Taking DFIG-based wind turbines as an example, the control model of the wind turbines participating in frequency regulation is analyzed and established considering the virtual inertia control and the primary frequency control.

DFIG-based wind turbines lack intrinsic inertia from the system aspect for the reason that their mechanical rotor speed is decoupled with system frequency. However, by introducing an auxiliary virtual inertia control loop in the maximum power tracking loop of the DFIG rotor-side convertor, the wind turbines can also supply the power grid with the virtual inertia response. The rate of change of frequency, i.e. d f / d t , is the input of the virtual inertia control. The system frequency drops when the power grid suffers a power deficiency. The virtual inertia control shares part of the power deficiency by rapidly augmenting the active power output of the wind turbines. The active power increment Δ P i n W F comes from the released kinetic energy, as expressed in Eq. 1. It is conducive to alleviating the sudden change in the frequency of the power grid. The virtual inertia control provides the wind turbines with the ability to support the total system inertia. Δ P i n W F = − k i n W F d f d t (1)

Where k i n W F is the inertia time constant of the wind turbines; f is the system frequency.

Similar to the droop control of synchronous generators, the primary frequency control of the wind turbines is designed in this study. The frequency deviation, i.e. f − f n o m , is the input of the primary frequency control. When the system frequency drops due to the power deficiency, the active power increment provided by the wind turbines can be expressed as Δ P d W F = − k d W F ( f − f n o m ) (2)

Where k d W F is the droop control gain of the wind turbines participating in the primary frequency control; f n o m is the system nominal frequency.

The control model of the wind turbines participating in frequency regulation combines the virtual inertia control and the primary frequency control holistically. Figure 2 shows the control block diagram.

In Figure 2, T is filter time constant; Δ P W F is the active power increment provided by the control model of wind turbines participating in frequency regulation, as expressed in Eq. 3. Δ P W F = − k d W F ( f − f n o m ) − k i n W F d f d t (3)

At present, the participation of UHVDC transmission systems in frequency regulation mainly includes two frequency control modes based on the PI controller and the droop controller, respectively. In this article, the frequency control mode based on the droop controller is used as the primary frequency control of UHVDC. The control block diagram is shown in Figure 3.

In Figure 3, T 1 and T 2 are filter time constants; k d D C is the proportional coefficient of UHVDC; Δ P d D C is the active power increment of UHVDC participating in primary frequency control.

By introducing the virtual inertia control on the basis of the regular droop control, UHVDC is capable of participating in the process of the system inertia response. It helps to reduce the rate and range of the frequency deviation when the power grid suffers a huge power deficiency. The active power increment Δ P D C provided by UHVDC participating in frequency regulation can be expressed as follows: Δ P D C = − k d D C ( f − f n o m ) − k i n D C d f d t (4)

Where k i n D C is the differential coefficient of UHVDC.

Similar to the control model of wind turbines participating in frequency regulation established in Section 3.1, the droop control of UHVDC is mainly in response to the frequency deviation, while the virtual inertia control of UHVDC is mainly in response to the frequency differential quantity. Thus UHVDC can simultaneously participate in the process of the inertia response and the primary frequency control, the same as synchronous generators.

As shown in Figure 4, typical HVDC transmission system mainly consists of rectifier station, DC tansmission line and inverter station. In this paper, the virtual inertia control and the primary frequency control of UHVDC can be realized by modifying the UHVDC control systems. P D C _ r e f is the active power reference value of UHVDC, and P D C is the active power which needs to be provided by UHVDC. Δ f is the system frequency deviation.

The power regulation of UHVDC systems is rapid enough to ensure that the response time is no longer than 150 ms after a power step disturbance occurs. The frequency regulation process of the power system belongs to the electromechanical transient process, of which the timescale is usually second level. Therefore, the regulation process of the UHVDC systems can be neglected in the process of analyzing the UHVDC frequency regulation mechanism, and the UHVDC transmission power strictly tracks the reference command. In addition, the effects of the filtering link, the deadband link, and the power amplitude limiting link are further neglected to simplify the analyzing process.

Based on the analysis above, the equivalent frequency response model of the power system including the virtual inertia control and the primary frequency control of wind turbines and UHVDC is shown in Figure 5. Where Δ f r e f is the system frequency deviation reference value; P L _ r e f is the load power reference value; R S G is the equivalent droop parameter of the power grid; T G is the main servo time constant; T C H is the time constant of main inlet volumes and steam chest; T R H is the time constant of reheater; F H P is the fraction of total turbine power generated by high pressure (HP) sections; H e q and D are the inertia constant and the damping coefficient of the equivalent generator of the power grid, respectively; P m is the mechanical power provided by the synchronous generators in the power grid; P L is the load power of the power grid; P W F _ r e f and P D C _ r e f are the active power reference value of wind power and UHVDC, respectively; P W F and P D C are the active power provided by wind power and UHVDC, respectively; Δ P h is the actual magnitude of the active power deficiency.

Assume that a sudden increase of load occurs and results in a power deficiency Δ P d e . Based on Figure 5, the equivalent rotor motion equation of the power system (transferred into the time domain equation) can be represented as 2 H e q d Δ f d t = P m 0 + Δ P m + Δ P W F + Δ P D C − P e 0 − D Δ f − Δ P d e (5) where P m 0 and P e 0 are the initial mechanical power and electromagnetic power of the power system, respectively; Δ P m is the mechanical power increment provided by the synchronous generators; Δ P W F and Δ P D C are the power increment provided by the wind power and UHVDC, seperately.

When we study the frequency characteristics of the power system integrated with wind power and UHVDC, one of the difficult problems we face with is the calculation of the system equivalent inertia constant H e q . For most situations, the inertia constant of the synchronous generators is a definite number. However, it is hard to analyze and calculate the equivalent inertia constants of the wind turbines and UHVDC. In the adaptive UFLS schemes, the actual magnitude of the power deficiency is commonly calculated as follows Δ P h = 2 H e q f n o m d f C o I d t (6)

It is obvious from Eq. 6 that we can calculate H e q precisely after we obtain the power disturbance variation Δ P around the time when the operating status of the power system changes or the disturbance occurs, as well as the RoCoF of CoI d f C o I d t , as expressed in Eq. 7. H e q = Δ P f n o m 2 d f C o I d t (7)

Furthermore, in order to reduce the error of calculating the equivalent inertia constant H e q , the study employs the method as follows: by maintaining the current operating state of the power system unchanged and setting L different and known power disturbance variation Δ P s e t , l , the corresponding RoCoF of CoI d f C o I d t can be calculated. Solve all the values of the equivalent inertia constant H e q ,   l correponding to Δ P s e t , l according to Eq. 7. Then calculate the mean value of H e q ,   l as the setting value of the equivalent inertia constant of the power system, which can be represented as H e q = ∑ l = 1 L H e q , l L = ∑ l = 1 L Δ P s e t ,   l f n o m 2 L d f C o I d t (8)

After the system equivalent inertia constant H e q is obtained, calculate the actual magnitude of the power deficiency Δ P h , 1 at the time when the system frequency drops to the frequency threshold in the first stage of UFLS.

Assume that the steady-state frequency after UFLS is f s . As f s < f n o m , the steady-state frequency deviation is Δ f s = f s − f n o m . Considering the participation of the wind turbines and UHVDC in primary frequency control, Δ P s refers to the active power provided by the primary frequency control of the synchronous generators, the wind turbines, and UHVDC, together with the effect of load regulation, as expressed in Eq. 8. Δ P s = − ( k L + k G + k d W F + k d D C ) Δ f s (9) where k L and k G are the unit regulation power of the load and the synchronous generators, respectively.

Then the total amount of load to be shed P s h e d , ∑ can be calculated as (Yang, 2007) Δ P s h e d , ∑ = Δ P h , 1 − ( k L + k G + k d W F + k d D C ) P L s Δ f s ∗ 1 − ( k L + k G + k d W F + k d D C ) Δ f s ∗ (10) where P L s is the load of the power grid in the steady state; Δ f s ∗ is the per unit steady-state frequency deviation.

Then the total amount of the load will be shed by stages. It is obvious from Eq. 9 that the primary frequency control of the wind turbines and UHVDC leads to the increase in their active power output in steady state, thus reducing Δ P h , 1 .

Firstly, determine the stages, frequency thresholds, load shedding percentage in each stage, and steady-state recovery frequency in the UFLS control strategy.

In the process of UFLS, the first frequency threshold should not exceed 49.25 Hz to fully use the rotating reserve capacity of the power system. The typical frequency difference between the stages is 0.2∼0.25 Hz and 5∼8 stages are commonly set. Based on the UFLS schemes of actual power grids, this paper sets four basic stages with the corresponding frequency thresholds of 49.2, 49.0, 48.8, 48.6 Hz, and the time delay of 0.2 s. The load shedding percentages in the basic stages are 20, 25, 25, and 30%, separately.

Afterward, determine the location and the amount of load to be shed in the UFLS control strategy.

In the actual operation of UFLS, the load of the scattered nodes needs to be shed. The load shedding location can be selected and the load shedding amount can be allocated based on the load shedding sensitivity index (Yang and Cai, 2016). The load shedding amount of the n th node of the power grid Δ P s h e d , n can be determined as Δ P s h e d , n = Δ P s h e d , i ϕ n ∑ n = 1 N ϕ n (11) where Δ P s h e d , i is the total amount of load to be shed in the i th stage; ϕ n is the load shedding sensitivity of the load node, directly related to the electrical distance from the load node to the disturbance node; N is the total number of the load nodes.

Finally, design the UFLS implementation strategy.

In this study, the UFLS control strategy is implemented as shown in Figure 6. The corresponding steps can be described as follows:

1) Set the frequency threshold f i and the load shedding percentage k i in each stage. Predefine the steady-state recovery frequency f s . Calculate Δ P s according to Eq. 9. Set i = 1 .

It can be seen from Figure 6 that when the system frequency reaches the threshold of the i th stage, i.e. f ≤ f i , UFLS is started in accordance with the load shedding percentage in each stage k i . After completing load shedding in the i th stage, detect the system frequency. If d f d t < 0 and f ≤ f i + 1 , it is clear that the load shedding amount is not enough to avoid the frequency from declining. Then the next stage of UFLS is triggered. Conversely, it means that load shedding has already restrained the descending of the system frequency. The frequency does not fall below the frequency threshold in the ( i + 1 ) th stage. The UFLS process ends.

In this case, when t = 5   s , a 300 MW load surge at Bus 21 occurs. This disturbance is used to imitate the power deficiency caused by new energy or conventional generators off-grid. Simulate and compare the effects of four frequency control modes on the system frequency response after the disturbance: 1) both the wind turbines and UHVDC participate in frequency regulation; 2) only the wind turbines participate in frequency regulation; 3) only UHVDC participates in frequency regulation; 4) neither the wind turbines nor UHVDC participates in frequency regulation. The simulation results are shown in Figure 8.

It is revealed from Figure 8 that when neither the wind turbines nor UHVDC participates in frequency regulation, the maximum frequency deviation is the largest and the steady-state frequency is the lowest of the four frequency control modes. Besides, the frequency nadir drops below 49.2 Hz, violating the frequency threshold of the first stage. Once the wind turbines or UHVDC participates in frequency regulation, the absolute maximum frequency deviation decreases by 0.4 Hz, and the steady-state frequency is higher. When both the wind turbines and UHVDC participate in frequency regulation, the maximum frequency deviation and the steady-state frequency deviation are the minima. It can be inferred that the participation of the wind turbines and UHVDC in frequency regulation can effectively ameliorate the system frequency characteristics. The combined action of the virtual inertia control and the primary frequency control significantly decreases the maximum frequency deviation and the steady-state frequency deviation. Thus the dynamic process and the trajectory of the system frequency are notably impacted by the participation of the wind turbines and UHVDC in frequency regulation.

For cases in Sections 5.2, 5.3, and 5.4, a 780 MW load surge at Bus 21 at the time t = 5   s is used as the disturbance to imitate the power deficiency caused by new energy or conventional generators off-grid.

In this case, both the wind turbines and UHVDC in the test system possess the capability of virtual inertia control actually. However, to illustrate the impact of the virtual inertia control of the wind turbines and UHVDC on UFLS, we consider four different situations in the process of formulating four UFLS schemes respectively: 1) both the wind turbines and UHVDC participate in virtual inertia control; 2) only the wind turbines participate in virtual inertia control; 3) only UHVDC participates in virtual inertia control; 4) neither the wind turbines nor UHVDC participates in virtual inertia control. Then the four UFLS schemes are implemented on the same test system in which both the wind turbines and UHVDC participate in virtual inertia control, separately. The simulation results are shown in Figure 9 and Table 1.

It can be seen from Figure 9 and Table 1 that, the steady-state recovery frequency in scheme 1 is the highest, followed by scheme 3 and scheme 2, while in scheme 4 is the lowest. The reason is that for one thing, the virtual inertia control of the wind turbines and UHVDC is considered in scheme 1 so that the calculated inertia constant H e q is the largest. However, scheme 2 only accounts for the virtual inertia control of the wind turbines, and scheme 3 only takes the virtual inertia control of UHVDC into account. Thus the calculated H e q in scheme 2 and scheme 3 is less. As scheme 4 does not consider the virtual inertia control of the wind turbines or UHVDC, the calculated H e q in scheme 4 is the least. For another, it can be inferred from Eq. 10 that the further calculated total amount of load to be shed Δ P s h e d , ∑ is the largest in scheme 1, followed by scheme 3 and scheme 2, while in scheme 4 is the least. Thus the steady-state recovery frequency in each scheme has certain differences.

The simulation results in this case also demonstrate that when the virtual inertia control of the wind turbines and UHVDC is taken into consideration, scheme 1 can calculate the actual magnitude of the power deficiency more precisely and reflect the effect of the virtual inertia control on UFLS more objectively. Obviously, the effect is significant.

In this case, to illustrate the impact of the primary frequency control of the wind turbines and UHVDC on UFLS, design and contrast four different UFLS schemes: 1) UFLS scheme considering the primary frequency control of both the wind turbines and UHVDC; 2) UFLS scheme only considering the primary frequency control of the wind turbines; 3) UFLS scheme only considering the primary frequency control of UHVDC; 4) UFLS scheme without considering the primary frequency control of wind turbines or UHVDC. Then each of the four schemes is implemented on the test system with the primary frequency control mode corresponding to the scheme itself. The simulation results are shown in Figure 10 and Table 2.

It can be observed from Figure 10 and Table 2 that, the steady-state recovery frequency is almost the same in the four schemes. However, the amount of load to be shed Δ P s h e d , ∑ in scheme 1 is 560 MW, which is 73 MW, 68 MW, and 144 MW less than that in scheme 2, scheme 3, and scheme 4, respectively. This shows that the magnitude of the power deficiency is partly offset by the primary frequency control of the wind turbines and UHVDC in scheme1, resulting in the decrease in the amount of load to be shed by 144 MW compared with scheme 4. Schemes 2 and scheme 3 respectively take into account the primary frequency control of wind turbines and UHVDC. The part of the magnitude of the power deficiency offset by the primary frequency control is less than that in scheme 1. Thus the amount of load to be shed in scheme 2 and scheme 3 is more than that in scheme 1. As neither the primary frequency control of the wind turbines nor of UHVDC is taken into account in scheme 4, more load needs to be shed to maintain the same steady-state recovery frequency as that in scheme 1, scheme 2, and scheme 3. To conclude, the primary frequency control of the wind turbines and UHVDC has a prominent effect on the steady-state recovery results and the amount of load to be shed.

In this case, simulations are conducted to compare three different UFLS schemes. Scheme 1 is the scheme proposed in this paper, which is performed according to the implementation strategy of UFLS in Figure 5. Scheme 2 is the conventional UFLS scheme in literature (Rudez and Mihalic, 2011). Scheme 3 is the adaptive UFLS scheme in literature (Song et al., 2014) without considering the virtual inertia control and the primary frequency control of the wind turbines and UHVDC. Compare the frequency response curves and the steady-state results of all the schemes in the process of UFLS. The simulation results are shown in Figure 11 and Table 3.

It can be seen from Figure 11 and Table 3 that all the schemes complete the action process of UFLS through four stages of load shedding, and the steady-state recovery frequency is close. However, the load shedding amount in scheme 1 is evidently less than that in scheme 2 and scheme 3 in each stage and in total. The reasons for the difference in the load shedding amount are as follows. On one hand, the actual magnitude of the power deficiency Δ P h , 1 is calculated in scheme 1 considering the virtual inertia control and the primary frequency control of the wind turbines and UHVDC. On the other hand, the total amount of load to be shed Δ P s h e d , ∑ is calculated in scheme 1 considering the primary frequency control of the wind turbines and UHVDC. Thus the simulation results show that when taking into account the virtual inertia control and the primary frequency control of the wind turbines and UHVDC, the load shedding amount can be significantly reduced on the premise of reaching the steady-state recovery frequency. Thus it is conducive to the improvement of the power supply reliability of the power grid and the reduction of the loss caused by load shedding.