A Review of State-of-the-art Flexible Power Point Tracking Algorithms in Photovoltaic Systems for Grid Support: Classification and Application

Mina Haghighat; Mehdi Niroomand; Hossein Dehghani Tafti; Christopher D. Townsend; Tyrone Fernando

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A Review of State-of-the-art Flexible Power Point Tracking Algorithms in Photovoltaic Systems for Grid Support: Classification and Application PDF

- ORCID：
Mina Haghighat ¹
✉
- ORCID：
Mehdi Niroomand ¹
✉
- ORCID：
Hossein Dehghani Tafti ²
✉
- ORCID：
Christopher D. Townsend ²
✉
- ORCID：
Tyrone Fernando ²
✉

1. the Department of Electrical Engineering, University of Isfahan, Isfahan, Iran； 2. the Department of Electrical, Electronic and Computer Engineering, University of Western Australia, Crawley WA 6009, Australia

Updated：2024-01-22

DOI：10.35833/MPCE.2022.000845

OUTLINE

Abstract

To maximize conversion efficiency, photovoltaic (PV) systems generally operate in the maximum power point tracking (MPPT) mode. However, due to the increasing penetration level of PV systems, there is a need for more developed control functions in terms of frequency support services and voltage control to maintain the reliability and stability of the power grid. Therefore, flexible active power control is a mandatory task for grid-connected PV systems to meet part of the grid requirements. Hence, a significant number of flexible power point tracking (FPPT) algorithms have been introduced in the existing literature. The purpose of such algorithms is to realize a cost-effective method to provide grid support functionalities while minimizing the reliance on energy storage systems. This paper provides a comprehensive overview of grid support functionalities that can be obtained with the FPPT control of PV systems such as frequency support and volt-var control. Each of these grid support functionalities necessitates PV systems to operate under one of the three control strategies, which can be provided with FPPT algorithms. The three control strategies are classified as

① constant power generation control (CPGC), ② power reserve control (PRC), and ③ power ramp rate control (PRRC). A detailed discussion on available FPPT algorithms for each control strategy is also provided. This paper can serve as a comprehensive review of the state-of-the-art FPPT algorithms that can equip PV systems with various grid support functionalities.

Keywords

Maximum power point tracking (MPPT); flexible power point tracking (FPPT); power reserve control (PRC); power ramp rate control (PRRC); low voltage ride-through (LVRT); constant power generation (CPG).

2023.

A. Variables

$τ_{s t a t i c}$ Static filtering effect

$τ_{d y n a m i c}$ Dynamic filtering effect

$Δ p$ Power reserve

$C_{p v}, C_{d c}$ Photovoltaic (PV) panel capacitor and DC-link capacitor

$D$ Duty cycle of DC-DC converter

$D_{m a i n}, D_{r i p p l e}$ Main duty cycle of DC-DC converter and perturbation signal

$f_{s, d c d c}$ Switching frequency of DC-DC converter

$f_{s w, i n v}$ Inverter switching frequency

G Irradiance

$i_{p v}$ PV output current

$i_{p v}^{*}$ PV current reference

$i_{m p p}$ PV current at the maximum power point (MPP)

$i_{l i m i t}$ Current limit

i_d, i_q Grid current converted to dq coordinates

$i_{l, c p g}^{*}$ Inductor current reference from constant power generation

$i_{l, m p p}^{*}$ Inductor current reference from the maximum power point tracking (MPPT) algorithm

$i_{l}^{*}$ Inductor current reference

$I_{m a x}$ The maximum value of inductor current

$I_{0}$ Constant current

$I r r$ Irradiance

$L_{b o o s t}$ DC-DC boost converter inductor

$L_{i n v}$ Grid connection inductor filter

m Integer number

$p_{p v}$ PV power

$p_{p v}^{'}$ Modified PV power

$p_{p v}^{0}$ Updated PV power after mT

$p_{m p p}$ The maximum PV power

$p_{f p p}$ Power reference calculated by grid support block

$p_{l i m i t}$ Power limit

$p_{a v a i}$ Available PV power

$P_{m i n}$ The minimum power

$p_{o l d}$ PV power in the previous time-step

$P W M_{i n v}$ , $P W M_{b}$ Pulse width modulation for inverter and DC-DC converter

dp^* Differences between PV power and power reference

$R_{r}^{*}$ Power ramp-rate reference

$R_{l i m}$ Power ramp-rate limit

S_rated Rated power

$T_{s t e p}$ Calculation time step

T Sample period of MPPT algorithm

$t_{1}, t_{2}$ Time intervals 1 and 2

$T h r$ Threshold value

$v_{p v}$ PV voltage

$v_{p v}^{*}$ PV voltage reference

$v_{m p p}$ PV voltage at MPP

$v_{f p p, l}$ , v_fpp_,_r PV voltages corresponding to the left and right flexible power points

$v_{g}, i_{g}, Z_{g}$ Grid voltage, grid current, grid impedance

$V_{d c}$ DC-link voltage

$V_{s t e p}$ Calculation voltage step

B. Subscripts and Superscripts

* Reference

cpg Constant power generation

g Grid

mpp MPP

min, max Minimum, maximum

st, tr Steady-state and transient

I. Introduction

WITH the increase of environmental concerns due to environmental pollution and global warming, together with the high consumption demand of energy for industrialization and manufacturing, the electrical industry has focused more on the evolution of renewable energy sources in recent years. Due to distinguishing benefits of photovoltaic (PV) generation such as reduced panel costs, low maintenance, high quality-factor, and easy installation for any desired capacity, PV systems are developing rapidly, especially for grid-connected applications [

1].

The maximum power point tracking (MPPT) operation is essential in many applications to generate the maximum revenue and energy yield [

2], [3]. However, the output power of the PV systems with MPPT operation cannot be flexibly controlled, because it follows the available power in the PV source, which depends on environmental conditions such as irradiance and temperature [4]. As the penetration level of PV systems increases, existing challenges pose critical problems to the stability and reliability of the power system. These challenges can include: ① reverse power flow from load towards generation units during the peak period of PV power generation (e.g., midday); ② grid-voltage fluctuations due to the sudden changes in the environmental conditions such as passing clouds; ③ reduction of system inertia and frequency regulation capability of the system operator due to the replacement of conventional synchronous generators with inverter-based systems; and ④ higher harmonic distortion levels in small islanded power systems [5]. In order to ensure the stability and reliability of the power system and reduce the adverse effects of high penetration of PV systems, power system operators are constantly updating the network codes and standards for connecting PV systems to the main grid. According to the updated grid codes, PV systems are required to provide several ancillary services such as voltage support, frequency response, harmonics compensation, and reliability and efficiency enhancement. Some of these features can be provided by flexible injection of active and reactive power into the network, according to the grid operating condition [6].

There are several ways to fulfill flexible active power control for PV systems.

One possible solution is to use energy storage systems. In this method, energy storage devices are controlled to absorb or release energy based on the active power control demands. By doing so, the maximum energy yield is harvested from the PV system and if this value is not required by the grid, the excess power is stored in the battery system. In this way, energy is stored during a high generation period and it is delivered when the available PV power falls (e.g., at night) [

7]. However, this method has some drawbacks such as high cost for the initial investments, energy recovering periods, and limited lifetime. Furthermore, by integrating batteries into PV systems, the overall system cost and complexity rise [8].

Flexible active power control can also be directly achieved in PV systems by replacing the MPPT algorithms with flexible power point tracking (FPPT) ones. In this way, the PV system operates at a reduced power level instead of the maximum power point (MPP) according to the requirements of power grid. This algorithm does not require any additional hardware, which makes it very attractive with a lot of potential applications in the existing or future PV systems. The active power control through FPPT algorithm is more cost-effective than other solutions. Furthermore, the system lifetime improves because of the reduced thermal stress of the converter [

9]. As shown in Fig. 1 [9], the FPPT algorithm regulates the operating point of the PV array corresponding to the power reference. Due to the non-monotonic characteristics of the P-V curve, there are two possible operating points resulting in the same value of power reference. The operating points are nominated as flexible power points (FPPs), i.e., FPP-L and FPP-R, which are located on the left side and right side of MPP, respectively [9]. When the power limit is less than the maximum available power, the operating point is moved to the left or right side of the MPP, i.e., FPP-L or FPP-R, respectively. Also, when the power limit is greater than the available power (e.g., for low irradiance conditions), the maximum available PV power is extracted. Therefore, according to Fig. 1, the FPPT algorithm sets the operating point in

M P P_{2}

. As can be observed from Fig. 1, the irradiance changes have a relatively small effect on the PV voltage at MPP.

Fig. 1 Concept of FPPT along with stability issues when operating point moves to the right side of MPP.

The flexible active power control schemes can be classified as: ① constant power generation control (CPGC); ② power reserve control (PRC), also called delta power control; and ③ power ramp rate control (PRRC) [

10], [11], as shown in Fig. 2 [12]. To provide each of these grid support functionalities, some specific FPPT strategies should be adopted in PV systems. This paper allocates each of these grid support functionalities with the corresponding FPPT algorithm in the literature. Such a comprehensive review of FPPT control modes for PV systems, with respect to standard requirements, is not currently available in the existing literature (to the best of the knowledge of the authors). This paper also provides a comprehensive overview of CPGC, PRC, and PRRC. The FPPT algorithms in this paper are classified, and the advantages and disadvantages of each algorithm are also reviewed and compared.

Fig. 2 Different active power control schemes for grid-connected PV systems in grid codes.

The remainder of this paper is organized as follows. Section II describes the overview of the PV system. Section III reviews the main grid support functionalities in PV systems. It also allocates each of these grid support functionalities with one of the FPPT control modes of PV systems, being CPGC, PRC, and PRRC. In Section IV, the available CPGC algorithms are reviewed and categorized. A comparison is also made between different CPGC algorithms and the advantages and disadvantages of each algorithm are analyzed. Section V provides a review and comparison between different PRC algorithms. The available PRRC algorithms are described in Section VI. Finally, a summary of conclusions is given in Section VII.

II. Overview of PV System

The main configurations of grid-connected PV systems are single- and two-stage power conversion topologies, as demonstrated in Fig. 3. The details of these PV system structures and performance descriptions of blocks in Fig. 3 can be found in [

9]. The “PV voltage reference computation (FPPT or MPPT)” block determines PV voltage reference in accordance with the power reference in the characteristic curve of the power voltage (P-V). This block is particularly considered in this paper and different control algorithms in prior artworks will be classified and compared due to their performances. The PV voltage control block adjusts the PV voltage to the voltage reference.

Fig. 3 Configurations of grid-connected PV systems. (a) Single-stage power conversion topology. (b) Two-stage power conversion topology.

III. FPPT Algorithms for Grid Support

As the penetration of PV systems in the power grid increases, these systems must support the grid in addition to generating the power. A description of some of the required grid support functionalities is provided in the following subsections.

A. Voltage Support

According to the standards, to support grid voltage, the injection or consumption of reactive power for PV systems is required, which is achieved by inverter control. Figure 4 shows the volt-var response (Q(V)) for different standards [

12], [13]. When the voltage at the point of common coupling (PCC) is smaller than the rated range, an amount of reactive power, based on the volt-var curve, must be injected into the network to increase the grid voltage. Also, when the voltage is above the nominal range, the inverter must consume an amount of reactive power, based on the volt-var curve, to help reduce the voltage at the PCC. Given the limited current rating of inverter, the amount of active power needs to be reduced, based on the required reactive power injection to the grid. As a result, the FPPT operating mode is required to support the grid voltage.

Fig. 4 Volt-var response for different standards.

As shown in Fig. 4, there is no deadband for volt-var response in Danish standard TR 3.2.2 and IEEE 1547 category A, which means that PV inverters with FPPT functionality participate in voltage regulation frequently. For standards with large dead-bands (i.e., AS 4777-2, TOR D4, and CEI 0-21), the response would rarely be activated even with the function enabled. In VDE 4105 as well as IEEE 1547 category B, the narrow dead-bands (3%) allow easier activation of volt-var response, but VDE 4105 has a relatively large reactive power range (up to 50% of $S_{r a t e d}$ ), which requires higher reactive power capability from the inverters.

B. Low Voltage Ride-through (LVRT)

If the PV systems are disconnected from the grid during low voltage conditions, problems such as power outages and voltage flickers occur on the grid. In order to eliminate the effects of these problems, the LVRT capability is recommended as an ancillary service in PV systems. During a low voltage fault, the grid voltage peak is smaller than the nominal value. Under this condition, if the system operates in the MPPT mode, the component of grid injection current increases. If this injected current exceeds the nominal inverter current rating, it will damage the inverter. If the injected power to the grid is reduced and the system continues to operate in the MPPT mode, the power input to the DC-link becomes greater than the output power, which increases the DC-link voltage. Hence, if the overvoltage is not limited, it will damage the DC-link capacitor. Therefore, in order to prevent overcurrent in the inverter and overvoltage in the DC-link, the active power generated by the PV unit should be reduced. As a result, in order to reduce the power generated by the PV unit, it is sufficient to move the operating point of the PV unit from MPP to a lower power using FPPT algorithms. Also, the LVRT capability, in addition to preventing the above problems, injects the reactive power to the grid during low voltage faults in order to improve the grid voltage [

14].

C. Reverse Power Flow

High penetration of PV systems in distribution networks can lead to reverse power flow from load towards generation units. In this case, the generated power from PV systems can be larger than the load demand of the distribution network (e.g., during mid-day), and this reverse power flow can lead to overvoltage in the distribution network. To solve this problem, when the grid voltage reaches the allowable limit, the active power output of PV units should be limited to a certain level. Therefore, by controlling the flexible active power, the overvoltage can be prevented during the peak period of PV power generation [

15]. This requirement is defined in the network codes of different countries. For example, in Germany, PV systems must be able to limit the maximum power to 70% of

S_{r a t e d}

[16].

D. Grid Voltage Fluctuations

Another possible problem is grid voltage fluctuation due to the fluctuating nature of solar irradiance. This problem is especially evident in small-scale PV systems. Passing the clouds could easily cover the main area of the panel. Rapid changes in PV power (due to rapid changes in irradiance) can cause grid voltage fluctuations with high PV penetration. Hence, the allowable power ramp rate is defined in various grid codes and standards [

17]. The power ramp rate requirements of various standards are listed in Table I [10]-[13], [18], [19]. The implementation of these standards can also be achieved by flexible active power control.

TABLE I Power Ramp Rate Requirements of Various Standards

Grid code	Positive power ramp rate	Negative power ramp rate
HECO [10]	2 MW/min	2 MW/min
Hawaii [10]	1 MW/min	1 MW/min
PREPA (Puerto Rico) [10]	10% per min	10% per min
EIRGRID (Ireland) [10]	30 MW/min	No requirement
Germany [11]	10% per min	No requirement
Australia [13]	16% per min	No requirement
Denmark [12]	100 kW/s	100 kW/s
ENTSO-E (Europe) [18]	No requirement	No requirement
National standards (China) [19]	10% per min	No requirement

E. Grid Frequency Support

When the grid is affected by frequency deviation, PV inverters must participate in supporting the grid frequency by changing the output active power. Frequency regulations including frequency droop control and inertial response are becoming essential in power grids with high penetration of PV systems. Accordingly, the frequency-Watt control is introduced in the network instructions to avoid instability problems, which is called frequency response [

11]-[13]. Figure 5 shows the international standards for active power control for grid frequency stabilization [11]-[13], [20]. The values of

f_{1}, f_{2}, \dots, f_{5}

are defined in different grid codes. In the range of

[f_{2}, f_{3}]

, the power reserve value

Δ p

is taken into account. Therefore, if the grid frequency is less than

f_{2}

, the PV system will be able to maximize the extracted PV power. If the grid frequency is between

f_{1}

and

f_{2}

, the maximum available power is injected into the grid. For frequencies above

f_{3}

, the power is reduced based on the droop relationship determined in the grid codes. Also, for frequencies above 52 Hz, the system must be disconnected from the network. Accurate frequency measurement is also necessary to perform frequency control [21]. According to Fig. 3, the “grid support” block calculates the power reference for the “PV voltage reference computation” block. To support the grid frequency, this block calculates the PV power reference based on the grid frequency and grid demands. Therefore, to further reduce system power fluctuations on the network, flexible active power control must be strengthened and integrated with frequency control, thus avoiding instability and overloading problems.

Fig. 5 Frequency response defined in international network codes.

F. Grid Support Functionalities and FPPT Strategies

Table II summarizes the FPPT operating modes to be implemented for each of the above-mentioned grid support functionalities. For example, the implementation of CPGC helps provide LVRT capability for grid-connected PV systems. In order to increase the voltage at PCC during the voltage sags, active and reactive power should be injected into the grid simultaneously. To avoid exceeding the maximum current rating of the inverter, the active power should be reduced to a certain value [

14]. PV power conversion systems with the ability to provide ancillary services such as reactive power support and LVRT capability can help increase system stability and prevent power quality problems. Furthermore, by using a thermally optimized operation, improvements in overall system reliability can be achieved [22]. Other issues are the reverse power flow from load towards generation units and over-voltage. These problems can be solved by CPGC algorithm. In fact, the CPGC algorithm ensures that the peak power injected from the PV system is within the power network capacity. Also, in order to support grid frequency (e.g., frequency droop control and inertia response), it is necessary to implement PRC. By implementing PRC, flexible grid frequency regulation can be provided. Another issue is related to the oscillating nature of solar energy, which can cause oscillations in the power injected into the grid. As the penetration of grid-connected PV systems increases, more power fluctuations are injected into the grid. Rapid changes in PV power can lead to fluctuations in grid voltage, thus challenging system stability. Therefore, PRRC has been introduced in grid codes to reduce power fluctuations and thus reduce the frequency change rate [15].

TABLE II Relation Between Grid Support Functionalities and FPPT Operating Modes

Grid requirement	FPPT operating mode
Frequency support	PRC (steady state) CPGC (frequency transient state)
Voltage support	CPGC
LVRT	CPGC
Solving grid voltage fluctuation problem	PRRC
Solving reverse power flow problem	CPGC

IV. CPGC

CPGC, also called power limiting control or absolute active power control, is defined to regulate the output power from PV panels to a specific reference value. The concept of this operating mode is illustrated by area 4 in Fig. 2. Fast dynamic response and low power oscillation in the steady state are two key factors under CPGC [

23]. Basic concepts of the CPGC have been introduced in [4], [15], [23]-[25], which concentrate on the stability issues and mandatory maintenance costs of PV systems.

A. Classification of CPGC Algorithms

As aforementioned, this paper aims at investigating the algorithms that can provide flexible active power control for PV systems by moving the operating point without additional components. In this subsection, different strategies of CPGC algorithms are classified and described. CPGC is performed in two ways: ① CPGC based on converter control loop modification (DC-DC converter controller in two-stage PV system structure or inverter controller in single-stage PV system structure); ② CPGC based on the modification of the “voltage reference computation” block. In the first method, a typical MPPT algorithm is implemented in the “voltage reference computation” block (see Fig. 3). In this method, the converter controller is modified to reduce the power level [

14], [23]-[27]. The computation block of the voltage reference is modified. Therefore, the “PV voltage reference computation” block adjusts the voltage reference of PV panels based on the power reference according to the P-V characteristic curve depicted in Fig. 1. Accordingly, this method does not require any change in the converter controller, and a conventional voltage controller is performed in the “PV voltage control” block [9], [28]. The algorithms of these two methods are described in the following parts.

1)　CPGC Based on PV Voltage/Power Control Loop

Available algorithms in this group can be classified into five categories in the following.

1) CPGC with direct power control (CPGC 1)

The PV output power can be limited to the desired value through the closed-loop control and a saturation block [

15], [24], as shown in Fig. 6, where PWM is short for pulse width modulation. When the maximum available power is less than the limit value, the maximum available power is injected into the grid and the PV system operates in MPPT mode. As

p_{m p p}

reaches

p_{l i m i t}

, the power reference

p_{p v}^{*}

will be limited to a constant level, thus PV system will enter into the CPGC mode [29]. The operational principle can be formulated as:

p_{p v}^{*} = \{\begin{array}{l} p_{m p p} & p_{p v} \leq p_{l i m i t} \\ p_{l i m i t} & p_{p v} > p_{l i m i t} \end{array}

(1)

Fig. 6 CPGC 1 with direct power control.

2) CPGC with current limiting control (CPGC 2)

Conforming to the P-V curve, the PV voltage $v_{p v}$ is approximately constant on the right side of the MPP (which is called the constant voltage region) [

23], [30]. Hence, the PV output current

i_{p v}

can be used as a control parameter to perform CPGC on the right side of MPP. To run CPGC, the reference current must be limited to a certain level

i_{l i m i t}

[29], which is expressed as:

i_{l i m i t} = \frac{p_{l i m i t}}{v_{p v}}

(2)

The structure of CPGC 2 is shown in Fig. 7 [

23], [30]. The main advantage of CPGC 1 and CPGC 2 is that they do not require switching between different operating modes. They are also able to regulate power under environmental changes because the PV voltage reference is persistently calculated by the MPPT algorithm. The disadvantage of CPGC 1 and CPGC 2 is that the MPPT block can lose the correct operating point, because the voltage/current reference calculated by the MPPT algorithm is modified in the saturation block [9].

Fig. 7 CPGC 2 with current limiting control.

3) CPGC with inductor current reference calculation (CPGC 3)

In [

23], the DC-DC converter current reference is calculated according to the power limit (refer to Fig. 8 [23]). The inductor current reference

i_{l}^{*}

is determined using the MPPT algorithm and power limitation algorithm, and then the lowest one is selected. The current reference

i_{l, c p g}^{*}

is computed continuously. MPPT loop is only implemented when MPPT is the actual mode (

i_{l, m p p}^{*} < i_{l, c p g}^{*}

). Otherwise, the MPPT mode is frozen and the last calculated PV voltage reference from the MPPT mode is used for computing the inductor current reference. Then,

i_{l, m p p}^{*}

is limited to I_max, which is

i_{l, c p g}^{*}

plus a constant current that is adjusted based on the inductor current and the size of the PV capacitor. This saturation with anti-windup is applied for faster response and to prevent voltage drop after switching to the MPPT mode.

Fig. 8 CPGC 3 with inductor current reference calculation.

4) CPGC with multi-mode operation (CPGC 4)

CPGC can be obtained through a multi-mode operation, as depicted in Fig. 9. The PV voltage reference, related to the power reference in P-V characteristic curve, is calculated [

4], [15], [31]. When

p_{p v} < p_{l i m i t}

, the MPPT mode is activated and PV voltage reference

v_{p v}^{*}

is computed via the implemented MPPT algorithm. When

p_{p v} \geq p_{l i m i t}

, the MPPT mode is frozen and the CPGC mode is activated. The duty cycle D is computed according to the error between

p_{p v}

and

p_{l i m i t}

. The transition between the operating modes results in the complexity of the design of the control variables. A fast change from MPPT to CPGC also may introduce instability [15].

Fig. 9 CPGC 4 based on multi-mode operation.

5) CPGC with PV power based or DC-link voltage based delta-voltage control (CPGC 5)

The schematic of CPGC 5 is shown in Fig. 10 [

14], [26], [27]. When

p_{p v} < p_{l i m i t}

, the MPPT algorithm is performed to compute the PV voltage reference. When

p_{p v} \geq p_{l i m i t}

, the MPPT mode is frozen and the final value of computed

v_{m p p}

is recorded. Then, a positive

Δ v_{p v}

is added to

v_{m p p}

. It should be mentioned that

Δ v_{p v}

can be calculated according to the error between

p_{p v}

and

p_{l i m i t}

[26] or based on the energy in the DC-link capacitor [27]. According to Fig. 10, a limiter is used to ensure only a positive

Δ v_{p v}

is added to

v_{m p p}

. Therefore, the operating point moves to the right side of the MPP.

Fig. 10 CPGC 5 with delta-voltage control. (a) Based on DC-link voltage. (b) Based on PV power.

2)　CPGC Based on Direct Computation of Voltage Reference

The CPGC can not only be used with a modification of the PV voltage control loop, but also can be attained with direct computation of the voltage reference [

9], [15]. For realizing the CPGC concept, the algorithm should be operated in one of two modes: ① MPPT mode; and ② CPGC mode. When the PV output power is lower than the power limit, MPPT operation is activated and PV voltage reference

v_{p v}^{*}

is specified by the MPPT algorithm. If the PV power exceeds the power limit

p_{l i m i t}

, the CPGC mode should be activated. The algorithms of this group can be classified into three categories, which are described below.

1) CPGC with constant voltage step values for MPPT and CPGC modes (CPGC 6)

The algorithm presented in [

28], [29], [32], [33] has two operating modes including MPPT and CPGC. If the operating mode is MPPT, the controller determines

v_{p v}^{*} = v_{m p p}

with a conventional MPPT algorithm (e.g., perturb and observe (P&O)). If the operating mode is CPGC, the voltage reference is determined based on the power limit using the power control algorithm, as illustrated in Fig. 11 [28], [29], [32], [33].

Fig. 11 CPGC 6 with direct computation of voltage reference with constant voltage step.

As a result, there is no need to change the control of the DC-DC converter or inverter connected to power grid. Consequently, this control algorithm has computational complexity since the voltage reference is calculated in two separate algorithms for the CPGC and MPPT modes. To achieve small power oscillation during the MPPT mode, the voltage step ( $v_{s t e p} = v_{s t e p, m p p}$ ) and time step ( $T_{s t e p} = T_{s t e p, m p p}$ ) values of the voltage reference computation algorithm are considered to be relatively small and large, respectively. For obtaining a fast dynamic response, $v_{s t e p, c p g}$ and $T_{s t e p, c p g}$ are considered to be relatively large and small, respectively, during CPGC mode.

2) CPGC with an adaptive voltage step under transient and steady-state conditions (CPGC 7)

In CPGC 7, the voltage step is computed based on steady-state or transient operating conditions, as shown in Fig. 12 [

28]. During the CPGC operating mode, a relatively small time step and high voltage step are selected to improve transient response under fault conditions. Under the normal condition (i.e., without grid fault), the algorithm identifies steady-state or transient conditions. According to the difference between

p_{p v}

and

p_{l i m i t}

(i . e ., |d p| = |p_{p v} - p_{l i m i t}|)

and comparing it with the threshold value

d p_{t h}

, the operating mode is classified into transient and steady-state conditions. A hysteresis band is implemented to avoid consecutive transitions between the steady-state and transient conditions. During the CPGC mode, the transient response and power oscillation are enhanced compared with the CPGC algorithm with constant voltage step as in [28].

Fig. 12 CPGC 7 with direct computation of voltage reference with adaptive voltage step.

3) General CPGC algorithm with adaptive voltage step (CPGC 8)

A general CPGC algorithm with adaptive voltage step (CPGC 8) was proposed in [

34], [35], as shown in Fig. 13. Here, a general algorithm is applied for both MPPT and CPGC modes. Consequently, transition changes between two operating modes are eliminated. This algorithm has two main computation steps: voltage step and voltage reference computation. The voltage step is adjusted adaptively based on the transient or steady-state mode in order to improve the performance. Therefore, this algorithm is robust for fast irradiance changes. In the next step, the calculated voltage step is selected to obtain the voltage reference. A general algorithm for voltage reference computation is implemented based on the operating mode. In this algorithm, a constant time step is applied for all operating modes. Consequently, the design of control parameters and the implementation of the algorithm are simpler than the CPGC 7 [9], [36].

Fig. 13 CPGC 8 with adaptive voltage step.

B. Experimental Results of CPGC Algorithms

A scaled-down 1.1 kVA two-stage PV system is experimentally implemented to compare the steady-state and dynamic performances of the studied CPGC algorithms, as shown in Fig. 3(b). A photo of the experimental setup is shown in Fig. 14.

Fig. 14 Experimental setup.

The PV panel is simulated using a Chroma 62000H-S solar array simulator, and the grid is simulated using a Cinergia grid emulator. A two-stage PV system is set up using IMPERIX’s H-bridge module and the control is implemented with IMPERIX’s B-BOX RCP control platform. Experimental setup and simulation parameters are shown in Table III.

TABLE III Experimental Setup and Simulation Parameters

Parameter	Value
$p_{m p p}$	1.1 kW
$v_{m p p}$	150 V
$v_{d c}$	250 V
$C_{p v}$	0.5 mF
$L_{b o o s t}$	2 mH
$f_{s, d c d c}$	10 kHz
$v_{g}$	110 V
$f_{s w, i n v}$	10 kHz
$L_{i n v}$	5 mH

Between CPGC 1 and CPGC 2, which adjust the PV power by controlling the power/current limit, CPGC 2 is selected for implementation. CPGC 3 and CPGC 4 have a multi-mode operation and their performances are similar, so only CPGC 4 is tested. Also, the performances of CPGC 6 and CPGC 7 are similar, so CPGC 6 is chosen for experimental evaluation. The operating point of CPGC 6 and CPGC 8 can be chosen both on the right and left sides of the MPP. The operating point of these algorithms is considered on the right side of the MPP. Three experimental cases have been carried out to evaluate the performance of the algorithms under the step increase and decrease of power reference as well as under the irradiance changes.

Case 1: the dynamic performance of the investigated algorithms is verified and compared under a step change of power reference from 550 W to 1000 W. The results are shown in Fig. 15. A step increase in power reference from 550 W to 1000 W occurs at $t = 0.04 s$ , as observed in Fig. 15(a) and (c). As can be observed from Fig. 15(b) and (d), the operating point of all algorithms is set on the right side of MPP. This is because when the power reference increases, $v_{p v}$ decreases to adjust $p_{p v}$ to the new reference value. According to Fig. 15(a) and (c), CPGC 2 has a slower dynamic response than others. CPGC 4 has a faster dynamic response than CPGC 2, although the PV power has a relatively large difference from its power reference after increasing the power reference. CPGC 5 has reached its final value with high speed within 0.06 s. However, this algorithm also has a large tracking error in a steady state. CPGC 6 uses a constant voltage step in all operating modes, so this algorithm has a low dynamic response. Compared with other algorithms, CPGC 8 reaches a new power reference with a small tracking error. Also, it has a high dynamic response and the PV power is set to its reference value within 0.07 s. The reason for this good performance is the use of an adaptive voltage step. The voltage step in this algorithm is set based on the operating point and operating mode (i.e., steady-state or transient). Note that the dynamic responses of CPGC 6 and CPGC 8 can be improved by choosing a smaller time step. The time step for executing these algorithms is 0.02 s.

Fig. 15 Performance comparison of different CPGC algorithms under sudden increase of power reference. (a) PV power for CPGC 2, CPGC 4, and CPGC 5. (b) PV voltages for CPGC 2, CPGC 4, and CPGC 5. (c) PV power for CPGC 6 and CPGC 8. (d) PV voltages for CPGC 6 and CPGC 8.

Case 2: the performance of the algorithms under a step reduction of the power reference from 1000 W to 450 W has been investigated, and the results are shown in Fig. 16. According to Fig. 16(b) and (d), when the power reference decreases, $v_{p v}$ increases to adjust $p_{p v}$ to the reference value. Therefore, the operating point of the algorithms is set on the right side of the MPP. In this case, the same results as in Case 1 can be obtained for dynamic response and tracking error. For example, according to Fig. 16(b), CPGC 2 and CPGC 4 have a large tracking error in the transient mode, and CPGC 2 has a fast dynamic response. CPGC 8 has a small tracking error and fast dynamic response. However, the dynamic response of CPGC 6 and CPGC 8 can be significantly improved by choosing a smaller time step.

Fig. 16 Performance comparison of different CPGC algorithms under sudden decrease of power reference. (a) PV power for CPGC 2, CPGC 4, and CPGC 5. (b) PV voltages for CPGC 2, CPGC 4, and CPGC 5. (c) PV power for CPGC 6 and CPGC 8. (d) PV voltages for CPGC 6 and CPGC 8.

From the experimental results in Figs. 15 and 16, it is clear that CPGC 5 with proportional-integral (PI) controller shows a faster response compared with other algorithms. The main reason, in this case, is the exponential response of the PI controller, compared with the linear response of other algorithms that change the voltage reference in steps. Based on the chosen voltage/time step, the response of other algorithms can be faster or slower than the PI-based CPGC. However, the main disadvantage of PI-based CPGC is the lack of intended functionality under environmental changes. The main reason for such a disadvantage is the lack of consideration of non-linear features of the P-V curve. However, the algorithms based on P&O scan through the P-V curve, and accordingly, they can adjust the operating point under environmental changes.

Cases 3 and 4: in these cases, the performances of the algorithms under rapid irradiance changes have been investigated and evaluated. The evaluation results of cases 3 and 4 are shown in Figs. 17 and 18, respectively. Before $t = 5 s$ and after $t = 40 s$ , the performance of CPGC algorithms in low irradiance conditions is shown. Before $t = 5 s$ , the irradiance is $300 W / m^{2}$ . Under low irradiance conditions, the maximum available PV power is extracted from the PV panels and the PV voltage is set to be $v_{m p p}$ .

Fig. 17 Performance comparison of different CPGC algorithms under rapid changes of irradiance when operating point is set on right side of MPP. (a) PV power for CPGC 2 and CPGC 4. (b) PV voltage for CPGC 2 and CPGC 4. (c) PV power for CPGC 6 and CPGC 8. (d) PV voltage for CPGC 6 and CPGC 8.

Fig. 18 Performance comparison of different CPGC algorithms under rapid changes of irradiance when operating point is set on left side of MPP. (a) PV power for CPGC 6 and CPGC 8. (b) PV voltage for CPGC 6 and CPGC 8.

Under a time interval of $t = 5 s$ to $t = 10 s$ , the irradiance increases from $300 W / m^{2}$ to $1000 W / m^{2}$ . In the interval between $t = 35 s$ and $t = 40 s$ , the irradiance decreases from $1000 W / m^{2}$ to $300 W / m^{2}$ . Two different power reference values, i.e., $75 %$ and $25 %$ of the available PV power p_avai, are considered to evaluate each algorithm. CPGC 5 assumes that $v_{m p p}$ remains constant during the CPGC mode. Since this assumption is not valid in environmental changes, CPGC 5 is not able to adjust the power under the irradiance changes. Therefore, in this case, CPGC 5 has not been tested. As mentioned before, CPGC 6 and CPGC 8 can move the operating point to both the right and left sides of the MPP. In this experimental case, the dynamic performance of these algorithms has been evaluated on both sides of the MPP.

According to the results shown in Figs. 17 and 18, the maximum available PV power is extracted from the PV string before $t = 5 s$ . After $t = 5 s$ , the irradiance increases until it reaches $1000 W / m^{2}$ . Therefore, the PV power increases up to the reference value. According to the results, two power reference values, i.e., $75 %$ and $25 %$ of the available power, are considered that the PV power is limited to the reference values. Each algorithm has a different tracking error. To compare the algorithms, the tracking error in steady or transient state, i.e., $T E_{s s}$ or $T E_{t r}$ , is calculated as:

T E_{s s} / T E_{t r} = \frac{\int |p_{p v} - p_{l i m}| d t}{\int |p_{p v}| d t} \times 100

(3)

To calculate the tracking error in transient state, the integral of the above equation is calculated between the time interval in which the algorithms are in the transient state. Also, to calculate the tracking error in steady state, the integral of (3) is calculated between the time interval in which all algorithms operate in steady state.

The total tracking error is defined as:

T E = \sqrt[]{T E_{t r}^{2} + T E_{s s}^{2}}

(4)

In this study case, the tracking errors of the investigated algorithms are calculated and shown in Table IV. According to Table IV, the tracking error of CPGC 2 is larger than that of other algorithms when the power reference is $25 %$ of the available PV power. Also, in general, the tracking error on the right side of MPP is larger than that on the left side. In addition, the tracking error of CPGC 8, for both applied power references, is smaller than that of other algorithms when the operating point is set on the left side of the MPP. Relatively low power fluctuations on the left side of MPP and the use of an adaptive voltage step are the reasons for the better performance of CPGC 8 compared with other algorithms.

TABLE IV Comparison of Tracking Error of Investigated Algorithms

Algorithm	Tracking error (%)
Algorithm	$p_{p v}^{*} = 25 % p_{a v a i}$	$p_{p v}^{*} = 75 % p_{a v a i}$
CPGC 2	11.22	2.99
CPGC 4	10.27	4.75
CPGC 6 (right side of MPP)	12.21	3.13
CPGC 8 (right side of MPP)	8.54	2.19
CPGC 6 (left side of MPP)	4.09	2.13
CPGC 8 (left side of MPP)	2.87	1.42

C. Comparison of CPGC Algorithms

A comprehensive comparison of the above-mentioned CPGC algorithms is provided in Table V. Several features such as ability to track the MPP, operation region (being right or left side of the MPP), dynamic response, computational complexity, and main advantages/disadvantages are compared for different CPGC algorithms.

TABLE V Comparison of Various CPGC Algorithms

Algorithm	Reference	Tracking of MPP	Transition between modes	Operation region	Dynamic response	Power fluctuation in steady state	Operating under environmental changes	Tracking error	Computational complexity	Main advantages (+) and disadvantages (-)
CPGC 1, CPGC 2	[15], [24]	Yes	No	Right	Very slow	Low	Yes	High	Low	- Not applicable to various MPPT algorithms - Unstable under small power reference value
CPGC 3	[23]	Yes	Yes	Right	Slow	High	Yes	Very high	Low	+ Easy calculations - Large power oscillations in steady state because of transitions between operating modes
CPGC 4	[4], [15], [31]	Yes	Yes	Right	Slow	High	Yes	Very high	Low	- Large power oscillations in steady state because of transitions between operating modes
CPGC 5	[14], [26], [27], [37]	No	Yes	Right	Fast	Low	No	High	Low	- Improper for a long time - Don’t work under environmental changes
CPGC 6	[28], [29], [32], [33], [38]	Yes	Yes	Right/left	Slow	High	Yes	Low	High	- Slow dynamic response - Unstable under a small power reference values
CPGC 7	[28]	Yes	Yes	Right/left	Fast	Low	Yes	Low	High	- Transition between operating modes
CPGC 8	[34], [35]	Yes	No	Right/left	Fast	Low	Yes	Very low	Very high	- Complex calculations

1) $T E_{s s}$ : this index is computed using (3) for the steady-state operation of algorithms, where $p_{l i m} = 500 W$ and $I r r = 1000 W / m^{2}$ .

2) Transient tracking error under step change of the power reference $T E_{t r 1}$ : this index is computed using (3) for the transient operation of the algorithms, where $p_{l i m}$ undergoes a step change from $500 W$ to $1000 W$ , and irradiance $I r r$ is held constant at $1000 W / m^{2}$ . The period of calculating this index is set equal to the longest period in which all the algorithms reach their new steady-state values.

3) $T E$ is computed based on (4) with the inclusion of $T E_{s s}$ and $T E_{t r 1}$ .

4) Transient tracking error under ramp change of the irradiance $T E_{t r 2}$ : since some of the algorithms are incapable of tracking the power reference under environmental changes, this index is used to differentiate the performance of the algorithms under environmental changes. $p_{l i m}$ is taken as $750 W$ , while the irradiance $I r r$ decreases linearly from $1000 W / m^{2}$ to $400 W / m^{2}$ in $0.1 s$ .

All the aforementioned parameters are computed and presented in Table VI.

TABLE VI Assessment of Tracking Error Metrics of CPGC Algorithms

Algorithm	TE_ss (%)	TE_tr₁ (%)	TE_tr₂ (%)	TE (%)
CPGC 2	4.8	3.5	17.5	5.9
CPGC 4	6.8	4.5	20.3	8.2
CPGC 5	0.5	0.6	72.5	0.8
CPGC 6 (right side of MPP)	5.2	7.1	11.3	8.8
CPGC 6 (left side of MPP)	6.0	8.9	14.6	10.7
CPGC 8 (right side of MPP)	4.0	1.7	10.7	4.4
CPGC 8 (left side of MPP)	2.1	2.9	9.2	3.6

CPGC algorithms with the modification of the MPPT control loop have several drawbacks. For instance, CPGC 1 and CPGC 2 do not work with different MPPT algorithms. The MPPT algorithm must be able to compute the current reference. Also, the computed current reference is modified in the PV voltage controller, which can make the operating point move in the incorrect direction. In CPGC 3, CPGC 4, and CPGC 5, the controller switches to MPP and CPGC modes, and large power fluctuations occur during transition between the two modes. During the operating mode of GPGC 5, the MPPT algorithm is stopped and the previous MPP voltage is used. Environmental conditions are assumed to be constant during CPGC operation in this algorithm. Therefore, GPGC 5 is only suitable for implementation in a short time, like short-time grid faults. In CPGC algorithms, by modifying the MPPT algorithm, the voltage reference corresponding to the power reference is computed and entered into the voltage controller of the converter. Hence, no changes in the DC-DC/DC-AC converter controller are required and the easier implementation of these algorithms can be provided. Another advantage of these algorithms is the ability to move the operating point flexibly to the right or left side of the MPP.

During the CPGC operation, a constant voltage step is applied in CPGC 6. In this algorithm, if a small voltage step is used, the dynamic response will slow down while a large voltage leads to high power fluctuations in the steady state. To solve this problem, CPGC 7 uses a large voltage step in transient state and a small voltage step in steady state. However, these algorithms have high power oscillations in steady state based on the operating point of PV arrays. In order to improve the previous algorithms, CPGC 8 uses an adaptive voltage step according to the operating point and operating mode of the PV array. Therefore, this algorithm achieves fast dynamics and low power fluctuations. The disadvantage of this algorithm is the high complexity of calculations.

As evidenced in Section IV-B, when the power reference values are relatively small, the activity on the right side of the MPP leads to greater power fluctuations. Conversely, by shifting the operating point to the left side of MPP, low power oscillations can be achieved, while quick dynamics can be attained by utilizing an adaptive voltage step, as executed in CPGC 8. The tracking error values, showcased in Table IV, validate the superior execution of CPGC 8 in comparison to other existing algorithms in the literature. Thus, among all the scrutinized algorithms, CPGC 8 achieves improved performance in most areas.

V. PRC

The aim of PRC is to keep a predefined amount of power as a reserve in the PV system during steady-state operation. This power reserve can be used during grid voltage/frequency transient. The basic concept of PRC is demonstrated in area 2 of Fig. 2 and Fig. 19 [

39]. In this algorithm,

p_{p v}

is obtained by subtracting the required amount of power reserve

Δ p

from the maximum available PV power

p_{a v a i}

as:

p_{p v} = p_{l i m i t} = p_{a v a i} - Δ p

(5)

Fig. 19 Concept of PRC with P-V curve of PV panels.

Accordingly, the PV output power follows the dynamics of $p_{a v a i}$ . $Δ p$ is an input for this application, which can be defined based on the power system operator regulations [

40]-[42]. Since

p_{a v a i}

is dependent on solar irradiance and temperature, effectively tracking the requested power reserve under dynamic conditions and observing MPP are the main challenges in implementing PRC algorithms [43]. The dynamic conditions are indicated by black, blue, and red lines in Fig. 19. Several solutions for the measurement of

p_{a v a i}

have been proposed in the prior art works [39]-[45] as:

1) Using an accurate measurement of the solar irradiance and temperature combined with the PV array characteristic model. This solution is effective but not common for residential and commercial-scale PV systems since additional sensors for measuring irradiance/temperature will raise the complexity and cost of the PV system. Furthermore, the model of the PV array should be very accurate, which is typically not possible, because of aging or faults [

40]-[42].

2) Applying artificial intelligence (AI) techniques based on historical operation and climatic data [

44], [46], [47]. This solution requires the availability of big data and considerable calculation processing in order to obtain an accurate result. However, this solution may become easier and more accurate due to the evolution of signal and data-processing systems and the advancement of available digital processing units [48].

3) Curve-fitting approximation of the P-V characteristic. Curve-fitting methods usually depend on a model-based approach, so these methods are sensitive to parameter variation. Complete curve-fitting is cumbersome due to the sophisticated operating point sampling [

49]. The least-square (LSQ) method is presented in [43], which samples a large data set of past measurements (i.e., current and voltage values of PV panel). With this method, not only

p_{a v a i}

is estimated in real time, but also the complete P-V curve can be attained. This method uses a non-simplified single-diode model and the five parameters of the model, and thus the control implementation appears to be more challenging [39]. In [50]-[53], the quadratic curve-fitting nethod is used. References [50] and [51] sample three points by Newton quadratic interpolation and the selection of the three sample points may affect the accuracy of MPP estimation. The estimation accuracy usually is compromised in quadratic curve-fitting methods because of curve-fitting approximation [43].

4) Combining MPPT and CPGC modes. The estimation of $p_{a v a i}$ can be performed by the concept introduced in [

8], [54]. This solution is performed by combining MPPT and CPGC modes. In this solution, one PV string operates in MPPT mode to monitor the actual maximum power and other PV strings operate in CPGC mode to provide delta power control. PV strings are located close to each other. Therefore, PV strings are assumed to have similar power production profiles. This method is suitable for large PV systems with similar components and conditions [8], [54].

5) Employing a hybrid operation between the MPPT and CPGC modes in one single PV system. In this method, the system periodically enters the MPPT mode in order to estimate $p_{a v a i}$ . Then, CPGC mode is employed to provide a power reserve as demanded. For following the PRC constraints, the peak power during MPPT mode should be buffered through DC-link capacitors. However, the increasing voltage of DC-link raises safety concerns without proper control [

55].

6) Using empirical models [

39], [45]. In this method, the maximum power is estimated by sampling a number of operating points and estimating the short-circuit current and Lambert-W function. A sampling of operating points is required. In this method, due to the aging of the components, the accuracy of the experimental models is affected. In addition, using many approximations leads to unavoidable errors [56].

A. Classification of PRC Algorithms

As mentioned before, in contrast to the CPGC mode, in which a constant power reference is applied, the power reference in PRC algorithms dynamically changes to obtain delta power constraints. Thus, the available PV power is estimated at first. Then, a control strategy is employed to achieve the power reserve. There are two solutions to effectively track the required power reserve under dynamic conditions: ① PRC based on the PV voltage control, and ② PRC based on the power control. In the first solution, according to the P-V characteristic curves, the “voltage reference computation” block (refer to Fig. 3) calculates the voltage reference of the PV panels based on the power reference. In the second solution, the “PV voltage control” block is modified. In this type, the converter controller is modified and the PV power is directly regulated rather than the voltage. Details of these two types of PRC solutions are presented in the following parts.

1)　PRC with PV Voltage Control

Available algorithms in this group can be classified into four categories in the following.

1) PRC with curve-fitting methods (PRC 1)

This algorithm with curve-fitting method was presented in [

45], [57] (refer to Fig. 20).

Fig. 20 PRC 1 with curve-fitting method.

First, the required voltage reference is calculated according to the power reference (i.e., the difference between the maximum estimated power $p_{m p p}$ and the required reserve power $Δ p$ ) by curve-fitting methods. The calculated voltage reference is then entered into the “PV voltage control” block to adjust the PV voltage to the voltage reference. So far, different curve-fitting methods for PRC have been introduced in the literature. For example:

① Newton quadratic interpolation is used in [

50], [51], and [53] to obtain the voltage reference complying with the power reference. ② A segmental linear fitting curve is used in [58] to calculate the suboptimal power-voltage curve. This paper also uses the variable voltage step when calculating the voltage reference to reduce fluctuations in the steady state. ③ Fitting the curtailment power-current curve is also presented in [45], [57] that calculates the voltage reference with the variable voltage step.

2) A hybrid operation of MPPT and CPGC (PRC 2)

A hybrid operation of MPPT and CPGC modes was proposed in [

54], [55] (refer to Fig. 21). In general, the performance of this algorithm is similar to CPGC 6. When the PV power is less than the power reference, an MPPT algorithm is used to increase the PV power toward the power reference. Otherwise, the PV voltage is continuously perturbed to the left or right side of MPP to reduce the PV power towards the reference value. This algorithm exhibits a relatively slow dynamic response, because it is based on a multi-step process: the operating point of PV array is adjusted with several iterations to reach the desired power level [42].

Fig. 21 PRC 2 with a hybrid operation of MPPT and CPGC.

3) Voltage regulator based on movement to constant current region (PRC 3)

In this algorithm [

39],

v_{p v}

and

i_{p v}

are sampled continuously. Then,

i_{m p p}

v_{m p p}

, and

P_{a v a i}

can be determined in turn by estimating the short-circuit current

I_{s c}

and the Lambert-W function. Figure 22 shows the total steps for estimating

P_{a v a i}

on the I-V characteristic curve of the PV panel. Then, the current changes relative to the voltage changes of two consecutive operating points are measured as:

m (n) = \frac{Δ i}{Δ v} = \frac{i (n) - i (n - 1)}{v (n) - v (n - 1)}

(6)

Fig. 22 The maximum power estimation process for PRC 3.

where $m$ is the ratio of the change in current to the change in voltage; $i (n)$ and $V (n)$ are the current and voltage sampled in step $n$ , respectively; and $i (n - 1)$ and $V (n - 1)$ are the current and voltage sampled in step $n - 1$ , respectively.

Then, $m (n)$ is compared with the slope of the I-V curve in the current-source region (i.e., the left side of MPP). Therefore, it is determined in which region the operating point is located. If the operating point is on the right side of MPP, the operating point shifts to the left side of MPP with a large step size. When the operating point is on the left side of MPP, a large step size should be used if the operating point is too far from the power reference $p_{p v}^{*}$ ; otherwise, the proposed algorithm around $p_{p v}^{*}$ will be perturbed by the small voltage step size. Therefore, the PV power will be set to the reference value. The schematic of this algorithm is shown in Fig. 23 [

39].

Fig. 23 PRC 3 with movement to constant current region.

4) Lookup table (PRC 4)

In one control step, this algorithm converts an active power command to a DC voltage command. The DC voltage command is given to a conventional PV voltage controller (e.g., a PI controller) to adjust the PV voltage to the reference value. A three-dimensional lookup table (LUT) was proposed in [

42], as illustrated in Fig. 24. The LUT takes power command, measurements of irradiance

G

, and panel temperature

T

, and uses a trilinear interpolation between them to find the PV voltage

v_{p v}

according to the desired power. However, the size of LUT can easily become very large. Therefore, a control loop should be added to reduce the size of LUT. Non-idealities such as module mismatch, non-uniform aging, and soiling will lead to some losses of accuracy of this algorithm. The machine-learning techniques can also be used to continuously update the LUT based on operational data [42].

Fig. 24 PRC 4 based on LUT.

2)　PRC with PV Power Control

The algorithms of this group can be divided into two categories.

1) Power limit controller (PRC 5)

The power limit controller was used in [

40], [59], [60]. In this algorithm, the power reference is fed to the power limit control block (refer to Fig. 25). The saturation block ensures that the PV power reference does not exceed the available PV power. In [61], after estimating the maximum power and calculating the power reference, a control algorithm similar to CPGC 4 is used. In this algorithm, the PV power reaches the reference value using a PI controller. However, the accurate tracking of a specific power reference is impossible, since the PI controller regulates the operating voltage [43]. However, due to the non-monotonic of the P-V curve, the accurate tracking of a specific power reference with a simple PI controller will not be effective [43].

Fig. 25 PRC 5 with power limit controller.

2) Power regulator based on the modified version of P-V curve (PRC 6)

A control scheme is presented in [

43] for direct adjustment of PV power by modifying the P-V curve. The block diagram of this solution is shown in Fig. 26 [43], [56]. Since the relationship between the power and duty cycle is not monotonic, a modified version of P-V curve is provided first. The modified P-V curve is obtained as:

p_{p v}^{'} = \{\begin{array}{l} p_{p v} & v_{p v} \geq v_{m p p} \\ 2 p_{m p p} - p_{p v} & v_{p v} < v_{m p p} \end{array}

(7)

Fig. 26 PRC 6 with modified version of P-V curve.

Also, the modified version of P-V curve is shown in Fig. 27 [

43]. The modified PV power

p_{p v}^{'}

is then sent to the PI controller. The PI controller adjusts the duty cycle of the DC-DC converter for operating at a specific power reference. PRC 6 is effective for tracking power reference. This algorithm always maintains the operating point to the right side of MPP. If the operating point is to the left side of MPP, instead of the actual measured power, the power changed from (7) is given to the PI controller. This results in a large negative error that moves the operating point to the right side of MPP. In [56], the operating point is chosen on the left side of MPP. Thus, a pseudo monotonic relationship is obtained between power and duty cycle. Therefore, the control is performed in all available power ranges (from near zero to 100%) in continuous mode without the need to switch between operating modes (such as MPPT or reserves).

Fig. 27 Modified version of P-V curve to ensure that operating point is on right side of MPP.

B. Comparison of PRC Algorithms

The main specifications of the above PRC algorithms are given in Table VII.

TABLE VII Comparison of Various PRC Algorithms

Algorithm	Reference	Transition between modes	$p_{r e f}$ location	Dynamic response	Power fluctuation in steady state	Operating under environmental changes	Tracking error	Computational complexity	Main advantages (+) and disadvantages (-)
PRC 1	[ 45], [ 50]-[53] [ 57], [58]	Yes	Right/left	Medium	Medium	Yes	Low	High	$-$ The effect of selecting sampling points on accuracy of control method
PRC 2	[54], [55], [61]	Yes	Right/left	Slow	High	Yes	Low	Medium	$-$ Slow dynamic response
PRC 3	[39], [62]	Yes	Left	High	Medium	Yes	Low	high	$-$ Need of knowledge of five parameters of PV model
PRC 4	[42]	No	Right	Very fast	Low	Yes	Low	Very high	$-$ High cost and complexity
PRC 5	[ 40], [59], [ 60]	No	Right	Fast	Very high	No	Very high	Very low	$-$ Lack of accuracy
PRC 5	[61]	Yes			High	Yes		Low	$-$ Large steady-state power oscillations
PRC 6	[43], [63]	No	Right	Very fast	Low	Yes	Very low	Low	$+$ A fast way for tracking power set-point
PRC 6	[56]	No	Left	Very fast	Low	Yes	Very low	Low	$+$ A fast way for tracking power set-point

PRC 1 needs to switch between operating modes (MPPT or CPGC). PRC 1 has better performance in terms of steady-state error and convergence rate compared with conventional P&O based solutions although the accuracy of PRC 1 may be affected by the selection of sampling points.

In PRC 2 and PRC 3, typical MPPT algorithms such as perturb and observe (P&O) are adapted to track a power reference. These algorithms rely on a multi-step process that results in a relatively slow response to frequency events. However, the dynamic response can be improved by using the adaptive voltage step technique. These algorithms first adjust the operating point of the PV array $v_{p v}$ and after the stability of the system, they measure the output power, and adjust the operating point again iteratively until the desired power level is provided. In PRC 2 and PRC 3, transitions between the operating modes (e.g., MPPT or reserves) are also necessary, which complicates the design of control parameters [

62].

PRC 4 is a straightforward and very effective solution. This algorithm has a very fast and accurate response to frequency events. However, the additional sensors of solar irradiance and temperature are required, which increases the cost and complexity of the system. This algorithm has high complexity and volume of computations. Non-ideality factors also cause the loss of the accuracy of PRC 4.

PRC 5 is very simple and does not need transitions between various operating modes. Nevertheless, this algorithm is not apt enough to track the MMP $p_{m p p}$ if $p_{p v}$ is smaller than the power reference. Hence, this algorithm seems less appropriate for a long period of time.

PRC 6 is a quick and effective way of tracking power set-point. This algorithm has efficient and reliable performances under different operating conditions. This algorithm does not require any transition between operating modes (MPPT or CPGC) [

43]. The operating point is allocated on the right side of MPP, which can introduce the instability issue under fast reduction of the irradiance (e.g., the operating point goes beyond the open-circuit voltage of the PV array). In addition, the operating point on the right side of MPP causes large power oscillations for relatively small power reference values.

VI. PRRC

In PRRC, the power ramp rate is limited to a certain value as defined by the standards and grid codes, as shown in area 3 of Fig. 2. Figure 28 also shows the concept of PRRC on the P-V curve. When the power ramp rate is below the allowable level $R_{l i m}$ , the controller extracts the maximum available power from the PV array and operates in MPPT operating mode. This is shown in Fig. 28 with the operating path A to B. If the power ramp rate exceeds the limit, the ramp rate should be reduced by reducing the power. Therefore, according to Fig. 28, the operating path is from point B to point C or D.

Fig. 28 Concept of PRRC with P-V curve of PV panels.

A. Classification of PRRC Algorithms

It is clear that the PV power ramp rate should first be measured to perform PRRC. In [

17] and [64], the power ramp rate is continuously calculated by measuring the amount of PV power change over a period of time according to:

R (t) = \frac{Δ p_{p v}}{m T} = \frac{p_{p v} (t + m T) - p_{p v} (t)}{m T}

(8)

To measure the power ramp rate, it is very important to choose the appropriate value for $m$ . A small value of $m$ leads to large fluctuations in the measured ramp rate, which is due to the inherent fluctuations of the MPPT algorithm. A large value of $m$ also reduces the speed and results in a delay in measuring the power ramp rate. It is also possible to use a moving average or low-pass filter before measuring the power ramp rate in order to reduce fluctuations in the measured ramp rate and improve the measurement [

65]. However, the use of a moving average or low-pass filter may reduce the measurement accuracy and deviate the ramp rate calculations from the actual value. Also in [66], to improve the measurement, the power ramp rate is calculated as:

R (t) = \frac{Δ p_{p v}}{Δ t} = \frac{p_{p v} (t) - p_{p v}^{0} (t)}{Δ t}

(9)

In the above equation, if the measured ramp rate is less than the allowable ramp rate, $p_{p v}^{0} (t)$ is regularly updated after each $m T$ . Otherwise, $p_{p v}^{0} (t)$ is updated after $T$ and the ramp rate in each computation cycle (i.e., after each $T$ ) is calculated continuously.

Another solution to measuring the power ramp rate is proposed in [

67], which uses an additional sampling at each computation step. In this method, the effect of fluctuations caused by the MPPT algorithm is eliminated when measuring the power ramp rate, and the power ramp rate due to irradiance changes is calculated. This method is able to detect rapid changes in irradiance. Therefore, the controller speed will be very high when performing PRRC.

Several methods have been reported in the literature for performing PRRC based on FPPT without additional components, which can be divided into three categories.

1) PRRC with constant ramp rate control (PRRC 1)

Constant ramp rate control is the most straightforward algorithm, which limits the change rate of PV power to a certain value $R_{l i m}$ . These algorithms set the voltage reference to control the boost converter. In [

68], a gradient-descent optimization algorithm is applied to obtain the operating voltage, but this control has heavy computations due to optimization. This algorithm also has high power fluctuations that occur during the search process [17]. A PRRC is also proposed in [69], which perturbs the PV voltage in the reverse direction of MPP. However, this algorithm is only able to perform PRRC in slow irradiance changes. A P&O based power ramp rate control is proposed in [17] to limit the power ramp rate according to demand. In this algorithm, during slow irradiance changes, when the power ramp rate is less than the limit, the controller operates in MPPT mode. When the power ramp rate exceeds the limit value, the controller moves the operating point to a point away from the MPP, thereby reducing the change rate of PV output power. The control structure and block diagram of PRRC algorithm are demonstrated in Fig. 29 [17], [64], [67].

Fig. 29 PRRC 1 with constant ramp rate.

PRRC solutions, without using the energy storage in PV systems, can only reduce the power ramp rate under irradiance increase conditions. Under irradiance reduction conditions, to limit the power ramp-down rate, the PV system should provide more power than the available power, which is not possible without a storage system. So far, several solutions have been introduced in the literature to control the power ramp-down rate without using an energy storage system. For example, by forecasting the weather from nearby satellites or sites, as well as using sky cameras, it is possible to predict the occurrence of a decrease in the power ramp rate, and as a result, the power ramp rate can be slowly reduced before irradiance reduction [

5]. In [64], the power ramp-down rate is controlled by clusters of PV sources. In this strategy, hybrid PRRC-CPGC controllers are adopted for each cluster. Each PV cluster consists of

n

PV strings with a separate DC-DC converter attached to each string. A separate controller is provided for each converter, some of which operate in PRRC mode and some in CPGC mode. Under irradiance reduction conditions, insufficient power required to control the power ramp-down rate is received from the PV strings for which the controller operates in CPGC mode. In the case of irradiance reduction, the operating point of these PV strings is adjusted in MPP to provide the required additional power. Also in [66], the operating point is usually set at an optimal point other than MPP. During the decrease of irradiance conditions, the operating point is transferred to a point with a higher power on the P-V characteristic curve and provides the additional power required to control the power ramp-down rate.

2) Static and dynamic PRRC (PRRC 2 and PRRC 3)

In these two algorithms, the “PV voltage control” block is modified. The control structure of these algorithms [

70], [71] is shown in Fig. 30. The PV system with static PRRC releases active power in an uncontrolled manner without considering any ramp requirement and it does not consider the duration of the transient state [70]. Dynamic PRRC can overcome the limitation of static PRRC. In this algorithm, the filtering effect

τ_{d y n}

is dynamically changed based on the power oscillations and the imposed ramp rate. The value of

τ_{d y n}

oscillates between a large value and a small value. A large value of

τ_{d y n}

means a low-pass filter with slow characteristics. In this algorithm, the ramp rate and duration of the irradiance change are not measured. Therefore, the value of

τ_{d y n}

gradually changes to provide the desired ramp rate [71]. This gradual change of

τ_{d y n}

causes the system to have a slow dynamic response.

Fig. 30 Control structure of PRRC 2 and PRRC 3.

B. Simulation Results of PRRC Algorithms

To show the importance of power ramp rate measurement for PRRC implementation, two algorithms presented in [

17] and [67] are simulated and the results are compared. The algorithms presented in [5], [17], [64], [68], [69] use (9) to measure the ramp rate. Whereas, the algorithm presented in [67] performs an additional sampling in the middle of each computational time step of the PRRC algorithm. The ramp rate will be calculated in the second half of each calculation time step. The simulations are carried out on a

1.1 k W

two-stage PV system shown in Fig. 3(b). The system parameters are considered equal for a fair comparison between the performance of the two algorithms. The parameters of the simulated PV system are presented in Table III. The sampling time of PRRC algorithm

T

is selected as

0.01 s

. Since the importance of power ramp rate measurement in fast irradiance changes increases, simulations have been performed in fast irradiance changes. The simulation results are shown in Fig. 31. To simulate the PRRC algorithm in [17], the sampling period of the ramp rate measurement algorithm is selected as

0.03 s

(i.e.,

Δ t = m T

and

m = 3

in (9)).

Fig. 31 Performance comparison of algorithms presented in [

17] and [67] under rapid increase of irradiance. (a) Irradiance. (b)

p_{p v}

. (c)

v_{p v}

. (d)

R_{p v}

As shown in Fig. 31(d), the power ramp rate limit of $900 W / s$ is adopted. Before $t = 0.5 s$ , the solar irradiance is constant and the available power $p_{a v a i}$ is $550 W$ . In $t = 0.5 s$ , the irradiance increases from $500 W / m^{2}$ to $1000 W / m^{2}$ in $0.25 s$ . In $t = 0.75 s$ , the available power $p_{a v a i}$ reaches $1.1 k W$ . The operating point for the PRRC is set on the left side of the MPP. Hence, according to Fig. 31(b) and (c), the PV voltage is reduced to adjust the PV power. As shown in Fig. 31(d), the instantaneous power ramp rate $R (t)$ for [

17] exceeds the limit value over a period of time, which is due to the delay in the measurement of the power ramp rate. The algorithm presented in [67] measures the power ramp rate quickly and has a very fast dynamic response.

C. Comparison of PRRC Algorithms

The main features of the above-mentioned PRRC algorithms are summarized in Table VIII.

TABLE VIII Comparison of Various PRRC Algorithms

Algorithm	Reference	Ability to control ramp-up rate	Ability to control ramp-down rate	Speed of ramp rate measurement	Dynamic response	Computational complexity	Power oscillation	Main advantages (+) and disadvantages ( $-$ )
PRRC 1	[68]	Yes	No	Slow	Low	High	Very high	$-$ Heavy calculation burden due to optimization
	[69]	Yes	No	Slow	Low	Low	High	$-$ Work under slow irradiance changes
	[17]	Yes	No	Slow	Medium	Low	Medium	$+$ Simple calculation
	[5]	Yes	Yes	Slow	Medium	Low	Medium	$-$ Need of a forecasting method
	[64]	Yes	Yes	Slow	Medium	Medium	Medium	$-$ Implementation complexity due to PV system clustering
	[66]	Yes	Yes	Fast	Medium	High	Medium	$-$ Decreased efficiency due to working at suboptimal power under normal conditions
	[67]	Yes	No	Very fast	Very fast	High	Low	$+$ Very high dynamic response
PRRC 2	[70]	Yes	Yes	No measurement	Low	Low	High	$-$ Ignoring the demand for ramp rates
PRRC 3	[71]	Yes	Yes	No need to measure ramp rate (predictive method)	Low	High	Low	$+$ Applicable for large-scale PV system

PRRC 1 is a simple algorithm to limit high power ramp rates. In this algorithm, the controller of the connected converter to the PV string does not need to be changed and only the MPPT algorithm should be modified. This algorithm requires a forecasting method to limit the ramp-down rate or the system should normally operate at a sub-optimal operating point other than MPP to be able to control the power ramp-down rate. PV system with PRRC 2 reduces ramp rate unconditionally without considering any ramp rate requirements. With PRRC 3, the duration of transient state is not considered and the limitation of PRRC 2 is overcome. In this algorithm, the power oscillations and the ramp rate limit are considered. However, this algorithm has a slow dynamic response.

VII. Conclusion and Future Directions

A classification and a comprehensive review of FPPT algorithms in the literature have been provided in this paper. A classification of these FPPT algorithms (i.e., CPGC, PRC, and PRRC) has also been provided. One of the main contributions of this paper is to classify the relation between each of these FPPT algorithms and grid support functionalities. The available solutions in the literature for each of these FPPT classifications are described in this paper and their features are extensively compared. The comparison shows that CPGC algorithms work better in most fields by directly calculating the PV voltage reference according to the PV power reference. These algorithms do not have a multi-mode transition. Also, the operating point of PV arrays can be flexibly transferred to the right or left side of MPP. The voltage control block of the PV system does not change in these algorithms. Additionally, the adaptive voltage step leads to low power fluctuations in a steady-state and rapid dynamic response. Among PRC algorithms, a control scheme with modification of P-V curve, which enables direct power regulation, rather than the voltage, has a better response and is effective in tracking the power set-point. Also, a summary review of different ramp rate control algorithms has been performed. Studies show that performing an additional sampling operation in the middle of each computational cycle increases the speed of measuring the power ramp rate and improves the performance of the PRRC algorithm.

In light of the discussions in this paper, the following directions are suggested as emerging research areas.

1) PRC under partial shading conditions. There are multiple local MPPs under partial shading conditions. In this case, the estimation of the maximum available power for PRC is challenging. Emerging solutions are yet to be proposed to estimate the available power without distorting the output power of the PV system.

2) Virtual power plants (VPPs) using PV systems with FPPT functionality. Conventionally, VPPs mainly rely on energy storage systems (ESSs) such as batteries, supercapacitors and hydrogen fuel cell systems, to deliver the required grid functionalities, like contingency frequency control ancillary services [

72], [73]. Conventional solar systems operate with their maximum available power. However, the intermittent nature of these resources results in fluctuations of the injected power to the grid, which is conventionally compensated by continuous charging/discharging of ESSs to deliver the grid requirements in VPPs. This fact results in a shortening of the lifetime of ESSs and increases maintenance and replacement costs of the system because the efficient lifetime of most ESS technologies, e.g., Lithium-ion battery, highly depends on the number of charging/discharging cycles [74]. The power reserve in PV systems can be treated as virtual energy storage. In this case, the coordinated control between the PV systems and energy storage systems can be conceptualized to form a VPP.

3) Battery lifetime extension in microgrids using FPPT operation of PV system. Due to the high penetration of the installation of PV systems in microgrid systems, these PV systems play an important role in the control and stability of the microgrids. Conventionally, in stand-alone microgrids with PV systems, battery energy storage systems are mainly used to regulate the voltage and frequency and deal with the power mismatch between supply and demand. This continuous battery operation leads to shortening the life span of battery systems. However, the FPPT operation in PV systems can be used as the main asset in regulating the voltage and frequency of the stand-alone microgrid. In this way, the battery system can stay in standby mode with reduced charging/discharging cycles, increasing the lifespan of battery.

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