Coordination between the central control unit and local control function of a photovoltaic system under the uncertainties of sunlight and three-phase unbalanced loads

At present, high penetration of photovoltaic (PV) systems on low voltage (LV) distribution systems is increasing worldwide because of several favourable conditions, such as government policies, decreasing cost of PV technologies, and environmental awareness. How-ever, varying sunlight and three-phase unbalanced load conditions can result in voltage violation, especially an overvoltage problem, and voltage unbalanced conditions that dete-riorate the power quality. Therefore, disconnection of PV systems, especially on the downstream node, can occur due to the overvoltage protection of the PV system, which results in PV owners losing revenue from selling electricity. Moreover, some electrical appliances can be damaged from voltage unbalanced conditions. To support a high PV penetration and prevent these adverse impacts, this study applies a control strategy involving coordination between the Central Control Unit (CCU) and Local Control Functions (LCFs) of PV systems. The CCU applies the Adaptive Tabu Search (ATS) technique to search for the optimal LCF parameter setting of PV systems and adjusted this weekly. The optimization problem is the maximization of real power generation from all PV systems under varying (uncertain) sunlight and three-phase unbalanced loads. MATLAB programming is used for the Newton–Raphson power ﬂow simulation on a modiﬁed 19-node distribution system.


INTRODUCTION
Currently, fossil-fuel-fired electricity generation is being partially but increasingly replaced by renewable electricity generation because of the latter's desirable outcomes, such as sustainability, no operation fuel costs (excluding manufacturing and installation costs), and a reduction of greenhouse gases. Many different renewable resources, including wind, biomass, and Photovoltaic (PV), can be used for electricity generation in transmission and Medium Voltage (MV) distribution systems, but only PV generation is currently selected as a viable option for suitable connections in Low Voltage (LV) distribution systems. This is because of the technological advancements and reasonable prices of PV systems for residential owners.
In LV distribution systems, small-scale PV systems actually cause a small impact. However, LV distribution systems presently face a high penetration of PV systems that can bring  [1,2]. These include (i) a loss of all PV generation because of the overvoltage protection of the PV system, where most of the PV systems in the downstream node are consequentially disconnected, and (ii) voltage unbalance from connected single-phase PV systems, which can damage some poly-phase appliances.
To support high PV penetration and prevent the consequent adverse impacts, grid reinforcements can be applied, including (i) installing an On-Load Tap Changer (OLTC), (ii) installing an energy storage system, and (iii) changing the conductor size of the LV feeder [2,3]. However, installing an OLTC has the limitation that it significantly increases the cost of the MV/LV distribution transformer and is unable to change tap positions frequently when voltage variation occurs on the LV feeder due to intermittent sunlight. Energy storage systems, which have been shown to be flexible tools for peak-shaving, power shifting, and electrical backup, are still very expensive. Finally, changing to a larger conductor size requires investment in a new line conductor.
The first approach considers directly controlling each PV system from a Central Control Unit (CCU) at a Distribution System Operator (DSO). The CCU needs to (i) apply real-time optimization and (ii) use a very reliable communication system for frequently sending and receiving commands. Therefore, this approach requires the high investment of high-performance computer and very reliable communication system. CCU in [4] regulates only the reactive power output from each PV system to minimize the system loss. In [5][6][7], CCU regulates the maximum allowable real power output and the reactive power output from each PV system to satisfy the weighted sum of the multiobjective optimization problems, which consist of the system loss minimization and the power output maximization from PV systems.
The second approach considers a self-controlling PV system through a Local Control Function (LCF), based on the local condition of the PV system itself. This approach is a low-cost investment, as there is no communication system involved. The LCF parameter is fixed by DSO since the installation of PV systems. For the relevant researches [8][9][10][11][12], the voltage regulation through the LCF application is studied. Here, the local control Q(U) function application changes the reactive power output when the voltage at the connection point of the PV system changes [8][9]. Alternatively, the local control P(U) function changes the real power output when the voltage at the connection point of the PV system changes [10]. Finally, a PV system with the application of various LCFs is studied [11][12], where the coordination of P(U) and Q(U) LCFs is recommended for the effective application of supporting high PV penetration in an LV distribution system.
The third approach considers the coordination between the CCU and the LCFs of PV systems. The CCU receives the local measurement data from smart meters and PV systems infrequently, such as every half or one day. After receiving the data, the CCU will assess and send the optimal LCF parameter back to PV systems in a schedule such as one day or one week. Finally, PV systems will receive and be updated that optimal LCF parameter. A PV system will then operate according to its received LCF parameter and the local condition of the PV system itself. For the example, more real power output is reduced when the voltage at the connection point of the PV system increases. Due to the infrequent sent and received data, this approach eliminates the need for high investment of highperformance computer and very reliable communication system as required in the first approach. Moreover, the capability of remotely scheduling the adjustment of the LCF parameter of this approach can support PV systems to optimally respond following the load and sunlight variations, where the second approach cannot. Therefore, this approach can be considered as the effective approach for leveraging the old-fashioned distribution system to the smart grid. In [13][14][15], various LCFs are considered, i.e., Q(P) LCF in [13], Q(P) LCF with real power limitation in [14], and Q(U) LCF in [15]. For the operation of Q(P) LCF, the reactive power output will be changed when the power output from the PV system changes. The CCU adjusts the LCF parameter only for voltage regulation in [13], power output maximization from PV systems in [14], and system loss minimization in [15].
From the previous research [4][5][6][7][8][9][10][11][12][13][14][15], their disadvantages can be expressed as follows: (i) They consider the LV distribution system as a three-phase balanced system [4,5,8,10,11], which is inaccurate because the loading of any LV distribution system is inherently unbalanced due to many unequal single-phase loads and PV systems and the non-symmetrical conductor spacing of three-phase overhead line segments; (ii) considering the connections of only a single-phase PV system [6,7,9,[12][13][14][15] or a three-phase PV system [4,5,8,10,11], which is incorrect because LV distribution systems are presently connected by both singleand three-phase PV systems; (iii) the uncertainties of sunlight and load are not considered, and the adjustment from the CCU is, therefore, not reliable for application in a real LV distribution system because the load and sunlight are varied; (iv) the two conflicting problems, which consist of the system loss minimization and the power output maximization from PV systems, are applied in [5][6][7] through the weighted sum method. However, it is unclear how to configure the optimal weighting factors. Therefore, the optimization result may be questioned whether it is optimal or not [16].
In this paper, the applied control strategy involves coordination between the CCU and the LCFs of PV systems to support high PV penetration and prevent the consequent adverse impacts. The advantages of this control strategy are already mentioned. The LCF of each PV system, which is the coordination of P(U) and Q(U) LCFs, is applied as the recommendation in [11,12] for the effective application of supporting high PV penetration in an LV distribution system. The CCU adjusts the LCF parameter of PV systems weekly following the result of the proposed optimization process using the Adaptive Tabu Search (ATS) technique, where the proposed optimization process also considers the uncertainties of sunlight and threephase unbalanced loads. The proposed optimization problem is mainly based on the power output maximization from PV systems to satisfy overall PV owners whose electrical sellings are maximized. The system loss is considered as the constraint to satisfy the National Electricity Authority (NEA), which needs to operate the distribution system with low system loss, as determined by the system loss limitation. According to the power flow analysis, the three-phase unbalanced LV distribution system and the connections of both single-and three-phase PV systems are considered. The Power Flow Algorithm (PFA) with the LCFs of PV systems as presented in [17] is applied, and MAT-LAB is used for the programming of this PFA. Numerical simulations are tested on a modified 19-node distribution system.
For the structure of this paper, the impacts of high PV penetration and the control strategy, which is the coordination between the CCU and the LCFs of PV systems, is described in Section 2. After that, the details of the LCF of each PV system are described in Section 3, while the details of the CCU are clarified in section 4. Section 5 focuses on the proposed optimization process for searching for the optimal LCF parameter setting of PV systems. Section 6 expresses the numerical simulations. Finally, the conclusions of this paper are drawn in Section 7.

IMPACTS OF HIGH PV PENETRATION AND THE CONTROL STRATEGY
The installation of more PV systems in an LV distribution system can cause adverse impacts as follows.

Loss of all PV generation
A traditional PV system operates on a unity Power Factor (PF) with no LCF, and so the real power output from this PV system will generate at the Maximum Power Point (MPP), and the reactive power output from this PV system cannot be regulated for voltage support. Therefore, the loss of all PV generation is likely to occur. For example, with an LV distribution system that is connected by two traditional PV systems, when the load is at a peak, the voltage will increase along the LV feeder due to real power injection from these PV systems, as shown in Figure 1(a). However, the voltage is further increased over the overvoltage limit when the intermittent system load is decreased, as shown in Figure 1(b). Then, the overvoltage protection of the PV system will operate, whereby the PV system in the downstream node is disconnected, and so the loss of all PV generation at the downstream node occurs. An LV distribution system with Unbalanced installation from single-phase PV systems more connected PV systems will face more losses of all PV generation.

Voltage unbalance
At present, LV distribution systems are increasingly being connected by many single-phase PV systems. If the connections of each phase PV system is unbalanced, as shown in Figure 2, then a voltage unbalanced condition occurs and the power quality is deteriorated. The effect of a voltage unbalanced condition is the ability to cause damage to all poly-phase loads, especially threephase induction machines. Additionally, current unbalance can be created from a three-phase induction machine at a voltage unbalanced condition and the heat that is then produced in the windings degrades and damages the machine. From the IEC 61000-2-2 [18], the VUF is defined to be not more than 2%, where the VUF can be calculated from Equation (1) [18]; where V ne is the negative-sequence voltage (V) and V po is the positive-sequence voltage (V).
To support a high PV penetration and prevent these adverse impacts, this study uses a control strategy of coordination between the CCU and the LCFs of PV systems. The CCU has the duties to receive the local measurement data from smart meters and PV systems and assess the optimal LCF parameter of PV systems in a schedule such as every half day or one day or week. Each PV system will receive that optimal LCF parameter for updating and operate following its local condition. For the example, the real power limitation is changed when the voltage at the connection point of the PV system changes. The advantages of this control strategy are already stated in Section 1, but in brief are (i) no need for high-performance computer and a very reliable communication system, and (ii) the CCU adjusts the LCF parameter remotely to suit the sunlight and load variation. In this study, the CCU readjusts the LCF parameter weekly. A schematic diagram of this control strategy is shown in Figure 3, where i is any node including a point of common couple (PCC) in the LV distribution system; n is the total node number in the LV distribution system; P i,meter + jQ i,meter is the load at PCC i , which is seen by smart meter (VA); P i,load + jQ i,load is the   (2); where P i,pv + jQ i,pv is the power output from the connected smart PV system at PCC i (VA), and P i,MPP is the generated power (W) at the MPP from the PV array, which can be calculated as previously reported [17].

THE LCF OF EACH PV SYSTEM
The LCF in this study consisted of P(U) and Q(U) functions, which are characterized as a piecewise linear function. This characteristic has been applied for a global LCF in PV systems [19]. Both the P(U) and Q(U) functions in a PV system operate simultaneously on the operational region, as shown in Figure 4, where S i,max is the maximum apparent power of the PV system (VA); Q i,con is 0.5 × S i,max ; P i,con is √ (S i,max ) 2 − (Q i,con ) 2 or around 0.866 × S i,max . When the PV system generates an apparent power output at P i,con + jQ i,con (VA), the power factor is around 0.866. The operation of both P(U) and Q(U) func- tions in a PV system is assumed that the real and reactive power outputs can be changed simultaneously and smoothly when the voltage at the connection point of PV system changes. In addition, more accurate model of a three-phase PV system is considered as the positive-sequence current generation source [17]. The details of the P(U) and Q(U) functions are described in Sections 3.1 and 3.2, respectively.

The P(U) function
When the voltage at the PCC reaches an abnormal voltage setting, a traditional PV system must trip due to the operation of the abnormal voltage protection [20]. Consequently, the loss of all PV generation occurs. Therefore, a P(U) function can be applied in a PV system to prevent loss of all PV generation by voltage-rise relief, where the real power output from the PV system will be reduced according to the operation of the P(U) function when the voltage at the PCC rises. The characteristic of P(U) function is shown in Figure 5, while the equation of the P(U) function for both single-and three-phase PV systems is shown in Equation (3).
where V low and V up are the lower and upper voltage limit (pu.); V i,op is the local voltage of connected PV system at node i (pu.) which is equal to |V i | if the PV system is singlephase type connected at phase ; if the PV system is three-phase type; is any phase (A, B or C). For the other variables, their meanings are shown in Table 1. The adjustable parameters and their limits are summarized in Table 2.

The Q(U) function
Currently, PV systems are permitted to generate reactive power to mitigate the voltage rise [19]. In this study, the Q(U) function is applied, as shown in Figure 6, where the reactive power output is changed when the voltage at the PCC changes. The equation of the Q(U) function for both single-and three-phase PV systems is shown in Equation (6).   (13) and (14) Variable Meaning where, the meaning of the variables in Equation ( (8) are shown in Table 3. The adjustable parameters and their limits are summarized in Table 4.

THE CCU
The CCU is presented schematically in Figure 7 and contains the four main parts of the (i) uncertainty analysis unit, (ii) PV system database, (iii) LV grid database, and (iv) optimization part.

Uncertainty analysis unit
The uncertainty analysis unit acknowledges the data, which consists of household loads, sunlight, and ambient temperature, through smart meters and a weather sensor. For household loads, they can be derived from Equation (2). The main function of this unit is the uncertainty prediction of sunlight, three-phase unbalanced loads, and ambient temperature one week ahead for applying in the optimization part (Subsection 4.4). The predicted uncertainty is based on the normal distribution curve, shown in Figure 8, where x is any data (sunlight, load, ambient temperature, or assessed MPP); and x mean , x max , and x min are the mean, maximum, and minimum values of the normal distribution curve, respectively. Note that, x mean , x max , and x min are based upon the premise that predictions one week ahead are possible. In this paper, each load in the LV distribution system that is at the same phase (A, B, or C) is assumed to have the same normal distribution curve. Moreover, the uncertainty prediction for one week ahead is considered only during the daytime since, during this period of time, a PV system can generate power output. This prediction is assumed to be at a very high degree of accuracy. The mean-max-min scenario is then presented to cover the predicted uncertainty, as shown in Table 5, where L i,mean , L i,max , and L i,min are obtained from the predicted uncertainties of the three-phase unbalanced loads (pu); ir mean and ir max are obtained from the predicted uncertainty of sunlight (kW/m 2 ); ir min is initial sunlight at 0.05 kW/m 2 that the PV system can initially operate from [21]; tem p mean , tem p max , and tem p min are obtained from the predicted uncertainty of the ambient temperature ( o C); MPP i,mean is calculated from ir mean and tem p mean (W); MPP i,max is calculated from ir max and tem p min (W); MPP i,min is calculated from ir min and tem p max (W). From Table 5, case z1 is focused on because this case is most likely to happen or is at the mean values of the aforementioned normal distribution curves. Moreover, cases z2 to z17 must also be considered because they are the boundaries or max-min scenario following the aforementioned normal distribution curves. Note that, an initial sunlight at 0.05 kW/m 2 is determined but the sunlight at 0 kW/m 2 is not. This is because this study determines that an LV distribution system is strong enough to hold on the system limit when there is no PV connection. The mean-max-min scenario in Table 5 is applied later in the optimization problem (Section 4.4), as this problem is for searching for the optimal LCF parameter setting of PV systems one week ahead.

4.2
The PV system database The PV system database stores the details of the PV systems as follows: (i) The connection point (node i and ) of each PV system, and (ii) the specification of each PV system. It is used for the PFA in the proposed optimization process, as discussed in Section 5.

The LV grid database
The LV distribution system, which is regulated by the CCU, has to store the configuration details in the LV grid database for use in the proposed optimization process (Section 5). The configuration details are the (i) base voltage, (ii) base VA, (iii) voltage limits, (iv) line flow limits, (v) distribution transformer capacity, (vi) impedance matrix of the LV distribution system, and (vii) the maximum load data in VA, which is defined as 1 pu. As an example of the load calculation, if the maximum load at any node i and phase is 500 + j100 VA and L i,mean is 0.5 pu, the L i,mean in VA is then calculated as 0.5 × (500 + j 100), which is 250 + j 50 VA.

Optimization part
The main function of the optimization plot is to find the optimal LCF parameter setting of PV systems that satisfies the optimization problem as follows: subject to: where z is any case from {z1, z2, … , z17}; w z is the weighting factor at case z; P i,z,pv is the real power output from the PV system at node i, phase , and case z (W); P loss,z is the system loss at case z (W); Loss MLNP is the system loss when the condition of LV distribution system is at maximum load on case z2 and no PV connection (W); Le 1% is the 1% of Loss MLNP (W); V e 1% is 1% of (V up − V low ); I i− j ,z are the line current between node i and j at phase and case z (A); I i− j ,max is the line current limit between node i and j at phase , and case z (A); S MV ∕LV z is the used capacity of the MV/LV transformer at case z (VA); S MV ∕LV max is the capacity limit of the MV/LV transformer (VA); and VU F i,z is the VUF at node i and case z.
From Equations (9)- (16), this optimization problem is mainly based on the three following factors: The satisfaction of overall PV owners From Equation (9), the overall real power output from the PV systems is maximized and they will not be disconnected at a low load condition. Moreover, each case of the mean-max-min scenario is integrated in Equation (9) by multiplication of the weighting factor. Note that, case z1 has the highest likelihood to occur because this case is at the mean value of the normal distribution curve. Therefore, case z1 is focused and the weighting factor of the case z1 will be higher than the boundary case (z2 to z17), where w z1 is 1 and the others are 0.1. Although the overall real power output from PV systems is maximized according to Equation (9), some PV owners, especially on downstream nodes, may get a disadvantage from operation of the P(U) function, where the real power output from the PV system will be reduced to maintain the system voltage within the limit. It seems unfair, but the PV system can still generate some real power despite occurring loss of all PV generation from PV disconnection.

Satisfaction of the NEA
Traditionally, an LV distribution system is used to serve electricity to household load, as shown in the example in Figure 9(a), where the system loss at peak load is around 250 W or Loss MLNP is 250 W. Currently, PV systems are increasing in LV distribution systems, where PV owners need to sell electricity to the NEA. As shown in Figure 9(b), the PV output is 2,830-j995.54 VA at peak load. There is reactive power absorption from this PV system for voltage rise relief. The resultant system loss is 216.72 W, which is less than the Loss MLNP . The NEA gets the advantage from this PV connection of a reduced system loss at a peak load. However, when the LV distribution system is at a light load and the PV system tries to inject a maximum power output, the system loss result may be worse, as shown in Figure 9(c), where the system loss is 667.13 W. A worse system loss is an unfair burden on the NEA despite power purchase at maximum PV output. Therefore, PV systems must not cause a higher system loss than Loss MLNP , as shown in Equation (12). The optimal PV output  Tables 2 and 4. According to Figure 9(c), the power output of the PV system can be readjusted to satisfy the required maximization of real power output while keeping the system loss limit to within 250 W, as shown in Figure 9(d). For the constraint in Equation (12), it is used for the satisfaction of NEA.

Constraints in the LV distribution system
The 17 cases of the mean-max-min scenario from Table 5 are subjected to a power flow analysis to cover the uncertainty prediction one week ahead. Through the LCF parameter adjustment of PV systems, the power flow result reveals that in all 17 cases the mean-max-min scenario must be maintained within the system limit, according to Equations (13)- (16). From Equation (13), the system voltage results must remain within the voltage limit, while Equations (14) and (15) indicate that the power flow results must be maintained within the line flow and the capacity limit of the MV/LV transformer, respectively. Finally, the IEC 61000-2-2 standard [18] defines that the VUF limit in an LV distribution system shall not exceed 2%, as shown in Equation (16). Note that the optimization problem in Equations (9)-(16) problem is based on the set {z1, z2, … , z17} which does not consider the uncertainties thoroughly. It means that other set, or out of the set {z1, z2, … , z17}, are not considered and those sets may cause the over limit in Equations (17) and (18). Therefore, Equations (17) and (18) are replaced by Equations (12) and (13) with the error factors, Le 1% and V e 1% . Furthermore, although the weighting factors (w z1 , w z2 , … , and w z17 ) are used, they are used in the same problem as shown in Equation (11) but in dif-ferent cases from z1 to z17.

THE PROPOSED OPTIMIZATION PROCESS
In this study, ATS is applied to find the solution to the optimization problem, as shown in Equations (9)- (16). The solution is selected from the LCF parameter setting of PV systems that causes the maximum objective value. The details of ATS are described in Section 5.1 and the objective value calculation from the optimization problem following Equations (9)-(16) is explained in Section 5.2.

Use of the ATS
The ATS is a meta-heuristic method that uses the current solution to move iteratively towards a better solution in its current neighbourhood region. The iteration continues until the local optimum is found. Additionally, ATS has an adaptive radius technique to increase the local optimum searching performance. This adaptive radius technique has the advantage that a large neighbourhood region can be decreased to a smaller one for a more accurate search for the optimal solution. Moreover, the backtracking technique of ATS can find other paths to move to for finding a better solution, but the adaptive memory, called the Tabu list, must be applied to prevent using the same path as before. The ATS has been applied previously [22,23], where it is claimed that the ATS is better than other methods, such as the Simulated Annealing (SA) and Hill-Climbing Method (HCM). This is because ATS can cope with the optimization problem with many free variables. Furthermore, many local optimal results can be obtained and the best result can be selected from these local optimal results. Figure 10 shows a sample moving path of ATS towards a local optimum point with the adaptive radius and the backtracking technique.

Objective value calculation
According to the optimization problem, written in Equations (9)-(16), the objective value calculation from the LCF parameter setting PV systems can be summarized into the following five steps, and shown in the flow chart in Figure 11.  Tables 2  and 4. STEP 2: At each iteration, each member from {z1, z2, … , z17} will be selected until all members are selected. Note that, each member from {z1, z2, … , z17} will have different data, as shown in Table 5.
STEP 3: From the obtained data in STEP 2, the PFA with the LCFs of PV systems [17] is performed. Then, the power flow result, which consists of the real and reactive power output from each PV system, system voltage, system loss, line flows, the used capacity of the MV/LV transformer, and VUFs, is obtained. Note that this PFA [17] is described in Appendix A.3. STEP 4: From the power flow result in STEP 3, F ob,z is calculated from Equation (11). Moreover, the power flow result is compared to the Equations (12)- (16) and Equation (19) is used to indicate the qualification of the power flow result, where pen z will be zero if the power flow result is within the Equations (12)- (16) or pen z will be more than zero if it is outside these constraints. After that, if all members from {z1, z2, … , z17} have not been selected, then go to STEP 2.
where, nb is the total branch number of an LV distribution system; and M p1 , M p2 ,M p3 , M p4 , and M p5 are constant values.

SIMULATION RESULTS AND DISCUSSION
This section expresses the effectiveness of the control strategy, which is the coordination between the CCU and the LCFs of PV systems, with a high PV penetration support. The test system which is the 19-node distribution system is detailed in Appendix A.1. The forecasted load, sunlight, and ambient temperature data (from 6.00 to 18.00 h) for the next week, shown in Appendix A.2, is assumed to happen. As stated in Section 4, the uncertainty analysis unit of the CCU then predicts the accurate uncertainties of three-phase unbalanced loads, sunlight, and ambient temperature, one week ahead. The predicted uncertainties in this study, as shown in Figure 12, are assessed from the data in Appendix A.2 and are transformed into the mean-max-min scenario ( Table 5). The simulation results are divided into five parts: (i) No PV connection; (ii) slight PV penetration; (iii) high PV penetration; (iv) non-optimal parameter setting of the LCF; and (v) optimal parameter setting of the LCF.

No PV connection
To begin with, there is no PV connection in the 19-node distribution system. The simulation is at the maximum load in case z2 with the voltage profile shown in Figure 13 and a Loss MLNP of 2,633.25 W.

Slight PV connection
In this subsection, there is a slight PV connection and the operation of the PV system has a PF of 1 pu. For example, the 19-  Table A5), where (i) this PV system is a threephase connection type; and (ii) the rated output of this PV system is 10,000 VA. According to the forecasted data for the week ahead in Appendix A.2 and PV18 with PF of 1 pu., the PFA [17] is performed and the results of the maximum and minimum voltage, maximum VUF, real power output from PV18, and system loss are obtained as shown in Figure 14, where the maximum or minimum voltage is obtained from any node that has a maximum or minimum voltage compared with another node, and the maximum VUF has the same meaning. From Figure 14, the voltage (215.60-246.72 V) and VUF (≤1.98%) results are within their respective limits. For PV18, it can generate at MPP or no real power limitation. Moreover, the maximum system loss is 1,908.29 W, which is less than Loss MLNP . Thus, a slight PV connection reduces the system loss in an LV distribution system.

High PV penetration
In the future, LV distribution systems may face a high PV penetration because of government policies. Therefore, the simulation in this section is based on a high PV penetration in which the 19-node distribution system has 18 PV connections. The overall PV capacity is 127.8 kW or 102.24% of the MV/LV transformer. According to the forecasted data for the week ahead in Appendix A.2 and PV systems with each PF of 1 pu., the PFA [17] is performed, and the power flow result is shown in Figure 15. Note that this simulation does not determine the PV disconnection. From Figure 15, the voltage results (223.74-268.16 V) are over the voltage limit, whereas the VUF results (≤1.61%) are within the VUF limit. For PV1-PV18, they generate a real power output at MPP or no real power limitation. Moreover, the maximum system loss is 7,195.15 W, which is more than Loss MLNP . Thus, a high PV connection can cause an overvoltage problem, where many PV systems will be disconnected due to their overvoltage protection, and so cause an increasing system loss. To prevent the impact from this high PV penetration, the control strategy of coordination between the CCU and the LCFs of PV systems is applied in the next subsection.

6.4
Non-optimal parameter setting of the LCF The coordination between the CCU and the LCFs of PV systems is applied in this subsection. The non-optimal objective is shown in Equations (22)-(25), where only the voltage, line flow, and used capacity of the MV/LV transformer are regulated under the limits following z ∈ {z1, z2, … , z17}. Applying ATS, the LCF parameter setting result of PV systems is obtained as shown in Table 6. According to the forecasted data for the week ahead in Appendix A.2 and the LCF parameter setting in Table 6, the PFA [17] is performed, and the power flow result is shown in Figure 16 where the voltage results (212.97-242.80 V) are within the voltage limit, but the VUF results (≤3.03%) exceed the VUF limit. For PV1-PV18, they generate a real power output with P(U) function with a maximum overall real power output of only 19,735.48 W. Moreover, the maximum system loss is 4,631.76 W, which is more than the Loss MLNP . Therefore, the LCF parameter setting from Table 6 will disappoint PV owners and the NEA because of the reduced sale of real power output from the PV systems and the greater system loss, respectively. Moreover, the VUF results are over the limit that can cause damage to poly-phase loads, especially three-phase induction machines. In the next subsection, the CCU applies the optimal objective in Equations (9)- (16) to satisfy both the PV owners and the NEA and to maintain the system constraints.

6.5
Optimal parameter setting for the LCF In this section, the coordination between the CCU and the LCFs of PV systems is applied to the optimization problem in Equations (9)- (16), and the LCF parameter setting result of PV systems is shown in Table 7. According to the forecasted data for   Table 7, the PFA [17] is performed, and the power flow result is shown in Figure 17.
From Figure 17, the voltage (220.94-252.26 V) and VUF (≤1.67%) results are within their respective limits. For PV1-PV18, they generate a real power output with a P(U) function with a maximum overall real power output of 82,402.12 W. Moreover, the maximum system loss (2,578.27 W) is less than the Loss MLNP . Therefore, the optimal LCF parameter in Table 7, which is obtained from the proposed optimization process, can satisfy (i) the PV owners by maximizing the real power output from PV systems, (ii) NEA by limiting the system loss and (iii) the system constraints.

CONCLUSION
Currently, the number of PV connections is increasing in LV distribution systems, and so a high PV penetration with the consequent adverse impacts can occur in the near future. These adverse impacts consist of (i) a loss of all PV generation because the overvoltage protection of the PV system is operated resulting in most of the PV systems in the downstream node being disconnected, and (ii) voltage unbalance from connecting single-phase PV systems, which can damage some poly-phase appliances. In this study, a control strategy that coordinates the CCU and the LCFs of PV systems is applied to support a high PV penetration and prevent these adverse impacts. This has the benefits of (i) no need for high-performance computer and very reliable communication system; (ii) the LCF parameter can be reset by the CCU remotely and optimally following variation in the sunlight and load. The proposed optimization process based on ATS is used in the CCU for finding the optimal LCF parameter, which is used to update PV systems in the next week. The LV distribution model is more accurate under the three-phase unbalanced system and the connections of both single-and three-phase PV systems. The numerical simulations are tested on the 19-node distribution system with high PV penetration, and the proposed optimization process can find the optimal LCF parameter of PV systems in the next week to satisfy (i) overall PV owners by maximizing the real power output from PV systems, (ii) NEA by limiting the system loss, and (iii) the system constraints.

APPENDIX A
The important data which is used in this paper can be shown in the followings.

A.1 Test system details [17]
The 19-node distribution system, as shown in Figure A1, is used as the test system in this study and consisted of: Base voltage of 230 V, line to neutral; Rated MV/LV transformer of 125 kVA; Voltage limit between 0.9-1.1 pu. or 207-253 V; VUF limit less than 2%; Impedance matrix of each branch, which has two types (A1 and A2), as shown in Table A1; Maximum load (or at 1 pu.) of each node and each phase is shown in Table A2; The 19-node distribution system [17]     Specification of the utilized PV module as shown in Table A3; Specifications of the utilized PV system as shown in Table A4;  Table A5 where each PV system is named following PV1-PV18. The overall capacity of PV systems is 127.8 kW, or 102.24% of the MV/LV transformer.

A.2 Forecasted data
The forecasted data at day time from 6.00 to 18.00 hr. for the next week, as shown in Figure A2, is assumed to happen. The only daytime data is presented because, during this period of time, a PV system can generate power output. Note that each node in the 19-node distribution system is assumed to have the same load profile as shown in Figure A2(a-c).

A.3 Numerical Simulation Using The Power Flow Algorithm With The LCFs Of PV Systems [17]
This paper uses the PFA with the LCFs of PV systems as presented in [17] for the numerical simulation. When the threephase loads, sunlight, and ambient temperature change, this