4.1. Adaptive Coordinated Control of VIC and VDC Based on Supercapacitor–Lithium Battery
From the analysis in
Section 3.3, it can be seen that the energy storage involved in VIC can increase the system inertia, the energy storage output is proportional to the rate of change of frequency when a sudden change in the system frequency needs to respond quickly to inhibit the change of frequency, and at the same time there is the disadvantage of inhibiting the recovery of the frequency after the frequency deviation reaches the extreme value. Energy storage involved in the VDC when the output and the frequency deviation is proportional to the frequency in the entire FR cycle can be effective in inhibiting the deterioration of the frequency, however, VDC requires energy storage to produce power for a long period of time, which requires energy storage to be configured with a higher FR capacity. It can be seen that VIC and VDC should be used before the frequency reaches the extreme value, and only VDC should be used after the extreme value point to ensure the effect of frequency regulation. However, the literature [
18,
19,
20,
21] suggests that a single energy storage to implement the above strategies at the same time cannot reflect the characteristics of the energy storage involved in the VIC and VDC at the same time, which ignores that the characteristics of the VIC and VDC for the energy storage power and capacity requirements are different, therefore, in order to give full play to the advantages of the power-type and energy-type energy storage in the two modes of FR control, this paper further puts forward a supercapacitor–lithium-battery-based adaptive VIC and VDC control. An adaptive coordinated control strategy of VIC and VDC is further proposed in this paper.
At present, the most commonly used and the most mature energy storage is based on lithium batteries as the main energy-based energy storage, which is characterized by high energy density and low power density. Supercapacitor-based power-type energy storage is less used in the field of FR, which is characterized by high power density and small energy density, which is due to the high cost and small capacity of supercapacitors, which are not suitable for today’s drastic load disturbances in systems.
Table 1 demonstrates the performance comparison between the typical power-type and energy-type energy storage [
14]. It can be seen that power-based energy storage is suitable for VIC due to its high power density and fast response to frequency-changing signals, while energy-based energy storage is suitable for VDC due to its high energy density, which can leave a sufficient FR margin to perform FR tasks throughout the FR cycle.
In summary, in order to solve the limitations of a single control method on the frequency control effect and make full use of the complementary advantages of VIC and VDC, this paper firstly proposes an adaptive coordinated control strategy of VIC and VDC. When the system frequency changes abruptly (i.e., energy storage is needed for inertial support), since VDC can improve the frequency control effect throughout the frequency control cycle, the control strategy of superposition of VIC and VDC should be adopted at this time; when the frequency deviation reaches the maximum value, since VIC will inhibit the frequency recovery instead, only the VDC control strategy should be adopted at this time. When the frequency deviation reaches the maximum value, the VIC will inhibit the frequency recovery, and only the VDC control strategy should be adopted. Then, considering that power-based energy storage is applicable to VIC and energy-based energy storage is applicable to VDC, the output power of hybrid energy storage and its auxiliary thermal power units to participate in the primary FR of the regional grid are obtained in the dynamic model as shown in Formula (10) and
Figure 3.
where
and
are the FR transfer functions of the supercapacitor and lithium battery, respectively.
From Formula (10) and
Figure 3, the frequency deviation under the control strategy of this paper is given as
Further, the initial frequency rate of change and the steady-state frequency deviation can be calculated as
4.2. Improved Generalized Logistic Function Design Method Based on Energy Storage Output Constraints
When the energy storage battery responds to the demand of system frequency regulation, if it has been operating with a given inertia/sag coefficient, it is very easy to saturate or exhaust the energy storage capacity due to the excessive frequency deviation in some time periods. In previous studies, many experts and scholars have improved the fixed inertia/sag coefficient control [
22,
23], and the more typical ones are the variable coefficient control [
24], however, the previous control strategies focus on establishing a simple linear constraint between the storage inertia/sag coefficients
and
and the SOC. This alleviates the problem of overcharge and overdischarge of the energy storage battery to a certain extent, but at the same time, there are two main problems: one is weakening of the fast response characteristics of the energy storage battery, and the other is a secondary perturbation of the system frequency when its own SOC reaches the critical point.
Therefore, when introducing the variable coefficient control, it is necessary to consider that when the storage SOC is in a relatively good interval, it should be a priority to ensure the FR demand and participate in the FR control with a high inertia/sag coefficient; and when the SOC is in a relatively poor interval, the storage should be less charged and less discharged or even not charged and not discharged in order to ensure that the SOC is maintained in a reasonable range and to leave the FR margin for the subsequent cycle and reduce the storage life loss. This paper is based on a generalized logistic curve, which is often used as an S-shaped curve that mimics similar population growth, as shown in Formula (13). The curve initially grows slowly, with the fastest growth rate at the center point, and then gradually slows down, and the overall growth rate is characterized by slow–fast–slow. In this paper, the generalized logistic function is improved by combining the relationship between the energy storage output and SOC, so that the discharge/charge of the energy storage can be limited as much as possible when its SOC is small/large, i.e., its corresponding inertia/sag control coefficients are lowered, and the output of the energy storage can be unrestricted as much as possible when the SOC is in a better state.
where
K is the maximum value;
P0 is the initial value, affecting the logistic function slope at the maximum (hereinafter referred to as the center point) of the location, P0. The smaller the function of the center of the curve from the
SOC = 0.5, the closer the curve, so this paper takes the
P0 to 0.01; n represents the curve change as fast or slow (i.e., the slope of the center point); the appropriate transformation of Formula (13) can be obtained with the curve shown in
Figure 4, and its expression is as follows:
In summary, the flowchart of the hybrid energy storage adaptive VIC and VDC coordinated control strategy proposed in this paper taking into account SOC optimization is shown in
Figure 5.
In order to quantitatively analyze the effectiveness of the strategies proposed in this paper, this paper defines the evaluation indexes of maximum frequency deviation Δfm, frequency decline rate Vm, and steady-state frequency deviation Δfs to evaluate the effectiveness of FR and the SOC of energy storage under different strategies, as follows.
- (1)
Primary FR Effectiveness Indicators
In the typical step load disturbance, so that the initial moment is t0, the initial frequency deviation is Δf0. When the frequency deviation reaches the maximum value of the moment for the frequency deviation that at this time is set to tm, it can be defined as the frequency rate of descent for the Δfm; the frequency deviation begins to recover until it reaches the steady-state moment Vm when the steady-state frequency deviation is set to Vm = (Δf0 − Δfm)/(tm − t0). Δf0, t0 are taken to be 0. Obviously, the smaller the value of Δfm, Vm, and Δfs, the more pronounced the effect of frequency regulation.
Under continuous load disturbance, all frequency deviation values in the sampling points can be measured. So that there are n sampling points, regarding Δfi for the ith sampling point of the frequency deviation value, the root mean square value of is calculated and, obviously, a smaller value of the frequency regulation effect is better.
- (2)
SOC Maintenance Effectiveness Indicators
In the same way as for the frequency deviation metric under continuous perturbation, the root mean square value of the SOC deviation (i.e., the degree of deviation from the optimal SOC0 = 0.5) is taken to be , and it is clear that the smaller the value, the better the SOC maintenance effect.