Joint Control Strategy of Energy Storage System and Cutting Machine for Transient Stability of Direct Current Locking Rear Delivery Terminal System

Abstract

With the gradual operation of large-capacity HVDC transmission, HVDC), the characteristics of the “strong and weak communication” of the power grid are increasingly obvious. The power impact of the DC line after locking has a great impact on the power angle stability of the system and seriously threatens the transient stability of the delivery end system. By establishing the equivalent model of the AC/DC system with the energy storage power station and analyzing the transient process after DC locking, we propose a control strategy for the transient stability of the energy storage system and the delivery system after DC locking. This strategy controls the charge and discharge of the energy storage system by collecting real-time power angle and voltage data of the grid, uses the equal area rule, and initiates the cutting machine after the energy storage system is withdrawn. To verify the validity and correctness of the proposed method, a simulation analysis was performed in a modified cross-flow CEPRI-36 node AC–DC system.

1. Introduction

Due to the imbalance of energy distribution and load distribution in China, high-voltage direct current transmission technology with a large transmission capacity, a long transmission distance, and a small footprint is being used more and more widely in China [1].

At present, China has completed 15,800 KV DC transmission projects represented by Hami to Zhengzhou, Ximeng to Taizhou, and Yunnan to Guangdong; three DC transmission projects from Qinghai to Henan, Shaanxi to Hubei, and Yazhong to Jiangxi are under construction. With the progress of technology, the transmission capacity of high-voltage DC transmission has been significantly improved; however, DC blocking due to phase change failure and other reasons will cause a huge impact on the frequency of the whole system, the power consumption of the generator, and the voltage of the bus [2,3]. A DC blocking fault may lead to a power imbalance between the generation side and the load side, which results in over-frequency at the sending end of the grid and low frequency at the receiving end [4,5]. In addition, the active power surplus at the sending grid often results in a large power shortage at the receiving grid, which seriously affects the transient stability of the entire grid [6]. With a large number of new energy sources such as photovoltaic and wind power connected to the grid, the power balance of the power system will be further hit, and once the grid power is out of balance, it may lead to large-scale blackouts of factories and residences, or even cause the collapse of the power system [7,8]. Through an in-depth study of DC circuit breakers, the literature [9,10] proposed the unbalanced power redistribution characteristics after DC circuit breaker closure, which makes the unbalanced power of the units effectively regulated, but with the increase in thermal units, this regulation effect is weakened, which affects the power angle stability of the whole grid.

In case of transient power angle instability, the method of cutting off the unit power is generally adopted to control the system at the sending end to restore the stability of the system by regulating the DC power [11]. The literature [12] quantifies the transient stability stabilization problem caused by the simultaneous phase change failure of multiple DCs based on the contact line stability index and proposes a DC power compensation modulation method to cope with the phase change failure of multiple DCs based on the shock energy of the phase change failure. In the literature [13], a control strategy to reduce the wind turbine output while removing some capacitors to improve the transient voltage and power angle stability of the system after DC blocking is given by analyzing the wind power extra-high voltage DC outgoing system. In the literature [14], a normalized evaluation index for mutual emergency power support of multiple DCs is established for multi-delivery DC systems; a method is proposed to improve the transient power angle stability through the emergency power support of other DC lines after the blocking of one DC line.

Recent studies have shown that battery energy storage systems have good prospects for regulating the transient stability of power systems. According to the consistency algorithm proposed in the literature [15], the advantages of multiple resources such as photovoltaic, energy storage, and flexible load can be fully utilized to realize the frequency regulation control of the receiver system after DC line blocking. In the literature [16], a voltage control method is proposed by the energy storage system to provide transient voltage support to the distribution network in case of DC blocking. In the literature [17], a joint stabilization control measure to solve the transient overvoltage problem after DC blocking by pumped storage units, power-based energy storage, and wind turbines was proposed. The literature [18] analyzed the battery storage system to improve the transient stability of the power system based on the extended equal area rule and illustrated the effects of different capacity configurations and different access locations on the transient voltage, and generator power angle. Studies have shown that joint cutter load-cutting techniques can effectively achieve transient stability control [19] and can calculate the exit time of energy storage systems; however, these calculation methods are often not accurate enough to determine the exit time of energy storage.

In this paper, by establishing an equivalent model of an AC–DC system containing an energy storage plant and analyzing the transient process of the AC–DC system after DC lockout, we propose a control strategy for the transient stabilization of the delivery system after DC lockout through the joint action of the energy storage system and cutter measures. The strategy controls the charging and discharging of the energy storage system by collecting real-time power angle and voltage data from the grid; the reference cut-off amount is found out by simplified calculation on the basis of the equal area rule, and the cut-off operation is performed after the energy storage system is withdrawn. Finally, simulation analysis is performed in the modified CEPRI-36 node AC system to verify the effectiveness of the proposed method.

2. Equivalent Model of AC/DC System of Energy Storage Plant

Usually, the power imbalance at the receiving end caused by DC blocking first occurs as an out-of-step phenomenon between two groups of machines. By analyzing the disturbance trajectory, we can classify the sending units into two categories [20]: one is the leading unit S and the other is the remaining unit A. In this paper, the AC–DC equivalent system of the counting and storage power plant is analyzed, and its equivalent model is obtained as shown in Figure 1.

In Figure 1, the leading cluster S and the remaining cluster A together form the region 1 equivalence unit G₁, $E_1$, $E_2$ for the generator equivalence potential. ${\delta }_1$, ${\delta }_2$ is the generator power angle. $U_1$, $U_2$ is the bus voltage amplitude. ${\theta }_1$, ${\theta }_2$ is the bus voltage phase angle. $X_1$, $X_2$ is the equivalent reactance of the AC system. $X_{12}$ is the equivalent reactance of the contact line between areas 1 and 2. $P_{L1}$, $P_{L2}$, $P_{L3}$ is the load power. $P_D$ is the DC line transmission power. $P_{E1}$, $P_{E2}$ is the electromagnetic power emitted by the generator. $S_B=P_B+j{Q}_B$ is the energy storage charging and discharging power from the equivalent model of Figure 1. The equations of motion of the rotor in the two regions are:

$$\{\begin{array}{l}\frac{d^2{\delta }_1}{d{t}^2}=\frac{P_{M_1}-P_{E_1}}{M_1}\\ \frac{d^2{\delta }_2}{d{t}^2}=\frac{P_{M_2}-P_{E_2}}{M_2}\end{array}$$

(1)

where $P_{M1},P_{M2}$ is the generator equivalent mechanical power of the sending and receiving system; $M_1,M_2$ is the generator equivalent inertia time constant of the sending and receiving system.

It is assumed that there is a weak interconnection between areas 1 and 2, whose contact line reactance is much larger than the generator equivalent reactance, which can be approximated as ${\delta }_1\approx {\theta }_1$, ${\delta }_2\approx {\theta }_2$. The equations of motion of the rotor in the two regions are:

$$\{\begin{array}{l}\frac{d^2{\delta }_1}{d{t}^2}=\frac{1}{M_1}\left(P_{M_1}-\frac{U_1{U}_2}{X_{12}}\sin {\delta }_{12}-P_D-P_{L_1}-P_B\right)\\ \frac{d^2{\delta }_2}{d{t}^2}=\frac{1}{M_2}\left(P_{M_2}+\frac{U_1{U}_2}{X_{12}}\sin {\delta }_{12}+P_D-P_{L_2}\right)\end{array}$$

(2)

where ${\delta }_{12}$ is the difference in generator power angle for regions 1 and 2, and the two regional systems are converted to the form of a single machine system according to Equation (2)

$$\frac{d^2{\delta }_{12}}{d{t}^2}=\frac{P_{M_1}}{M_1}-\frac{P_{M_2}}{M_2}-\frac{1}{M_1}{P}_D-\left(\frac{1}{M_1}+\frac{1}{M_2}\right)\frac{U_1{U}_2}{X_{12}}\sin {\delta }_{12}-\frac{P_{L1}}{M_1}+\frac{P_{L2}}{M_2}-\frac{P_B}{M_1}$$

(3)

System stable operation $P_B=0$, ignoring the generator governor action and load power changes, Equation (3) is reduced to Equations (4)–(6), $P_M$ is the equivalent mechanical power, and $P_{E\max }^{\mathrm{I}}$ is the equivalent electromagnetic power maximum.

$$P_M=\frac{P_{M1}}{M_1}-\frac{P_{M2}}{M_2}-\frac{P_D}{M_1}-\frac{P_{L1}}{M_1}+\frac{P_{L2}}{M_2}$$

(4)

$$P_E^{\mathrm{{\rm I}}}=(\frac{1}{M_1}+\frac{1}{M_2})\frac{U_1{U}_2}{X_{12}}\sin {\delta }_{12}=P_{E\max }^{\mathrm{I}}\sin {\delta }_{12}$$

(5)

$$\frac{d^2\delta }{d{t}^2}=P_M-P_E^{\mathrm{I}}$$

(6)

After DC blocking, the blocking pole transmission power drops to 0, and the electrical power $P_B$ fed into the grid from energy storage is shown in Equation (7), where ${\delta }_S$ and ${\delta }_A$ are the S- and A-group equivalent power angles, respectively. $K_B$ is the active regulation factor of energy storage. The equivalent mechanical power $P_M^{\prime }$ and equivalent electromagnetic power $P_E^{\mathrm{II}}$ are shown in Equations (8) and (9).

$$P_B=K_B\sigma =K_B({\delta }_S-{\delta }_A)$$

(7)

$$P_M^{\prime }=\frac{P_{M1}}{M_1}-\frac{P_{M2}}{M_2}-\frac{P_{L1}}{M_1}+\frac{P_{L2}}{M_2}$$

(8)

$$P_E^{\mathrm{I}\mathrm{I}}=P_{E\max }^{\mathrm{I}}\sin {\delta }_{12}+\frac{K_B}{M_1}\sigma$$

(9)

3. Energy Storage System and Cutter Joint Control Strategy

3.1. Equivalent Area Rule for Counting and Energy Storage Systems

For the sending AC/DC system, after DC blocking, the transmission power of the blocking pole drops to zero, and there is a large power surplus in the sending system and a large power deficit in the receiving system. The large amount of surplus active power at the delivery end is transferred to the adjacent AC line. If the fault time is short, the system can usually resume normal operation after fault removal; however, for long-time faults, prolonged DC blocking can cause the whole system to exceed its stability limit, so protective control measures are required [21]. In the case that the fault cannot be removed in time, the transient power accumulated in the system after lockout can seriously threaten the stable operation of the system. Based on the response time of the energy storage power plant in milliseconds and the advantage of rapid charging and discharging, the energy storage power plant is put into operation first at the $t_a$ moment. Considering the delay of the fault signal and the cut-off command, as well as the limitation of the energy storage system’s own capacity, part of the generator set of the sending system is removed at the $t_a$ moment. The rapid input of the energy storage system can quickly reduce the acceleration area generated after DC blocking and increase the deceleration area thus reducing the cut-off volume, where ${\delta }_0$, ${\delta }_a$, ${\delta }_b$, and ${\delta }_u$ are the stable balance point after DC line lockout, the equivalent power angle at the moment of energy storage system input, the equivalent power angle at the moment of the energy storage system exit, and the unstable balance point after DC lockout, respectively. $P_M$, $P_M^{\prime }$, and $P_{M1}$ are the equivalent mechanical power of the AC/DC system in stable operation, the equivalent mechanical power after DC blocking, and the equivalent mechanical power after taking cutting measures; $P_E^{\mathrm{I}}$ and $P_E^{\mathrm{I}\mathrm{I}}$ are the electromagnetic power curve after DC blocking and the electromagnetic power curve after the energy storage system is put in, respectively.

In Figure 2, when ${\delta }_a$ corresponds to the moment $t_a$ energy storage is put into operation, the equivalent electromagnetic power curve rises to $P_E^{\mathrm{I}\mathrm{I}}$. The shaded part B is the acceleration area increased after the energy storage is put into operation. At this point, the acceleration area that has been accumulated by the system is $S_A$, as shown in Equation (10).

$$S_A={\displaystyle {\int }_{{\delta }_0}^{{\delta }_a}\left(P_M^{\prime }-P_E^{\mathrm{I}}\right)}d\delta$$

(10)

The equivalent mechanical power is further reduced to $P_{M1}$, $P_M^{\prime }=P_{M1}-\Delta P$ by removing part of the generator and reducing the generator output in the destabilized region at the corresponding moment $t_b$ of ${\delta }_b$. The shaded part C is the increased deceleration area after the cutter. When the system is in a critical steady state, the area of the shaded part A is equal to the sum of the areas of B and C, as shown in the following equation.

$$S_A=S_B+S_C$$

(11)

3.2. Electromechanical Transient Model and Control Strategy for Energy Storage System

The active power $P_B=K_B\sigma$ fed into the grid by the energy storage system is configured with an active regulation factor based on the current grid structure of the grid and the parameters of each generator.

The electromechanical transient model of the energy storage system is mainly aimed at modeling the grid-connected converter (PCS) and its control system. The PCS is an important link in the bidirectional transfer of energy from the storage battery to the grid, and the impact of the battery energy storage on the transient electromechanical stability focuses on the embodiment of its grid-connected characteristics, so there is no need to accurately model the characteristics of the battery, and it can be modeled according to the converter’s grid-connected control strategy. The electromechanical transient model of the energy storage system is mainly modeled for the PCS and its control system, as shown in Figure 3, which is divided into four modules: active/reactive power outer loop control, PCS inner loop control, charging and discharging power limitation, and grid-connected interface.

Real-time $\delta$ and $V$ data are collected from the grid, and the difference is made with the given values to obtain $\Delta \delta$ and $\Delta V$ as the input values of the outer loop control module, and the inner loop input signals $P_{set}$ and $Q_{set}$ are obtained through the proportional–integral regulator. The inner loop control is a PCS module, where the values of $P_{set}$ and $Q_{set}$ after rectification by negative feedback links are Park-transformed and simplified equivalent to obtain the first-order dynamic links to obtain the output active and reactive commands. The internal and external loop control structure is shown in Figure 4.

The charging and discharging power limiting module is detailed in the literature [16] as shown in Equation (12).

$$\{\begin{array}{c}{P}_{\min }<P<P_{\max }\\ Q_{\min }<Q<Q_{\max }\\ 0.1\le SOC\le 0.9\\ Q_{\max }=\sqrt{V_{AC}{}^2{I}_{\max AC}{}^2-P^2}\\ \left|P\right|\ge \sqrt{V_{AC}{I}_{\max AC}}\\ P={\eta }_{bat}{P}_{DC}\\ -I_{\max }\le I\le I_{\max AC}\end{array}$$

(12)

where: $P_{\max }$, $P_{\min }$ are the limit values of active power for charging and discharging of the energy storage station; $Q_{\max }$, $Q_{\min }$ are the limit values of reactive power for charging and discharging of the energy storage station; $I_{AC}$, $V_{AC}$ are the bus current and voltage of the AC side of the PCS; $I_{\max AC}$ is the limit value of the current of the AC side; $P_{DC}$ is the active power of the DC side; and ${}_{ }{\eta }_{bat}$ is the efficiency of energy conversion of the PCS. From the perspective of battery safety and life, the depth of charge, and discharge constraints, with the battery pack SOC at more than 90% of the capacity, the battery can only be discharged and cannot be charged when the discharge SOC is less than 10%, in order to protect the battery life to stop discharging.

The grid-connected interface module converts the active/reactive output commands into the real part of the current imaginary parts $Ip$ and $Iq$ to feed into the grid as shown in Equation (13), where $Vp$ and $Vq$ are the real and imaginary parts of the voltage at the grid-connected point.

$$\{\begin{array}{l}{I}_p=\frac{P{V}_p+Q{V}_q}{V_p^2+V_q^2}\\ I_q=\frac{P{V}_q-Q{V}_p}{V_p^2+V_q^2}\end{array}$$

(13)

3.3. Triangular Approximation Simplification Strategy for the Reference Cutter Volume

The acceleration area a and deceleration area b in Figure 2 are given by Equations (13) and (14), respectively:

$$\begin{array}{l}{S}_A={\displaystyle {\int }_{{\delta }_0}^{{\delta }_a}{P}_M^{\prime }}-P_E^{\mathrm{I}}d\delta \\ =P_M^{\prime }\left({\delta }_a-{\delta }_0\right)+P_{E\max }^{\mathrm{I}}\left(\cos {\delta }_a-\cos {\delta }_0\right)\end{array}$$

(14)

$$\begin{array}{l}{S}_B={\displaystyle {\int }_{{\delta }_a}^{{\delta }_b}{P}_E^{\mathrm{I}\mathrm{I}}}-P_M^{\prime }d\delta \\ =P_{E\max }^{\mathrm{I}}(\cos {\delta }_a-\cos {\delta }_b)+\frac{K_B}{M_1}\sigma ({\delta }_b-{\delta }_a)-P_M^{\prime }({\delta }_b-{\delta }_a)\\ \end{array}$$

(15)

The calculation of the unstable equilibrium point ${\delta }_u$ in Figure 2 is cumbersome and not conducive to real-time online applications. In this paper, a simplified method is proposed to solve the problem of unstable equilibrium point after using the cutting machine, which transforms the iterative solution of nonlinear equations of the original method into linear relational equations, and this method can effectively reduce the computation, especially it is more convenient and fast in real-time online applications, and the detailed method description is shown below.

In Figure 2, the arc between the moment when the energy storage system is pushed out corresponding to $({\delta }_a,P_E^{\mathrm{I}})$ and the unstable equilibrium point $({\delta }_u,P_{M1})$ after cutting the machine is approximated by a line segment. The line segment passes through the point $({\delta }_a,P_E^{\mathrm{I}})$, whose slope k is equal to the slope of the electromagnetic power curve $P_E^{\mathrm{I}}$ at the point $({\delta }_a,P_E^{\mathrm{I}})$ and intersects the equivalent mechanical power $P_{M1}$ at the point $({\delta }_u^{\prime },P_{M1})$. The amount of machine cutting is $\Delta P$, and then:

$$k=\frac{\Delta P}{{\delta }_u^{\prime }-{\delta }_b}$$

(16)

After approximate calculation, the increased deceleration area after machine cutting is a triangle area:

$$S_C=S\approx \frac{1}{2}\Delta P({\delta }_u^{\prime }-{\delta }_b)$$

(17)

when $S_B+S_C\ge S_A$, the system can remain stable, so use the critical steady state of $S_A=S_B+S_C$ to calculate Equations (12), (13) and (16), which will be combined

$$\{\begin{array}{l}{S}_A=P_M^{\prime }\left({\delta }_a-{\delta }_0\right)+P_{E\max }^{\mathrm{I}}\left(\cos {\delta }_a-\cos {\delta }_0\right)\\ S_B=P_{E\max }^{\mathrm{I}}(\cos {\delta }_a-\cos {\delta }_b)+\frac{K_B}{M_1}\sigma ({\delta }_b-{\delta }_a)-P_M^{\prime }({\delta }_b-{\delta }_a)\\ S_C=\frac{1}{2}\Delta P({\delta }_u^{\prime }-{\delta }_b)\end{array}$$

(18)

Solving Equation (17) yields the expression for the reference cutter quantity as

$$\Delta P=\sqrt{2k(S_A-S_B)}$$

(19)

The accuracy of the calculation is also ensured by using the triangular approximation method on the basis of avoiding solving nonlinear algebraic equations, and the cutter instantaneous quantities are substituted into Equation (19) to obtain the cutter quantity $\Delta P^{\prime }$.

$$\Delta P^{\prime }=\frac{M_G}{M_1}\Delta P$$

(20)

where $\Delta P$ is the equivalent cut-off volume of the single infinity system; $M_G$ is the inertia time constant of the unit being cut off.

3.4. Optimal Cutting Strategy in Combination with Energy Storage Plant

In today’s stability control systems, the way to solve the best cutting machine solution mostly uses the exhaustive method. However, this approach must consider all possible cutting solutions, and the considered cutting solutions increase exponentially in the form of cutting machine objects. Additionally, as the power system evolves, more possible solutions may appear. Therefore, when a DC blocking fault occurs, the response time under fault operation with this approach is far beyond the grid’s requirement for a fast cut machine to cut the load for the control system.

In this paper, we propose an optimal cutter strategy combining energy storage plants, based on the exhaustive method, to reduce the computational effort and solve the optimal cutter problem quickly by calculating only the cutter combinations that are likely to be optimal. After calculating the reference cut-off amount $\Delta P^{\prime }$ according to the analysis in Section 3.3, the difference between the actual cut-off amount and $\Delta P^{\prime }$ in the region is minimized as the objective function of this strategy, and this objective function is as follows:

$$\min \left|n_1{p}_1+n_2{p}_2+n_3{p}_3+\cdots +n_m{p}_m-\Delta P^{\prime }\right|$$

(21)

where $p_1,p_2,p_3.\cdot \cdot \cdot ,p_{\mathrm{m}}^{}$ is the actual operating capacity of each generator, respectively; $n_1,n_2,n_3\cdot \cdot \cdot ,n_m$ is the number of units of each generator removed.

After cutting according to the results of the above cutting combination, the generator with the largest relative angle in the leading generator group is removed as a priority.

It is worth noting that in practical applications, in order to maintain the long-term stability of the system, when a transient instability occurs in the system, only up to one-third of the current output power of the generator can be removed, and if the system still cannot restore stability, the cutter operation needs to be taken again. The control strategy flow of the cutter measure and energy storage system jointly acting on the transient stability of the AC–DC system proposed in this paper is shown in Figure 5 and described as follows:

(1)

After the DC line blocking occurs, collect real-time generator data for single infinity system equivalence and calculate the acceleration area based on the equivalent power angle information at the moment of energy storage input.

(2)

Configure the charging and discharging power of the energy storage power station and put it in the energy storage power station for transient stability control.

(3)

After the energy storage plant is put into operation, the generator’s power angle, speed, and electromagnetic power data are collected in real time, and the electromagnetic power curve is least-squares fitted to calculate the reference cut-off amount.

(4)

Exit the energy storage system and calculate the best cut-off combination, and take effective cut-off measures according to the calculation results.

(5)

Re-evaluate the transient stability of the system. If the system restores stability, exit the emergency control state; if the system is still unstable, recalculate the cut-off amount.

4. Simulation Analysis

4.1. Simulation Example

The network structure of the AC–DC system used in this paper is shown in Appendix A, using a modified CEPRI-36 node AC–DC system. Region a and region b serve as the sending and receiving ends of the AC–DC system, respectively, and are connected by a 500 KV high-voltage DC transmission line in between. In addition, the two regions are connected by an AC transmission line that connects nodes 24a and 24b. The system has a baseline capacity of 100 MVA and a total installed capacity of 39.1 pu. The tide results are used as transient initial values in the time domain simulation. The DC line operation is bipolar, with a total simulation time of 10 s and an integration step of 0.01 s. The parameters of the generator set are shown in Appendix B, and the parameters of the DC line are shown in

Table 1. Unipolar parameters of DC line.

Parameters	Rectifier Side	Inverter Side
BUS	BUS16a	BUS16b
AC side voltage $V_{ac}/kV$	226.47	218.32
DC transmission current $I_{dc}/kA$	0.8	0.8
DC side voltage $V_{dc}/kV$	500	476.14
DC line transmission power $P_d/MW$	225.78	221.56
Reactive power compensation capacity $Q_c/M\mathrm{var}$	300	300

.

4.2. Simulation Analysis of Joint Control Strategy of Energy Storage System and Cutting Machine under DC Blocking Condition

When the power system operates steadily up to 1 s, the HVDC transmission line (16_a,16_b) has a bipolar DC lockout. Due to the short response time of the energy storage system and the rapid charging and discharging process, the energy storage system can be put into operation within 0.1 s after the fault occurs. Considering the signal transmission as well as the cut-off time delay, the cut-off operation takes up to 0.9 s to operate. When the DC line is locked, the transmitted power drops sharply to 0 within 1 s. This triggers a huge power shock, which destabilizes the system at the sending end, and the power angle curve of generator sets 1–8 is shown in Figure 6.

As can be seen from Figure 6, generating units 1–4 and 7 constitute the leading units, while generating units 5, 6, and 8 constitute the remaining group.

The rated output power of energy storage $P_B=3$ pu. is configured according to the 36-node grid structure and generator parameters at the sending end. The charged and discharged active power of the energy storage system after it is put into operation is shown in Figure 7. By collecting real-time power angle data at the grid-connected node, the energy storage system acts quickly and is put into operation at 1.1 s and exits operation at the 2 s moment when the cut-off control measures are executed.

By analyzing the power angle $\delta$ and $P_E$ electromagnetic power and mechanical output power $P_M$ of the engine after the failure, we can perform a single infinity (OMIB) model fit using Equations (4)–(9) to obtain the relevant power angle and power characteristics, and we present the results in Figure 8.

The actual power cut is 4.171 pu. calculated according to Equation (19), and the optimal cut combination allocation method according to Equation (20) is as follows:

(1)

Unit 1 is cut at BUS1 bus, the cut ratio is 33%, and the active power is 181.5 MW.

(2)

Unit 2 is removed at BUS2 bus with a 33% removal ratio and 198 MW of active power.

(3)

Unit 3 is removed at BUS3 bus, with the removal ratio of 10% and the active power of 60 MW.

Firstly, the effectiveness of the joint control of the energy storage system and the cutter measures in this paper is verified, and the cutter control is carried out with the traditional exhaustive method, and the actual cutter volume is 5.782 pu., and the traditional scheme is compared to highlight its advantages. The power angle curves and equivalent power angle curves of the two schemes under transient stability control are shown in Figure 9 and Figure 10, and the relative power angle of each generator is shown in Figure 11.

The results in Figure 9 show that, after the cut-off amount is determined, the present scheme and the conventional scheme are equally capable of restoring stability to the system that is about to become unstable.

However, it can be seen from Figure 10 that the equivalent power angle curve oscillates more when the exhaustive method is used, which is close to 160°, while the highest equivalent power angle value is only 145° and the overall oscillation amplitude is smaller under the strategy of this paper.

Figure 11a–e shows that after the transient stabilization control by the joint control strategy proposed in this paper, the relative power angle between the overrunning and lagging groups, which is about to become unstable, is effectively restored to stability. The joint control strategy proposed in this paper can effectively suppress the speed of power angle oscillation, so it has a certain reference value in transient stability control.

5. Conclusions

In this paper, an equivalent model of an AC–DC system is established to obtain a single infinity equivalent system of an AC–DC system taking into account an energy storage system. By analyzing the transient process of the single infinity system, a control strategy is proposed for the transient stabilization of the sending system after DC blocking through the joint action of the energy storage system and cutting machine measures.

(1)

This control strategy is based on the advantages of millisecond response times and the rapid charging and discharging of the energy storage system. The rapid input of the energy storage system can reduce the acceleration area after DC lockout and increase the deceleration area to reduce the cut-off volume, thus reducing the economic loss caused by the cut-off.

(2)

This strategy calculates the reference cutting volume by triangle approximation and then allocates the optimal cutting machine combination scheme, which is simple to calculate.

(3)

By adopting the joint control strategy proposed in this paper, it can effectively ensure the system continues to operate in the case of loss of stability and can effectively reduce the magnitude of power angle swing, which provides an important reference for transient stability control.

(4)

The relevant conclusions provide new ideas for future HVDC transmission planning and operation as well as energy storage plants to enhance the transient stability of AC–DC transmission systems.