Selection of Inertial and Power Curtailment Control Methods for Wind Power Plants to Enhance Frequency Stability

Abstract

As renewable energy penetrates the power system, system operators are required to curtail output power from generation units to balance the power supply and demand. However, large curtailment from wind power plants (WPPs) may instantly cause excessive output power decrement, causing system frequency to drop significantly before reaching its nominal value. In order to solve this problem, this paper proposes a cooperative control framework to determine the operation of WPPs in two control methods, which are the stepwise inertial control (SIC) method and the curtailed control method. The proposed framework first determines the WPPs to operate in the curtailed control method to provide the required power curtailment. Next, it determines the WPPs to operate in the SIC method considering their releasable kinetic energy to provide an effective inertial response and compensate for the sudden excessive output power decrement caused by other WPPs operated in the curtailed control method. Therefore, each WPP is operated in one of two control methods to provide required power curtailment while reducing the sudden excessive output power decrement. To verify the effectiveness of the proposed cooperative control framework, several case studies are carried out on the practical South Korea electric power system.

1. Introduction

Worldwide, many countries are installing the high penetration of renewable energy, especially wind and solar, for the transition to renewable energy sources. According to the report from the International Renewable Energy Agency (IRENA) [1], the capacity of renewable energy in 2020 was 291.7 GW in the United States, 100.6 GW in Canada, 55.4 GW in France, 47.4 GW in the United Kingdom, 32.9 GW in Sweden, 894.9 GW in China, 103.5 GW in Japan, and 134.3 GW in India. In particular, the renewable energy capacity of South Korea in 2020 was 21 GW, and the wind and photovoltaic take the largest portion. Moreover, the South Korean government has planned to increase the renewable energy generation rate to 20% by 2030. To do so, they are planning to install wind power plants (WPPs) and photovoltaic up to 17.7 and 5.7 GW, respectively, until 2030.

However, many studies have reported that high renewable energy penetration may cause several stability problems [2,3,4,5,6]. In terms of frequency stability, the renewable energy penetration replaces the conventional synchronous generators (SGs) participating in various ancillary services, resulting in various frequency stability problems. For example, when a large disturbance occurs in the power system, conventional SGs provide power reserve and inertial response (IR) to support the frequency stability. However, distributed generators (DGs) normally operate on the maximum power point tracking (MPPT) control method, which cannot provide additional frequency stability support. Therefore, the penetration of DGs operating on this control method decreases the frequency stability supports.

For the power system with a low wind power penetration level (WPPL), the WPPs operating in the MPPT control method have caused a minor frequency stability problem. However, as WPPL increases, WPPs operating on this control method are causing severe frequency stability problems [7]. Moreover, the variability and uncertainty of renewable energy resources are causing severe problems in the power supply and demand. Therefore, the system operator may require WPPs to operate in different control methods other than the MPPT control method to provide frequency stability support [8,9] and curtail a certain amount of power to maintain the power balance [10]. The control methods for WPPs other than the MPPT control method are summarized in Figure 1.

To solve the frequency stability problem caused by high WPPL, researchers have developed a control method for WPPs to provide IR. In order to provide IR by WPPs, there are two types of virtual inertial control (VIC) methods, which are the frequency-based inertial control (FBIC) method and the stepwise inertial control (SIC) method [11,12,13]. These two control methods provide the IR by the kinetic energy from the WPPs. However, while the former provides the IR based on system frequency change, the latter is independent of the system frequency change and provides the IR according to its control scheme. Therefore, the SIC method is applied more variously for applications.

On the other hand, WPPs operated by the curtailed control method can provide power reserve when a disturbance occurs in the power system. For the curtailed control method, there are proportional curtailment control (PCC) and constant curtailment control (CCC) methods [14]. The former curtails the output power of WPP according to its proportional coefficient. Therefore, depending on the wind speed, the size of the power curtailment differs. On the other hand, the latter curtails constant output power.

Moreover, as the WPPL increases, maintaining the balance between power supply and demand is becoming more important than ever. Moreover, the amount of required power curtailment increases for high WPPL. However, excessive output power decrement instantly occurs from WPPs in the process of switching from the MPPT control method to the curtailed control method. As a result, this causes the system frequency dip before reaching its nominal value. In particular, if this frequency dip is beyond the dead-band of the governor, it will cause other SGs to compensate for the power loss. This paper proposes the design of a cooperative control framework, which determines each WPP operation in curtailed control and SIC methods. Therefore, when system operators require power curtailment to maintain the power balance, the WPPs operating by the former provide the required power curtailment, and other WPPs operating by the latter compensate for the excessive output power decrement by IR.

This paper is organized as follows. Section 2 describes the operation of the WPPs, including MPPT control, curtailed control, and SIC methods. In Section 3, the proposed cooperative control framework implementation is described with its theoretical analysis. Section 4 describes the characteristics of the practical South Korea electric power system and verifies the effectiveness of the proposed framework with several case studies using the DIgSILENT PowerFactory^® (Version 2018, DIgSILENT GmbH, Gomaringen, Germany) [15]. Finally, conclusions are given in Section 5.

2. Wind Power Plants Operation

2.1. Characteristics of Permanent Magnet Synchronous Generator and MPPT Control Method

In this paper, a type-4 wind turbine generator, which is a permanent magnet synchronous generator (PMSG), is considered for wind power. Generally, PMSG consists of a rotor side converter (RSC), DC-link circuit with a capacitor, and grid side converter (GSC) [16]. Moreover, the PMSG control system provides a reference signal for pitch control, RSC control, and GSC control methods. Furthermore, depending on the power system condition, the active power reference (P_ref) is determined based on MPPT control, VIC, and curtailed control methods.

Besides the power reference determined by each control method, the mechanical power from the wind source is obtained and calculated as

$$P_{mec} = \frac{1}{2}\rho \pi R^2{V}_{wind}^3{C}_P(\lambda ,\beta )$$

(1)

where P_mec is the mechanical power extracted from the wind, ρ is the air density of 1.225 kg/m³, R is the rotor radius of 46.5 m, V_wind is the wind speed, and C_P is the power coefficient based on tip speed ratio (λ) and pitch angle (β). Normally, WPPs are operated by the MPPT control method to provide maximum power in a steady state [17]. As shown in Figure 2, the active power reference is determined by the MPPT curve, P_MPPT, when rotor speed (ω_r) is between the minimum speed limit (ω_min) and maximum speed limit (ω_max). Moreover, P_MPPT is calculated as

$$P_{MPPT}({\omega }_r) = \frac{\pi \rho R^5{C}_{P,opt}}{2{\lambda }_{opt}^3} \times {\omega }_r{}^3 = k_{opt} \times {\omega }_r{}^3$$

(2)

where C_P,opt and λ_opt are the optimal C_P and λ values determined by the MPPT control method, respectively, and k_opt is the coefficient of the MPPT curve. In this paper, C_P,opt is set to 0.447 with β at 0 and λ_opt at 7.2.

2.2. Curtailed Control Method

As system operators need to maintain the power balance, they may require WPPs to operate in the curtailed control method considering the wind condition. As mentioned previously, there are CCC and PCC methods to curtail output power from WPPs. However, power curtailment by the former method is only available at a specific output power level [14]. Therefore, the latter method is preferably applied to curtail output power from WPPs. The curtailed power using the PCC method is defined as

$$P_{cur}({\omega }_r)={\alpha }_{cur}\times P_{MPPT}({\omega }_r)$$

(3)

where P_cur is the power reference by the PCC method and α_cur is the coefficient for the curtailed power curve. Therefore, when WPP switches from the MPPT control method to the PCC method, the output power decreases by ΔP_down as

$$\begin{array}{ll}\Delta P_{down}({\omega }_r)& =P_{MPPT}({\omega }_r)-P_{cur}({\omega }_r)\\ & =(1-{\alpha }_{cur})\times P_{MPPT}({\omega }_r)\end{array}$$

(4)

As shown in Figure 3, the output power is decreased from point A to B when WPP is switched from the MPPT control method to the PCC method. However, the output power cannot maintain the power at point B. This is because a difference exists between the mechanical power and active power reference. Therefore, the rotor speed is accelerated by the swing equation as

$$2H{\omega }_r\frac{d{\omega }_r}{dt} = P_{mec} - P_{ref}$$

(5)

where H is the inertia constant of the PMSG. As a result, the rotor speed is accelerated from point B to C, which is the intersection of the P_ref and P_mec. Therefore, it can be concluded that when WPP switches from the MPPT control method to the curtailed control method, the active power immediately decreases from point A to B and then reaches point C. In other words, when WPPs are required to curtail by ΔP_cur, the unwanted power decrement of ΔP_dec occurs. Moreover, ΔP_dec becomes significant as WPPL and the required power curtailment increases.

2.3. Virtual Inertial Control Method

While conventional SGs provide various frequency responses, such as power reserve and IR, renewable energy-based DGs are less capable of providing these frequency responses. However, recent studies have developed a VIC method for WPPs to provide IR with the releasable kinetic energy stored in the rotating rotor. Therefore, WPPs can provide similar IR as conventional SGs and support frequency stability when a large disturbance, such as a generation trip occurs in the power system [11,12,13].

As mentioned previously, there are FBIC and SIC methods for the WPP VIC method. The WPPs operated by the FBIC method provide the IR based on the frequency deviation and rate of change of frequency change (RoCoF) [13]. On the other hand, WPPs operated by the SIC method provide the IR independently from the frequency but based on the deceleration and acceleration stage [11], as shown in Figure 4. As P_ref is increased from P₀ to P_up by the SIC method, the right term of the swing equation of Equation (5) becomes negative. As a result, the rotor speed starts to decelerate right after P_ref is increased from P₀ to P_up. Then, to recover the rotor speed to ω₀, the SIC method decreases the P_ref from P_up to P_down.

After the SIC method has been developed in [11], many studies have improved this SIC method to provide active power more effectively and improve the frequency stability [18,19]. While the SIC method in [11] increases power by 0.1 pu without considering the WPPL or wind condition, the SIC method recently developed in [19] increases the power regarding the prevention of secondary frequency dip while providing effective support for frequency nadir. Therefore, this SIC method increases the power by ΔP_SIC as

$$\Delta P_{SIC} = \left[P_{\mathrm{T-}\lim }({\omega }_0) - P_0\right] \times ({\omega }_0^m-{\omega }_{\min }^m)$$

(6)

where P_T-lim(ω₀) is the power at ω₀ based on the torque limit, and m is an index depending on the WPPLs. Note that m is decreased as WPPL increases. This is because if each WPP provides the same amount of ΔP_SIC in high WPPL, the power decrement after frequency nadir arrestment (point C’ in Figure 5) also becomes high. As a result, this may cause other conventional SGs with a slow frequency response speed to compensate, causing a secondary frequency dip. Therefore, ΔP_SIC is decreased by reducing m in Equation (6) when WPPL increases. After frequency nadir is arrested, P_ref is decreased from point C’ to D’, and enters the acceleration stage to recover the rotor speed to ω₀.

3. Proposed Cooperative Control Framework

As the WPPL increases, power curtailment becomes essential to balance the power supply and demand. However, as mentioned previously, the increment on required power curtailment can cause significant ΔP_dec, resulting in a severe frequency dip before reaching its nominal value. As shown in Figure 6, when WPPs are switched from the MPPT control method to the curtailed control method, in order to maintain the power balance and restore the frequency from f₀ to nominal frequency (f_norm), the output power of the WPPs is instantly decreased further by ΔP_dec. As a result, the frequency falls significantly before reaching f_norm, and this problem becomes severe as WPPL is increased. Moreover, suppose the frequency falls beyond the dead-band of the governor before reaching f_norm. In that case, it will activate the governor response from SGs to compensate for the power loss using the primary frequency reserve.

In order to solve this frequency dip problem, the proposed cooperative control framework determines the overall WPPs operation in the SIC and curtailed control methods to provide the required power requirement while improving the frequency dip. The main reason for the frequency dip occurrence during the power curtailment is the sudden significant output power decrement from WPPs. To solve this problem, the proposed framework operates some WPPs by the SIC method during the power curtailment. Therefore, they instantly increase the power by providing IR for a short period to compensate for the power decrement, and, after providing IR, they decrease the power back to its initial value (see Figure 5). As a result, the excessive power decrement of ΔP_dec caused by the curtailed control method may be compensated while improving the frequency dip without disturbing the frequency recovery to f_norm.

The overall procedure to implement the proposed cooperative control framework is shown in Figure 7, and the detailed operations are explained below. Note that the SIC method in [19] is used for the VIC method, and CCC and PCC methods are considered for curtailed control methods in the proposed framework.

• Stage I—As power curtailment is required to maintain the power balance, parameters including the iteration number (k) and the total sum of the power curtailment from WPPs (P_cur,tot) are initialized. Then, the proposed coordination control framework begins. In this stage, the framework firstly assigns the WPPs to be operated by the PCC method to provide the required power curtailment (P_cur,req). Considering the technical operation limit [10], α_cur is assumed to be 5%. Note that WPPs are assigned to be operated by this method until P_cur,tot becomes higher than P_cur,req.
• Stage II—As P_cur,tot becomes larger than P_cur,req in the previous stage, the system operator needs to decrease the P_cur,tot to curtail the exact amount of P_cur,req. If WPPs curtail more than P_cur,req, the frequency will not recover to f_norm but will converge to a lower value. Therefore WPP_k is operated by the CCC method to curtail the exact amount of insufficient power curtailment (ΔP_cur,CCC). As a result, while WPP₁ to WPP_k−1 are operated by the PCC method with α_cur of 5%, WPP_k is operated by the CCC method with ΔP_cur,CCC to curtail the exact amount of P_cur,req.
• Stage III—After determining the WPPs to be operated by the curtailment control method (PCC and CCC methods), the other WPPs are determined to be operated by the SIC method to compensate for the power decrement caused by other WPPs operated by PCC and CCC methods. To do so, the total available IR for WPP_k+1 to WPP_n (ΔP_SIC,tot) is calculated as

  $$\Delta P_{SIC,tot}={\displaystyle \sum _{i=k+1}^n\Delta P_{SIC,i}}$$

  (7)

Figure 7. Implementation of the proposed cooperative control framework.

Figure 7. Implementation of the proposed cooperative control framework.

However, if ΔP_SIC,tot is larger than the required power curtailment, it will cause another power imbalance. Therefore, ΔP_SIC for each WPP is modified considering the required power curtailment as

$$\Delta P_{SIC\_mod,i} = \left[P_{\mathrm{T-}\lim ,i}({\omega }_0) - P_{0,i}\right] \times ({\omega }_0^m-{\omega }_{\min }^m)\frac{P_{cur,req}}{\Delta P_{SIC,tot}}$$

(8)

Therefore, the other WPPs (WPP_k+1 to WPP_n) provide IR to compensate for the power decrement without causing a power imbalance.

In summary, when a large amount of power is curtailed from WPPs, excessive power decrement instantly occurs during the power curtailment, which causes a significant frequency drop before the frequency recovers to f_norm. To solve this problem without disturbing the power balance, the proposed cooperative control framework operates WPPs partially by the SIC method to provide instant frequency support. In particular, the curtailed control method is first applied to WPPs with PCC methods, and then the CCC method is applied to provide the exact power curtailment of P_cur,req. Moreover, the other WPPs that are not operated by the curtailed control method are operated by the SIC method considering the P_cur,req to compensate for the excessive power decrement.

4. Simulation Results

To verify the effectiveness of the proposed cooperative control framework, several case studies are carried out on the practical South Korea electric power system using the DIgSILENT PowerFactory^® software to provide an effective solution for power curtailment.

4.1. Characteristics of South Korea Electric Power System

In the practical South Korea electric power system, there are about 400 SGs with a power capacity of 145 GW. Moreover, the load demand and power supply for one day during winter in 2020 used in the simulation are about 82.4 and 83.9 GW, respectively. Furthermore, the load demand and the power generation considering the types of SGs are given in

Table 1. Load demand and power generation according to areas in winter of early 2020.

Area No.	Area Name	Load Demand (MW)	Power Generation
			Nuclear (MW)	Coal (MW)	Combined Cycle (MW)	Others (MW)	Total (MW)
1	Seoul/Gyeonggi	26,115	0	0	9717	5214	14,931
2	Incheon	7056	0	4826	4697	0	9523
3	Gangwon	2615	0	2820	0	1204	4024
4	Chungcheong	14,096	0	16,886	1835	359	19,080
5	Jeolla	8642	5201	1111	3637	715	10,664
6	Gyeongsang	23,871	11,791	6786	3902	3242	25,721

according to the provinces with six areas. Therefore, the South Korea electric power system has regional characteristics. As given in Table 1, area 1, which includes the capital Seoul of South Korea, has the largest load demand. However, it is observed that the power generation in area 1 is much lower than the load demand. Therefore, power is transmitted from the other areas through a high-voltage transmission line, such as 345 and 765 kV transmission lines. Moreover, the types of SGs and their roles are different among areas. For example, nuclear power plants, which take charge of base load power plants, are primarily located in areas 5 and 6. On the other hand, the coal power plants, which take charge of the load-following power plant, are primarily located in area 4. Lastly, the peaking power plants are practically located in areas 1 and 2.

For wind resources, the currently installed capacity of WPPs is only about 1000 MW in the South Korea electric power system, which is much lower than conventional SGs. However, the South Korean government has planned to install 17.7 GW of WPPs by 2030. Therefore, in this paper, according to the South Korean government’s renewable energy policy and basic plan for long-term electricity supply and demand [20], 20 WPPs shown in Figure 8 are considered. Moreover, their capacity is given in

Table 2. Hosting capacity of 20 WPPs.

Capacity (MW)
WPP1	WPP2	WPP3	WPP4	WPP5	WPP6	WPP7	WPP8	WPP9	WPP10
200.1	299	299	220.8	167.9	218.5	170.2	637.1	46	400.2
WPP11	WPP12	WPP13	WPP14	WPP15	WPP16	WPP17	WPP18	WPP19	WPP20
1499.6	119.6	1499.6	878.6	154.1	1000.5	1000.5	278.3	1499.6	41.4

, and the total capacity is about 10 GW. Furthermore, since the simulation environment of the South Korea electric power system is based on winter in early 2020, the wind speed scenario is based on January 2020 and February 2020, as given in

Table 3. Wind speed of 20 WPPs for all cases.

	Wind Speed (m/s)
	WPP1	WPP2	WPP3	WPP4	WPP5	WPP6	WPP7	WPP8	WPP9	WPP10
Case 1 (January)	6.5	7.3	6.8	7.7	6.4	6.7	8.7	8.2	8.7	6.8
Case 2 (February)	6.8	8	7.2	6.8	6.3	6.4	8.7	7.5	7.5	6.7
	WPP11	WPP12	WPP13	WPP14	WPP15	WPP16	WPP17	WPP18	WPP19	WPP20
Case 1 (January)	7.4	8	8.5	7.4	7.5	8.1	9	7.6	8.8	7.4
Case 2 (February)	6.9	8.6	8.2	7.9	8.2	7.1	9.1	6.7	8.4	7.4

.

4.2. Case 1—Required Power Curtailment of 606 MW

As shown in Figure 9, because of the power imbalance, the initial center of inertia (CoI) frequency [21] is 60.035 Hz, which is higher than f_norm of 60 Hz. Note that the CoI frequency, f_COI, is calculated as

$$f_{COI}=\left({\displaystyle \sum _{j=1}^m{H}_{SG,j}{S}_{SG,j}{f}_{SG,j}}\right)\times {\left({\displaystyle \sum _{j=1}^m{H}_{SG,j}{S}_{SG,j}}\right)}^{-1}$$

(9)

where H_SG,j and S_SG,j are the inertia constant and capacity of the j-th SGs, and f_SG,j is the measured frequency of the bus that is connected to the j-th SGs. However, there are many SGs and buses in a practical large-scale power system, making it impossible to measure the frequency of every bus to obtain f_COI. Therefore, the frequency of SGs with the largest capacity in each area is selected and measured to obtain f_COI.

In case 1, due to wind conditions based on January, 606 MW is required for power curtailment to balance the power supply and demand. In order to curtail 606 MW, WPP operations are determined using the proposed cooperative control framework shown in Figure 7. As a result, WPPs (WPP₁ to WPP₉) are operated by the PCC method with an α_cur of 5%, and WPP₁₀ is operated by the CCC method with a constant power curtailment of 69.8 MW. On the other hand, when power curtailment occurs from WPPs (WPP₁ to WPP₁₀), other WPPs (WPP₁₁ to WPP₂₀) are operated by the SIC method. Note that, since ΔP_SIC,tot (210 MW) is much lower than P_cur,req (606 MW), ΔP_SIC for WPPs (WPP₁₁ to WPP₂₀) are not modified by Equation (8).

As shown in Figure 10, WPPs (WPP₁ to WPP₁₀) determined to be operated by the curtailed control method are curtailed at 20 s. As a result, the imbalance of power supply and demand is solved, and f_COI starts to decrease from 60.04 Hz to f_norm. However, while 606 MW is curtailed from WPPs, an additional 230 MW of excessive power decrement occurs in the power system. Therefore, as shown in Figure 9, f_COI drops significantly to 59.964 Hz before recovering to 60 Hz. To solve this problem, the proposed cooperative control framework operates WPP₁₁ to WPP₂₀ by the SIC method. Thus, they provide an IR of 210 MW at 20 s to compensate for the power decrement. As a result, it clearly shows that the f_COI dip is significantly improved to 59.983 Hz (see the dashed red line in Figure 9).

Table 4. Summary of WPPs operation and numerical results for case 1.

WPP No.	Control Method	P0 (MW)	ΔPcur (MW)	ΔPdec (MW)	ΔPSIC (MW)
WPP1	PCC	44.2	30.6	11.5	-
WPP2	PCC	93.4	64.3	24.4	-
WPP3	PCC	75.5	52.2	19.7	-
WPP4	PCC	81	55.7	21.2	-
WPP5	PCC	35.4	24.5	9.2	-
WPP6	PCC	52.8	36.5	13.7	-
WPP7	PCC	90	61.7	23.6	-
WPP8	PCC	282.1	193.6	73.9	-
WPP9	PCC	24.3	16.7	6.4	-
WPP10	CCC	101.1	69.8	26.4	-
WPP11	SIC	488.1	-	-	30.8
WPP12	SIC	49.2	-	-	3
WPP13	SIC	739.6	-	-	43.9
WPP14	SIC	286	-	-	17.5
WPP15	SIC	52.2	-	-	3.5
WPP16	SIC	427	-	-	28.4
WPP17	SIC	587.4	-	-	29.9
WPP18	SIC	98.1	-	-	5.1
WPP19	SIC	820.7	-	-	47.4
WPP20	SIC	13.5	-	-	0.9
Total	-	4441.6	605.6	230	210.4

summarizes the operation of 20 WPPs during the power curtailment.

4.3. Case 2—Required Power Curtailment of 337 MW

In case 2, the imbalance between power supply and demand raises the f_COI to 60.015 Hz. Note that the f_COI exceeds f_norm by a smaller amount than that of case 1. This is because the total power generated from the overall WPPs is smaller than case 1 due to the wind conditions. In order to balance the power supply and demand, 337 MW is required for power curtailment. To solve this problem, the proposed cooperative control framework is applied to determine the 20 WPPs operation. In general, the power system is operated by each area rather than operating the entire system as one large area. Therefore, the proposed framework is applied in each area to determine the operation of WPPs for this case study. However, since there are fewer WPPs in areas 1, 2, and 4, the operation of WPPs in these areas is considered simultaneously. Thus, in order to curtail 337 MW, each area is curtailed by 84.3 MW. As a result, the framework determines WPPs (WPP₁, WPP₄, and WPP₅) to be operated by the curtailed control method (PCC method), which provides power curtailment. Moreover, WPP₂, WPP₆, WPP₁₁, and WPP₁₆ are operated by the CCC method to balance the power supply and demand precisely for each area. Note that WPPs are not operated by the PCC method for areas 5 and 6 since WPPs (WPP₁₁ and WPP₁₆) operated by the CCC method can provide the required curtailment for each area. Finally, the remaining WPPs are operated by the SIC method to provide IR and compensate for the instant power decrement during power curtailment.

As shown in Figure 11, f_COI is over 60 Hz during 0 s to 20 s due to a power imbalance of 337 MW. After determining the WPPs operation using the proposed cooperative control framework, WPPs are curtailed at 20 s to balance the power supply and demand, making f_COI recover to f_norm, which is 60 Hz. However, as shown in Figure 12e, an additional power decrement of 428 MW occurs during power curtailment. As a result, a frequency dip occurs, making f_COI decrease to 59.952 Hz before reaching 60 Hz. In order to solve this problem, the proposed coordination control framework additionally operates WPPs (WPP₃, WPP₇, WPP₈, WPP₉, WPP₁₀, WPP₁₂, WPP₁₃, WPP₁₄, WPP₁₅, WPP₁₇, WPP₁₈, WPP₁₉, and WPP₂₀) by the SIC method as soon as power curtailment occurs from other WPPs. As a result, the frequency dip is increased to 59.98 Hz.

Table 5. Summary of WPPs operation and numerical results for case 2.

WPP No.	Control Method	P0 (MW)	ΔPcur (MW)	ΔPdec (MW)	ΔPSIC (MW)
WPP1	PCC	50.6	35.1	13.2	-
WPP2	CCC	122.9	49.2	54.9	-
WPP3	SIC	89.6	-	-	9.5
WPP4	PCC	55.8	38.7	14.6	-
WPP5	PCC	33.8	23.7	8.8	-
WPP6	CCC	46.0	21.9	18.9	-
WPP7	SIC	90.0	-	-	9.7
WPP8	SIC	215.9	-	-	26.0
WPP9	SIC	15.6	-	-	1.7
WPP10	SIC	96.7	-	-	7.3
WPP11	CCC	395.8	84.3	180.3	-
WPP12	SIC	61.1	-	-	5.5
WPP13	SIC	664.0	-	-	84.4
WPP14	SIC	347.9	-	-	35.8
WPP15	SIC	68.2	-	-	7.4
WPP16	CCC	287.7	84.3	137.2	-
WPP17	SIC	607.2	-	-	58.3
WPP18	SIC	67.3	-	-	5.8
WPP19	SIC	713.8	-	-	92.9
WPP20	SIC	13.5	-	-	1.5
Total	-	4043.3	337.2	427.9	345.8

summarizes the operation of 20 WPPs during the power curtailment.

In summary, it is clearly shown from cases 1 and 2 that a large amount of power curtailment causes instant power decrement during a switching process from the MPPT control method to the curtailed control method. Moreover, this causes a significant frequency dip before reaching f_norm. To solve this problem, the proposed cooperative control framework determines WPP operation in three control methods, which are the PCC, CCC, and SIC methods. Therefore, the proposed framework operates WPPs that could provide required power curtailment for power balance while also providing IR to compensate for the instant power decrement. The results show that frequency dip during the power curtailment is significantly improved using the solution by the proposed framework.

5. Conclusions

This paper proposed the new cooperative control framework between the curtailed control and virtual inertial control (VIC) methods to minimize the instant power decrement during the power curtailment and improve the frequency dip. To do so, this paper first analyzed the power loss that occurs in the process of switching from the maximum power point tracking control method to the curtailed control method, which caused a severe impact on frequency stability during the frequency recovery. In order to solve this problem, the proposed cooperative control framework determined the WPP operation in the proportional curtailment control (PCC) and constant curtailment control (CCC) methods to provide the required power curtailment. Then, it operated the rest of the WPPs by the stepwise inertial control (SIC) method to provide an inertial response with the consideration of the power balance.

The effectiveness of the proposed coordination framework was verified with several case studies on the practical South Korea electric power system. The results show that the proposed coordination framework successfully determined WPP operation in the PCC, CCC, and SIC methods to provide the required power curtailment and compensate for the excessive power decrement. Therefore, it is expected that the proposed framework would provide a promising solution on power curtailment and enable the high penetration of WPPs to the power system.