Optimal connection of wind turbines to distribution grid to minimize power loss

This research aims to connect wind turbines to a distribution grid to minimize the power loss and to satisfy the grid’s normal operating condition. The proposed algorithm will determine optimal positions, optimal operation mode and wind turbine type. We must choose the best operation mode from available modes including the constant power factor mode and the constant voltage mode. According to the optimal operation mode, we decide the optimal setting data of wind turbine. This algorithm is coded in MATLAB software and implemented to IEEE 33-buses distribution grid. Noted that in this research, we tested two cases including the original IEEE 33-buses grid and its modification where the power system connected to this grid at multi-position. Results indicated that the proposed algorithm could determine the number of wind turbines, position, optimal operation mode, wind turbine type and the priority order of wind turbine installation to minimize power loss. Moreover, results were also compared to that of other algorithms.


INTRODUCTION
Renewable energy resources have been considered and exploited in many countries in the world; they have contributed an essential part of demand [1]. For solar energy, solar farms are in the range of several kW to MW, and hence, it can integrate to distribution grids quite conveniently. Unlikely, the wind turbine (WT) rating is often several ten kW to MW and wind plants are often connected to transmission grid [2]. However, in areas with low wind potential, we only use small WTs, and they are connected to distribution grids.
For distribution grids, the high-power loss and low node voltage are serious issues [3]. To improve these problems, distributed generators (DG) are recommended to install in the distribution grid. However, determining the optimal position to install is an important issue, and until now, many methods were proposed to tackle this problem [4]- [20]. These methods can be generally divided into three groups. The first group took the economic problem into account [4]- [11]; most research focused on the minimal active power loss [4]- [11] and the maximal electrical energy capture [10]; some of them, authors took the cost and profit maximization into account [10]. The second group concerns technical issues like power quality, stability, and so on [10]- [12]; some research focused on the voltage stability improvement [10]- [12]. The final group considers multi-objective [14]- [20]; at least two objectives from the technique and economic issues is expected to obtain; in this group, the combination of optimal power loss and voltage stability is well-known [15]- [20]. Generally, authors mainly focused on algorithms to obtain the cost function and they did not consider the type of DG (WT, diesel or photovoltaic); the DG unit in these studies often operates in either power quality (PQ) mode or photovoltaic (PV) mode, and authors did not consider which the operation mode is the best [5], [12]. Moreover, the DG units' rating is normally an available value, for example 100 kW, 160 kW, 200 kW, and hence, the DGs' size determined by algorithms is often different from available sizes and we must choose an approximate size; this can make the cost function fail.
In terms of WT, WTs are classified into two groups including fixed speed wind turbine (FSWT) and variable speed wind turbine (VSWT) [21]. For FSWT, it consumes the reactive power from the grid because it is connected directly to the grid [21], and this can make the power loss of the grid increase. For VSWT, if a doubly feed induction generator (DFIG) is used, a power converter with 30% of the DFIG capacity must be installed in the rotor side [21]; and hence, the DFIG turbine is named partial-power-converter based WT (PCWT); by contrast, in the case of a synchronous generator, the converter rating is the same as the generator rating, and hence, it is called full power converter based WT (FCWT) [21]; a VSWT can operate in either the constant voltage mode (CVM) or the constant power factor mode (CPFM) [21]; and noted that the reactive power capacity limitation of PCWT is different from that of FCWT [22]. Practically, VSWT can withdraw a higher energy than FSWT. Hence, in this research, we only use VSWT, and we consider both VSWT type and its operation mode.
This research's objective is to minimize the power loss of a distributed grid by using VSWT. Firstly, we will determine the optimal position where the wind turbine is connected; secondly, the VSWT type, optimal operation mode (OOM) and setting parameters of each VSWT are suggested. The proposed algorithm is coded in MATLAB, and we will test two cases of IEEE 33-bus grid including the original IEEE 33-bus grid and its modification that multi-nodes are connected to the power system. Results are analyzed and compared to those without WTs, and we also compare these results to that of some previous methods.

ALGORITHM OF OPTIMAL WIND TURBINE CONNECTION IN A DISTRIBUTION GRID
To reduce the power loss in a distribution grid, we can install WTs to supply the power to local loads. Here, WT installation must ensure that the power loss in the grid in total, ∆P, is minimum, and constraints including the nodes' voltage limitation and all lines' overload condition are satisfied. Hence, the cost function and constraints are described as (1)-(3), where, is the number of lines in the grid; ∆p is the power loss on the ℎ line; is the voltage at the ℎ node; and , are the current on the line, connecting between the ℎ node and the ℎ node, and its load capacity; and and are the voltage limitations at the ℎ node. To obtain the power loss minimization (PLM), we propose an algorithm to determine the number, position, operation mode, and type of WT as Figure 1.

Main algorithm
The idea of this algorithm is step by step increase in the WT number to determine the optimal connection of each WT. It means we determine the optimal position, OOM, and WT type based on (1)-(3); when the optimal position of the first WT was determined, we suppose that the first WT is already connected to that position, and the next, we consider the second WT; this is repeated until all WTs ( , ) are considered. When all WTs have been considered, we decide the optimal WT number. This algorithm, Figure 1(a), is explained as: − Step 1: reading the grid's data including the node type, magnitude and phase angle of voltage buses, load power, the generation power and its reactive power limitation at nodes, lines' impedance, line's capacity, and so on. The set of all parameters is named . In this step, we use Newton Raphson method to determine ∆P, and the minimum voltage, , in the base case which WTs have not yet connected to the grid. After running the base case, we set = 1, −1 = , and −1 = . Here, is the ℎ WT corresponding to the ℎ stage and −1 is the minimum voltage in this grid in the ℎ stage. Step 2: setting the data of the distribution grid = −1 . − Step 3: checking the minimum voltage −1 . If −1 ≥ 95%, we go to Step 4, otherwise, we go to Step 5. − Step 4: setting = 95% of the rated value, , and going to Step 6. − Step 5: setting = −1 and going to Step 6. − Step 6: determining the optimal position, OOM and type of the ℎ WT. Assuming that ∆ is minimum when the ℎ WT is connected to the ℎ node. Hence, we obtain the optimal position ( ℎ ); , ∆ ; OOM ( or ), and WT type ( ). For more detail, we can refer to Figure 1 Step 8: updating data: assuming that the ℎ WT optimal position is the ℎ node, we update the generated active power at the ℎ node ( , ) as , = , −1 + . If OOM is CPFM, the type of ℎ node is node, the reactive power , = , tan , the voltage at the ℎ node = 1 , and the WT type at the ℎ stage is PCWT or FCWT. If OOM is CVM, the type of ℎ node is node, , = 0, = , the type of WT: . − Step 9: moving to the ( + 1) ℎ WT and then return to Step 2.

Algorithm determining the optimal operation mode (OOM)
This algorithm, Figure 1(b), aims to determine OOM of the ℎ WT if it is connected to the ℎ node. Here, we compare the power loss in total of the grid as WTs at the ℎ node in CPFM, ∆ , , to that in CVM , ∆ , . For CPFM, we must obtain the optimal power factor , as the algorithm in Figure 1(c). For CVM, we must obtain the optimal voltage , and the WT type , as the algorithm in Figure 1(d). Noted that if the ℎ WT operates in the power factor mode, , can be set either PCWT or FCWT. The algorithm's outputs consist of OOM, the power loss ∆ , the minimum voltage , and the ℎ WT type, , . This algorithm is described as: − Step 6a: starting the first node in the list of load node = 1. − Step 6b: using , to calculate and choose OOM as the ℎ WT connected to the ℎ node. Here, we set , = and update the generation power at the ℎ node , , = , Step 6c: using , to determine the optimal power factor of this WT. In this step, we obtain ∆ , , , , , , , , . The detail of this step is described in Figure 1(c).

Algorithm determining the optimal power factor mode
The algorithm described in Figure 1(c) is to decide the optimal power factor of the ℎ WT connecting to the ℎ node. By varying the power factor from +95% to -95% [23] with 10% each step, we run Newton Raphson program to decide the optimal power factor based on PLM. This algorithm is described as: − Step 6c1: setting = 1. − Step 6c2: defining a new set of data, , to calculate in the case of the ℎ WTs at the ℎ node in CPFM. Here, we set , , = , . − Step 6c3: computing the power factor and reactive power of the ℎ WT at the ℎ node as . If one of these constraints is violated, we can set ∆ , , = . − Step 6c5: checking value. If = 11, we move to Step 6c6. Otherwise, we move to Step 6c7. FCWT. We finish this algorithm.

Algorithm determining the optimal voltage mode
This algorithm, shown in Figure 1(d), determine the optimal voltage at the ℎ node where the ℎ WT is connected. Here, we change step by step the voltage at this ℎ node from 95% to 105% of the rated value to determine the optimal voltage value that we obtain PLM. From the required reactive power and WT's reactive power capability at PV nodes, we determine WT type. This algorithm is described as − Step 6d1: setting ℎ = 1. , the type of WTs at ℎ node is PCWT. If above conditions are failed, we set ∆ , ,ℎ = . − Step 6d6: checking the voltage condition. If , ,ℎ < 1.05, we move to Step 6d7, otherwise, Step 6d8 is done. − Step 6d7: increasing ℎ to ℎ = ℎ + 1 and return to Step 6d2. − Step 6d8: determining the , ,ℎ is the optimal voltage if ∆ , ,ℎ = min{∆ , ,1 , ∆ , ,2 , … , ∆ , ,11 }. We set ∆ , = ∆ , ,ℎ , − This algorithm is finished.

RESULTS AND DISCUSSION
To test the proposed algorithm, the IEEE 33-bus distribution grid as Figure 2 is used. In this figure, the grid with continuous line is the original IEEE 33-bus distribution grid [24] while that with dotted line is the modified configuration of this grid. The structure and parameters of the modified IEEE 33-bus distribution grid is completely the same as the original case; the different point is that the modified grid is connected to the power system at multi nodes as the discontinuous line. Noted that the parameters of the original IEEE 33-bus grid data are taken from [24] and each WT in this research is 100 kW [25]. With the parameters of 100 kW WT [26], the reactive power range of PCWT is approximate to from -80 to 75 kVAr while that of FCWT is from -40 to 40 kVAr.

Original IEEE 33-bus distribution grid
We suppose that the 1st node is connected to the power grid and its voltage is always remained at 12.66 kV (the rated value). By running the proposed algorithm, results are shown in Table 1. As can be seen from Table 1, to minimize the power loss in the original IEEE 33-bus distribution grid, we must install 32 WTs of 100 kW at 15 nodes. The node requiring the highest number of WTs (9 WTs) is the 30 th node; the next node is the 25 th node, the 17 th node, and the 32 nd node with 6, 4, and 2 WTs, respectively; for the other 11 nodes, we only install 1 WT for each node. Concerning to OOM, WTs at three nodes including the 17 th node, 25 th node, and 30 th node must operate in CVM; and the voltage at these nodes is always kept at 101%, 99.5% and 100%, respectively; WTs at other nodes must operate in the CPFM with the power factor of 95%. This table also indicates that only WTs at the 25 th node and the 30 th node must employ PCWT whereas other nodes, WT can be either FCWT or PCWT.  Figure 3(a) indicates the voltage profile in the distribution grid before and after installing 32 WTs. By installing WTs as Table 1, the voltage profile in the grid is improved significantly. At the 18 th node, before installing WTs, the voltage is only around 91.5% of 12.66 kV, it is lower than the allowable operation range (95-105%); however, after installing 32 WTs, it increases to 101%. Likely, many nodes including the 7 th to 17 th nodes and the 26 th to 33 rd nodes, the voltage data increases from below 95% to over 99% of 12.66 kV. Generally, nodes' voltage is almost from 99% to 101% and it is in the allowable operation range.
Concerning the power loss on lines, by installing 32 WTs as Table 1, the active power loss on branches is reduced significantly as shown in Figure 3(b). Clearly, on lines near the source, the power loss is reduced significantly from several ten kW to below than 3 kW, taking the line from the 2 nd node to the 3 rd node for an example. However, on the 16 th line which is connected from the 16 th node to the 17 th node, the power loss is higher than that before installing WTs because the power flows from the 17 th node to the 16 th node to supply the load at the 16 th node. The active power loss in total is reduced from 202.68 to 18.04 kW.  As above results, we obtain PLM when we install 32 WTs. However, if the investment is low, we can install a few WTs as Table 2 indicates the priority order of WT installation. It is noted that the operation mode of WTs at the ℎ node is decided by the newest operation mode or the nearest priority order. For example, we only invest 15 WTs; and according to this table, we suggest as following: we install 4 WTs at the 30 th node, 2 WTs at the 17 th and 32 nd node, 1 WT at each node including the 3 rd , 11 th , 13 th , 14 th , 15 th , 18 th , and 31 st nodes; only WTs at the 17 th node operates to remain 98% of the rated voltage whereas WTs at other nodes must generate at 95% power factor; the power loss in this grid after installing 15 WTs is reduced from 202.68 to 56.75 kW. Moreover, it is important to note that in this distribution grid, before WTs' installation, the voltage at the 7 th -18 th nodes and the 26 th -33 rd nodes are normally below 95%, hence, if we install a few WTs, the voltage at these nodes cannot be improved significantly although the power loss is reduced. Hence, we must install up to the 9 th WT, the voltage at all nodes can satisfy the allowable range.
In comparison to other methods in [4], [5], with the proposed algorithm, the power loss is far lower than that with others although DGs' capacity in total is quite similar. With the proposed algorithm, the power loss is reduced to 18.70 kW by installing 3,200 kW of WT whereas with the methods in [4], [5], the power loss still remains quite high, 72.85 and 51.5 kW by installing 3,040 and 3,111 kW (3,660 kVA/pf=0.85) of DG, respectively. The last column in Table 3 indicates that with the proposed algorithm, the percentage of loss reduction is highest 90.77% whereas they are 75.59% and 65.3% for algorithms in [4], [5], respectively. To compare the efficiency of WT installation, we calculate the percentage of loss reduction per 1 kW of generator. As the last column of Table 3, with the proposed method, this data is 0.0283%/kW while others are below 0.025%/kW. Obviously, the efficiency of the proposed method is higher than that of other methods. Obviously, with the proposed algorithm, we can determine the number and position of WTs to obtain PLM of a radial distribution grid. Results also indicate OOM and the type of WTs.

Modified IEEE 33 bus distribution grid
The objective of this section is to test a distribution grid where is connected to the power system via multi-nodes. Hence, we suppose that the IEEE 33 bus distribution grid is connected to the power system via three nodes including the 1 st , 18 th , and 33 rd nodes as Figure 2. These nodes are called source nodes and they are operated as swing buses. By running the proposed algorithm, we obtained results as Table 4. As can be seen from Table 4, to get PLM in this distribution grid, we need to install 34 WTs at 16 nodes. The 25 th and 29 th nodes are required to install the highest number of WTs, 6 WTs for each node. The 9 th , 24 th , and 7 th nodes are also required 5, 4, and 2 WTs, respectively. At other nodes including the 2 nd , 13 th , 14 th , 16 th , 17 th , 20 th , 21 st , 22 nd , 27 th , 30 th , and 31 st nodes, we only install one WT at each node. Almost all WTs at nodes are recommended to operate at 95% power factor except WTs at the 17 th , 20 th , 24 th , and 29 th nodes which are operated in CVM, 100% of the rated value. Moreover, only WTs at the 20 th , 24 th , and 29 th nodes are required to employ PCWT while at other nodes, either PCWT or FCWT can be employed. The total power loss in this grid after installing 34 WTs is 4.048 kW, it cut off 43.676 kW. Figure 4(a) shows all nodes' voltage before and after installing WTs. Obviously, before installing WTs, the nodes' voltage is in the allowable range (95-105% of the rated value) and it is improved significantly after installing WTs. In fact, before installing 34 WTs, the voltage at the 8 th to 12 th and 24 th to 30 th nodes is quite low, below 98.5%, but after installing 34 WTs, they are approximately to the rated value. This can be explained by the following reasons. Firstly, installing WTs at many nodes to directly supply the local load leads to reduce the power flow on lines, and hence, the voltage loss on lines is reduced. Secondly, some WTs are operated in CVM to retain the rated voltage at the connected node, and as a result, the voltage at vicinity nodes are improved.
Beside the voltage loss on lines, the power loss on lines is also reduced significantly as Figure 4(b). Obviously, because many WTs are connected to the 9 th and 29 th nodes, it makes the power flow on the 8 th line and the 29 th line higher than that of without WT, the power loss on these lines becomes higher. However, before connecting WTs, the power loss on the second line is over 12 kW but after installing 34 WTs, it is reduced to below 0.5 kW and this is also seen at many lines such as the 1 st , 16 th , from 23 rd , and 30 th lines. The main reason is that WTs supply directly power to the local load and it makes the power flow on lines decrease. Consequently, the power loss in total is reduced from 47.72 to 4.05 kW.  The priority order of WT installation is indicated in Table 5. The principle of determining the operation mode of WTs at the ℎ node up to the ℎ order is likely to the Table 4. As can be seen from this table, the 25 th node is firstly prioritized because it is quite far from swing nodes and its load power is highest; the first 3 WTs are prioritized to connect to the 25 th node; the next 2 WTs should install at the 9 th node and so on.

CONCLUSION
This paper presents an algorithm to determine the optimal number of WTs such that the power loss in a distribution grid becomes minimum. Beside the optimal number of WTs, this algorithm also determines the optimal location, OOM and the type of WTs. This algorithm was verified via the IEEE 33 bus distribution grid and its modification. Results indicated that the algorithm could give better results than that of other algorithms.

ACKNOWLEDGMENT
This work was supported by The University of Danang, University of Science and Technology, code number of project: T2022-02-07.