1. Introduction
Most recently, stand-alone microgrids are involved in a great transition with the high penetration of renewable energy sources (RESs) by replacing conventional diesel synchronous generators. In other words, for microgrids, which were previously operated with only diesel generators, the entire topology of system is being changed in the form of distributed energy resources (DERs) [
1,
2]. In this case, the entire planning process must be redesigned to ensure stable operation of the microgrid. However, the high penetration of RESs, which are mainly wind turbine (WT) and photovoltaic (PV) generators, may increase the uncertainty in the power system while causing large frequency variations. Therefore, stand-alone microgrids, which are isolated from the main grid, must include dispatchable generators in order to overcome the uncertainty from RESs.
The size and placement of RESs can be optimized using electrical system data (e.g., frequency limits, voltage limits, system protection equipment, settings, etc.) and RES data (e.g., type of generator, operation modes, potential locations, etc.) [
3]. Furthermore, the system design, which can ensure frequency stability, is necessary because the frequency relay in the microgrid operates when the system frequency varies beyond its limits while causing unwanted blackout. Thus, the frequency stability must be considered to calculate the maximum penetration capacity of RESs for a stand-alone microgrid with high renewable penetration.
Several studies [
4,
5,
6,
7,
8,
9,
10,
11] were carried out for the stability of system frequency when the level of renewable penetration was increased. In Reference [
4], the system frequency response was analyzed for different wind power penetration levels, and an optimal parameter range for a controller was derived. Also, the method to increase the penetration level of RESs by using the storage characteristics of an energy storage system (ESS) was described in Reference [
5]. In Reference [
6], inertial control for a WT was proposed to stabilize the stand-alone microgrid. In addition, the control method of ESS was proposed to accommodate wind power fluctuations in [
7]. The genetic algorithm (GA)-based method was proposed in Reference [
8] for an optimal charging/discharging scheduling of ESSs, which are interconnected with PV. Furthermore, the integrated wind, solar, and energy storage plant, which mitigates power generation with a complementary generation profile, was introduced in Reference [
9]. Hence, to increase the renewable penetration level of the grid, various frequency control methods were studied. In Reference [
10], the ESS provided inertial and primary reserves to enhance the frequency stability, and it was sized in terms of required power and energy. Also, the supplementary droop control method was introduced to improve the stability of the microgrid in Reference [
11]. However, it is essential to precisely determine the maximum penetration capacity of PV because the PV generators lack adaptive control technologies, such as inertial control in WTs.
Few studies were reported on the capacity calculation of the RESs. Instead, most papers focused on the optimum sizing of ESS. In Reference [
12], the methodology for planning the energy and power capacity of ESS was proposed in order to smooth the fluctuation from RESs. The ESS sizing method to increase the renewable penetration in terms of grid frequency deviations was introduced in Reference [
13]. In Reference [
14], the probabilistic approach for the optimal capacity specification of renewable integrated ESS was tested using real wind data. The assessment of maximum capacity for DERs was given in Reference [
15]. However, multiple operation scenarios must be analyzed by using a probabilistic method, which is time consuming.
In this paper, an algorithm to evaluate the maximum penetration capacity of PV is proposed. It determines the capacity of the PV based on both maximum quasi-steady-state (QSS) and instantaneous frequency deviation limits, which are given by the system operator reflecting the characteristics of the microgrid. Then, the magnitude of a credible contingency event is derived by using the dynamic droop equation while considering the droop coefficient and reserve powers at the initial and post-contingency state of diesel generators. Thereafter, the maximum penetration capacity of PV is evaluated from the perspective of QSS frequency. Finally, a time-domain simulation is carried out to determine whether the frequency stability of the microgrid is ensured based on the required limits of the QSS and instantaneous frequency. In conclusion, the main contributions of this paper are summarized as follows:
The maximum penetration capacity of PV is evaluated to satisfy the frequency stability of a stand-alone microgrid;
A new dynamic droop equation is derived by considering both the droop coefficient and reserve power of each generator instead of the droop coefficient for entire system;
Case studies are carried out by using the practical data of stand-alone microgrid in South Korea.
This paper is organized as follows: firstly, a theoretical background for four stages of the frequency responses for a stand-alone microgrid is described in
Section 2. Then, the method to evaluate the maximum penetration capacity of PV is proposed in
Section 3. A model of a practical stand-alone microgrid with diesel generators, PV generators, and ESSs is described in
Section 4. Next, several case studies are carried out on the stand-alone microgrid with high renewable penetration by using both analytic analysis and time-domain simulations based on DIgSILENT PowerFactory
® software in
Section 5. Finally, conclusions are given in
Section 6.
2. Frequency Response of Microgrid with High Renewable Penetration
Most power systems have hierarchical controls to eliminate power imbalances rapidly and reliably after a disturbance, by which the system frequency is reduced from its nominal value,
fnom, by more than a deadband,
fdb. They can be divided into three levels, which are the primary, secondary, and tertiary controls. However, the frequency response behavior can be classified into four stages, as shown in
Figure 1 [
16]. The first stage is the inertial response, which is uncontrolled because the power imbalance is instantaneously and naturally resolved by the stored kinetic energy of synchronous generators. In other words, the power output will be increased for a short time as the rotational energy in the synchronous generator is released to mitigate the fluctuation in system frequency. The second stage is the primary frequency response (PFR), in which the power imbalance is eliminated by the power output control of each generator, depending on the frequency deviation. With this control, also referred to as droop control, the system frequency is settled to the QSS value,
fQSS, where a power balance is ensured. Then, the secondary frequency response (SFR) follows to compensate for the system frequency deviation from its nominal value (i.e., 60 Hz). Finally, the tertiary frequency response (TFR) relates to long-term operations making the generators operate at their optimal point.
In the stand-alone microgrid, the system frequency lasts at
fQSS for a long duration since the secondary control acts more slowly than in larger power systems. Furthermore, the minimum instantaneous frequency,
fmin, occurs during the PFR stage as shown in
Figure 1. Both the deviation of QSS and instantaneous frequency should not exceed their limits (Δ
fQSS,max and Δ
fins,max, respectively) to ensure the frequency stability of the stand-alone microgrid. Therefore, the maximum penetration capacity of PV must be evaluated in terms of
fQSS and
fmin, which are described in the subsequent sections.
2.1. Quasi-Steady-State Frequency
The droop control is generally used as the primary control in a microgrid [
17]. When a number
n of generators in a power system utilize the droop control, the deviation of system frequency for the QSS, Δ
fQSS, can be calculated for the entire system according to the droop equation as follows:
where the
Rsys is the droop coefficient of the entire power system, and the Δ
P is the deviation of active power generation caused by a disturbance. The
Ri and
Pi,max are the droop coefficient and maximum power output limit of the
i-th generator, respectively. However, when the renewable penetration level of system is high, the reserve power of each generator may be insufficient even if the reserve power of all generator is enough. If the power output of diesel generator reaches its limit before the system frequency settles, both
Rsys and
fQSS will decrease. Therefore, Δ
fQSS must be calculated by considering the reserve power of each diesel generator.
2.2. Instantaneous Frequency
When the system frequency is significantly reduced, load shedding may be induced to prevent the outage in the generator from rotating beyond the operating speed range. Therefore, the instantaneous frequency must be maintained higher than the outage point. Both the system droop coefficient and inertia constant of the system are important factors for computing
fmin, which is observed in the PFR stage. The system inertia constant,
Hsys, is calculated as follows:
where the
Hi and
Si are the inertia constant and apparent power of the
i-th generator, respectively. However, because the exact value of
fmin is difficult to calculate, the swing equation is used to indirectly assess the value. The effect of the inertia on the system frequency is given as follows:
where the
df/
dt is the rate of change of frequency (RoCoF), and
Pm and
Pe are the mechanical power and electrical power, respectively. From Equation (4), it is obvious that the grid with a larger inertia constant will have the higher
fmin. However, the RoCoF is also affected by the response time of how closely
Pm follows the reference signal,
Pe. Therefore, the response time of a generator is difficult to obtain numerically. Instead, it can be estimated from time-domain simulations.
6. Conclusions
This paper proposed a new method for evaluating the maximum penetration capacity of a photovoltaic (PV) generator for a practical stand-alone microgrid with high renewable penetration. The credible contingency event was calculated for the microgrid using the dynamic droop equation, which incorporates the relationship between the deviation in system frequency and the size of active power disturbance in real time. By considering both quasi-steady-state (QSS) and instantaneous frequency, the maximum capacity of PV for a given number of diesel generators can be evaluated. As the result, the generation composition of microgrid can be determined to achieve the highest renewable penetration level with or without the ESS. Moreover, the relationship between the additional capacity of PV and ESS was analyzed to select the optimal size of ESS.
To verify the effectiveness of the proposed algorithm, several case studies were carried out by using both mathematical and simulation-based analyses. The results showed that the proposed evaluation method could only determine the maximum penetration capacity of PV and size of the credible contingency event in terms of QSS frequency. Therefore, time-domain simulations must be carried out to access whether the system frequency varies beyond the maximum instantaneous frequency deviation limit.