In this paper, a hybrid energy storage device combining battery and supercapacitor is used to extend the service life of the energy storage device and realize the efficient use of its capacity. The charge and discharge limits of supercapacitors are set to 20% and 80%, and the battery in hybrid energy storage equipment can participate in power balance when the state of charge is 10%–90%. If there here are only batteries in the grid, it is also possible to use only one form of energy storage to achieve the expected control goals.

The electronic power converters equipped with HESDs have great potential for power regulation. Although the active and reactive powers can be regulated independently by vector control, the HESDs still cannot provide power support due to the decoupled operation between the HESDs and SGs. The inherent inertia of SGs is useful for reducing the rate of change of system frequency by absorbing or releasing the kinetic energy stored in the rotating rotor. Thus, A new frequency-coupled relationship should be established between the HESDs and SGs to provide effective power support.

The static energy stored in the battery can be regarded as a new energy source of virtual inertia. The state of charge (SOC) γ _SOC of the battery is defined as γ S O C = Q B − ∫ i B d t Q B (1) where Q _B and i _B are the capacity, and output current of the battery, respectively. The static energy W _B stored in the battery can be expressed as W B = ∫ u B i B d t = u B Q B γ s o c − 0 (2) where u _B is the output voltage of the battery, and γ _SOC-0 is the initial value of γ _SOC.

From (2), the expression of W _B can be transformed as follows: W B = ∫ u B i B d t ω e d ω e / p n 2 ω e p n 2 d ω e = ∫ p n 2 u B Q B d 1 − γ S O C ω e d ω e ω e p n 2 d ω e (3)

In transient events, the SGs regulate kinetic energy to provide frequency support. Thus, the SGs are coupled with one another by the system frequency. It is worth noting that the kinetic energy E _k is determined by the inherent inertia, which can be expressed as follows: E k = ∫ 1 p n 2 J S ω e d ω e = 1 2 p n 2 J S ω e 2 (4) where J _S, p _n, and ω _e are the inherent inertia, pole pairs, and angular velocity of the SG, respectively.

According to (4), W _B can be converted into kinetic energy, which is given by W B = ∫ J B V ω e p n 2 d ω e = E k B (5) where J _BV and E _kB are the virtual inertia and virtual kinetic energy of the battery, respectively.

The conversion relationship between the static energy of the battery and the kinetic energy of the SG is established by (5). The virtual inertia J _BV of the battery can be further expressed as J B V = ω e Δ γ S O C γ S O C _ 0 ω S u B Q B γ s o c − 0 ω e 2 = J S k B E k B 2 E k (6) where ω _S is the variation of system angular velocity ω _e, ∆γ _SOC is the variation of γ _SOC, γ _SOC-0 is the initial state value of γ _SOC, and k _B = ω _e∆γ _SOC /(γ _SOC-₀ ω _S) is defined as the SOC adjustment coefficient of battery.

In HESD, the static energy stored is stored in the super capacitor can also be utilized to provide the virtual inertia response. The SOC ρ _SOC of the super capacitor is defined as ρ S O C = Q C − ∫ C d u C Q C (7) where Q _C and u _C are the capacity and output voltage of the super capacitor, respectively.

The static energy W _C stored in the super capacitor can be expressed as W C = ∫ C u C d u C = u C Q C ρ S O C − 0 (8) where ρ _SOC-0 is the initial value of ρ _SOC, and C is the capacitance of the super capacitor. The expression of W _C given in (8) can be transformed as follows: W C = ∫ C u C d u C ω e d ω e / p n 2 ω e p n 2 d ω e = ∫ p n 2 u C Q C d 1 − ρ S O C ω e d ω e ω e p n 2 d ω e (9)

According to (4), the static energy W _C can be converted into kinetic energy, which is given as follows: W C = ∫ J C V ω e p n 2 d ω e = E k C (10) where J _CV and E _kC are the virtual inertia and virtual kinetic energy of the super capacitor, respectively.

The conversion relationship between the static energy of the super capacitor and the kinetic energy of the SG is given by (10). The virtual inertia J _CV of the super capacitor can be further expressed as J C V = ω e Δ ρ S O C ρ S O C _ 0 ω S u C Q C ρ S O C _ 0 ω e 2 = J S k C E k C 2 E k (11) where ∆ρ _SOC is the variation of ρ _SOC, ρ _SOC-0 is the initial state value of ρ _SOC, and k _C = ω _e∆ρ _SOC/(ρ _SOC-₀ ω _S ) is defined as the SOC adjustment coefficient of the super capacitor.

The virtual inertia of the HESD, which is composed of a battery and a super capacitor, is given by J H V = J B V + J C V = J S E k B k B + E k C k C 2 E k (12)

Referring to the concept of inertia time constant of SGs, the virtual inertia time constant H _HV of the HESD can be defined as follows: H H V = J H V ω e 2 / 2 p n 2 S H (13) where S _H is the rated capacity of the HESD.

According to (12) and (13), the virtual inertia of the HESD is no longer constant and is mainly determined by the coefficients k _B and k _C. It can be found from Eqs 5, 10 that the static energy of the battery and super capacitor can be utilized for frequency support in the form of virtual kinetic energy. In theory, the virtual inertia couples the HESD with the system frequency by releasing or absorbing the virtual kinetic energy.

During the initial transient period, the system frequency change can be reduced with the increase of system inertia. However, subsequently, a larger inertia still prevents the frequency from recovering to the normal value, and as a result, the recovery time is increased. Moreover, the slower attenuation of the rotor angle of the SG causes it to oscillate unnecessarily.

The oscillation process of angular velocity and rotor angle of a SG after the application of a perturbation is shown in Figure 3. The oscillation period can be divided into two stages: 1) Phase A with ω _S = ω _e-ω ₀>0 and dδ/dt > 0, 2) Phase B with ω _S = ω _e -ω ₀<0 and dδ/dt < 0. As Figure 3 shows, the rotor angle δ increases during phase A. Increased inertia is useful for reducing the deviation of the rotor angle, and the system stability can be enhanced. However, if the power system enters phase B, the fixed inertia will prevent the rotor angle from going back to the initial value, resulting in a continuous oscillation.

To address this issue, the virtual inertia is regulated in the proposed control scheme to transfer the transient energy from the SGs to HESDs during different oscillation stages of the rotor angle. The energy transfer controller of the frequency-coupled HESD is designed as P v = H v ω S d ω S d t 2 (23) where H _v is the inertia coefficient of HESD with H _v>0, and ω _S is the angular velocity deviation.

Under the proposed control scheme, the rotor motion equation of the power system can be expressed as follows: H S d ω S d t = P m − P e − P v − D S ω S (24)

Substituting (23) into (24), we get H v ω S d ω S d t 2 + H S d ω S d t = P m − P e − D S ω S (25)

Using the small disturbance analysis method, the linear equation is obtained as H S + 2 H v ω S 0 ⋅ d Δ ω S d t + D S + H v d ω S 0 d t 2 ⋅ Δ ω S = Δ P (26)

The eigenequation of the system is obtained as H S + H A d 2 δ d t 2 + D S + D A d δ d t = Δ P (27) where H _A = 2H _v ω _s0 is the inertia of the additional controller, and D _A = H _v(dω _s0 /dt)² is the damping of the controller.

During phase A, ω _s0 > 0, and thus the positive inertia is provided by the proposed controller. The rotor angle will change slowly with the addition of virtual inertia. However, during phase B, ω _s0 < 0, the virtual inertia is negative, and thus the rotor angle recovers quickly due to the decrease of system inertia. This new dynamic performance of the rotor angle is desirable for achieving system stability. In addition, the damping coefficient D _A of the proposed controller is always positive. Thus, the controller can contribute to the improvement of the system damping characteristics.

To further verify the positive impact of the proposed control scheme on the system transient stability, the transient energy transfer between the SGs and HESDs is analyzed using the Lyapunov direct method. Figure 3 shows that both angular velocity ω _e and rotor angle δ increase during phase A. If the fault is cleared in time at point c, the rotor angular velocity ω starts to decrease. However, it is still higher than the initial velocity ω ₀, and thus the rotor angle continues to increase. During phase B, both the angular velocity ω and rotor angle δ decrease before ω _e returns to its initial value. After crossing the point k, ω _e increases. However, δ decreases until ω returns to its initial value again.

The analysis of the dynamic performance of the rotor angle under the proposed control shows that a slower change and faster recovery of the rotor angle can be achieved during phases A and B, respectively. Obviously, during phase B, lower inertia will accelerate the recovery of the rotor angle. However, the oscillation amplitude and time increase during phase A due to the higher inertia. Therefore, it is imperative to analyze the transient energy change that takes place during phase A.

According to (24), under the proposed control scheme and ignoring the system damping, the transient energy of the power system can be expressed as E = E S + E H (28) where E _S is the inherent energy of SGs, E _H is the additional energy generated by the energy transfer controller. E S = ∫ δ 0 δ c P m − P e 2 d δ + ∫ δ k δ t P e 3 − P m d δ (29) E H = ∫ δ 0 δ c − P v d δ + ∫ δ k δ t P v d δ (30) where δ ₀ is the initial value of the rotor angle, δ _c and δ _t are the rotor angles at fault clearing time and time t, respectively, δ _k is the rotor angle at the stable equilibrium point, and P _e2 and P _e3 are the electromagnetic powers before and after the fault is cleared, respectively.

According to (28), under the proposed control scheme, the system transient energy is composed of the inherent energy of the SGs and the additional energy generated by the energy transfer controller.

(1) During the fault period, the angular velocity and rotor angle are in the intervals [ω ₀,ω _c] and [δ ₀,δ _c], respectively. In this period, the additional energy E _HA generated by the energy transfer controller can be expressed as E H A = ∫ δ 0 δ c − H v ω S d ω S d t 2 d δ = − H v ∫ 0 ω c − ω 0 ω S 2 d ω S d ω S d t = − H v 3 ω c − ω 0 3 ⋅ d ω S d t (31)

During this accumulation phase of acceleration energy, the angular velocity increases, i.e (ω _c-ω ₀)³ > 0, and dω _S/dt>0. Consequently, the acceleration energy generated by the energy transfer controller satisfies E _HA<0. Therefore, the energy transfer control can transfer the acceleration energy from the SG to the HESD and reduce the accumulation of acceleration energy.

(2) After the fault is cleared, the angular velocity and rotor angle are in the intervals [ω _c,ω _f] and [δ _c,δ _f], respectively. In this period, the additional energy E _HD generated by the energy transfer controller can be expressed as follows: E H D = ∫ δ c δ f H v ω S d ω S d t 2 d δ = H v ∫ ω c − ω 0 ω f − ω 0 ω S 2 d ω S d ω S d t = H v 3 ω f − ω 0 3 − ω c − ω 0 3 ⋅ d ω S d t (32)

During this transformation stage of deceleration energy, the angular velocity decreases, i.e (ω _f-ω ₀)³-(ω _c-ω ₀)³ < 0, and dω _S/dt < 0. Consequently, the deceleration energy generated by the energy transfer controller satisfies E _HD>0. Therefore, the HESD can be used to provide energy support and increase the conversion of deceleration energy under the energy transfer control.

It is obvious that under the proposed control strategy, the accumulation of acceleration energy decreases and the transformation of deceleration energy increases throughout phase A. According to the Lyapunov method, both the oscillation amplitude and time of the rotor angle can be reduced by sharing the transient energy between the SG and HESD. Thus, a stronger stability of the rotor angle can be achieved, thanks to the more efficient power control.

According to (6) and (11), the energy variation of HESD can be expressed as Δ E k B + Δ E k C = 1 2 p n 2 J B V ω S 2 + 1 2 p n 2 J C V ω S 2 (33)

The energy variation generated by energy transfer controller can be expressed as follows: Δ E H = ∫ H v ω S d ω S d t 2 d δ (34)

The relationship between virtual inertia of HESD and H _v can be expressed as 1 2 p n 2 J B V + J C V ω S 2 = ∫ H v ω S d ω S d t 2 d δ (35) H v = 3 J B V + J C V 2 ω S d ω S / d t (36)

The structure of the HESD transient energy transfer controller is shown in Figure 4, in the control system, the variable u _pv and i _pv are the reference voltage and reference current of the photovoltaic respectively; u _abc* is the three-phase reference voltage for DC/AC converter pulse width modulation; u _dc* and u _dc are DC reference voltage and output voltage of DC/AC converter; i _d* and i _q* are the reference current of the d and q axes of the DC/AC converter respectively; P _ES is the output power reference value of the HESD; i _C is the output current of the supercapacitor; i _B and i _C are the current reference value of the storage battery and the supercapacitor respectively. As shown, four modules are added to the control system of HESD. According to (36), the virtual inertia of the battery and super capacitor is calculated to set the energy transfer control parameter H _v. The angular velocity signal is introduced to calculate the output power of the proposed controller P _v. After the fluctuation of PV is suppressed, the surplus power P _ES is then sent to the power distribution module. The inertia support is provided by the super capacitor at first after the power reference instruction is received. The remaining power difference (P _v–P _C) is compensated by the energy stored in the battery to obtain the desired inertia response. The power provided by PV and HESD (P _pv + P _ES) flows into AC power grid through DC/AC converter, in which the voltage and current dual closed-loop control is adopted.

Differential control is easy to generate high-frequency signals, resulting in a decrease in frequency quality and an increase in the probability of miss operation of the additional controller. Therefore, a first-order low-pass filter is set in the angular velocity detection link to filter out the high-frequency signal and eliminate its influence on the system frequency.

To demonstrate the effectiveness of the proposed control scheme, a test system is carried out, of which structure in shown in Figure 5. In the test system, the SGs and PV arrays are rated at 160 kVA and 100 kW, respectively. The HESD consists of a battery and a super-capacitor with capacities of 50 Ah and 10 F, respectively. The PV array and HESD were connected to the grid through bus B₇, with loads L₁ and L₂ of 150 kW and 100 kW, respectively. The solar irradiance was set to 1000 W/m².

To illustrate the impact of energy transfer between the SGs and HESD on the system transient stability, the following three cases are considered. 1) Case A: without any additional control scheme. 2) Case B: VSG control scheme Ref. (Torres et al., 2014). 3) Case C: under the proposed control scheme in Figure 5 (k _B = 0.1, k _C = 0.2, H _v = 5.6).

Due to the duration of common power disturbances, such as generator cut-off, high-power load switching, and other events, is much longer than the time required for inertial support. Therefore, this paper treats ΔP _d as a step signal, and conservatively evaluates controller performance regardless of the disturbance duration. To illustrate the performance of the proposed control scheme for system frequency, load L₁ is increased by 50 kW at 18s. Experimental results of the system frequency f, output active power P _G of SG₁, and output active power P _E of HESD in cases A-C are compared in Figures 6A–C. In the simulation model, the synchronous generator contains primary and secondary frequency regulation modules, which are close to the frequency regulation mode of the actual power grid. Among them, the primary frequency adjustment is differential regulation, and the secondary frequency adjustment is non-differential regulation. When the synchronous generator starts the secondary frequency regulation, the frequency of the system under situation A-C can be restored to 50 Hz.

In case A, the system frequency performance during the initial period mainly depends on the inherent inertia of the SGs. However, among all three cases, the largest frequency drop of around 0.5 Hz is observed for Case A due to the lowest inertia, as shown in Figure 6A. Since the synchronous generator equips a secondary frequency regulator in the simulation system, which contains the PI controller. Thus, in the dynamic process, the inevitable overshoot of the system frequency can be observed. In all three cases, the overshoot of case A was observed to be the largest since case A had the lowest damping.

In case B, virtual inertia is provided by the HESD under the VSG by detecting the frequency variation. As shown, the frequency deviation is reduced to around 0.25 Hz. Before the system frequency drops to its minimum value, the positive power support is generated by the VSG, and thus the rate of change of system frequency is reduced with the addition of virtual inertia. However, once the system frequency begins to recover, the HESD still prevents the frequency from going back to its normal value, and the active power generated by the VSG is negative for the increased load. Thus, a slower system frequency recovery is observed.

In case C, under the proposed control scheme, the rate of change of the frequency drop is reduced similar to that in case B. More importantly, the best system frequency recovery performance is attained because the HESD always maintains a positive power support to share the load demand with the SGs. Thus, the recovery period of system frequency is the shortest for case C among all three cases.

(a) Case A: without additional control (b) Case B: VSG control (c) Case C: under the proposed control

To illustrate the performance of the proposed control scheme on system damping, a 0.1s three phase short-circuit fault is applied on bus B₉ at 18s. The experimental results of the rotor angle δ, system frequency f, angular velocity ω, tie-line transmission power P _T, output active power P _E and output active power P _G of SG1 for cases A–C are compared in Figures 7A–C.

As Figure 7A shows, a continuous rotor angle oscillation can be observed in the absence of any additional control. Although the power system stabilizers are applied to the SGs in the test system, the system damping is still insufficient. In the test system with a high penetration of PV generation, there is still a lack of regulators. Obviously, the ability of HESDs to dampen the oscillation is important.

However, in case B, the virtual inertia is provided by the HESD. Although the frequency stability can be improved as verified in Section 5.2 (case B), an unexpected rotor angle oscillation is likely to be caused by the addition of virtual inertia. As Figure 7B shows, the maximum swing amplitude of the rotor angle is increased from 5.2° to 7.25°. Compared with case A, a more serious oscillation of the rotor angle is observed. Moreover, it is harder for the SGs to damp the oscillations of ω, P _T and P _G. The main reason for this phenomenon is that during different oscillation phases of the rotor angle, the frequency coupled HESD with a constant inertia produces a negative damping effect.

In case C, as Figure 7C illustrates, the oscillation amplitude of δ is reduced to around 2.75°, and the oscillation durations of δ, ω, P _T and P _G are shortened to 3.2 s. Obviously, the proposed control scheme improves the system transient stability. The test results demonstrate that the transient energy transfer between the SGs and HESD is beneficial for increasing the system damping.