Review of reactive power dispatch strategies for loss minimization in a DFIG-based wind farm

: This paper reviews and compares the performance of reactive power dispatch strategies for the loss minimization of Doubly Fed Induction Generator (DFIG)-based Wind Farms (WFs). Twelve possible combinations of three WF level reactive power dispatch strategies and four Wind Turbine (WT) level reactive power control strategies are investigated. All of the combined strategies are formulated based on the comprehensive loss models of WFs, including the loss models of DFIGs, converters, ﬁlters, transformers, and cables of the collection system. Optimization problems are solved by a Modiﬁed Particle Swarm Optimization (MPSO) algorithm. The effectiveness of these strategies is evaluated by simulations on a carefully designed WF under a series of cases with different wind speeds and reactive power requirements of the WF. The wind speed at each WT inside the WF is calculated using the Jensen wake model. The results show that the best reactive power dispatch strategy for loss minimization comes when the WF level strategy and WT level control are coordinated and the losses from each device in the WF are considered in the objective.


Introduction
Wind energy has become the leading renewable energy in the world. In 2015, the increase in wind generation was equal to almost half of the global electricity growth. In Europe, wind energy overtook hydropower as the third largest source of power generation, with a 15.6% share of the total power capacity [1]. In the same year, the total wind generation in Denmark consisted of 42 percent of the Danes' electricity consumption [2].
The high percentage of wind power penetration will influence the system stability [3]. In order to deal with this issue and to have the ability to integrate more renewable energies, power system operators have imposed strict grid codes for Wind Farms (WFs). For large WFs, one of the mandatory requirements is to provide voltage and reactive power support [4,5], including the voltage ride through under fault conditions [6,7] and the reactive power provision under steady states. Both of these functions need WFs to provide extra reactive power [8], which may increase the active power losses in devices providing the reactive power. The loss of the active power will affect the benefits of the WF owners and reduce their initiative to participate in the reactive power support. Therefore, the idea of considering the reactive power as an ancillary service and allowing different providers to compete in electricity markets is proposed in [9].
Traditionally, there are few suppliers of reactive power support when it is needed in a particular location, because reactive power does not travel far on the transmission line, which limits the competition for this service [10]. However, as the penetration of renewable energy increases, especially the highly distributed generation penetration, there will be more reactive power suppliers in a region, which increases the practicability to introduce the reactive power market to clear the reactive power This paper reviews the WT level reactive power control strategies and the WF level reactive power dispatch strategies, and compares all of the possible combinations of WF level reactive power dispatch strategies and WT level reactive power control. The loss models for all of the devices that will cause active power and reactive power losses are also given in this paper. The twelve combined reactive power dispatch strategies are evaluated on a WF with 40 NREL 5MW reference WTs under a series of cases. A modified particle swarm optimization (MPSO) algorithm is adopted to solve the optimization problem. The wind speed at each WT inside the WF is calculated using the Jensen wake model [23]. Since the WF active power dispatch is not the main concern in this paper, the MPPT control is used on each WT. The results show that the best reactive power dispatch strategy for loss minimization occurs when the WF level strategy and WT level strategy are coordinated and the losses from each device in the WF are considered in the objective.
The paper is organized as follows. Section 2 reviews the WF reactive power sources and the loss models. Section 3 introduces the reactive power control strategies inside a DFIG based WT system. Section 4 states the reactive power dispatch strategies within a WF. Section 5 introduces the combinations of WT level control and WF level dispatch, and the optimization method. The effectiveness of these strategies is calculated and analyzed in different case studies in Section 6. Finally, conclusions are drawn in Section 7.

Reactive Power Sources and Loss Models
Many sources can be used to regulate the reactive power for the WF, like capacitor banks, STATCOMs, SVCs, load tap changers (LTCs), and WTs [12]. Capacitor banks are discrete reactive power sources, so they are usually used in relatively old WFs. The LTC is only equipped on the transformer connected to the grid, because the transformers equipped with the WTs do not need to have LTCs [5]. Meanwhile, the LTC connected to the grid will not influence the losses related to reactive power dispatch inside the WF. Therefore, in modern WFs, the reactive power dispatch is usually between STATCOMs, SVCs, and WTs equipped with power electronic devices, which are all continuous reactive power sources. In addition, the loss models of the components inside STATCOMs and SVCs are similar to the loss models of the components inside DFIG-based WTs. Therefore, only the DFIG-based WTs are considered as reactive power sources in this paper.
In DFIG-based WFs, the active power losses mainly arise from the WTs, the transformers for WTs, and the transmission cables. The active power losses inside a WT are illustrated in Figure 1, which consist of friction loss of the mechanical part, core loss and copper loss inside the DFIG, and losses in the converters and the filter. The friction loss and core loss can be considered constant under a certain operating point [24], and therefore, they are not considered in this paper. one is the traditional way used in many WFs and the second one is a newly developed which aims at minimizing the wake effects inside the WF [22]. This paper reviews the WT level reactive power control strategies and the WF level reactive power dispatch strategies, and compares all of the possible combinations of WF level reactive power dispatch strategies and WT level reactive power control. The loss models for all of the devices that will cause active power and reactive power losses are also given in this paper. The twelve combined reactive power dispatch strategies are evaluated on a WF with 40 NREL 5MW reference WTs under a series of cases. A modified particle swarm optimization (MPSO) algorithm is adopted to solve the optimization problem. The wind speed at each WT inside the WF is calculated using the Jensen wake model [23]. Since the WF active power dispatch is not the main concern in this paper, the MPPT control is used on each WT. The results show that the best reactive power dispatch strategy for loss minimization occurs when the WF level strategy and WT level strategy are coordinated and the losses from each device in the WF are considered in the objective.
The paper is organized as follows. Section 2 reviews the WF reactive power sources and the loss models. Section 3 introduces the reactive power control strategies inside a DFIG based WT system. Section 4 states the reactive power dispatch strategies within a WF. Section 5 introduces the combinations of WT level control and WF level dispatch, and the optimization method. The effectiveness of these strategies is calculated and analyzed in different case studies in Section 6. Finally, conclusions are drawn in Section 7.

Reactive Power Sources and Loss Models
Many sources can be used to regulate the reactive power for the WF, like capacitor banks, STATCOMs, SVCs, load tap changers (LTCs), and WTs [12]. Capacitor banks are discrete reactive power sources, so they are usually used in relatively old WFs. The LTC is only equipped on the transformer connected to the grid, because the transformers equipped with the WTs do not need to have LTCs [5]. Meanwhile, the LTC connected to the grid will not influence the losses related to reactive power dispatch inside the WF. Therefore, in modern WFs, the reactive power dispatch is usually between STATCOMs, SVCs, and WTs equipped with power electronic devices, which are all continuous reactive power sources. In addition, the loss models of the components inside STATCOMs and SVCs are similar to the loss models of the components inside DFIG-based WTs. Therefore, only the DFIG-based WTs are considered as reactive power sources in this paper.
In DFIG-based WFs, the active power losses mainly arise from the WTs, the transformers for WTs, and the transmission cables. The active power losses inside a WT are illustrated in Figure 1, which consist of friction loss of the mechanical part, core loss and copper loss inside the DFIG, and losses in the converters and the filter. The friction loss and core loss can be considered constant under a certain operating point [24], and therefore, they are not considered in this paper.

Loss Model of DFIG
The copper losses of the DFIG can be calculated using: where R s and R r are the stator and rotor resistance, respectively. The calculation of the currents of the stator and the rotor can be given in [25].

Loss Model of Converters and the Filter
According to [26,27], the loss of a converter can be expressed as: where I rms is the rms value of the sinusoidal current, and a l and b l are the power module constants, which can be expressed as: where V IGBT is the voltage across the collector and emitter of the IGBT, E ON + E OFF represents the turn-on and turn-off losses of the IGBTs, E rr is the turn-off (reverse recovery) loss of the diodes, I C,nom is the nominal collector current of the IGBT, f sw is the switching frequency, and r IGBT is the lead resistance of the IGBT. The loss of the filter can now be calculated by: where I gd and I gq are the d-axis and q-axis currents of the RSC and the GSC, respectively, and can be calculated using the equations described in [25]. Thus, the total loss of a WT, P loss WT , is: P loss WT = P Cu + P loss RSC + P loss GSC + P loss f ilter

Loss Model of Transformers
The transformer loss P loss trans can be expressed by the equation in [28]: where β, P 0 , and P k are the load ratio, no-load loss, and load loss, respectively. The reactive power loss of the transformer is neglected in this paper.

Loss Model of Cables
The power loss in cable ij can be expressed by [29]: where V i , V j are the voltage at bus i and bus j, respectively, I ij is the cable current measured at bus i and defined positive in the direction i → j , and I ji is the cable current measured at bus j and defined positive in the direction j → i .

Reactive Power Control Inside a DFIG based WT System
The reactive power control strategies inside a DFIG based WT system are reviewed in this section. The typical control flow of the converters inside a DFIG based WT system is shown in Figure 2.

Reactive Power Control Inside a DFIG based WT System
The reactive power control strategies inside a DFIG based WT system are reviewed in this section. The typical control flow of the converters inside a DFIG based WT system is shown in Figure 2. is set by the WT controller. Therefore, the reactive power reference for GSC can be calculated by: The total reactive power requirement can be provided by either RSC or GSC, or the combined effort of both RSC and GSC.

Strategy 1:
This strategy is proposed in [30,31]. The reactive power required by the WF controller is only provided from the stator side. In this case, the reactive power is controlled by the RSC, which also controls the WT active power. In the RSC controller, the q-axis current of the DFIG rotor rq I is controlled to regulate the stator reactive power s Q . This method is commonly used, but it will cause more copper loss inside the DFIG if the required power factor is far from the unity power factor.

Strategy 2: ref
In this control concept, the reactive power is only provided by the GSC [30,32]. In this case, GSC is responsible for regulating the reactive power and keeping the dc-link voltage constant, which are controlled by the q-axis current gq I and d-axis current gd I , respectively. This method can fully utilize the capacity of the GSC, but it will increase the losses from the GSC and the filter and the copper loss is not minimal.

Strategy 3: Minimum Copper Loss Control
The copper loss minimizing strategy is proposed in [33,34]. This method regulates reactive power using both the RSC and the GSC. The reactive power sharing between the RSC and the GSC can be derived using the method described in Equation (11). The optimal reactive current rqopt I  can be derived by equating the derivative of the copper loss with respect to rq I  to zero. The result can be expressed as: The total reactive power reference of the WT, Q re f WT , is received from the WF controller, while the reference of reactive power from the stator of the DFIG Q re f s is set by the WT controller. Therefore, the reactive power reference for GSC can be calculated by: The total reactive power requirement can be provided by either RSC or GSC, or the combined effort of both RSC and GSC. This strategy is proposed in [30,31]. The reactive power required by the WF controller is only provided from the stator side. In this case, the reactive power is controlled by the RSC, which also controls the WT active power. In the RSC controller, the q-axis current of the DFIG rotor I rq is controlled to regulate the stator reactive power Q s . This method is commonly used, but it will cause more copper loss inside the DFIG if the required power factor is far from the unity power factor.

Strategy 2: Q
In this control concept, the reactive power is only provided by the GSC [30,32]. In this case, GSC is responsible for regulating the reactive power and keeping the dc-link voltage constant, which are controlled by the q-axis current I gq and d-axis current I gd , respectively. This method can fully utilize the capacity of the GSC, but it will increase the losses from the GSC and the filter and the copper loss is not minimal.

Strategy 3: Minimum Copper Loss Control
The copper loss minimizing strategy is proposed in [33,34]. This method regulates reactive power using both the RSC and the GSC. The reactive power sharing between the RSC and the GSC can be derived using the method described in Equation (11). The optimal reactive current I rqopt can be derived by equating the derivative of the copper loss with respect to I rq to zero. The result can be expressed as: Then, the optimal stator side reactive power can be calculated using the steady-state voltage equations of the DFIG in [25]: Further, the reference reactive power of the GSC can be calculated by Equation (9). This method can minimize the copper losses in the DFIG. However, it may increase the losses from the GSC and the filter, which contributes to a significant part of the total loss.

Strategy 4: Minimum WT Loss Control
A strategy which shares the reference reactive power of the RSC and the GSC to minimize the total loss is proposed in [35,36]. The sharing ratio is iteratively calculated and a look-up table is formed, which can be used to set the reactive power reference for the GSC controller and the RSC controller. The loss of the filter is included in the objective function in [37] for minimizing the total electrical losses inside the DFIG-based WT system. The authors derived an equation to calculate the reference of the q-axis rotor current I re f rq with the changing variables P mec and Q re f WT . However, this equation is derived based on the piecewise-linear model of the converter loss, which will cause errors. The proper Q re f s and Q re f g of each WT can also be dispatched by the centralized WF controller [25]. However, this will increase the computational burden on the centralized WF controller. In fact, the optimal Q re f s can be found by solving an optimization problem in Equation (12) under certain P mec and Q re f WT , which is an extension to the method proposed in [35,36].
Min Q re f s P loss WT .
The constraints for this optimization problem include Equation (9) and the WT reactive power limits.

Range of Reactive Power
The range of Q s is mainly constrained by the rated rotor side current, which is the rated RSC current I rated con and the rated stator current I rated s [31]: The range of Q g is determined by the rated current of the GSC [31]: These constraints are nonlinear constraints and the currents are calculated using the steady state equations of the system.

Reactive Power Dispatch Strategies within a WF
Besides the WT level reactive power control strategy, the WF level reactive power dispatch strategy is critical to the total loss minimization in WFs. This section reviews the reactive power dispatch strategies within a WF.

Strategy A: Proportional Dispatch
The traditional dispatch strategy is the proportional dispatch, which distributes the reference reactive power required by the WF operator proportionally among all the operational WTs based on their available reactive power [38][39][40][41][42]. This scheme can be expressed using the following equation: where Q re f WTi and Q max WTi are the reference reactive power and the available reactive power of WT i , respectively, and Q Total re f is the WF total reactive power requirement. This method has the advantage that it can be easily implemented and can ensure that the reactive power reference of each WT does not exceed its limit. However, the active power losses are not considered.

Strategy B: WF Transmission Loss Minimization
This strategy minimizes the active power losses along the transmission system in a WF, which includes the transmission cables and the transformers for WTs [12,[43][44][45][46]. The optimization objective for this strategy is: where P loss trans i and P loss Cable k represent the active power losses for the i-th transformer and the k-th cable, respectively.
This strategy aims at minimizing the active power losses along the transmission system; however, the active power losses inside the WTs are not considered, which are actually responsible for a great share of the total loss.

Strategy C: WF Total Loss Minimization
This strategy includes the losses along the transmission system, as well as the losses inside the WTs, in the objective [25,47,48]. Thus, the optimization problem can be written as: s.t. This strategy considers all of the losses inside the WF in the optimization objective, which is promising for producing the lowest active power loss for the WF.

Combinations of WT Level Control and WF Level Dispatch and the Optimization Method
The reactive power control strategies at the WT level can affect the total loss inside the WT under certain P mec and Q re f WT . If the wind distribution and the active power control strategy for each WT are determined, the reactive power dispatch strategy at the WF level will influence not only the transmission losses, but also the losses inside the WTs. Therefore, from the WF controller's perspective, it is reasonable to find the possible combinations of reactive power control strategies at the WT level and reactive power dispatch strategies at the WF level to check which combination gives the best performance.

Combinations of WT Level Control and WF Level Dispatch
Based on the aforementioned description, there are twelve reasonable combinations of WT level control and WF level dispatch strategies, which are listed in Table 1. Strategy C4 [25] Many of the combined strategies have been proposed in previous literature. For example, Strategy A1, which is the combination of Strategy A and Strategy 1, has been introduced in [38][39][40][41]. This method is the most common and basic strategy used in WF control.
Strategy C4 is the combination of the WF total loss minimization strategy at WF level and minimum WT loss control at WT level. This strategy has the best chance to reach the minimum active power loss for the WF; however, it may be very difficult to implement because of the complexity. There are different ways to implement Strategy C4. The scheme proposed in [18] uses the centralized WF controller to dispatch the optimal Q re f s and Q re f WT to each WT, which will change the control strategy of the WT, i.e., each WT should receive two references from the WF controller. Besides, this method doubles the optimization variables, and will thus demand many more computational resources for the WF controller.
In this paper, the optimization problem of Strategy 4 is considered as the inner loop of the optimization problem of Strategy C. The problem is formulated as Equation (12)  the optimization problem of Strategy C, the optimal Q re f s is found by searching the lookup table, which saves computational effort for the WF controller.
In order to calculate the currents of the cables and the voltages of each bus, the AC power flow should be implemented. However, it is not easy to include the AC power flow in the optimization problem. In this paper, the AC power flow is computed using the Newton-Raphson method and is considered as an inner loop of the optimization problem. The solutions giving infeasible power flow will be excluded.

Optimization Method
The problems for WF dispatch strategies B and C are nonlinear and non-convex, and therefore, the PSO algorithm is chosen to provide the solution [49]. In order to improve the performance of standard PSO, a linearly time-varying acceleration constant is applied, as suggested in [49]. It modifies the velocity updating method with a high cognitive constant (c 1 ) and low social constant (c 2 ), and gradually decreases c 1 and increases c 2 to search the entire search space, rather than to converge towards a local minimum: where k is the iteration number and k max is the maximum iteration number. A method for improving the convergence speed of the Modified PSO (MPSO) is properly handling the constraints. In this paper, a penalty factor method [50] is adopted to handle the constraints, where the objective function for strategies B and C will be defined by: where P loss WF is the total loss of the WF; λ 1 and λ 2 are the penalty factors for the equality constraints and inequality constraints, respectively; and ceq and c are the equality constraints and inequality constraints for the optimization problem, respectively, which can be expressed as: where the tolerance of the voltage violation V viol is selected as 0.05 in this paper, the unit for all the variables in ceq is kW, and all of the variables in c are in per unit system. The penalty factors λ 1 and λ 2 are chosen as 0.03 and 100, respectively.

Case Study
In this paper, a WF with 40 NREL 5MW reference WTs is used to test the combined strategies, as shown in Figure 3. The distance between WTs in the prevailing wind direction is 8 rotor diameters and in the non-prevailing wind direction is 6.7 rotor diameters. The red square is the substation and the number besides the red stars indicates the predefined WTs' sequence number. The blue line shows the cables connecting the WTs and the substation. The cables are 630, 500, 300, 240, or 95 mm 2 (chosen by load) XLPE-Cu cables, which are operated at a 66 kV nominal voltage. The parameters of the WTs are the same as in [25]. The MPSO method is employed to solve the optimization problems.
(chosen by load) XLPE-Cu cables, which are operated at a 66 kV nominal voltage. The parameters of the WTs are the same as in [25]. The MPSO method is employed to solve the optimization problems.

Case I: V = 10 m/s, Wind Direction = 240°
Considering the wake effect, the wind velocities in front of each WT are different. By using the traditional MPPT control strategy of WTs, the active powers of each WT will be different if the wind velocities are below the rated value. Since the reactive power dispatch between WTs is highly related to their active power, the active power distribution in the WF should be calculated beforehand. In this paper, the wakes are calculated by the Jensen model and the wake combination refers to the multiple wake model in [33]. In this scenario, the wind velocities at each WT are shown in Figure 4. The performances of four WT control strategies with each WF dispatch strategy are shown in Figure 5. As can be seen, the total loss of the WF using WT control Strategy 4 (the red dashed line) is always optimal with all three WF dispatch strategies. Meanwhile, the WT control Strategy 1 (the blue dashed line) is the second best. Using WT control Strategy 4, the total losses are almost the same as when  Considering the wake effect, the wind velocities in front of each WT are different. By using the traditional MPPT control strategy of WTs, the active powers of each WT will be different if the wind velocities are below the rated value. Since the reactive power dispatch between WTs is highly related to their active power, the active power distribution in the WF should be calculated beforehand. In this paper, the wakes are calculated by the Jensen model and the wake combination refers to the multiple wake model in [33]. In this scenario, the wind velocities at each WT are shown in Figure 4. (chosen by load) XLPE-Cu cables, which are operated at a 66 kV nominal voltage. The parameters of the WTs are the same as in [25]. The MPSO method is employed to solve the optimization problems.

Case I: V = 10 m/s, Wind Direction = 240°
Considering the wake effect, the wind velocities in front of each WT are different. By using the traditional MPPT control strategy of WTs, the active powers of each WT will be different if the wind velocities are below the rated value. Since the reactive power dispatch between WTs is highly related to their active power, the active power distribution in the WF should be calculated beforehand. In this paper, the wakes are calculated by the Jensen model and the wake combination refers to the multiple wake model in [33]. In this scenario, the wind velocities at each WT are shown in Figure 4. The performances of four WT control strategies with each WF dispatch strategy are shown in Figure 5. As can be seen, the total loss of the WF using WT control Strategy 4 (the red dashed line) is always optimal with all three WF dispatch strategies. Meanwhile, the WT control Strategy 1 (the blue dashed line) is the second best. Using WT control Strategy 4, the total losses are almost the same as when  The performances of four WT control strategies with each WF dispatch strategy are shown in Figure 5. As can be seen, the total loss of the WF using WT control Strategy 4 (the red dashed line) is always optimal with all three WF dispatch strategies. Meanwhile, the WT control Strategy 1 (the blue dashed line) is the second best. Using WT control Strategy 4, the total losses are almost the same as when Q WF re f is −0.1 pu and 0 pu. That is because the minimum loss for the DFIG is reached when absorbing a portion of reactive power from the stator side. Therefore, the best Q WF re f for the minimal total loss should lie between 0 pu and −0.1 pu. By the same reason, WT control Strategy 3 (the black dashed line) causes more loss than WT control Strategy 2 (the green dashed line) when Q WF re f is larger than zero. Since WT control Strategy 4 has the best performance of the four WT control strategies, it is used as the base WT control strategy to compare the performances of the WF dispatch strategies. The results are shown in Figure 6, from which it can be seen that WF dispatch Strategy C exhibits the best performance, while WF dispatch Strategy B causes the largest total loss. Besides, the WF total loss is higher when WF ref Q is positive rather than negative, though the absolute value of WF ref Q is the same.
That is also because the loss in the DFIG is minimal when absorbing a portion of reactive power from the stator side. Since WT control Strategy 4 has the best performance of the four WT control strategies, it is used as the base WT control strategy to compare the performances of the WF dispatch strategies. The results are shown in Figure 6, from which it can be seen that WF dispatch Strategy C exhibits the best performance, while WF dispatch Strategy B causes the largest total loss. Besides, the WF total loss is higher when Q WF re f is positive rather than negative, though the absolute value of Q WF re f is the same. That is also because the loss in the DFIG is minimal when absorbing a portion of reactive power from the stator side. Since WT control Strategy 4 has the best performance of the four WT control strategies, it is used as the base WT control strategy to compare the performances of the WF dispatch strategies. The results are shown in Figure 6, from which it can be seen that WF dispatch Strategy C exhibits the best performance, while WF dispatch Strategy B causes the largest total loss. Besides, the WF total loss is higher when WF ref Q is positive rather than negative, though the absolute value of WF ref Q is the same.
That is also because the loss in the DFIG is minimal when absorbing a portion of reactive power from the stator side. The losses using Strategies A4, B4 and C4 are shown in Table 2. It can be seen that the losses inside the WTs and the losses on the transformers using Strategy A4 are the minimum. The losses along the cables using Strategy B4 are the minimum; however, the losses inside the WTs and the losses from the transformers using Strategy B4 are the highest, and the total loss using Strategy B4 is the highest. This means that Strategy B4 can minimize the losses in the cables, but increases the losses in the WTs and transformers more significantly. None of the losses on individual parts using Strategy C4 are optimal, but the total loss using Strategy C4 is the minimum, which means the minimal total loss is reached as a compromise of the trend to minimize the losses along the cables and the trend to minimize the losses in the WTs and transformers.  Figure 7. The total loss in direction 240 • is lower than that in other wind directions, because the stronger wake effects in this direction make the wind power at downwind WTs lower, which leads to reduced losses in the WF. However, the loss reduction in this direction is higher than those in other directions. The reason for this is that stronger wake effects cause a higher diverse for the wind distribution in the WF, and thus a higher diverse for the active power distribution. A higher diverse in active power generates more space for reducing the total loss by properly dispatching the reactive power.   Figure 7. The total loss in direction 240° is lower than that in other wind directions, because the stronger wake effects in this direction make the wind power at downwind WTs lower, which leads to reduced losses in the WF. However, the loss reduction in this direction is higher than those in other directions. The reason for this is that stronger wake effects cause a higher diverse for the wind distribution in the WF, and thus a higher diverse for the active power distribution. A higher diverse in active power generates more space for reducing the total loss by properly dispatching the reactive power.

Case III: Total WF Loss in a Year
In this case, the effectiveness of Strategies A4, B4 and C4 are evaluated in a year. The wind data is obtained from a WF called FINO 3, where the wind speeds are sampled per 3 hours, and then averaged each day. The wind rose is plotted with the intervals of wind directions and wind velocities as 5° and 4 m/s, respectively, as shown in Figure 8.

Case III: Total WF Loss in a Year
In this case, the effectiveness of Strategies A4, B4 and C4 are evaluated in a year. The wind data is obtained from a WF called FINO 3, where the wind speeds are sampled per 3 hours, and then averaged each day. The wind rose is plotted with the intervals of wind directions and wind velocities as 5 • and 4 m/s, respectively, as shown in Figure 8. With the data from the wind rose, the total loss using Strategies A4, B4 and C4 are calculated at each wind speed and summed up as the total loss in one year at each WF ref Q , as seen in Figure 9. calculated in every case, the WF reactive power dispatch Strategy C4 can ensure minimal active power losses among all of the twelve combined strategies. Meanwhile, Strategy A4 is the second best for loss minimization. However, the implementation of Strategy A4 is much easier than the implementation of Strategy C4, because Strategy C4 needs to solve a nonlinear and nonconvex optimization problem, which requires more computing resources. Therefore, Strategy A4 can be a good choice in WFs with limited computing resources.

Conclusions
The total loss in a WF with twelve possible combinations of three WF reactive power dispatch strategies and four WT reactive power control strategies is calculated and compared in different cases. The following conclusions can be drawn based on the results and analysis:

•
The reactive power control strategies on the WF level and the WT level interact with each other and should be considered at the same time to achieve a further loss reduction. With the data from the wind rose, the total loss using Strategies A4, B4 and C4 are calculated at each wind speed and summed up as the total loss in one year at each Q WF re f , as seen in Figure 9. Compared with Strategy A4, Strategy C4 can save around 0.3 GWh electricity when operating at Q WF re f = 0.33 pu for the whole year. The saving amount of Strategy C4 reaches around 1 GWh when compared with Strategy B4, which is the largest saving amount for every Q WF re f . Based on the results calculated in every case, the WF reactive power dispatch Strategy C4 can ensure minimal active power losses among all of the twelve combined strategies. Meanwhile, Strategy A4 is the second best for loss minimization. However, the implementation of Strategy A4 is much easier than the implementation of Strategy C4, because Strategy C4 needs to solve a nonlinear and nonconvex optimization problem, which requires more computing resources. Therefore, Strategy A4 can be a good choice in WFs with limited computing resources. With the data from the wind rose, the total loss using Strategies A4, B4 and C4 are calculated at each wind speed and summed up as the total loss in one year at each WF ref Q , as seen in Figure 9. Based on the results calculated in every case, the WF reactive power dispatch Strategy C4 can ensure minimal active power losses among all of the twelve combined strategies. Meanwhile, Strategy A4 is the second best for loss minimization. However, the implementation of Strategy A4 is much easier than the implementation of Strategy C4, because Strategy C4 needs to solve a nonlinear and nonconvex optimization problem, which requires more computing resources. Therefore, Strategy A4 can be a good choice in WFs with limited computing resources.

Conclusions
The total loss in a WF with twelve possible combinations of three WF reactive power dispatch strategies and four WT reactive power control strategies is calculated and compared in different cases. The following conclusions can be drawn based on the results and analysis:


The reactive power control strategies on the WF level and the WT level interact with each other and should be considered at the same time to achieve a further loss reduction.

Conclusions
The total loss in a WF with twelve possible combinations of three WF reactive power dispatch strategies and four WT reactive power control strategies is calculated and compared in different cases. The following conclusions can be drawn based on the results and analysis: • The reactive power control strategies on the WF level and the WT level interact with each other and should be considered at the same time to achieve a further loss reduction.
• When considering the loss minimization in the WF, the losses of every device, including the losses of the generators, converters, filters, transformers, and cables should be included in the objective at the same time, because reducing the losses on parts of the devices may increase the losses on the other parts. • The dispatch of reactive power is strongly related to the distribution of the active power. The stronger the wake effect is, the larger the improvement is when using the optimal dispatch strategy. • The WF losses are lower when Q WF re f is negative, which is because the copper loss on the DFIG is minimal when the stator absorbs a certain amount of inductive reactive power. • Strategy C4 can give the minimum WF active power loss, but Strategy A4 can be a good choice in WFs with limited computing resources.
The combined strategies can be implemented in the WF energy management system. For future research, different active power dispatch strategies can be combined with the optimal reactive power dispatch strategy.