Cooperative Primary Frequency Regulation Strategy of Wind Storage System Based on Variable Inertia Coefficient

Direct-drive permanent magnet synchronous wind turbine-generator (PMSG) is connected to the grid through the rotor side and grid side converter. The rotor speed is decoupled from the grid frequency, so PMSG output power cannot respond to the change in system frequency. However, with the gradual increase of wind power penetration, the static stability of system frequency is weakened, so the new grid-connected wind farm should have the ability of active frequency support. This paper proposes a cooperative primary frequency regulation (PFR) strategy for wind storage systems based on variable inertia coefficient. PMSG provides inertia based on the distribution of rotational kinetic energy and modifies the polarity of the inertia coefficient at the frequency recovery stage to speed up the frequency recovery. Droop control is realized by energy storage and variable power tracking control (VPPT). Energy storage and VPPT respectively suppress the frequency decrease/increase and only participate in the down/up single-side PFR, which can reduce the energy storage configuration capacity. And a safety discharge coefficient considering the state of charge (SOC) is introduced to prevent over-discharge of energy storage devices when outputting energy. Finally, the PFR capability of PMSG under the proposed control strategy is verified by simulation results.


Introduction
In the face of increasingly prominent environmental pollution and energy shortage, wind power generation technology has been widely concerned by scholars because of its environment-friendly [1] .However, the Direct-drive permanent magnet synchronous wind turbine generator (PMSG) works in maximum power point tracking (MPPT) mode, and the rotor speed under decoupling control is not affected by the grid frequency.PMSG output power cannot respond to the change in system frequency.With the increase of wind power generation in the power grid, the total inertia of the system decreases, and the safe problem of the system frequency becomes more and more prominent.Therefore, more and more countries and power grid companies require that grid-connected wind farms should have active frequency support capability.
To endow the wind farm with frequency regulation capability, the current mainstream way is to build additional controllers for a frequency change, mainly including virtual inertia control (VIC), droop control (DC), and integrated control of additional energy storage.The VIC provides an inertia response for the system by controlling PMSG to simulate the inertia response of a traditional synchronous generator.The DC is used to reserve the mechanical reserve participating in the primary frequency regulation (PFR) in advance by de-loading.The integrated control of additional energy storage uses the fast charging and discharging capacity of the energy storage device to conduct PFR in conjunction with PMSG.
For VIC, in [2], the frequency deviation function is used as the additional torque set point of the wind turbine generator to couple the rotor speed with the power system frequency and improve the kinetic energy release capability.In [3], an additional controller with VIC and DC is added to the original MPPT control loop, which improves the inertia support capacity of the wind power system, but may cause the secondary frequency drop.In [4], it proposes a nonlinear virtual inertia controller based on the objective holographic feedback theory to avoid the secondary drop caused by traditional control but ignores the problem that excessive inertia support leads to the difficulty of a speedy recovery.And it also does not consider the different kinetic energy reserves caused by different rotor speeds under different wind speeds.
For DC, in [5], it proposes to use pitch angle control of PMSG to realize PFR, but the response speed is slow.And frequent adjustments will wear the mechanical components of PMSG, thus increasing the maintenance costs.In [6], it proposes the overspeed de-loading operation control method, which allows the wind turbine to reserve power in advance to participate in PFR.Although the method is effective, the regulation margin of overspeed de-loading is limited.And the adjustment speed of the pitch angle is slow, and there is mechanical loss.They all sacrifice the power generation efficiency of wind turbines.
Therefore, the integrated control of additional energy storage and wind turbines has been widely studied.In [7], combined with the advantages of more cycles of supercapacitors and high power density, the supercapacitor is configured in parallel to the DC bus of the wind turbine to provide inertia support.But the required capacity is large, and the economic cost is high.
Given the problems existing in the above research, this paper fully considers the rotor kinetic energy reserve at different rotor speeds and SOC of the stored energy, proposing a PFR strategy of PMSG with variable coefficient VIC.In the frequency support stage, energy storage and VPPT work together to reduce steady-state frequency deviation (SFD).Variable coefficient VIC is used to reduce the maximum frequency deviation (MFD).In the frequency recovery stage, modify the polarity of the inertia coefficient to help the system frequency recover quickly.In addition, the energy storage device only participates in single-side PFR, greatly reducing the energy storage configuration capacity and improving the operation economy.Finally, a four-machine two-area model is built in Matlab/Simulink.The simulation results show that its inertia support and frequency recovery are significantly improved compared with traditional VIC and DC.

Variable coefficient VIC
By increasing the number of poles, the wind wheel of PMSG is directly connected to the generator rotor without the gearbox, which improves the reliability of the wind turbine.It also makes the generator size of PMSG very large and the diameter of the blade very long.Therefore, much kinetic energy is stored in the rotating mass of the blades and generator rotors of PMSG, which can be used to simulate the inertia response of the synchronous generator.
When PMSG operates at the rotor speed of ω r , the rotor kinetic energy can be expressed as where J is the total rotational inertia of the PMSG generator and prime mover.When the electromagnetic torque T e and mechanical torque T m of PMSG are unbalanced, the rotor speed will change, and the rotor speed dynamics can be obtained as where D is the damping coefficient, and ω N is the rated rotor speed.When the rotor speed of PMSG changes from ω 1 to ω 2 , the released kinetic energy ΔE of the rotor is To prevent the rotor of PMSG from losing stability, the rotor speed of PMSG is limited to 0.7 p.u. ~ 1.2 p.u. From Equation (2), it can be calculated that one PMSG of rated capacity S N =1.5 MW, rated speed ω N =1.833 rad/s, total inertia J=4.853×10 6 kg•m 2 , working at rated speed ω N , the maximum kinetic energy of rotor can be released is 4.158 MJ.Supposing that PMSG continues to participate in the inertia support at 10% of the rated capacity, the inertia support time Δt of PMSG working at the rated speed can be calculated is where P N is the rated electromagnetic power of PMSG, and P e is the electromagnetic power output at time t.From Equation ( 4), the maximum inertia support time of PMSG can reach 4.73 s.It can be seen that using the rotor kinetic energy stored in the wind wheel and rotor to provide inertia support can supply short-term and rapid frequency support at the beginning of frequency change.It can effectively reduce the MFD of the system and improve the transient stability of the system frequency.
Simulate the inertia characteristics of the synchronous generator.The control principle of PMSG based on VIC is shown in  PMSG works in MPPT mode without disturbance.When the frequency suddenly changes due to the source or load disturbance, VIC responds to the change rate of frequency and outputs the inertia support power ΔP 1 to participate in frequency regulation, which can be calculated as where K d is the inertia coefficient, which can reflect the equivalent inertia of the system.With the increase of K d , the equivalent inertia of the system will increase, the frequency change will slow down, and MFD will decrease.But the high-frequency oscillation will intensify.Therefore, the frequency measured by the phase-locked loop is usually processed by low-pass filtering and then output to the VIC part.In traditional VIC, K d is constant.However, PMSG works in unpredictable and fluctuating wind speed environments.Under MPPT control, the rotor speed of PMSG is constantly changing, and the rotor kinetic energy is also different.Therefore, the inertia support capacity of PMSG in the face of the same frequency change is different.From Equation (5), PMSG is required to provide the same inertia support power at different rotor speeds.So PMSG with too high (too low) rotor speed may be unstable when the system frequency increases (decreases) due to providing too large inertia support.
Therefore, to solve the above problem, a variable coefficient K considering the rotor speed of PMSG itself is introduced.K is equal to the ratio of the current rotor kinetic energy of PMSG to the rotor kinetic energy at the rated speed, which can be expressed as The optimized inertia support power is When PMSG works normally, the safe range of rotor speed is 0.7 p.u.~1.2 p.u.When the rotor speed is lower than 0.7 p.u. (higher than 1.2 p.u.), to prevent the rotor speed of PMSG from exceeding the limit to lose stability.PMSG should be prevented from releasing (absorbing) the rotor kinetic energy to participate in the inertia support by controlling K is 0.
At the initial stage of frequency change, VIC can suppress the frequency change.Extending the inertia support time can reduce the system frequency change rate and MFD.However, if the inertia support time is too long, it will hinder the system frequency recovery.Therefore, when the polarity of the frequency differential is detected to change, the polarity of K is also changed to speed up the frequency recovery, thus improving the frequency performance of the system.
When the frequency disturbance exceeds the frequency regulation threshold of 0.03 Hz, first detect the increase or decrease of frequency and then detect the rotor speed.Take the system frequency rise detected as an example.If the rotor speed ω r > 1.2 p.u., to prevent the rotor speed from rising to lose stability, control K=0, namely ΔP 1 =0, PMSG does not participate in inertia support.If the rotor speed ω r ≤ 1.2 p.u., output ΔP 1 is shown in Equation (7), and the polarity of K is changed at the same time when the polarity of frequency differential is detected to change.The whole variable coefficient VIC scheme is shown in

DC-based on the energy storage device and VPPT
VIC of PMSG can only provide short-term frequency support.Therefore, it is necessary to introduce DC to reduce the SFD of the system.The DC can be expressed as where ΔP 2 is the additional power of DC, K p is the droop coefficient, and Δf is the frequency deviation.
Combining Equations ( 7) and ( 8), the additional power provided by the integrated VIC and DC of PMSG participation in PFR is The additional power ΔP 2 of DC is generally supported by the de-loading reserve power of PMSG and the support power of the additional energy storage device.However, the traditional de-loading reserve requires PMSG to work in the de-loading mode, which reduces the wind energy utilization rate.Therefore, in this paper, additional energy storage devices and VPPT are utilized to participate in the PFR of PMSG. 1) When there is no disturbance, PMSG works in MPPT mode to maximize the utilization of wind energy.According to "The Test Method of Wind Turbine Generator," the frequency regulation dead band of PMSG is set as 0.03 Hz, and the PFR time is not more than 30 s.Moreover, the VIC and DC of PMSG simultaneously participated in PFR.
2) When the system frequency is detected to rise, PMSG participates in PFR through VPPT.In this case, the output electromagnetic power of PMSG is controlled from P MPPT to P VPPT , and electromagnetic torque T e is controlled to decrease.When the mechanical separator torque T m is greater than the electromagnetic torque T e , the rotor speed of PMSG will increase until the torque reaches balance again based on equation (2).The VPPT can be obtained as VPPT MPPT 2 MPPT p where P VPPT is the de-loading tracking power, and P MPPT is the maximum tracking power shown in Figure 3.

MPPT curve
VPPT curve Variable power tracking control principle 3) when the system frequency is detected as falling, PMSG works in MPPT mode, where is no standby power to participate in PFR.It needs to introduce an energy storage device to provide power support.Taking advantage of the modular function and fast charging/discharging characteristics of the supercapacitor, the supercapacitor is selected as the energy storage device in this paper.From Figure 4, the supercapacitor transmits active power to the grid side through the DC-DC converter in parallel at the side of the DC bus of the grid-connected PMSG.In case of lasting disturbance, due to the limited capacity of supercapacitors, to prevent the supercapacitors from continuously outputting energy with a large droop coefficient in DC equation ( 8), causing the problem of out-of-limit SOC, this paper proposes a dynamic discharge strategy of PMSG based on energy storage devices, that is, introducing a safety discharge coefficient K SC .As shown in Figure 5, When the SOC of the supercapacitor is low, K SC can dynamically adjust the active power output of the supercapacitor, which can avoid the over-discharge problem and improve the service life.And supercapacitor SOC is divided into discharge frequency regulation region and forbidden region.The discharge frequency regulation region is further divided into unconstrained discharge region and constrained discharge region.The dynamic discharge strategy is shown as follows.

Relationship between safety discharge coefficient and SOC
Combining Equation ( 8), the output active power P SC of PMSG, which is based on a supercapacitor with DC participation in PFR is The PFR strategy of PMSG based on variable coefficient VIC and coordinated control of energy storage and VPPT is shown in Figure 6.

Capacity configuration of supercapacitors
As mentioned above, when the energy storage is equipped to participate in the PFR of PMSG, it is necessary to reasonably configure the supercapacitor module to achieve economic operation.
According to [8], the discharge efficiency of a supercapacitor is 1) where R is the supercapacitor internal resistance, P d is the charging efficiency, γ = U min / U max is the voltage ratio, and U max is the maximum working voltage.The voltage of a single capacitor is about 2.5 V. Therefore, the maximum output power of a supercapacitor module composed of m groups in series and n groups in parallel is In traditional PFR strategy, the energy storage device can provide 30 s power support at a maximum of 10% of the rated power of PMSG.Combined with Equations ( 11) and ( 12), the actual output power of the supercapacitor considering SOC will be reduced.A 5 MW PMSG should be equipped with a capacity of (500×75%) kW × 30 s super capacitor module.

Simulation model
To verify the effectiveness of the cooperative PFR strategy of wind storage system based on variable inertia coefficient, this paper builds a four-machine two-area simulation model, as shown in Figure 7. Simulation model of four-machine two-region with PMSG wind farm G1, G2, and G3 are three thermal power plants with a capacity of 600 MW, which are equipped with the governor and have a PFR function.G4 is composed of 100 PMSG with a capacity of 5 MW, each of which is equipped with an energy storage device.L2 and L3 are, respectively, 900MW and 1,000 MW constant active loads.L1 is a 100 MW switchable load.The wind power penetration rate of the four-machine two-area system is about 21.7%.

Simulation analysis
To verify the effectiveness of the proposed strategy, this paper will observe the control effect in three modes: MPPT mode, traditional VIC and DC, and proposed control.At 10 s, the load is suddenly increased by 100 MW, and the dynamic response of system frequency and PMSG under each control mode is analyzed, as shown in Figure 8.As shown in Figure 8 (a), the MFD and SFD of the system have been effectively improved under the proposed strategy.The proposed variable coefficient VIC responds to the system frequency and rotor speed.Compared with the traditional VIC, it can not only release more rotor kinetic energy when the rotor speed is higher but also continue the short-term inertia support when the system frequency rises, accelerating frequency recovery speed (FRS) and improving the frequency dynamics.Specific indicators of response frequency MFD, SFD, and FRS are shown in Table 1.  9, Because of the introduction of the safety discharge coefficient K SC , when the supercapacitor SOC decreases to 40% at time t 2 , according to Equation (11), the output power will decrease.When the SOC drops to 10% at t 3 , to prevent out-of-limit SOC, the output power of the supercapacitor is controlled to be 0. Similarly, the system load suddenly decreases by 100 MW in 20 s, and the dynamic response of system frequency and PMSG are shown in Figure 10.Under

Conclusion
This paper proposes a cooperative PFR strategy for wind storage systems based on variable inertia coefficient, which can improve the frequency static stability of the power system and the economy of PMSG participating in PFR.
(1) Variable coefficient VIC is proposed considering the distribution of rotor kinetic energy in this paper.It introduces the ratio coefficient K of rotor kinetic energy to optimize the inertia support power provided by rotor kinetic energy.At the frequency recovery stage, where the frequency differential is 0, the FRS is accelerated, and the frequency response is optimized by changing the polarity of the inertia coefficient.
(2) The DC is composed of VPPT and a supercapacitor.The supercapacitor only participates in the lower single-side PFR when the frequency drops, which can reduce the energy storage configuration capacity and improve the frequency regulation economy.To prevent capacitor over-discharge, the safe discharge coefficient K SC considering SOC is introduced into the energy storage output part.
(3) The cooperative PFR strategy of the wind storage system based on the variable inertia coefficient proposed in this paper reduces the SFD from 0.09 Hz under MPPT control to 0.07 Hz, which decreases by 22.2%.The MFD decreased from 0.260 Hz to 0.116 Hz, reducing by 55.4%.The FRS has also been effectively improved.The above results verify the effectiveness of the proposed strategy.

Figure 1 .
Figure 1.Control principle of PMSG based on VIC.

Figure 7 ,
based on the Matlab/Simulink simulation platform.

Figure 8 .
Figure 8.Comparison of system frequency dynamic response when the load suddenly increases

Table 1 .
System frequency response index in case of sudden load increase

Table 2 .
VPPT, PMSG can reduce the output active power through rotor acceleration to suppress the frequency fluctuation and participate in PFR through integrated variable coefficient VIC.Comparison of system frequency dynamic response when the load suddenly decreases Compared with the MPPT mode, the MFD and SFD of the system under the proposed control are reduced by 56.0% and 33.3% respectively shown in Table2Compared with Traditional VIC and DC, FRS has been effectively improved.System frequency response index in case of sudden load decrease