A typical two-region model load frequency control is studied as an example, and a two-region grid frequency dynamic response model with energy storage involved in secondary frequency regulation is established based on the regional equivalence approach [19]. The model is shown in Fig. 1, and the parameters in the model are defined as shown in Table 1.

The model consists of a dispatch centre and a control unit for FM power supplies to enable primary and secondary FM. Area 1 is configured with 1 conventional unit and k BESS for FM, for a total of 1 + k FM power supplies, while area 2 is configured with only conventional units to achieve FM.

The conventional unit is a reheat-type thermal power unit and the model mainly consists of a governor and a reheat-type turbine. The reheat-type thermal power unit model is shown in Fig. 2a.

The functional expression for the model is as follows:

(1)Gov_H(s)=ΔYΔf=11+sTG

(2)Gov_RT(s)=ΔPGΔY=FHP(1+sTCH)(1+sTRH)+FIP(1+sTCO)+FLP(1+sTCH)(1+sTRH)(1+sTCO)

(3)Ggi(s)=Gov_H(s)×Gov_RT(s)where, Δf is the system frequency deviation, ΔY is the change in turbine steam valve opening, ΔP_G is the change in turbine output power, G_gi(s) is the reheat thermal unit transfer function, Gov_−H(s) is the governor transfer function, Gov_−RT(s) is the turbine transfer function, T_CH, T_RH and T_CO are the high-pressure steam volume time constants, reheat steam volume time constants and low-pressure steam volume time constants, respectively. F_HP, F_IP and F_LP are the power coefficients of the high-pressure, medium-pressure and low-pressure cylinders, respectively.

The battery energy storage system is based on a first-order inertia model, which takes into account the charge state constraints of the system and can accurately simulate the dynamic characteristics of the energy storage system and the grid in the active exchange state. The model is shown in Fig. 2b.

In Fig. 2b: K_B is the output gain, T_B is the energy storage time constant, S_n is the rated capacity of the energy storage, SOC₀ is the initial state of charge, and ΔP_Bj(s) is the FM output of the energy storage system.

The functional expression for the model is as follows:

(4)GBj(s)=KB1+sTBwhere, G_Bj(s) is the transfer function of the battery storage system.

To prevent excessive power throughput range of the energy storage system, the range of SOC is constrained to be within the range of safe battery operation from the perspective of battery life, i.e.,

(5)QSOC min≤QSOC≤QSOC max

The two modes of signal assignment for BESS participation in AGC FM are Area Control Requirement (ARR) based signal assignment and Area Control Deviation (ACE) based signal assignment [20]. The two signals can be converted by a PI controller, i.e., by integrating the Area Control Deviation (ACE) signal the Area Control Requirement (ARR) signal is obtained.

As shown in Figs. 3a and 3b, the participation factor α (taking values in the range 0.1–0.9) determines the power output allocation of the two FM sources (conventional units and energy storage batteries) to the ACE or ARR signals; ΔPg_i(s) and ΔP_bj(s) determine the depth of power output after the allocation of the ACE or ARR signals; ACE(s) and ARR(s) are the signal inputs for the two control methods.

Ignoring the FM Deadband and limiting constraints, from Fig. 3a we have

(6)ACE(s)=−β1Δf1(s)

(7)Δf1(s)=ΔPG1(s)+ΔPF1(s)+∑j=1kΔPB1(s)−ΔPL1(s)Ms+D

(8){ΔPF1(s)=−K1Gg1(s)Δf1(s)ΔPG1(s)=(KP1+KI1s)ΔPg1(s)Gg1(s)∑j=1kΔPB1(s)=∑j=1kΔPbj(s)Gbj(s)

(9){ΔPg1(s)=αACE(s)∑j=1kΔPbj(s)=(1−α)ACE(s)

Of these, the models for reheat thermal units and energy storage batteries are

(10){Gg1(s)=FHP(1+sTCH)(1+sTRH)+FIP(1+sTCO)+FLP(1+sTCH)(1+sTRH)(1+sTCO)(1+sTG)GBj(s)=KB1+sTB

Rectifying Eqs. (6)–(10) yields the final expression for the ACE signal as

(11)ACE(s)=ΔPL(s)⋅βMs+D+K1Gg1(s)+αβ[(KP1+KI1s)Gg1(s)−∑j=1kGBj(s)]+β∑j=1kGBj(s)

As can be seen from Eq. (7), the ACE signal is not delayed without a PI control link, so the system can respond quickly to transient changes in the signal.

Similarly, from Fig. 3b, it follows that:

(12)ARR(s)=−β1(KP1+KI1s)Δf1(s)

(13)Δf1(s)=ΔPG1(s)+ΔPF1(s)+∑j=1kΔPB1(s)−ΔPL1(s)Ms+D

(14){ΔPF1(s)=−K1Gg1(s)Δf1(s)ΔPG1(s)=ΔPg1(s)Gg1(s)∑j=1kΔPB1(s)=∑j=1kΔPbj(s)Gbj(s)

(15){ΔPg1(s)=αARR(s)∑j=1kΔPbj(s)=(1−α)ARR(s)

Rectifying Eqs. (12)–(16) yields the final expression for the ACE signal as

(16)ARR(s)=ΔPL(s)⋅[β(KP1+KI1s)Ms+D+K1Gg1(s)+αβ(Gg1−∑j=1kGBj(s))+β∑j=1kGBj(s)]

From Eq. (12), it can be seen that there is a delayed effect on the ARR signal, which is better suited to respond to steady state changes.

From Eqs. (11) and (16), it can be seen that when the load perturbation ΔP_L1(s) and the participation factor α take a constant value, the amplitude of the ACE signal increases and then decreases with time until it tends to be smooth, while the amplitude of the ARR signal gradually increases with time and is smaller than the ACE signal at the beginning and larger than the ARR signal at the middle and end. The time domain curves of the difference between the two signals are shown in Fig. 4.

From Fig. 4, we can obtain a comprehensive allocation strategy for the system’s participation in the secondary FM for both signals, using whether the signal difference crosses the zero point as the timing for switching between the two modes.

(1) Signal difference before crossing the zero point

In the pre-FM period, when the ACE signal is gradually enhanced and larger than the ARR signal, it is conducive to the rapid recovery of the transient frequency deviation of the system, so the ACE control mode is adopted.

(2) Signal difference after crossing the zero point

In the middle and late stages of FM, the ACE signal is weakened while the ARR signal is gradually enhanced, at this time the ACE signal plays a suppressive role in the later FM, and the ARR control is conducive to improving the steady-state frequency deviation of the system, so the ARR control mode is adopted.

A two-layer fuzzy control strategy based on an integrated distribution model of the ARR and ACE signals, which takes into account the FM demand and FM capability to modify the participation and depth of output of the energy storage battery.

The first layer fuzzy controller takes the frequency regulation demand of the grid as the purpose, takes the system frequency deviation and the power signal allocated to the FM unit in ACE (or ARR) mode as the input quantity, derives the connection between the total power response and the grid frequency difference demand in both modes, and determines the participation factor of the energy storage; the second layer fuzzy controller considers the energy storage’s frequency regulation capability based on the SOC state, takes the output of the first layer fuzzy control and The second layer fuzzy controller considers the energy storage’s frequency regulation capability based on the SOC state, and uses the output of the first layer fuzzy control and the real-time SOC of the energy storage as the input quantity to derive the connection between the real-time SOC of the energy storage and the participation factor, to determine the actual depth of the energy storage output.

The double-layer fuzzy control can take into account the frequency regulation capability of the energy storage system based on meeting the demand for grid frequency regulation, thus avoiding the phenomenon of battery overcharge and over-discharge. The double-layer fuzzy control process in dual-signal mode is shown in Fig. 5.

In the combined allocation mode of both ARR and ACE signals, the first layer of the fuzzy controller takes the system frequency deviation Δf₁ and the power signal P_ACE (or P_ARR) allocated to the FM unit in ACE (or ARR) mode as input quantities for the FM demand of the grid, thus determining the participation factor α for the energy storage response.

The first level of the fuzzy controller is a two-dimensional control with the scale factors of the input quantities Δf₁, P_ACE (or P_ARR) and the scale factors of the output quantities α. k₁₁, k₁₂ and k₁₃ as shown in Eq. (17).

(17)k11=1Δfmaxk12={1Pd_maxη,PACE(PARR)>0ηPc_max,PACE(PARR)<0k13=1where, Δf_max is the maximum permissible interval for the secondary FM of the energy storage, P_c−max and P_d−max are the maximum charging and discharging power of the energy storage system, and η is the conversion efficiency of charging and discharging.

The Mamdani-type affiliation function is used. Δf₁(t) and P_ACE(t) (or P_ARR(t)) are the two inputs to the fuzzy controller, both in the theoretical domain of [−1,1]; α(t) is the output of the fuzzy controller, in the theoretical domain of [0,1]. The fuzzy subsets are taken as seven subsets such as NB (negative large), NM (negative medium), NS (negative small), ZO (zero), PS (positive small), PM (positive medium), and PB (positive large).

The control rule of the first layer of the fuzzy controller is: when the system frequency deviation Δf₁ and power signal P_ACE (or P_ARR) are larger, the energy storage equipment should play its advantage of quickly adjusting the larger deviation and increase the output to assist the traditional unit for frequency regulation, so the participation factor α of the energy storage system response should also increase; when the system frequency deviation Δf₁ and power signal P_ACE (or P_ARR) are smaller, the traditional frequency regulation unit should appropriately increase the output to prevent the energy storage system from operating too frequently, so the participation factor α of the energy storage system response should also be reduced. Next, the values of the affiliation functions for Δf₁(t), P_ACE(t) (or P_ARR(t)) and α(t) are defined as A_u1(t), A_u2(t) and A_u3(t), respectively. The final relationship between input A_u1(t), A_u2(t) and output A_u3(t) can be obtained as shown in Fig. 6, and the fuzzy control rule table is shown in Table 2.

The output fuzzy quantity A_u3(t) is anti-fuzzified using the area centre of gravity method to finally obtain the participation factor α(t) as shown in Eq. (18).

(18)α(t)=∫u11∫u12Au11(t)⋅u11(t)⋅Au12(t)⋅u12(t)du11du12∫u11∫u12Au11(t)⋅Au12(t)du11du12where, u₁₁, u₁₂ and u₁₃ are the values of Δf₁(t), P_ACE(t) (or P_ARR(t)) and α(t) after fuzzy quantization respectively, and A_u1(t), A_u2(t) and A_u3(t) are the values of Δf₁(t), P_ACE(t) (or P_ARR(t)) and α(t) after substitution respectively.

In the combined distribution mode of both ARR and ACE signals, the second layer of the fuzzy controller takes into account the FM capability of the battery and uses the participation factor α of the energy storage system and the real-time battery charge state quantity Q_SOC as inputs to determine the outgoing depth of energy storage P_out−1 (or P_out−2).

The second layer of the fuzzy controller is the same two-dimensional control, with the scale factors for the input quantities α and Q_SOC and the scale factors k₂₁, k₂₂ and k₂₃ for the output quantity P_out−1 (or P_out−2) as shown in Eq. (19).

(19)k21=1k22=1k23={ 1Pd_maxη,Pout−1(Pout−2)>0ηPc_max,Pout−1(Pout−2)<0

α(t) and Q_SOC(t) are the two inputs of the fuzzy controller, whose theoretical domain range is [0,1]; P_out−1(t) (or P_out−2(t)) is the output of the fuzzy controller, whose theoretical domain range is [−1,1]. The fuzzy subsets are taken as seven subsets such as NB (negative large), NM (negative medium), NS (negative small), ZO (zero), PS (positive small), PM (positive medium), and PB (positive large).

The control rule of the second layer of the fuzzy controller is: when the real-time charge state of energy storage battery Q_SOC is too large or too small, to prevent the energy storage system from being damaged by overcharge and over-discharge, the power out the depth of energy storage P_out−1 (or P_out−2) should be appropriately reduced as the participation factor α of the energy storage system increases; when the real-time charge state of energy storage battery Q_SOC is within the safe range, the power out the depth of energy storage P_out−1 (or P_out−2) should be appropriately increased as the participation factor α of the energy storage system increases to ensure the demand of system frequency regulation. Second, the values of the affiliation functions for α(t), Q_SOC(t) and P_out−1(t) (or P_out−2(t)) are defined as B_u1(t), B_u2(t) and B_u3(t), respectively. The final relationship between input B_u1(t), B_u2(t) and output B_u3(t) can be obtained as shown in Fig. 7, and the fuzzy control rule table is shown in Table 3.

The output fuzzy quantity B_u3(t) is anti-fuzzified using the area centre of gravity method, resulting in the output depth P_out−1 (t) (or P_out−2 (t)) as shown in Eq. (20).

(20)Pout−1(t)(Pout−2(t))=∫u21∫u22Bu21(t)⋅u21(t)⋅Bu22(t)⋅u22(t)du21du22∫u21∫u22Bu21(t)⋅Bu22(t)du21du22where, u₂₁, u₂₂ and u₂₃ are the values of α(t), Q_SOC(t) and P_out−1(t) (or P_out−2(t)) respectively after fuzzy quantization, and B_u1(t), B_u2(t) and B_u3(t) are the values of α(t), Q_SOC(t) and P_out−1(t) (or P_out−2(t)) respectively after substitution.

The equivalent model of a typical grid in two regions with energy storage participating in secondary frequency regulation shown in Fig. 1 is simulated in the Matlab/Simulink platform, with a conventional frequency regulation unit using a reheated thermal power unit rated at 750 MW (with a climbing rate of 25 MW/min) and energy storage with rated power and capacity of 10.5 MW and 1.5 MW/h, respectively. The rated frequency of 50 Hz and the maximum rated capacity of the unit is used as the reference value for the standardization. Two typical operating conditions, step disturbance and continuous disturbance are designed and simulated to test the effectiveness of the proposed control strategy (Scheme 3) against the fuzzy control without energy storage (Scheme 2) and without energy storage (Scheme 1). The system simulation parameters are shown in Table 4 [21,22].

To more intuitively compare the effects of the three schemes, a corresponding evaluation system is established based on the frequency regulation effect, power output and charge maintenance level. The smaller Δf_m, Δf_rms and V_m, the larger V_r, the smaller the frequency fluctuation after FM, and the better the FM effect; in terms of power output, two evaluation indicators, W_gen and W_BESS, can be used to compare the utilization rate of the units under the three schemes. The smaller the W_gen and W_BESS, the greater the utilization of the unit when the optimal FM effect is achieved; in terms of charge maintenance level, it contains two evaluation indicators, Q_SOC,ave and Q_SOC,rms, which can be used to compare the maintenance of the storage charge state under the three schemes. The closer the Q_SOC,ave is to the initial charge state value as well as the smaller the Q_SOC,rms is, the better the maintenance of the energy storage charge state is. The parameters of the evaluation index are defined as shown in Table 5.

In regions 1 and 2, step perturbations of 0.015 and 0.01 are added to ΔP_Li (the standardized value), respectively. To better verify the effectiveness of the method in this paper based on the evaluation system, the change curves of frequency deviation, traditional unit output, battery storage output and battery charge state under step perturbation for the three schemes are used for comparison.

Fig. 8a shows the curves of frequency deviation of the system after adding the step disturbance. From the picture, it can be seen that all three schemes can adjust the frequency deviation without a difference, but compared with Scheme 1 and Scheme 2, Scheme 3 is more sensitive to the disturbance and can restore the frequency deviation to 0 in a shorter time, and at the same time, the fluctuation of frequency deviation can be controlled in a smaller range during the recovery process. Fig. 8b shows the output change curve of the traditional unit after adding the step disturbance. From the picture, it can be seen that the traditional unit is always in the output state in the process of frequency regulation, and compared with Scheme 2, the traditional unit in Scheme 3 has less output in the process of frequency regulation, indicating that the conventional unit is more suitable for regulating the steady-state frequency deviation for a long time. Fig. 8c shows the power change curve of the energy storage unit after adding the step disturbance, and it can be seen from the picture that the energy storage unit is discharged and then charged until the end of frequency regulation, and then no more power is produced. Compared with Scheme 2, the energy storage unit in Scheme 3 has a smaller power output and a shorter power output time during the frequency regulation process. Fig. 8d shows the change curve of the charge state of the storage cell after adding the step disturbance. From the picture, it can be seen that the initial charge state of the storage unit is 0.5, and the charge state will gradually recover to the initial value after the end of FM. Compared with Scheme 2, the storage unit in Scheme 3 fluctuates less and recovers faster in the process of maintaining the charge level.

With the addition of continuous perturbation in region 1 as shown in Fig. 9a. To better verify the effectiveness of the method in this paper based on the evaluation system, the change curves of frequency deviation, traditional unit output, battery storage output and battery charge state of the three schemes under continuous perturbation is used for comparison.

Fig. 9b shows the change curve of frequency deviation of the system after adding continuous perturbation. From the picture, it can be seen that all three schemes can regulate the frequency deviation after adding continuous perturbation but compared with Scheme 1 and Scheme 2, Scheme 3 can control the frequency deviation within a smaller range in a shorter time, and at the same time, it can control the fluctuation of frequency deviation within a smaller range during the recovery process. Fig. 9c shows the output change curve of the traditional unit after adding the continuous disturbance, and it can be seen from the picture that the traditional unit continues to produce less output in the process of frequency regulation, compared with Scheme 2 in Scheme 3. Fig. 9d shows the change curve of the energy storage unit after adding continuous disturbance, from the picture, it can be seen that the energy storage unit is continuously charged and discharged during the process of frequency regulation, compared with Scheme 2, the energy storage unit in Scheme 3 is less charged and discharged during the process of charging and discharging and the time of discharging is shorter. Fig. 9e shows the change curve of the charge state of the storage battery after adding the continuous disturbance, from the picture, it can be seen that the initial charge state of the storage unit is 0.5, and the charge state of the storage increases when charging and decreases when discharging. Compared with Scheme 2, the storage unit in Scheme 3 fluctuates less and recovers faster in the process of maintaining the charge level.

The simulation results are analysed in terms of frequency modulation effect, power output and charge maintenance level. The evaluation results under the standardized values are shown in Tables 6 and 7.

(1) FM effects

From Tables 6 and 7 and Figs. 8a and 9b, it can be seen that Δf_m and Δf_rms of Scheme 3 are the smallest, and the V_m of Scheme 3 under step perturbation is reduced by 11.49% and 1.79% compared to Schemes 1 and 2, and the V_m of Scheme 3 under continuous perturbation is reduced by 8.87% and 1.55% compared to Schemes 1 and 2; the V_r of Scheme 3 under step perturbation is improved by 19.16% and 1.51% compared with Schemes 1 and 2, and the V_r of Scheme 3 under continuous perturbation is improved by 9.50% and 1.97% compared with Schemes 1 and 2. Therefore, the combined FM effect of Scheme 3 is the best.

(2) Power output

From Tables 6 and 7 and Figs. 8c and 9d, it is clear that the traditional unit in Scheme 3 has 12.91% and 2.57% lower output under step perturbation than Schemes 1 and 2, and the traditional unit in Scheme 3 has 25.85% and 3.34% lower output under continuous perturbation than Schemes 1 and 2. Therefore, the traditional unit in scenario 3 has the highest utilization rate.

From Tables 6 and 7 and Figs. 8b and 9c, it is clear that the energy storage unit in Scheme 3 has a 3.52% lower output under step disturbance than Scheme 2, and the energy storage unit in Scheme 3 has a lower and 1.92% lower output under continuous disturbance than Scheme 2. Therefore, the energy storage unit in Scheme 3 has the highest utilization rate.

(3) Charge maintenance level

From Tables 6 and 7 and Figs. 8d and 9e, it is clear that compared to Scheme 2, the Q_SOC,ave in Scheme 3 is closer to the initial charge state under both step perturbation and continuous perturbation, and the Q_SOC,rms in Scheme 3 is also smaller. Therefore, the charge maintenance level in Scheme 3 is the best.