Study on overvoltage suppression method of phase modulation of hydroelectric generating units and its cooperative optimization in new energy grid

When a significant portion of renewable energy is transmitted to the power grid through high voltage direct current, when the monopolar blocking occurs, as a result of the converter station’s filter and reactive power compensation equipment’s influence, overvoltage will be generated, which will cause harm to the new energy station, and even lead to large-scale new energy grid disconnection. This paper initially examines the mechanism behind overvoltage in a new energy power grid and then puts forward a method to restrain overvoltage by using phase modulation operation of hydroelectric generating units. To improve the phase modulation capability of hydroelectric generating units and optimize the utilization of new energy sources, this paper proposes a particle swarm optimization to determine the optimal phase modulation capacity. Finally, this paper builds an example of the PSASP platform to verify the correctness and effectiveness of collaborative optimization.


Introduction
In the past few years, as wind power, photovoltaic, and other new energy sources have been connected to the grid on a larger scale, the dynamic support capacity of the DC transmitting end system has been steadily decreasing [1].If the system fails and causes DC blocking, it will not only lose the transmission power but also bring a large impact on the weak AC grid at the transmitting end.As the removal of the converter station filter requires a certain response time, DC Monopolar Blocking will cause overvoltage in the sending AC system, seriously endangering the reliability of an abundance of power electronic equipment [2].For wind turbines with weaker high-voltage ride-through capability, large-scale disconnection may even occur during the overvoltage period of the system, to further excite the chain fault of the transmission end power grid.Hence, it is essential to take the required steps to improve the dynamic reactive power support capability of the new energy delivery system and reduce the potential overvoltage of the system.
Currently, extensive research has been conducted by both domestic and international scholars on the over-voltage issue of DC weak transmitting end system, which is mainly solved from two aspects: optimizing the power supply planning and dispatching scheme at the transmission end and improving the reactive compensation capability of the transmission end system.For the first method, Tamimi et al. propose a novel approach to maximize the scale of wind farms by analyzing the voltage instability mode of a weak transmitting end system [3].Wu et al. calculate the minimum ratio of conventional units in the bundling delivery system, which helps suppress the fluctuation of commutation bus voltage after the DC latching fault [4].However, these methods cannot solve the problem that the scale of new energy stations is still limited while sacrificing the flexibility of grid planning and dispatching.For the second method, Zhang studies the maintenance of the bus voltage at the grid-connected point of the wind farm by putting in a dynamic voltage restorer and other devices during the bus voltage surge stage [5].Li et al. conduct an in-depth comparative analysis of the decentralized access and centralized access to new energy systems of different reactive power compensation devices and prove through simulation that the decentralized access to new energy of reactive power compensation can better solve the problem of transient overvoltage of the system [6].
If there are a large number of hydroelectric generating stations in the DC outgoing transmission system, the structure of the hydroelectric generating unit is similar to that of the synchronous phase modifier, and the capacity of reactive power support and transient overvoltage suppression of the hydroelectric generating unit can be improved by switching the operation state or modifying the engineering structure of the hydroelectric generating unit, to enhance the integration of new energy sources.
The research on phase modulation of hydroelectric generating units at home and abroad focuses on the improvement and optimization of phase modulation technology to improve the phase modulation performance and stability of hydroelectric generating units.In addition, some studies have discussed the relationship between phase modulation technology and power system scheduling and stability [7].However, the research on the influence of enhancing the phase modulation capability of hydroelectric generating units on power grid safety and new energy consumption is still insufficient.
Based on the structural characteristics of the wind power-photovoltaic-hydroelectricity transmitting end system and the mechanism of over-voltage transfer, the hidden danger of over-voltage at the wind power-photovoltaic-hydroelectricity transmitting end is described.Against this background, the method of enhancing phase modulation function to restrain transient over-voltage is put forward.Then the cooperative optimization of enhancing phase modulation function and new energy is studied and analyzed.

Structural features of new energy grid
Figure 1 illustrates a typical green energy DC transmission system.In the transmitting end of the power grid, the wind turbine unit and the photovoltaic unit are the main power supply of the new energy cluster, and the hydroelectric generating unit is used as the rotating equipment to provide the voltage and inertia support for the system.The voltage stability of the new energy cluster is weak.Because of the power electronics' overload capacity and the control system's limitations, the short-circuit current of the wind turbine unit and the photovoltaic unit is only 1.5 times the rated current [8], and the short-circuit capacity provided by the new energy cluster is extremely limited.Therefore, as the proportion of wind farms and photovoltaic power stations grows, the effective short-circuit ratio experiences a decrease, and the voltage stability of the power grid is weakened.China has been putting significant effort into the development of new energy.In the past few years, the penetration rate of new energy at the transmitting end has been increasing, and the voltage-supporting capacity of the wind power-photovoltaic-hydroelectricity transmitting end power grid gradually decreased [9].
To sum up, amidst the trend of extensive integration of renewable energy sources, new energy delivery system often has problems such as weak grid structure, insufficient short-circuit capacity, and limited reactive power support to DC.In case of DC phase commutation failure and other faults, the reactive balance of the power grid at the transmitting end will be impacted instantaneously and the voltage will rise sharply.

DC monopolar blocking overvoltage in new energy grid
Direct Current Monopolar Blocking (DCMB) is a control strategy used to protect equipment and lines in an HVDC transmission system.In the HVDC transmission system, DC Monopolar Blocking is used to limit fault propagation and ensure the secure and stable functioning of the power grid.However, DC Monopolar Blocking will cause over-voltage in the transmitting end system.The relationship between the reactive power that is consumed by the converter of the DC system and the transmitted active power during regular operation of the DC system must adhere to a specific formula or relationship: (1) where and are reactive power consumption of DC converter, DC transmission active power, converter power factor angle, rectifier trigger angle, and commutation angle, respectively.In case of a DC blocking fault, the rectifier's trigger angle increases rapidly, and the active power of DC transmission drops instantaneously.The reactive power consumption of the DC system can be greatly reduced by Formula (1).Due to the time delay of AC filter equipment cut-off action, Qc cannot be reduced, so the reactive balance of the converter station is broken.In case of overvoltage on the converter station's AC bus, the overvoltage amplitude and reactive power surplus shall meet the following relationship: (2) where , , and are the overvoltage amplitude of the converter station's AC bus, the reactive surplus of the converter station, and the short-circuit capability of the transmitting end of the system, respectively.At this time, the excess reactive power at the transmitting end converter station is equal to the reactive power consumption of the DC system in the steady state.
In addition, when the new energy unit enters the low-voltage ride-through control link, the transient overvoltage is aggravated by the new energy active back-off [10].The characteristic of the low-to-high AC voltage of the power grid at the transmitting end will lead to reverse modulation of reactive power of the new energy generator unit and reactive power compensation device, further aggravating transient overvoltage [11].

Overvoltage suppression technology of phase modulation of hydroelectric generating unit
In the new energy power grid, hydroelectric generating units, as the key peak load and frequency regulation and reactive power support equipment, play an important role in post-fault overvoltage suppression.This section will discuss the application of the phase modulation function of hydroelectric generating units in overvoltage suppression.

Mechanism analysis of suppressing overvoltage using phase modifier
The fluctuation in the phase modifier's reactive power can be perceived as the aggregate of that represents spontaneous reactive component and that represents reactive component controlled by excitation.
The phase modifier's spontaneous reactive element is naturally generated by following the voltage change of the rectifier station's AC bus, and its instantaneous value is mainly determined by the direct-axis sub-transient reactance : ( where , , and are the voltage of the AC bus of the rectifier station before and after the fault, respectively, is the short-circuit reactance of the grid-connected transformer of the phase modifier, and is the initial value of the d-axis current in the rotating coordinate system.will decay over time to a steady-state value that is mainly determined by the d-axis steady-state reactance .The characteristics of the excitation control system shall be considered for the reactive component of excitation control of the phase modifier.The post-fault calculation formula is (4) where is the variable related to the parameters and time of the excitation control system.In Formulas ( 3) and ( 4), because is very small, the positive and negative of and are inversely related.For example, when the rectifier station voltage rises, , then , that the phase modifier absorbs the reactive power; otherwise, the phase modifier releases or emits reactive power.
PSASP is used to build a typical new energy DC-sending system.Within 0.5 s, the DC bipolar blocking problem manifests in the system.The bus voltage at the rectifier station and the reactive power coming from the regulator post-fault are both included in the study.
Figure 2 illustrates that the operation mode of putting the phase modifier into operation will directly prevent the rectifier station's AC bus voltage from briefly rising.This is because the phase modifier is in the state of absorbing reactive power after the DC blocking fault, which curtails the amount of transient overvoltage at the AC bus of the rectifier station and diminishes the surplus of reactive power at the rectifier station after the DC blocking.To sum up, the AC bus of the rectifier station experiences less transient overvoltage while the phase modifier is in operation after DC blocking by directly inhibiting the surge in the temporary voltage of the AC bus at the rectifier station.At the same time, the transmitting end of the new energy source experiences a system-level effect from the indirect inhibition, which lowers the power grid's transient overvoltage.

Analysis of phase modulation operation technology of hydroelectric generating unit
In the new energy power grid, the Hydroelectric Generating Units at the transmitting end have the capability of phase modulation operation, which makes them play a crucial part when overvoltage occurs in the power grid.Through the phase modulation operation, the hydroelectric generating unit can utilize its dynamic reactive capacity, that is, the excitation current can be adjusted, and the unit's reactive power output may be further controlled, so that the overvoltage problem of the system can be suppressed.The phase modulation operation is an effective overvoltage suppression strategy.Especially when the voltage on the electricity grid is too high, the phase modulation operation of the hydroelectric generating unit can absorb the redundant reactive power and assist the electrical grid in using the extra electricity to maintain the grid's voltage.
The phase modulation operation of the hydroelectric generating unit is caused by excitation low excitation, and the result is that the unit stably absorbs reactive power.The specific process can be analyzed based on the change of each electric quantity in the detailed dynamic model of the hydroelectric generating unit.The transfer function is shown in Figure 3 (all the electric quantities in the figure are established in the coordinate system).
' ' '' Based on the equivalent circuit of the synchronous motor, the stator current and can be described by the synchronous motor transient potential and , end voltage and , and transient reactance and , as shown in Formula ( 5). ( The output reactive power of the hydroelectric generating unit shall meet Formula (6).( 6) Substituting ( 5) into (6), Formula (7) of output reactive power of hydroelectric generating unit described by transient potential and , end voltage and , and transient reactance and can be derived.(7) Formula (7) shows that when the end voltage rises, the reactive output of the unit can be reduced by the characteristics of the synchronous motor.If the internal potential level of the unit is further reduced to a negative value, reactive power can be absorbed.
Formula ( 8) is the expression of the excitation system of the hydroelectric generating unit.The potential source-controllable rectification excitation system is used as an illustration. ( where the effective value of the voltage error signal is the result of the voltage reference value minus the effective value of end voltage, that is, Formula ( 9) is satisfied.( 9) Formula ( 10) is the relationship between excitation voltage and axis transient potential of the synchronous motor after Laplace transformation.
(10) According to Formula (10), after a significant increase in system voltage at the transmitting end, the voltage at the turbine end of the hydroelectric generating unit rises, and the excitation voltage is rapidly reduced by the hydroelectric excitation system, so that the transient potential of the axis is reduced after the time delay of , and the stator current generates the magnetizing armature reaction, thereby reducing the reactive output and even absorbing the reactive power.The selfregulation of the end voltage is realized.

Analysis of optimization technology of phase modulation operation of hydroelectric
generating unit in new energy grid By improving the phase modulation function of the hydroelectric generating unit, the loss of electricity during no-load operation can be reduced after the transformation is completed, and the generating capacity of the new energy generating unit can be increased, to gain benefits.However, both the transformation itself and the phase modulation operation need a certain cost, and the water is abandoned and the power generation is sacrificed.Therefore, it is necessary to analyze the phase modulation capacity to realize the synergistic optimization of the enhanced phase modulation function and the new energy.

Objective function
This paper calculates the economy according to the following energy yield function.
(11) where the power loss caused by abandoned water caused by no-load operation is .When using phase modulation mode, the phase modulation function requires a amount of power drawn from the system.The cost of the renovation is , and the increased capability for producing new energy is .The estimated phase modulation run time is ; the turbine generator unit is rated at ; the turbinerated flow is ; the initially estimated turbine no-load flow is calculated as 13% of the rated flow, i.e.
(12) The initial estimate of no-load running loss is obtained. (13) When using the phase modulation mode, it is estimated that phase modulation requires a amount of power to be absorbed by the system. (14)

Constraint conditions
For this reactive power optimization model, each node must satisfy the balance of active power and reactive power.
(15) where are the active and reactive power of the generator, DC transmission, and load node, respectively; are the voltage and phase angle of node and , respectively; are the branch conductance and susceptance; and is the number of nodes.The reactive power of the generator shall meet the following requirements: (16) where and are the lower and upper limits of the generator reactive power, respectively.The node voltage of the AC system shall meet the following requirements: (17) where and are the lower and upper limits of the node voltage, respectively.The node voltage includes not only the normal operation voltage but also the overvoltage generated after DC blocking.
(18) where and are the lower and upper limits of the planned capacity of the reactive compensation equipment, respectively.

Introduction to particle swarm optimization
The initialization of a collection of random particles is the first step in the stochastic optimization technique known as PSO.Particles control their mobility in solution space by determining their speed and direction based on their individual and swarm information.Each particle tracks two "optimum solutions" during the iterative solution process to update its speed and location.The updating procedure is as follows: where w is inertia weight, 1 c and 2 c are acceleration factors, and are random numbers between (0, 1), is the d-dimensional component of the optimal position vector of the ith particle at time k, and is the d-dimensional component of the optimal position vector of the population at time k.

Analysis of suppression of transient overvoltage by enhancing phase modulation function of hydroelectric generating unit
Figure 4 is the topology diagram of a certain area.The simulation experiment is carried out with this area as an example.The total installed capacity of new energy at the DC transmitting end in this area is 27, 000 MW, including 18, 000 MW of solar energy and 9, 000 MW of wind power.This area also has 12, 600 MW of installed hydroelectric generating.There is an extra-high voltage DC transmission line with a DC line rated voltage of ±800 kV in this area.The transmission distance is 1, 207 km.The operation mode is per day in the dry season, with hydroelectric generating output of about 2, 606 MW, thermal power output of about 1, 260 MW, wind power output of about 4, 590 MW, and photovoltaic output of about 9, 566 MW.Type 14 photovoltaic units and Type 13 wind turbines all adopt typical parameters that have not been modified, and the high voltage ride-through function is not enabled.The third phase commutation failure DC blocking fault occurs after 2 consecutive commutation failures.The near-zone new energy's highest transient voltage increase, as shown in Figure 5, is 1.383 p.u.

Case analysis of enhanced phase modulation function of hydroelectric generating unit and collaborative optimization of new energy
Simulation verification was performed by using the system shown in Figure 4. Considering the simultaneity, the system's overall maximum new energy production is 9, 200 MW.
The investment for enhancing the phase modulation function of each hydroelectric generating unit is shown in Table 1, including the price of phase modulation pressurized water system equipment, equipment re-supplied by the unit plant, civil engineering, removal, and installation costs.It is considered that the total investment of the phase modulation project is RMB 33.23 million yuan per unit.After the modification, the unit enters the pressurized water phase modulation operation, the overflow of the unit is zero, and the unit can generate reactive power required by the system only by absorbing small active power from the system.
According to the content of the third part, the optimization model is established and the PSO is used to analyze the example in this paper.The results are shown in Table 2.After calculation, it can be seen that the system has obvious effects on increasing new energy power generation, and its economy has been further improved.Therefore, the enhanced phase modulation function of hydroelectric generating station units can significantly increase the generation of new energy and improve the economy of system operation.

Conclusions
Aiming at the transient overvoltage problem in the new energy grid, a method of enhancing phase modulation function based on the hydroelectric generating unit is proposed.This technology utilizes the phase modulation function of the hydroelectric generating unit to realize the reactive voltage regulation by changing the operation state and the control strategy, to restrain the overvoltage of the power grid.The results of the analysis and example show that enhancing the phase modulation function can increase the generation of new energy and the economy of system operation.Especially when the rated power of the hydroelectric generating station unit is large and the no-load running loss is high, the economic benefit of enhancing the phase modulation function will be more obvious.

Figure 1 .
Figure 1.DC Outward Transmission System of New Energy.

Figure 3 .
Figure 3.The Transfer Function of Each Electric Quantity of the Dynamic Model of the Hydroelectric Generating Unit.

Figure 4 .
Figure 4. Grid Structure Topology in a Certain Area.

Figure 5 .
Figure 5. Transient Overvoltage of New Energy Unit After DC Fault.

Figure 6 .
Figure 6.Transient Overvoltage of New Energy Unit After DC Fault.
Control Effect of Suppressing Transient Overvoltage Response of Rectifier Station Phase Modifier.

Table 1 .
Investment to Enhance Phase Modulation Function of Hydroelectric Generating Units.

Table 2
Enhanced Phase Modulation Function of Three Hydroelectric Generating Stations.