Imbalance-based primary frequency control for converter-fed microgrid

Frequency droop control is a simple and effective frequency control method. However, it is not appropriate as a primary frequency control for microgrids with energy storage systems and voltage source converters (VSCs) owing to their slow response speed. In addition, it is difﬁcult to determine the grid balance only with frequency deviation. In this paper, a new converter-fed microgrid primary frequency control method based on the estimated active power imbalance for fast response and less variability in the transmission system is proposed. The active power imbalance is estimated via frequency deviation, frequency drop speed and the modiﬁed swing equation. The estimated imbalance indicates the status of the power imbalance more quickly and accurately than the frequency deviation. The proposed method does not require communication devices, responds quickly to frequency drops, and prevents unnecessary operation of the grid-connected VSC because it uses the estimated imbalance instead of the frequency or angle for droop control. Simulation results show that the proposed method is signiﬁcantly faster than frequency droop control methods, improves the rate of change of frequency and frequency nadir and reduces variability in the transmission system.


INTRODUCTION
Centralised power system and generation have been used for their efficiency and economic feasibility. However, as the construction of large-scale generators and transmission lines has become increasingly difficult, decentralised power systems and microgrids have attracted increasing attention. Microgrids are small independent power systems that can reduce or eliminate the need for central control [1][2][3][4]. Distributed energy resources (DERs) and energy storage systems (ESSs) are the main components of microgrids.
Droop control has been widely used for the primary frequency and voltage control of microgrids and conventional centralised power systems [5,6]. Conventional frequency droop control is based on frequency changes and does not require communication. However, frequency droop control is not optimal for controlling the DERs and ESSs in microgrids [5]. Furthermore, owing to its low transient response speeds, it is not suitable for performing rapid and large changes in load and generation [7,8]. Voltage source converters (VSCs) for DERs and ESSs can control the voltage angle, which changes the power-sharing between sources [9,10]. In angle droop control, each converter controls its angle via the droop. Compared to conventional frequency droop methods, the angle droop method provides better transient performance and smaller steady-state errors. However, angle droop control also has drawbacks when used for distributed control. The voltage angle is a relative value and requires a common reference. For this reason, global positioning system (GPS) timing receivers and communication devices are needed for angle droop control, making it more difficult to apply to real systems compared to the frequency droop control approach [8,11].
Frequency stability is related to how quickly the active power balance is restored. ESS and VSC have fast dynamics and can contribute significantly to frequency stability, but their performance is limited by slow response speed of frequency droop control. In recent years, several methods have been developed to overcome frequency droop control issues [12][13][14][15][16][17][18]. S-shape control for secondary control to output more power in the normal frequency range and reduce the power outside the normal range is prosed in [15]. In [16][17][18], cubic droop and sectional droop control are introduced to prevent unnecessary operation and fast motion characteristics in critical situations. However, these methods are still based on frequency deviation, and owing to the inertia of the power system frequency, the rate of change is slow compared to the active power imbalance. For a frequency-based droop, the deadband and droop ratio can be adjusted to improve the response speed [19]. However, in frequency-based droop control, if the deadband and droop ratio is adjusted to increase the response speed, it leads to an active power source problem of unnecessarily frequent operation. Therefore, the slow response speed issue of frequency droop control has not been solved.
Droop control is widely used for frequency regulation and microgrid control [20][21][22][23][24][25]. Conventional frequency droop control is a simple and effective control method, but it is not suitable for future power system equipment control owing to its low performance in distribution networks and transient situations [5]. To achieve fast and high performance in transient, microgrid states need to be identified quickly using minimal communication. Power system frequency variation is due to imbalances in the active power supply and demand. Therefore, the imbalances between supply and demand are the best indicators of the frequency state of a power system.
In this study, we develop a primary frequency control method for converter-fed microgrids. The proposed method has a fast response speed that prevents unnecessary operation, and it does not require communication equipment. In this method, primary frequency controls are based on active power imbalance estimated from the frequency deviation and the speed of the frequency drop. Because frequency fluctuations arise from active power imbalances, imbalance is a faster and more accurate indicator than frequency deviation. Using the estimated active power imbalance for control, instead of frequency deviation, there are several advantages over previous methods.
The dynamic response speed of the proposed method is much faster because it is controlled by imbalance rather than frequency. Due to the fast response speed of the proposed method, the active power balancing performance of ESS and VSC can be properly utilized, and frequency stability is greatly improved through this. Therefore, the transient performance of droop control and frequency stability are further improved. Furthermore, imbalance-based control minimises the operating point change of the grid-connected VSCs to minimise variability in a transmission system using microgrids. To minimise the impact on the transmission system, the VSC operating point change should be made only when the ESS and the governor response in the microgrid cannot handle the frequency fluctuation. Based on the estimated imbalance, the magnitude of the frequency drop can be identified more accurately, enabling the VSC to operate only when it is absolutely necessary. In the case of conventional frequency droop control, the deadband can be increased to minimise changes in the grid-connected VSC operation. However, this reduces the response speed of the frequency droop [19]. Unlike angle droop control, the proposed droop control method does not require communication between resources because the estimated imbalance is a synchronised value in the power grid.
The main contributions of the proposed microgrid control method over conventional ones can be stated as follows: • Faster response than frequency droop control • More accurate diagnosis of contingency in the power system • Less impact on the transmission systems • Efficient frequency regulation considering facility characteristics • Control without the requirement of additional communication devices or phasor measurement unit The rest of this paper is organised as follows. In Section 2, we describe the configuration and function of the converterfed microgrid and imbalance-based droop control method for microgrids. In Section 3, we present the simulation results and comparisons of the imbalance-based droop control and frequency droop control methods. In Sections 4 and 5, we present the discussion and conclusions.

IMBALANCE-BASED DROOP CONTROL FOR MICROGRID
In this study, the estimated active power imbalance is used for droop control. Using imbalance-based droop control, controllable equipment in a microgrid can operate and adjust faster than under frequency-deviation-based conventional droop control. Moreover, the VSC, which connects the microgrids to the main grid, adjusts the active power only when large power imbalances occur.

Converter-fed microgrid
A microgrid consisting of an ESS, distributed generation and grid-connected VSC can be operated in stand-alone and grid-connected modes via the VSC, which has a good dynamic performance for active and reactive power control and can operate bidirectionally [26]. Figure 1 shows the configuration of a converter-fed microgrid. In the grid-connected mode, the VSC can compensate for the variability in the microgrid and control the bidirectional power flow. In stand-alone mode, the microgrid is asynchronous and operates independently of the transmission system via the VSC. In this study, the photovoltaic (PV) array in the microgrid is not used for primary frequency regulation and is assumed to operate on maximum power point (MPP) [27].

Imbalance estimation
Electric power system frequency fluctuation is caused by active power imbalances between supply and demand in the power

FIGURE 1
Configuration of the converter-fed microgrid system. Because it is difficult to calculate the imbalance by accurately measuring the supply and demand in real-time, frequency deviation has been used for primary frequency control. In this study, the imbalance is estimated based on the swing equation.
The swing equation is a second-order differential equation that shows the swing of a synchronous machine. Assuming that the power system is a single large synchronous machine, the swing equation can be used to calculate the power system frequency fluctuation and active power imbalance [28]. The power system frequency dynamic with governor response is as follows [29]: where ΔP g and ΔP l are the changes in power generation and load, respectively, D is the load-damping constant, R is the governor response ratio of conventional generators, and H is the inertia of the power system. The active power imbalance P imb can be expressed as From Equations (1) and (2), we obtain If the primary reserve sources measure the time t and frequency deviation, as shown in Figure 2, the active power imbalance can be calculated using Equation (3). Because the FIGURE 2 Frequency fluctuation in the converter-fed microgrid electrical power system frequency is the same throughout the system, it can be measured at the point-of-common-coupling bus without remote communication. The power system inertia and load-damping constant are very important for imbalance calculations. The inertia and load-damping constants change excessively frequently to monitoring them in real-time. In this study, the inertia and load-damping constants are assumed to be the maximum values of a given power system. The estimated active power imbalance can be expressed as where D max is the maximum value of the load-damping constant, and R max is the maximum value of the governor response ratio of conventional generators of power system. Using the maximum value of the inertia and load-damping constants, the estimated imbalance is larger than the actual active power imbalance, ensuring a margin. The relative magnitude of the imbalance is used as an indicator of droop control.

Imbalance-based droop control for ESS and governor response
In the proposed microgrid control method, the governor response of combined heat and power (CHP) and an ESS are responsible for the primary frequency control. For the primary frequency control of the CHP generator and an ESS, the estimated active power imbalance in Equation (4) is used. Figure 3 shows the imbalance-based droop characteristics of the ESS and CHP in a microgrid.
As shown in Figure 3, the basic control characteristics of the proposed droop for the ESS and CHP are proportional, as is the case for conventional droop control. The major difference between the proposed and conventional droop control methods is that the former uses the estimated active power imbalance, as a control indicator, rather than the frequency deviation. The relationship between the ESS output deviation ΔP ESS and the estimated imbalance is given by where k ESS is the frequency response ratio of the ESS. The ESS adjusts the output P ESS by considering the scheduled output P Sch ESS and ΔP ESS as follows: From Equations (4), (5), and (6), we obtain In this paper, negative and positive values of the ESS output indicate charging and discharging, respectively. The imbalance- where k CHP,n is the frequency response ratio of the n th CHP. The CHPs adjust the output P CHP by considering the scheduled output P Sch CHP and ΔP CHP as follows: P CHP,n = P Sch CHP,n + P CHP,n From Equations (4), (8), and (9), we obtain If multiple ESSs with different performances and capacities are mixed in a microgrid, different droop coefficients for individual ESSs can be applied. The primary frequency control is a control that operates for a short period of time, and during this time, the state of charge of the ESS does not change significantly and does not affect control performance much.

Imbalance-based droop control for VSC
The objective of the grid-connected VSC is to minimise the active power adjustment of the VSC for primary frequency control to reduce its effect on the main grid. To achieve this, the deadband in the active power imbalance is set for the droop control, as shown in Figure 4. The VSC adjusts the active power only when a large active power imbalance occurs that is too large for the primary reserves in the microgrid. Consequently, the deadband of the imbalance-based droop control is determined from the capacity of the primary reserves in the microgrid, load-damping constant, and frequency regulation. The upper ΔP + imb,cri and lower critical imbalances ΔP − imb,cri are expressed as follows: where Δ f − reg and Δ f + reg are the lower and upper limits of the frequency, respectively, D min is the minimum value of the loaddamping constant, and P cap primary is the total capacity of the primary frequency reserve in the microgrid. For the reserve margin and error compensation, the load-damping constant is assumed to be a minimum value. From Equations (11) and (12), the upper and lower ranges of the deadband DB + and DB − are set as The participation rate c, which has a value between 0 and 1, is set as the degree of VSC participation during active power imbalance. Changes in the active power of the microgrid via the VSC are represented as follows: Figure 4 shows the imbalance-based droop control of the characteristics of the VSC obtained using Equation (15). The active power P VSC supplied to the microgrid via the VSC is where P Sch VSC is the scheduled active power supplied to the microgrid via the VSC. As shown in Figure 5, proposed method estimates the frequency imbalance from Equation (4) and uses it as a control input, unlike conventional methods that use frequency deviation as a control input. VSC can adjust the influence and independence on the main grid by applying participation rate c.

SIMULATION RESULTS
For the simulation, a converter-fed microgrid consisting of a CHP generator, a load, a photovoltaic (PV), an ESS and a   (Figure 1). The PV, ESS and demand data of the microgrid study by Tsukuba were used [30,31]. The total capacity of the PVs in the microgrid was 90.84 kWp, and the rated capacity and power of the ESS were 326 kWh and 90 kW, respectively. Three CHP systems with a capacity of 300 kW each were installed in the microgrid. The generalized model was used for CHP, ESS and VSC [28,32,33]. The inertia and loaddamping constants of the microgrid were assumed to be 7.6 and 3.565, respectively, which are the average values for the Korean power system [34,35]. The rated frequency of the microgrid was 60 Hz. Table 1 shows the parameters of the microgrid components used in the simulation. Mathematical models of power system frequency and MATLAB R2020a were used for the simulations [29].

Primary frequency control simulations
In this section, we report the results of the primary frequency control of the microgrid in the transient state. The purpose of this simulation was to verify the transient performance of the proposed control. The electric demand and PV output of the microgrid were 1000 and 35 kW, respectively. To test the primary frequency control, a large amount of generation tripping, which caused a decrease in frequency in the microgrid, was simulated in the microgrid at 1 s intervals. The role of the primary frequency reserve in this simulation was to maintain the frequency within the regulation range (±0.5 Hz) until the automatic generation control operated (10 s). Figure 6 shows the frequency fluctuation and active power output of the ESS and VSC at generator tripping of 100, 150, 200 and 300 kW. As shown in Figure 6(a,b), the ESS reacted quickly to the active power imbalance, but the VSC did not change its operation in the 100 and 150 kW generation tripping cases. Even though the 100 and 150 kW generation tripping cases were larger than the ESS capacity, the frequency could be maintained within the operating range by the load-damping characteristics and the governor response of the CHP. Therefore, the VSC did not need to change its active power flow from the transmission system. Using the imbalance-based droop control at the VSC, it was possible to prevent the VSC from unnecessary changes of operation. In contrast, the operation point of the VSC rapidly changed to maintain the frequency deviation in the regulation range in the frequency droop control.
Other simulations were performed under the same conditions for comparison with the conventional frequency droop in the two cases. Each case was set with a different deadband and percent droop to compare the response speed and VSC operation of the conventional and proposed methods. Because angle droop requires communication and GPS timing devices, it was excluded from this comparison. Table 2 lists the deadband and percent droops for two cases.
In case 1, a wide deadband of the VSC and a small percent droop were set to prevent the frequent operation of the VSC and to achieve a similar effect as the imbalance-based droop control. The percent droop is the percentage between the frequency change and the power output change. A lower percent droop indicates a greater the power output change for a given frequency change. Although the percent droop is generally set to 3-5%, in this study, it was set to 1% to increase the speed of the droop control. To prevent frequent operation of the VSC, a wide deadband was set (400 mHz). Figure 7 shows the frequency fluctuation and active power output of the ESS and VSC, respectively, at generator tripping of 100, 150, 200 and 300 kW in case 1.
As a wider deadband was set, the frequency droop control showed similar results to the imbalance-based droop control. The VSC did not change its active power flow from the transmission system in the 100 and 150 kW generation tripping, which could be compensated for by the ESS, governor response, and load damping in the microgrid. For the 200 and 300 kW generation tripping, which could not be compensated for by the microgrid, the VSC changed the active power and stopped the frequency drop, as shown in Figure 7(a,b). However, in the 200 kW generation tripping, the microgrid frequency exceeded the lower limit even though the VSC controlled a similar amount of active power to the imbalance-based droop control. By widening the deadband, the response of the VSC was slowed down, resulting in a greater frequency deviation compared to that of the proposed method. To reduce the frequency deviation in the 300 kW generation tripping, the deadband was narrowed to 250 mHz in case 2. The droop was increased to 2% to prevent frequent operation of the VSC. Figures 7 and 8 show the frequency fluctuation and active power output of the ESS and VSC at the 100, 150, 200 and 300 kW generator tripping in case 1 and case 2, respectively. By narrowing the deadband, the VSC could respond quickly to 300 kW generation tripping and maintain the frequency within the regulation range, as shown in Figure 8(d).
Although the frequency deviation was within the regulation range, the change in frequency was still slow compared to that achieved with the imbalance-based droop control. Moreover, Figure 8(b) shows that the VSC changed the active power supplied to the microgrid. The frequency droop with a narrow deadband inevitably affected the transmission system, even when the microgrid could compensate for the imbalance.

Comparison between proposed control and frequency droop control
The response speed and primary frequency control performance of the conventional and proposed methods were compared with the largest generation tripping in the microgrid (300 kW). As shown in the previous simulation, with 300 kW generator tripping, the ESS must be operated at the rated power and the operating point of the VSC must be adjusted to maintain the frequency. Table 3 shows the rise time (0-90%) and settling time (±5%) of the imbalance-based droop and frequency droop.
In comparing case 1 and case 2 of the frequency droop as shown in Table 3, there is no significant difference between the rise time and settling time because the ESS has the same droop ratio and deadband value. On the other hand, in the case of VSC, the rise time decreased from 732 to 659 ms owing to the reduction in the deadband and the increase in the droop ratio in case 2. However, even in case 2, the rise time is long compared to that of the imbalance-based droop because the frequency deviation reacts more slowly than the active power imbalance. For the imbalance-based droop, the rise times of the ESS and VSC are 38 and 89 ms, respectively.
The nadir of the frequency and rate of change of frequency (ROCOF) were calculated for quantitative analysis of the primary frequency control performance. The ROCOF was calculated as the average over time until the frequency reached its nadir. Table 4 lists the nadir and ROCOF for the imbalancebased droop and frequency droop, respectively. It can be seen that the imbalance-based droop significantly improved the nadir and ROCOF. In particular, the VSC reacted quickly at the beginning of the frequency drop, significantly reducing the ROCOF compared to the frequency droop control. In contrast, the frequency droop control in case 1 prevented the

FIGURE 9
Microgrid frequency and active power output of the ESS and VSC in cubic droop control with generation tripping of (a) 150, (b) 300 kW frequent operation of the VSC; however, the nadir was outside the frequency regulation range and the ROCOF was large. In case 2, in which the response speed was higher owing to the narrower deadband, the nadir and ROCOF were higher, but the response speed was still slower than that of the proposed method. In addition, the VSC changed the operation point even when it was not necessary and caused variability within the transmission system for 150 and 200 kW generation tripping. Cubic droop control and sectional droop control were recently proposed in [16][17][18] to achieve a fast response speed and prevent the unnecessary operation of frequency droop control. The cubic droop method controls the active power proportionally to the cube of the frequency deviation. The sectional droop control method reacts more sensitively to large frequency deviations by applying different droop ratios according to the frequency range. Simulations were performed to compare the latest frequency-based droop controls with the proposed imbalance-based droop control. Figures 9 and 10 show the microgrid frequency and active power change of ESS and VSC with generation tripping. Table 5 compares the  However, owing to frequency-based control limitations, the response speed is still slower than the proposed imbalancebased control. Additionally, unlike the imbalance-based droop control, both methods did not prevent unnecessary VSC operation for 150 kW generation tripping. Table 6 shows that the ROCOF of cubic control and sectional control is larger than that of the proposed method due to the slow response speed and that they cannot adequately cope with the initial stage of frequency fluctuation.

DISCUSSION
The frequency droop method is widely used because it is simple and effective, but it is not suitable for facilities with a fast response speed, such as ESS, owing to its slow response speed. Because the power system frequency change is induced by the integral of the active power imbalance over time, the frequency change lags behind the active power imbalance. The response speed of frequency droop can be improved by adjusting the droop ratio and deadband, but this causes excessively frequent operation. Methods to solve this problem have been proposed [12][13][14][15][16][17][18], but frequency-based droop control has limitations. To overcome the problem of frequency-based droop control in microgrids with ESS and VSC, a novel droop control method based on active power imbalance is proposed in this paper. Because the estimated active power imbalance precedes the frequency deviation, the response speed of the proposed droop control method is faster than the existing frequencybased droop control method. As shown in the primary frequency control simulation in Section 3.1, VSC did not unnecessarily change the operation for 100 and 150 kW generation tripping in the proposed method. For frequency-based droop, the deadband can be widened to achieve a similar effect, but this results in a slower response speed. As shown from the results of the comparative simulation in Section 3.2, the imbalance-based droop control method has a faster response speed and improved ROCOF when compared to the conventional frequency droop control, as well as the recent frequency droop controls. Moreover, for small-generation tripping, imbalance-based droop control prevents unnecessary VSC operation when compared to frequency-based droop controls, enabling more efficient system operation.

CONCLUSION
In this paper, we presented the imbalance-based droop control as a new primary frequency control method for converter-fed microgrids. The imbalance-based droop control uses the active power imbalance estimated from the swing equation instead of the frequency deviation. The proposed imbalance-based droop control method has a faster response speed than existing frequency-based droop control methods and a significantly lower rise and settling times of the ESS and VSC in the microgrid without additional communication devices or phasor measurement units. In addition, the ROCOF and nadir of frequency can be improved by fast response using estimated active power imbalance directly and it is possible to prevent unnecessary operation of the VSC for small-generation tripping.
We expect the proposed method to be utilized for the stable and efficient operation of power systems with numerous microgrids and inverter-based resources. In future research, various applications and filter designs for imbalance estimation will be studied.