Steady-state voltage-control method considering large-scale wind-power transmission using half-wavelength transmission lines

0 Introduction

In 2020,China announced the firm long-term target of peaking carbon emissions before 2030 and reaching carbon neutrality in 2060,regarded as a major fillip for the global fight against warming climate [1-2].Under the guidance of this target,clean energy,including wind power,has been rapidly developed in recent years [3].However,the inverse distributions of load centers and energy sources have increased the transmission and consumption issues of clean energy [4].Safe and reliable long-distance powertransmission technology has begun to attract considerable research interest.The half-wavelength transmission (HWLT)system is a type of three-phase AC power transmission,where the line length between its sending end (SE)and receiving end (RE)is approximately 3000 km for 50 Hz or 2500 km for 60 Hz [5].The minimum annual cost method indicates that ultrahigh voltage (UHV)HWLT is more economical than ± 800 kV and ± 1000 kV DC transmission[6].In different transmission scenarios,Samorodov G et al.reported that the investment for the single-circuit HWLT with reserve phase is considered to be 30% lower than that for HVDC [7].It has shown advantages for technical and economic perspectives,primarily for not requiring reactive compensation or intermediate substations between the terminals [8].

Some existing research results have made clear progress in the voltage-characteristic analysis of HWLT systems.Voltage profiles along the HWLT line are significantly affected by the transmitted active power and power factor.The peak voltage increases with an increase in active power or a decrease in power factor.Joule losses and corona losses were addressed in reference [9] and reference [10]to obtain more accurate voltage and current distribution regularities for a wide variety of load conditions.Reference[11] reported that grounding short-circuit faults can cause a partial power-frequency overvoltage.The fault location has a significant effect on the amplitude of the resulting overvoltage.In reference [12],the electromagnetic transient simulation under various operating conditions revealed that the overvoltage profiles of the closing operation of breakers has the shape of a “saddle,” with a high at both ends and a low in the middle.The need for a method of mitigating the severe resonant fault condition until the operation of a protection system is discussed,and such a method is proposed in reference [13].An alternative method of suppressing overvoltages is proposed using linesurge arresters directly at the phases in parallel with tower insulators [14].These reports indicate that HWLT systems have specific characteristics and behaviors,especially from the perspective of their voltage profiles [15].Compared with the conventional UHV transmission line,more severe partial overvoltages in some operating conditions will occur along the HWLT line.These voltage characteristics increase the complexity of voltage-regulation problems to some degree.

Automatic voltage control (AVC)is a representative voltage-regulation framework in modern power grids and has been shown to have superior control effect and robustness by engineering practices in many countries[16-18].Secondary voltage control (SVC)is a vital part of the hierarchical voltage-control structure and enables achievement of better voltage support through effective coordination between reactive power resources [19-20].Combined with HWLT systems,multiple technical issues need to be addressed in the steady-state voltage-control process.First,existing control strategies and objectives are not suitable for special characteristics of HWLT lines.Secondly,the remote geographical distance of HWLT lines causes a clear time delay or signal noise for control command communication.Thirdly,the stochasticity and volatility of wind power on the SE leads to fluctuations in power transmission,which may increase the partial overvoltage risk of HWLT lines.The main contributions of this study are as follows.

(1)The voltage-reactive power characteristics of the HWLT system have been detailed,and the complexity and particularity from a steady-state voltage-control perspective have been summarized.

(2)The HWLT line overvoltage risk-assessment function is deduced,considering large-scale wind-power transmission.More targeted voltage-control strategies will be employed based on different risk levels.

(3)An improved secondary voltage-control method is proposed herein.Considering the reactive powertransmission limits of the HWLT line,a multiobjective optimization model is developed.Independent control logic between the SE and RE without mutual communication is realized based on real-time electrical quantities of HWLT line terminals.

1 Reactive power-voltage characteristics of HWLT system

1.1 Mathematical description of HWLT system

The voltage and current profiles of a long transmission line can be expressed based on the distributed parameter model [12],given by (1).

where and respectively denote the voltage and current at x km from the RE,γ is the line propagation coefficient,and Zc is the line characteristic impedance.

Equation (1)shows that the voltage profiles are significantly affected by transmitted powers P2 and Q2.Consequently,a partial sustainable overvoltage may occur along a transmission line under specific load conditions.Taking a 1000 kV LGJ-8×500-type overhead transmission line as the test parameter [8],the maximum-voltage magnitudes with varying P2 or Q2 are presented in Fig.1.It can be observed that the maximum voltage typically increases with an increase in the active power.When Q2 = 0 and the active power exceeds the surge impedance loading (SIL),the peak voltage increases significantly,and conversely,when the active power is lower than SIL,there is no clear overvoltage.As Q2 increases,the curves tend to significantly increase.In summary,steady-state overvoltage results from an overload or a large reactive power transmission in the steady state.

Fig.1 Curves of the maximum voltage of HWLT line for different transmission powers

Based on (1),the maximum voltage along HWLT line Uline(P1,Q1,U1)and its location xmax can be deduced as follows:

Because of the reactive power self-balancing characteristic,the voltage-reactive power relationships between two terminals of the line are different from those of the short AC line.The SE voltage,U1,mirrors the RE voltage,U2,in magnitude under lossless hypothesis.There is no Ferranti effect in light-load operation,and no reactive compensation is required to balance the surplus reactive power along the HWLT line.However,in an actual project,the Joule losses are nonnegligible in a long transmission line,which introduces clear active power and voltage losses.

It can be concluded that the magnitude of voltage loss has a stronger correlation with active power than reactive power [21].To better describe this behavior,the variations in terminal voltages with transmitted power are presented in Fig.2.

Fig.2 Curves of voltage magnitudes of terminals for different transmission powers

The figure shows that the voltage loss increases with increase in P2 but varies slightly with Q2; the voltage loss is approximately proportional to P2.A clear voltage loss between the terminals of the HWLT line is observed in heavy-load conditions.

1.2 Difficulties encountered by HWLT system from a steady-state voltage-control perspective

The reactive power/voltage characteristics of HWLT systems are very different from those of conventional highvoltage AC transmission systems.The voltage-control difficulties can be summarized from three perspectives.

· The HWLT line itself neither absorbs nor generates reactive power at lossless hypothesis,but a large amount of reactive power transmission causes additional voltage fluctuations along the line.In certain operating conditions,local overvoltages cause insulation damage.Therefore,limiting the maximum voltage should be considered in steady-state voltage control,and restriction of the power factor should be regarded as an important control target.

· The voltage magnitude between the SE and RE presents a strong correlation.In the conventional zonedivision method,adjacent power grids should be classified in the same control zone based on the electric distance.In reality,in many countries such as China,the division of voltage-control zones is mainly based on administrative regions.Centralized control mode is not available for longdistance power-transmission systems,which may lead to control oscillations and reduce control reliability.

· In heavy-load conditions,there are clear voltagemagnitude differences between line terminals because of Joule losses.The normal operating voltages of load buses should be limited by a tolerance range to ensure security and stability of the power supply.The clear voltage loss decreases the feasible range and increases the difficulty of voltage regulation.The fluctuating power flow caused by sources of volatility,such as wind-power plants,further complicates the voltage control.

2 Half-wavelength line overvoltage riskassessment method considering largescale wind-power transmission

With an increasing installed capacity of wind-power plants,there are many scenarios involving the large-scale wind-power bases for long-distance transmission or bundled transmission with thermal power units in China [22-24].The stochasticity and volatility of wind power have significant effects on power-system security and stability [25-26].The uncertainty output on the SE leads to fluctuations in the transmission power,which increase the overvoltage risk of the HWLT line.The load fluctuation of the RE system can also affect the transmission power of HWLT line.The HWLT line overvoltage risk-assessment method is proposed herein,considering source-side and load-side uncertainty.

2.1 Wind-power probability-density function

When considering the real-time rolling solution of the HWLT line overvoltage risk,the time-series correlation of multi-period wind power should be utilized.In reference[27],the authors found that the t location-scale distribution is suitable for identifying the probability distribution of wind-power variations in the minute level.The t location scale can be acquired with appropriate displacement and expansion transformation of the t distribution.

where μw,σw,and v are the location,scale,and shape parameters,respectively.These parameters can be fitted based on the operating data of actual wind farms.

2.2 Load probability-density function

The Gaussian probability-distribution function has been used to describe the probability distribution of load uncertainty [28].The load active and reactive power probability models herein are given by (4).

where μP and σP are the mean and variance of the active power,respectively,and μQ and σQ are the mean and variance of the reactive power,respectively.

2.3 Overvoltage risk-assessment function of half-wavelength line

The samples of the bus voltage distributions can be obtained based on the probability power flow results calculated by the Monte Carlo simulation method.It is difficult to fit the obtained voltage-distribution samples with a certain probability model.Therefore,the use of a nonparametric estimation method of the kernel density estimation (KDE)is proposed.This method does not require prior knowledge of the data distributions and is employed to study the characteristics of the data samples themselves [29].The fitting function of the adopted KDE is as follows:

where xi is the ith fitting sample,n is the total number of samples,h is the fitting bandwidth,and K0 is the KDE function.

Typically,voltage distribution is continuous and smooth,which is suitable to be fitted according to the Gaussian kernel function.

where σk is the standard deviation of random variables,and is the expected value of random variables.

According to the maximum-voltage calculation function of the HWLT line,the maximum-voltage samples can be acquired.Then,based on equation (5)and (6),the approximate probability-density function,fvman(x),can be deduced,fitted by voltage data.Assuming that the maximum allowable voltage of an HWLT line is ,the overvoltage risk probability-calculation function is as follows:

The voltage-control models proposed in the next section will make adaptive adjustments according to overvoltage risk-assessment results.

3 Improved secondary voltage-control method

Based on the hierarchical voltage-control framework and considering the special characteristics of the HWLT line,an improved voltage-control method needs to be proposed.

3.1 Basic control logic

· Independent control mode.Based on the difference in the system structure and voltage sensitivity,the receiving and sending control zones will execute different control objectives.This control method maintains a high control reliability without a dependence on the remote communication of control signals.The basic control frame is shown in Fig.3.

Fig.3 Basic frame of independent control mode

The control objective of the RE zone is the same as that of a conventional SVC system.All reactive power compensation equipment in this zone is applied to track the pilot bus voltage reference value U2_ref to ensure the voltage quality of the loads.There is less load in the SE zone,where it can withstand greater voltage fluctuations.In order to avoid the control oscillations between two sides of the line,the SE zone will no longer have the voltage pilot bus.The maximum voltage value Uline(P1,Q1,U1)along the HWLT line can be calculated in real time by using the electrical quantities of line terminals,such as the voltage magnitudes and transmission power.When partial overvoltage occurs,the SE zone will adjust the reactive power output among different generators based on sensitivity information to restrict the reactive power transmission of HWLT line.It should be noted that the voltage level of the RE is determined by the pilot bus voltage reference,which is given by the prior voltage control level.If the SE units contain a large amount of fluctuating power sources such as wind power plants,it will cause obvious voltage fluctuations in the SE zone.Under this control mode,it is necessary to focus on the risk of wind power plant overvoltage tripping.Therefore,the voltage level of the pilot bus on the RE should not be too high,and overloads of the HWLT line should be avoided.

· Coordinated control mode.In the independent control mode above,the reactive power generators in the SE system only respond to the power factor adjustment of the HWLT line.It can be found that a large range of reactive power transmission is allowable without any overvoltage risk in light-load conditions of HWLT line.Because of the reactive power self-balancing characteristic,the reactive power at two terminals can maintain the same value.However,it should be noted that low-load operating conditions are not economical with a high power-loss rate.The power loss under different transmission conditions is detailed in Table 1,which suggests that if the active power is less than 2000 MW,the power-loss rate will clearly increase.If the active power exceeds 3000 MW,the power factor will be limited to prevent overvoltages.Considering both economy and voltage safety,the allowable reactive power range is-1500～+1500 Mvar when the active power-transmission range is 2000～3000 MW.Therefore,the coordinated control mode is proposed to maximize the use of the reactive power resources of the SE in specific operating conditions.The control frame of the coordinated control mode is shown in Fig.4.

Fig.4 Basic frame of the coordinated control mode

Table 1 Power loss under different transmission conditions

(P2,Q2)/MW,Mvar ΔP/MW ΔP/P1/% ΔQ/Mvar ΔQ/Q1/%(1000,0)229 18.7 3.49 —(1000,500)232 18.9 3.53 0.71(1000,1000)240 19.4 3.66 0.36(2000,0)266 11.7 4.05 —(2000,1000)276 12.1 4.22 0.42(2000,2000)308 13.4 4.71 0.23(3000,500)326 9.83 4.98 1.00(3000,1000)334 10.0 5.11 0.51(3000,1500)348 10.4 5.31 0.36

The main voltage-control objective of the RE zone is still tracing the pilot bus voltage as a reference.The SE control zone is used as a restricted reactive power source to participate in the voltage-control optimization calculation in the RE system.When the control signal is interrupted or the reactive power of the line exceeds the limit,the control mode will be automatically adjusted back to the independent control mode.The activation and switch conditions between two control modes will be further analyzed in the following section based on HWLT line overvoltage risk-assessment results.

3.2 Objectives and constraints

In this section,specific voltage control mathematical models under different operating conditions are given based on the overvoltage risk levels of HWLT line.For the entire SE and RE power grids,the purpose of implementing SVC is to prevent HWLT line overvoltage while maintaining the system voltage level within reasonable ranges.The proposed basic control principle is tracing the pilot bus voltage reference value in the RE system [30].With respect to the SE system,the main control objective is to adjust the power factor at the line terminal to avoid partial overvoltage.It should be noted that to facilitate the control of the power factor of the line terminal,the thermal power units in the SE system will operate in the constant power control mode,and the terminal voltage will become a free variable.It changes with the voltage level of the RE system and the active power transmitted by the HWLT line.The wind turbine units operate in constant power mode or constant power factor mode according to their own voltage regulation characteristics.In these control modes,the reference voltage value of the pilot bus should not be too high,which may lead to wind turbine tripping caused by overvoltage.Besides,reasonable reactive power distributions among generators can improve the power system security and reactive power utilization.Thus,another objective is to regulate the reactive power output of control generators distributed according to the rated value [31].

In order to adapt to the uncertainty of transmission power caused by strong fluctuation of energy sources,the voltage control mode and activating conditions are determined with reference to the overvoltage risk level of the HWLT line.The overall flow of the SVC of the HWLT system is shown in Fig.5.The overvoltage risk level is divided into three levels,and the control objective function and constraint conditions applied by the sending control zone and the receiving control zone are given as follows.

Fig.5 Overall flow of the SVC of the HWLT system

· Prisk = 0%.In this operating condition,the transmission line has no overvoltage risk.In independent control mode,the SVC in the SE zone will not be activated.With respect to the RE zone,supposing the reference value of pilot bus is U2ref,there are k generators applied in SVC and the variable parameters are terminal voltage of generators UG.The detailed objectives and constraints are listed as follows:

where ΔU2 is the voltage deviation of the pilot bus,ΔUG(i)is the terminal voltage adjustment value of generator i,ΔQR (i )is the reactive power deviation of generator i,Su (i)and Sqg(i )are the sensitivity matrixes of the terminal voltage of generator i to pilot bus voltage and reactive power output,respectively.All sensitivity information can be obtained using the perturbation method.

The constraints that are considered include primarily the reactive power limit of generators and the voltage limit of the pilot bus.U2min and U2max are the lower and upper voltage limits for the pilot bus,respectively,ΔUGmax(i ),QGmin(i ),and ΔQGmax(i)are the maximum adjustable voltage,minimum,and maximum reactive power generation of generator i,respectively.

When the reactive power resources of the RE zone are in short supply,the coordinated control mode can be activated,and the generators of the SE and RE can be applied to the control system simultaneously.Supposing there are k generators in the RE and p generators in the SE.The control variables are terminal voltages of generators.The objective function and constraint conditions of the coordinated control mode are shown as follows:

With the exception of the constraints mentioned in (11), and are respectively the lower and upper reactive power-transmission limits of the HWLT line.

· 0% ＜ Prisk ＜ 30%.In this level,the system has a certain risk of overvoltage.The objectives and constraints of the RE zone are the same according to equation (10)and (11).The objectives and constraints of the SE are listed as follows:

The variables that are not mentioned are defined below.ΔQline is the reactive power deviation of the terminal of the HWLT line,ΔQG (i )is the reactive power adjustment value of generator i,is the sensitivity matrixes of the reactive power output of generator i to the line terminal reactive power.

· Prisk ＞ 30%.There is a higher risk of overvoltage in this operating condition.The reactive power transmitted in the HWLT line should be strictly limited to 0 to lower the maximum-voltage value to the greatest extent.The objectives in the SE zone are:

If strict limitations on the reactive power transmission still cannot effectively reduce the risk of overvoltage,generator tripping in the SE should be activated to reduce active power along the HWLT line.

All of these voltage-control models can be solved using the linear goal programming method [8].

4 Case Study

In order to verify the effectiveness of the propose d voltage-control method for the “point-to-grid” HWLT transmission scenario including large-scale wind-power plants,a simulation calculation model is established based on the actual grid structure in East China,as shown in Fig.6.The SE system has a simple structure that is mainly composed of bundled wind power and thermal power plants,and the sending and receiving ends are connected through a 1000 kV UHV HWLT line.

Fig.6 The simulation secondary voltage-control zone of HWLT system

There are four 1000 MW thermal power plants in the RE control zone,and different wind-power penetration rates on the SE.The voltage-control measures include all generators and shunt capacitor/reactor banks in the control zone.Generator terminal voltages are allowed for the range of 0.9-1.1 p.u.; load bus voltages are allowed for the range of 0.95-1.05 p.u.,the sustaining overvoltage limit for HWLT line is 1200 kV.BUS_R is selected as the pilot buses.The SVC will be activated when the voltage deviation of the pilot bus with respect to the reference value exceeds 3 kV,or when the maximum-voltage profiles of the HWLT line exceed 1150 kV.For each wind farm,the output uncertainty is represented by the wind-power probability-density function,and the variables are μw = -7.4E-4,σw = 0.06,and v = 2.04.The time interval between two SVC processes is 10 s [32-33].

The power flow is obtained using the Matpower toolbox,and the optimizing calculation is solved using the LGP algorithm in MATLAB.

4.1 Control effects under different wind-power penetration conditions

In order to compare the control effects in different windpower penetration conditions,three simulation scenarios are established with penetration rates of 0%,40%,and 80%.The voltage pilot bus of the SE is BUS_R and the reference value is 0.98 p.u.Assuming that these three scenarios have the same initial state,the voltage of the pilot bus is Up = 0.949 p.u.,and the active power transmission of the HWLT line is 4750 MW; the maximum voltage along the HWLT line is UHWLT_max = 1175 kV.

Based on the probabilistic power flow calculation,the probability-density functions of HWLT line transmission power are shown in Fig.7.In contrast,with an increase in the wind-power penetration,the probability of extreme power fluctuations has increased sharply.The overvoltage risk for the three scenarios is 0%,1.6%,and 53.7%,respectively.The control objectives and constraints are according to the mathematical models of Prisk = 0%,0% ＜Prisk ＜ 30%,and Prisk ＞ 0%.

Fig.7 Probability-density function of transmission power considering different wind-power penetration rates

By applying the proposed SVC scheme,the voltage profiles along the HWLT line are shown in Fig.8.For the three different wind-power penetration scenarios,voltage fluctuations along the line have been significantly suppressed,and the peak voltage has been reduced from 1170 kV to 1086 kV.A comparison of control objectives results is shown in Table 2.The voltage deviation of the pilot bus has been limited within the allowable range,and the reactive power transmission of the HWLT line has been effectively suppressed.The generator’s adjustment operations of both the SE and RE are shown in Table 3.Simulation results show that considering the overvoltage risk of the HWLT line,the differentiated voltage-control models are more targeted.However,as the wind-power penetration rate increases,the effect of voltage regulation will decrease because the control capability of the windpower plants is ignored.As a result,for scenario 3,the control effects of the main objectives are worse than those of scenario 1 or scenario 2.Therefore,for a very intermittent energy system,the voltage support capabilities of wind turbines or photovoltaic power plants should be fully utilized.In addition,dynamic reactive power compensation equipment,such as synchronous compensators,can be considered to enhance voltage-control capabilities [34-35].

Fig.8 Comparison of control effects of voltage profiles along half-wavelength lines

Table 2 Comparison of control objectives in different scenarios

Reactive power of halfwavelength line/Mvar Initial state 0.031 872.8 Scenario 1 0.001 122.5 Scenario 2 0.001 49.6 Scenario 3 0.002 336.2 Voltage deviation of pilot bus/p.u.

Table 3 Voltage-control schemes in different scenarios.

Control schemes of generators/p.u.QG1 QG2 QG3 QG4 QG5 UG6 UG7 UG8 UG9 Initial state 674 674 769 417 417 1.00 1.00 1.00 1.00 Scenario 1 321 321 548 223 223 1.02 1.02 1.07 1.08 Scenario 2 89 — 270 — 135 1.02 1.02 1.03 1.05 Scenario 3 -327 — — — — 1.09 1.09 1.10 1.09

4.2 Control effects on a typical day

This section verifies the 15 min-level control effects of the proposed control method on a typical test day.The red curve in Fig.9 represents the power transmission demands through the HWLT line during the day.On this typical day,the thermal power units G2,G3,and G4 are applied to the operation.According to the wind power in the priority principle,the wind-power penetration rate of the SE system fluctuates within the range of 28%～100%,as shown by the dashed line in Fig.9.Owing to the fluctuations of transmission power and the changes of the wind-power penetration rate,the overvoltage risk is shown as the dotted line in Fig.10 in the time series.Control modes 1,2,and 3 respectively correspond to the mathematical models of Prisk= 0%,0% ＜ Prisk ＜ 30%,and Prisk ＞ 30%.After adopting the proposed SVC method,the maximum voltage of the HWLT line is limited within a reasonable range.As shown in Fig.11,the maximum line voltage of 1239 kV appears at 21:15,and it can be reduced to 1158 kV by applying reasonable control measures.The maximum voltages are still maintaining at high levels.Therefore,in certain operating conditions,the transmitted active power should be restricted to reduce overvoltage risks.

Fig.9 Transmission power fluctuations of HWLT lines in a single day

Fig.10 Overvoltage risk of half-wavelength line and its corresponding control modes

Fig.11 Maximum-voltage comparisons of HWLT line

5 Conclusion

An improved secondary voltage-control method is proposed herein to achieve suitable voltage regulation for large-scale wind-power transmission using a HWLT line.

(1)Independent control logic between SE and RE control zones without mutual communication is realized based on real-time electrical quantities of HWLT line terminals.SEs and REs of the HWLT line are divided into two separated control zones,which makes voltage control more reliable and effective.

(2)A multiobjective optimization model is utilized to limit the reactive power of the HWLT line and pilot bus voltage regulation.

(3)The HWLT line overvoltage risk-assessment method is deduced considering the stochasticity and volatility of wind power.Based on the overvoltage risk levels,more targeted voltage control modes and activating conditions are obtained.

The simulation results verify that the proposed voltage-control method can adapt to different wind-power penetration conditions.For the 15-min period,voltages of pilot buses can be regulated at acceptable levels,and the voltage profiles along the HWLT become flatter with lower overvoltage risk.

Acknowledgements

This work was supported by State Grid Corporation of China,Projects under Grant 520626200031 and National Natural Science Foundation of China,No.51877200.

Declaration of Competing Interest

We declare that we have no conflict of interest.