-large-scale renewable energies. The flexible multi-terminal DC grid technology is one of the effective techniques to solve this problem [1,2,3,4,5,6,7].

The traditional control strategy of converter stations focuses on the transmission power. The converter acts as a specified power supplier in the inverter side, or a load in the rectifier side. Thus, it plays a negative role in regulating the power of the entire grid [8,9,10,11]. As is well known, the purpose of traditional small-scale power grids interconnecting to larger grids is to enable each small grid to share the moment of inertia and frequency regulation function. Thus, they can support or act as a standby for each other to make the whole system more stable. If the converter stations are controlled as specified power suppliers or loads, it will greatly weaken the advantages of the interconnected system [12,13,14]. The proposed control strategy will solve this problem.

In order to ensure the steady operation of the multi-terminal high voltage direct current transmission based on voltage source converter (VSC-HVDC) grid, the basic control requirements are to maintain the stability of the DC voltage and to balance the DC power [15,16,17,18,19]. In order to keep the DC voltage stable and the system power balanced, both the voltage control and power control are commonly used [20,21]. At present, there are three main types of voltage control strategy: the voltage margin control, the voltage droop control, and the voltage droop control with a voltage margin [22]. These three control modes can realize the coordinated control of DC voltage and power, but they are lacking in a real-time interaction for the AC networks, and cannot provide a primary frequency control function for each sub-AC grid. Thus, scholars have put forward a method that combines the DC voltage power droop with the AC frequency power droop [1,23,24,25]. It can sustain DC voltage and provide the primary frequency control function to a sub-AC grid [16,17,18]. However, this control method is lacking in a dynamic flow balance method. During a load disturbance, this control method will lead to more transient power fluctuations [26].

This article proposes an improved droop control method. With every converter station using this control method in multi-terminal VSC-HVDC system, each AC system can share the primary frequency regulation service. All the generators can share their inertia in the hybrid AC/DC power system. The real-time interaction of each AC system is enhanced. Additionally, it is easy to apply the secondary frequency control method of traditional AC systems to the AC/DC hybrid system.

This paper proposes an improved control strategy based on the slope control of the DC voltage and AC frequency (V–f slope control), in which the virtual inertia is introduced. This paper is arranged as follows: In Section 2, the applied models of the whole hybrid AC/DC system are presented. Based on the model, in Section 3, the control strategy and the coordination method are proposed. In Section 4, the crucial parameters of the control strategy are discussed. In Section 5, the validity of the proposed control method is proved by simulation in Matlab/Simulink. Finally, the conclusion and the future work are presented in Section 6.

2. System and Model Description

2.1. DC Grid Description

The research object of this paper adopts a bipolar-operation, three-terminal HVDC system with a star topology. The bipolar-operation, three-terminal HVDC system of this paper is a hypothetical power system. The DC-side uses a unified rated voltage of ± 200 kV. DC lines adopt lumped parameters. The line capacitance effect is focused on the DC-side of the converter and the line inductance is ignored. The structure of the power grid is shown in Figure 1.

In Figure 1, areas A, B and C represent three asynchronous AC power grids. Point O is a node of the DC power grid. The multi-terminal DC power grid adopts overhead lines. These lines choose aluminum cable steel reinforced (ACSR)-720/50 with R = 0.04 (Ω/km), and adopt a four-splitting lead. The distances of OA, OB and OC are 100 km, 80 km and 40 km, respectively. The resistances of each line are:

$$\begin{array}{l}{R}_{AO}=0.04/4\times 100\times 2=2\mathsf{\Omega }\\ R_{BO}=0.04/4\times 80\times 2=1.6\mathsf{\Omega }\\ R_{CO}=0.04/4\times 40\times 2=0.8\mathsf{\Omega }\end{array}$$

(1)

2.2. AC Grid Description

In Figure 1, the three AC systems A, B and C are asynchronous; each AC system is represented by an equivalent source and load. The synchronous generator model represents the power source, and the equivalent model of each AC system is shown in Figure 2.

The terminal voltage of the synchronous generator is 10 kV and it is connected to the 110 kV lines through a 10/110 kV transformer. The equivalent concentrated load and the line impedance are connected to the 110 kV line. The parameters of the AC grid are shown in

Table 1. Parameters of AC generators.

Parameters/AC Area	A	B	C
Rated power (MW)	600	400	100
Initial power (MW)	488.70	246.16	81.45
Droop coefficient (Hz/MW)	0.0042	0.0168	0.025
Inertia constant (S)	6.5	6.5	6.5

and

Table 2. Parameters of AC line and load.

Parameters/AC Area	A	B	C
Initial load (MW)	380	180	240
Line impedance (Ω)	4 + j12.5	4 + j12.5	4 + j12.5
Rated power of transformer (MVA)	600	400	100

.

In addition, 2% of the power loss is considered as output power, and it is distributed by the generators of the three areas according to per unit of their rate capacities.

2.3. Converter Station Description

In fact, typical VSC-HVDC converter stations always adopt modular multi-level topologies. The main research point of this paper is the method for the coordinated control of AC/DC power, so the control problem of the converter component level is ignored. To simplify the problem, it uses three-phase, two-level, triple-arm bridges with IGBT power semiconductors to replace the actual modular multi-level topology model.

3. Proposed Control Method

The new control method is based on the speed droop characteristics of traditional AC power grids and the voltage droop control of traditional HVDC converter stations; thus, it inherits the characteristics of the two traditional control methods.

For VSC-HVDC transmission systems, it is assumed that the converter station V₂ is connected to the stable DC grid V₁ through line impedance, as shown in Figure 3.

The transmission power from the DC grid to the converter can be expressed by Equation (2):

$$P_2=\frac{\mathrm{\Delta }V}{R}\left(V_1-\mathrm{\Delta }V\right)$$

(2)

where P₂ is the transmission power of the converter station, V₁ is the voltage of the DC grid, and V₂ is the DC-side voltage of the converter station.

In Equation (2), if ∆V is much less than V₁, it can be ignored; then Equation (2) can be turned into Equation (3):

$$P_2\approx \frac{\mathrm{\Delta }V}{R}{V}_1=\frac{V_1^2}{R}-\frac{V_1}{R}{V}_2$$

(3)

From Equation (3), it can be illustrated that the power transferred from the DC grid to the AC area is inversely proportional to the voltage of the DC terminal. If V₂ < V₁, the converter acts as an inverter; otherwise, it acts as a rectifier. The characteristics are shown in Figure 4.

If the inverter acts as a power supplier in the AC side. It should be operated by the frequency and active power droop control to provide a primary frequency control function for the AC system. From the view of the rectifier side, it acts as a load of the AC-side. The control characteristic is that the frequency and active power are in a positive correlation. Therefore, the ideal control characteristic of the active power and frequency is shown in Figure 5.

As shown in Figure 4 and Figure 5, if the converter station operates in the inverter state, when the frequency of the AC system decreases, the AC side hopes to obtain more active power to support its frequency; thus, it requires the terminal voltage of the DC-side to be decreased to satisfy a more active power transmission. When the frequency of the AC system increases, the AC-side hopes to obtain less active power and the terminal voltage of the DC-side should be increased. This requires the AC system frequency and DC voltage control to positively correlate, as Figure 6 shows.

If the converter station operates in the rectifier state, the control principle is the same as for the inverter state.

Based on the analysis above, this paper proposes a control method. It puts the converter DC voltage and AC frequency in a positive relationship, as shown in Figure 6. In addition, to make the converter automatically sense frequency fluctuations of the AC system and supply energy to AC grids, the converter should make the AC frequency as feedback in the outer control loop. The virtual inertia is introduced in the control strategy, which makes the converter achieve dynamic power sharing, as for the traditional synchronous generator when a load disturbance occurs in the AC system [26,27]. Additionally, to ensure that the converter has the ability to support DC voltage, the converter should also make DC voltage a feedback in the outer control loop. The control loop is shown in Figure 7.

In Figure 7, ω is the sampled AC frequency; ω_ref is the reference AC frequency, which equals 100π rad/s; V_{dc_ref} is the reference DC voltage of the converter station; and K₁ is the slope coefficient of the AC frequency and DC voltage. When there is a need for AC systems to share the primary frequency regulation service, K₁ can regulate the dynamic power that each AC system should undertake. The transfer functions, Equations (4) and (5), can be obtained from Figure 7:

$$\mathrm{\Delta }T=(\mathrm{\Delta }{V}_{dc}-K_1\cdot \mathrm{\Delta }\omega )\cdot (\frac{K_i}{S}+K_p)$$

(4)

$$\frac{\mathrm{\Delta }\omega }{\mathrm{\Delta }T}=\frac{1}{S/K_3+K_2}$$

(5)

where K_p and K_i are the coefficients of the proportional-integral (PI) controller, ∆T is the intermediate variable, and K₂ and K₃ are the virtual inertia coefficients. These should be designed carefully to provide virtual inertia to AC grids.

4. Parameter Designs

The parameters of the new control method for the VSC-HVDC converter station are K₁, K₂, K₃, K_p and K_i. A suitable K₁ can sustain the AC frequency and DC voltage both at the scheduled level when the load increases suddenly in one AC system (as for the simulation presented in Section 5.1). The reasonable design of parameters K₂, K₃, K_p and K_i can smooth the frequency fluctuation of the AC system. The design principle should be based on the premise of satisfying the dynamic power sharing, and then making full use of the inertia of all generators in the entire system.

4.1. The Design of Slope Coefficient K₁

The DC voltage and AC frequency slope coefficient K₁ is a key parameter in the new control method. It has a similar design principle to the typical speed-droop characteristics of traditional power plants. With respect to the typical speed-droop characteristics of traditional power plants, it requires a load fluctuation ∆P within the range of ± 5%; the whole range of primary frequency control is released when the frequency error is about ± 200 mHz. Therefore, the speed-droop coefficient K is the ratio of the maximum relative power fluctuation and the maximum frequency relative deviation [23]. The speed-droop coefficient is calculated by Equation (6):

$$K=\frac{\mathrm{\Delta }P/P_n}{\mathrm{\Delta }f/f_n}$$

(6)

where K is the speed-droop coefficient, P_n is the active power of the AC system, and f_n is the rated frequency.

The method of designing the V–f control slope coefficient K₁ is proposed—refer to the typical speed-droop coefficient design of K. K₁ can be determined by the ratio of the maximum DC voltage relative deviation and the maximum frequency relative deviation. It can make the most of the permissible fluctuations of the DC voltage and AC frequency. It can be expressed by Equation (7). In this way, the slope coefficient of every converter station is equal. In fact, with respect to a multi-terminal VSC-HVDC system, the line impendence is very small, which results in a small deviation of the DC voltage among different converter stations.

$$K_1=\frac{\mathrm{\Delta }V/V_n}{\mathrm{\Delta }\omega /{\omega }_n}$$

(7)

It is assumed that the maximum DC voltage relative deviation is 10%. The frequency relative deviation is kept the same as for the traditional AC system (±200 mHz), and the base frequency is 50 Hz. The slope coefficient K₁ can be calculated to be 25 from Equation (7).

4.2. The Design of Inertial Coefficients K₂ and K₃

A reasonable design for the inertial coefficients can make the VSC-HVDC converters provide a virtual inertia to AC grids that is similar to that of the traditional synchronous generators. The virtual inertia plays an important role in damping the high frequency fluctuation of power, and smoothing the frequency variation in transient processes. Several studies have investigated the virtual inertia of virtual synchronous generators (VSGs). These generally made the virtual inertia coefficient equal to the moment of inertia of the synchronous generator, realizing the power sharing in the dynamic processes [26,27]. Therefore, the time constant of the converter’s frequency loop should equal the inertia time constant of the generator to achieve similar characteristics to the synchronous generator. In Figure 7, the relationship between ∆ω and ∆T is expressed as Equation (5), while the swing equation of the generator can be expressed as Equation (8) [28]:

$$\frac{\mathrm{\Delta }\omega }{\mathrm{\Delta }T}=\frac{1}{D+J\cdot S}$$

(8)

where ∆ω is the frequency deviation, ∆T is the deference of the turbine torque and the electromagnetic torque, D is damping torque coefficient, and J is the moment of inertia of the generator.

In fact, Equations (5) and (8) have a similar form. In Equation (5), the time constant of the frequency loop is K₂·K₃, making it equal to the inertia time constant of the generator. In this situation, the converters can provide virtual inertia to AC grids. A reasonable number for the inertia time constant is 5.2 [28]. Thus, Equation (9) can be obtained:

$$K_2\cdot K_3=5.2$$

(9)

This paper assumes that K₂ = 1; thus K₃ = 5.2, according to Equation (9).

4.3. The Design of the Reference DC Voltage of Each Converter

When setting the reference DC voltage of the converter station, the transfer power should be considered. Assuming point O (Figure 1) is the center, the voltage at point O is kept at 400 kV. In the initial state, the power of the generator in area A is 488.7 MW, and the load is 380 MW. Thus, area A needs to transfer 108.7 MW to the DC grid. Because point O is 400 kV, and the resistance from point O to station A is 2 Ω, the reference DC voltage of station A can be found from Equation (10):

$$\frac{108.7}{400}\times 2+400=400.54$$

(10)

Using the same method, the voltages of station B and C can be found; they are 400.26 kV and 399.68 kV. The parameters of the converter station are shown in

Table 3. Parameters of the converter station.

Parameters/AC Area	A	B	C
K1	25	25	25
K2	1	1	1
K3	5.2	5.2	5.2
Kp	1	1	1
Ki	100	100	100
Vdc_ref (kV)	400.54	400.26	399.68

.

Additionally, with respect to the AC voltage amplitude control, this study uses reactive power and voltage droop control [28]. The method of designing the droop coefficient is similar to that for the speed-droop coefficient, which was described in Section 4.1. The reactive power and voltage droop coefficient can be described mathematically by Equation (11) [28]:

$$K_Q=\frac{\mathrm{\Delta }Q/S_n}{\mathrm{\Delta }V/V_n}$$

(11)

where K_Q is the reactive power and voltage droop coefficient, S_n is the rating of the AC grid, and V_n is the rated AC voltage.

5. Simulation Study

To evaluate the proposed converter control strategy, an AC/DC hybrid parallel system model was built in Matlab/Simulink. For a special explanation, this control method was used for all converter stations in multi-terminal VSC-HVDCs. Two important functions were achieved by applying the new method. The first function was that it could realize asynchronous AC systems sharing their primary frequency control functions. The second function was that it was easy to apply the secondary frequency control method of traditional AC systems to the AC/DC hybrid system.

To evaluate the advantages of the proposed method, it was compared with the traditional V–f control method. The traditional V–f control method is proposed by reference [25].

5.1. Load Disturbances

At 10 s, a load increase of 45 MW in area C was simulated. Before t = 10 s, area A and area B transmitted 100 MW and 60 MW of active power to area C through the DC grid, respectively. At t = 10 s, the load in area C increased 45 MW suddenly; the response waves of the frequency of each AC area, the DC-side voltage, and the transmission power of each converter are shown in Figure 8. The response of the traditional control method [25] is shown in Figure 9.

In Figure 8, from the frequency waveform, when the load disturbance occurred in area C at 10 s, the frequencies of areas A, B and C decreased. With the frequencies decreasing, the generators of the three areas increased their active power outputs due to the effect of the frequency droop control of the generators. From the power waveform, when a load step occurred in area C, areas A and B transferred more active power to area C automatically, to balance the power of the entire system. Thus, areas A and B shared their primary frequency control function with area C. Because the three converter stations used the same control method, we can suppose that if the load increase occurred in area A or B, it is reasonable to consider that the frequency of all the AC areas would have decreased, and all the generators would have output more power to balance the increased load. Therefore, it is reasonable to conclude that all sub-AC systems can share the primary frequency control function.

The waveform of Figure 9 is similar to that in Figure 8, while the dynamic performance of Figure 9 is poor, as after 10 s, the frequency and DC voltage waveforms of Figure 9 have more fluctuation than the frequency and DC voltage waveforms of Figure 8. During load disturbance, the traditional control method will lead to more transient power fluctuations. This conclusion can also be found in reference [26]. Thus, it proves that the new control method is better than the traditional control method in terms of dynamic performance.

5.2. Secondary Frequency Control

Based on the simulation condition in Section 5.1, when the system became stable after load steps in area C, the active power of the generator in area B increased 45 MW at t = 60 s. This was just an imitation of secondary frequency control (considering that the generator in area B was the frequency control generator). The response waves of the frequency, the DC-side voltage, and the transmission power of each converter are shown in Figure 10. The response of the traditional control method is shown in Figure 11.

In Figure 9, both the AC frequency and DC voltage decreased after the load step occurred in area C at t = 10 s. The frequency waveforms of areas A, B and C were very similar. Thus, we could make an approximation, considering that the three frequencies were the same, to use their average value as the frequency of the hybrid AC/DC power system. In order to restore the AC frequency and DC voltage to the scheduled value, the secondary frequency control strategy could be introduced into the hybrid AC/DC power system. The average frequency was used to compute the output of the frequency control generator (e.g., the generator of area B). By increasing the active power output of the frequency control generator, the AC frequency and the DC voltage could be restored to the scheduled value. Therefore, when t = 60 s, the active power output of the generator in area B increased 45 WM (computed by using the decreased value of the average frequency).

As the frequency and DC voltage waveforms show in Figure 10, after the generator in area B increased 45 MW of active power at t = 60 s, the AC frequencies and DC voltages were restored to around the scheduled value. From the power waveform, the transmission power of station A was restored to the initial value. This means that the output of the generator in area A was restored to the initial value, while from the power waveform, the transmission power of station B increased (the waveform goes down, because it is a negative value). This means that the load step of area C was totally borne by the generator of area B. Thus, this demonstrates that, with the new converter control strategy, the AC/DC hybrid system could use the traditional secondary frequency control (the average frequency is considered as the frequency of the hybrid system). From this phenomenon, it is reasonable to suppose that when there is a power shortage in any AC area of the hybrid system, all the terminal DC voltages and all the AC area frequencies will decrease. In this situation, in order to restore the AC frequencies and DC voltages to the scheduled value, the secondary frequency control strategy of traditional AC systems can be used. Because all the frequencies of different AC areas are very similar, and active power can be transferred automatically to meet the need (without a specified value), by increasing the suitable amount of active power output of the frequency control generator, the AC frequencies could be restored to the scheduled value. Thus, it is reasonable to conclude that, with the new control strategy of the converter station, it is easy to apply the secondary frequency control method of traditional AC systems to the AC/DC hybrid system.

With the same simulation condition, the response of the traditional control method is shown in Figure 11. The waveforms of Figure 11 are similar to those of Figure 10, while the dynamic performance of Figure 11 is poor, as at t = 10 s and t = 60 s, the waveforms of Figure 11 have more fluctuation than for Figure 10. Thus, this proves that the new control method is better than the traditional control method in terms of dynamic performance.

6. Conclusions and Future Work

For the power balance control of multi-terminal VSC-HVDC systems, this paper improves the traditional converter station control mode by adopting the DC voltage and AC frequency slope (positive correlation) control mode. The paper adds a virtual moment of inertia into the control strategy. The control method has two functions. First, it supports different asynchronous AC systems sharing their primary frequency control function. Second, it is convenient for the AC/DC hybrid system to inherit the secondary frequency control methods of the traditional AC system. The simulation results prove that the new control method is better than the traditional control method in terms of dynamic performance.

The new control method of the VSC-HVDC converter station has some potential value for further study. The frequency control strategy, grid-on and isolated island operation strategy and stability analysis will be researched in a follow-up study.