Coordinated voltage/var control in a hybrid AC/DC distribution network
2020; Institution of Engineering and Technology; Volume: 14; Issue: 11 Linguagem: Inglês
10.1049/iet-gtd.2019.0390
ISSN1751-8695
Autores Tópico(s)Smart Grid Energy Management
ResumoIET Generation, Transmission & DistributionVolume 14, Issue 11 p. 2129-2137 Research ArticleFree Access Coordinated voltage/var control in a hybrid AC/DC distribution network Feng Qiao, School of Electrical and Information Engineering, The University of Sydney, Sydney, AustraliaSearch for more papers by this authorJin Ma, Corresponding Author j.ma@sydney.edu.au School of Electrical and Information Engineering, The University of Sydney, Sydney, AustraliaSearch for more papers by this author Feng Qiao, School of Electrical and Information Engineering, The University of Sydney, Sydney, AustraliaSearch for more papers by this authorJin Ma, Corresponding Author j.ma@sydney.edu.au School of Electrical and Information Engineering, The University of Sydney, Sydney, AustraliaSearch for more papers by this author First published: 08 April 2020 https://doi.org/10.1049/iet-gtd.2019.0390Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract A hybrid AC/DC distribution network (HDN) is formed after multiple hybrid AC/DC microgrids (MGs) and distributed generators (DGs) are integrated into the distribution network. Voltage/var control (VVC) in this evolved system constitutes a big challenge to system operators as a large variety of voltage control devices with quite different control characteristics are expected to be co-managed. This study proposes a coordinated VVC scheme to regulate voltage in an HDN by integrating power management model of hybrid AC/DC MGs into HDN's VVC model. The devices at HDN's level and those in MGs are allocated into two different models, and two models are linked via an approach called mathematical programmes with equilibrium constraints to achieve system-wide coordination. In the proposed VVC, mechanical devices such on-load-tap changer (OLTC) and shunt capacitor (SC) are scheduled every 2 h to save their lifetime, while the electronically interfaced DGs and MGs are scheduled every 30 min to leverage their fast power support. Case studies on a modified IEEE 33 nodes distribution system validate that the proposed VVC can effectively coordinate MGs' power support with OLTC, SCs, and DGs, and it constitutes significant improvements on power loss reduction and voltage quality compared with traditional VVC. Nomenclature t time interval t voltage of bus i Active and reactive power flow from bus i resistance and reactance from bus i to j nominal voltage of the system tap tap position of OLTC tap step of the OLTC position of the shunt capacitor i position step of the shunt capacitor reactive power compensation from shunt capacitor i active and reactive power consumptions at bus i active and reactive powers from the renewable generator at bus i active and reactive powers from the microgrid at bus i minimal value of variable * maximal value of variable * capacity of the renewable generator at bus i capacity of the interfaced transformer of the microgrid at bus i cost coefficient of variable * active power from the fuel-based distributed generator in AC and DC subsystems charging and discharging powers of the energy storage system in AC subsystem charging and discharging powers of the energy storage system in the DC subsystem active power from the renewable generator in AC and DC subsystems exchanged power through the interlinking converter between AC and DC subsystems exchanged power through the transformer between microgrid and distribution network state of charge of the energy storage systems in AC and DC subsystems charging and discharging efficiencies lower boundary of variable * upper boundary of variable * binary variables for the energy storage systems in AC and DC subsystems binary variables for the interlinking converter between AC and DC subsystems binary variables for the transformer between microgrid and distribution network 1 Introduction Driven by technology advancements in the power conversion, a large scale of electronically interfaced distributed generators (DGs) and hybrid AC/DC microgrids (MGs) are connected to distribution networks [1]. Consequently, a hybrid AC/DC distribution network (HDN) is formed, where multiple electronically interfaced power sources coexist with traditional voltage regulators such as on-load-tap changer (OLTC) and shunt capacitor (SC). To control various devices contributing to a satisfying voltage quality, it is required to merge them into one voltage/var control (VVC) scheme, in which their different controlling characteristics can be well developed. With the help of advanced communication system and control techniques, MGs and DGs equipped with power electronic devices perform better in terms of control speed [2–5], and their active and reactive powers can be simultaneously controlled to improve voltage quality under the high R/X ratio in the distribution network. By contrast, OLTCs and SCs can be only controlled regularly because they suffer from reduced lifetime if being frequently adjusted. There are plenty of literature leveraged different control characteristics of various devices to achieve VVC objectives in distribution networks. In [6], a VVC model is built, in which the reactive power from DGs is coordinated with OLTC and SCs to reduce power losses and the numbers of switching operations of OLTC and SCs. In [7], the inverter interfaced DGs, OLTC, and SCs are operated in different time scales to mitigate the fast voltage variation caused by stochastically varied renewable generation. A multi-temporal optimisation problem is formulated in [8] to control the voltage in a distribution network with various voltage/var regulators. The curtailment of DGs and loads are utilised in the model, and a metaheuristic algorithm is used to find the optimal solution. In [9], the electronically interfaced DGs and energy storage systems (ESSs) are controlled to regulate the system voltage, and both active and reactive powers are controlled through a coordination strategy according to their sensitivity to the voltage profile. After MGs are connected to distribution networks, VVC becomes more challenging as MGs' operational objectives could conflict with VVC task. However, the reported works regarding MGs' application in distribution networks mostly focus on energy management [10–13], while the literature investigating MG's participation in VVC is very limited. In [14], MGs' power injection is coordinated with OLTC and DGs to control the system voltage. Since the power exchange between the distribution network and each MG is determined by a pre-trained artificial neural network, the calculation accuracy cannot be guaranteed if the system parameters change. In [15], a decentralised VVC is proposed based on the multi-agent system to drive MGs to participate in voltage control. However, the coordination between MGs and other voltage regulators is not considered. In [16], a distributed VVC is proposed for multi-MG active distribution networks. The VVC is activated when the voltage boundaries of any MG are affected, and then the MG asks support from neighbouring MGs and distribution network operator (DNO) to restore its local voltage. However, this scheme also overlooks the coordination at the system level. Since the reactive power support from an MG is limited by its capacity and internal active power generation [17, 18], its active power management should be integrated into the VVC scheme. Furthermore, when the MG employs a hybrid AC/DC structure [19, 20], it is expected to address three distinct but interconnected entities (namely MG's AC subsystem, MG's DC subsystem, and the distribution network) by coordinating two bidirectional power flows (one is between two subsystems and the other is between the MG and the HDN). Consequently, the devices at the distribution network's level and those in MG's subsystems are expected to be interactively managed. The conflicts cannot be avoided when MG's power management and HDN's VVC have different objectives. Thus, it calls for a reformulated VVC model to coordinate the traditional voltage regulators such as OLTC and SC and the newly introduced controllers such as DGs and MGs to maintain voltage profile in the distribution network and resolve the possible conflicts between VVC objectives and optimal energy schedule in grid-tied MGs. This paper develops coordinated VVC strategies to optimise voltage profile in an HDN by coordinating various voltage/var regulators with different control characteristics, and major contributions of this work lie in three folds: (i) A game-based mathematical model is developed to give an integrated solution on HDN's VVC with the hybrid AC/DC MGs' own active power management conflicts considered. (ii) A coordinated multi-time scale control strategy is developed to leverage different control characteristics of the voltage regulators such as OLTC and SC in the traditional distribution network and those emerged with DGs and MGs. (iii) The active and reactive powers in the system are simultaneously controlled toward a reduction in power loss and satisfied voltage quality. This paper is organised as follows: Section 2 introduces the voltage control problem after MG's connection and gives a game-based view for solving this problem. Section 3 presents the VVC model and MG's power management model. Section 4 introduces the solution method and the multi-time scale application for the proposed VVC model. In Section 5, the effectiveness of the proposed method is validated on a modified IEEE 33 nodes distribution system, and it is compared with traditional VVC schemes to demonstrate its advantages. Section 6 concludes this paper and summarises merits and limitations of the proposed method. 2 Impact of a grid-tied MG on voltage control 2.1 Voltage variation after MG's integration The traditional VVC can be illustrated by (1) [21]. The secondary voltage of the transformer and the reactive power from the SC are coordinated to regulate the voltage (1)However, this scheme fails to maintain the voltage in an HDN after MG's connection. In Fig. 1, the downstream power injection is introduced from an MG. In this case, can be calculated by (2). It can be identified that will be increased if and take positive values or decreased if and are negative (2)The impact of the augmented power from MG on the VVC can be viewed from two aspects. On the one hand, if MG's power injection is only determined by its power management model, OLTC and SC should adjust more frequently to face the variation caused by and , and load might be curtailed to guarantee the voltage quality. On the other hand, if the power injection from MG can be properly controlled to mitigate the variation caused by load and distributed generation in the distribution network, reduced active power loss and better voltage quality can be expected. Fig. 1Open in figure viewerPowerPoint Schematic hybrid distribution network 2.2 Game-based view on VVC in a hybrid distribution network To utilise the power support from grid-tied MG while not deteriorating the voltage quality in the HDN, VVC should be redesigned by adding MGs' power injections as control variables. Furthermore, since the capacity of the converter constraints the reactive power support from MG, the active power management of the MG becomes coupled in the VVC scheme. Consequently, different operational objectives of MG and HDN could bring conflicts to each other. Fig. 2 shows Pmg –V2 curves using three different sets of set points for OLTC and SC on the hybrid distribution network in Fig. 1, and reactive power from MG is deactivated in three cases. It can be observed that Pmg needs to be accordingly adjusted in response to the variations on V1 and QSC in order to maintain the voltage of bus 2 within the range from 0.9 to 1.1 pu. The applicable range of Pmg would be fixed once the set points of OLTC and SC are determined. When the MGs are connected to the distribution network, the power exchange with the distribution network is expected to be determined not only by MGs' power management model but also the DNO, which wants to achieve the VVC objectives. Then, the possible conflict between DNO and MGs will occur. Fig. 2Open in figure viewerPowerPoint Pmg–V2 curves for various operation modes of OLTC and SC To solve this bi-lateral situation, where the interest of each and the conflict between them must be addressed, a game-based model is proposed here. The HDN and the hybrid AC/DC MG are considered as two distinct entities contributing to VVC objectives under a hierarchical structure. The VVC problem for the whole system is formulated based on the Stackelberg game theory, in which the HDN acts as the leader and the grid-tied MGs acts as the follower. The leader takes advantage of being the first mover, whereas the follower accordingly takes his optimal move after observes the leader's move and may slightly sacrifice his profits as being the latter mover. The equilibrium in the game can be described by (3) [22]. The leader takes his action x from set X, and the follower determines his action y from set Y. Their costs are and , respectively. The equilibrium of the game is a set of actions such that is the best response of the follower to the action , which solves the problem as shown in the equation below: (3)It is indicated in (3) that the leader in the game understands that the follower will always choose the best response to any action and chooses the action to minimise his cost. When the equilibrium point in (3) is reached in the VVC, the DNO profits the optimised VVC objectives while the MGs profit the minimised local operational cost they could have after considering DNO's VVC requirements. In the following section, the VVC model of the HDN and the power management model of the hybrid AC/DC MG are built, and solutions for the VVC task will be obtained by seeking the equilibrium among two models in the game. 3 Problem formulation 3.1 VVC model of HDN The VVC model of the HDN is formulated based on DistPF [21]. The objective function (4) consists of two parts. The first one minimises the active power loss in the distribution network, whereas the second one maintains the node voltages as much close as to the nominal value. The weights and are utilised to scale two objectives, and they can be altered when loads are updated at each time interval. It is worth noting that using the second objective is necessary for an HDN as the node voltage needs to be maintained as much close to the nominal value as possible to make the system robust for accommodating the intermittent output of downstream power sources (4)The equality constraints (5)–(9) represent the voltage and power balance of each bus. The inequality constraints (10)–(12) represent the operational limits of the bus voltage, SC, and OLTC. The limit on the reactive power injection from the renewable generators and grid-tied MGs are described by (13) and (14), respectively. In this paper, the MGs and DGs are electronically interfaced to the system via a converter or a solid-state transformer, so their power injection can be regulated in four quadrants [23, 24] (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 3.2 Power management model of hybrid AC/DC MG A hybrid AC/DC MG example is shown in Fig. 3, which can be easily transformed into any form of distribution network with AC or DC MGs. The objective function as defined in (15) consists of six terms. The first three penalise the usage of the fuel-based DGs and ESSs. The fourth term maximises the renewable generation by setting the coefficient as a negative value. The last two terms penalise the usage of the interlinking converter and the solid-state transformer, respectively. Fig. 3Open in figure viewerPowerPoint Schematic hybrid AC/DC MG The operational principles are stated as follows: (i) using the interlinking converter to balance the power supply between two subsystems is more efficient compared with exchanging power with the HDN; (ii) each subsystem obtains external power only if the local generation is fully loaded; and (iii) fuel-based generators should be the last to be dispatched since it is not environmental-friendly, whereas the renewable generation is highly prioritised. With the above principles, the rank, as indicated in (16), should be followed when setting the coefficients in the equation below: (15) (16)The power balance in AC and DC subsystems are described in (17) and (18). The AC subsystem is connected to the HDN, so its load can be supplied by either the local power sources or the power from the distribution network. The DC subsystem is supplied by either its local generation or the AC subsystem (17) (18)The fuel-based generators and renewable generators in AC and DC subsystems are limited by their upper and lower bounds, as indicated in (19), (20), (26), and (27). The upper boundary of the renewable generator is defined as its maximum generation obtained from forecasted data. Inequalities (21)–(25) and (28)–(32) are operational constraints of the ESSs in AC and DC subsystems. Their states of charge are updated by (25) and (32), and binary variables in (23) and (30) avoid them from simultaneously charging and discharging. The operation constraints of the interlinking converter and solid-state transformer are defined in (33)–(38) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) 4 Solution method and application procedures 4.1 Mathematical programmes with equilibrium constraints Under the theory of Stackelberg game, the optimum of the HDN's VVC model in Section 3.1 depends on the decision of the MG's power management model in Section 3.2. Conversely, the optimum of the model in Section 3.1 can be only sought if the power exchange between MG and HDN is determined by solving the power management model in Section 3.2. This nested feature increases the difficulty to get the equilibrium point in the game. In this paper, an approach called mathematical programmes with equilibrium constraints (MPECs) is employed to find the optimal solution for these two nested models [25]. By using MPEC, the optimal of MG's power management problem is described by its Karush–Kuhn–Tucker (KKT) conditions, and then the conditions are augmented to HDN's VVC problem as complementary constraints. Then, two nested models are transformed into one, in which the optimal of the MG's problem can be guaranteed at any feasible point of the HDN's VVC problem. The derivation of KKT conditions requires a linear problem; however, multiple binary variables exist in the MG's power management model in Section 3.2. A simple search method is used to handle the binary variables here. Moreover, the dual variables generated from deriving KKT conditions are relaxed via the Big-M method [26]. 4.2 Multi-time scale VVC application To leverage the fast control speed of the electronically interfaced MGs and DGs while to relieve the control burden of the OLTC and SCs, a multi-time scale application is chosen. Specifically, the MGs and DGs are adjusted every 30 min to face the changing loads in the HDN while the OLTC and SCs can be only adjusted every 2 h to limit their usage for saving their lifetime. The computation procedures are illustrated by the flowchart in Fig. 4. The forecast data of the load and renewable generation are input for each time interval. The OLTC and SCs will be fixed to their current positions if the time scale is in 30 min or set as controllable for the VVC model if the time scale is in 2 h. After setting the control state of the OLTC and SCs, the algorithm selects one combination of the binary variables and to link the HDN's VVC problem and the MGs' power management problem by using MPEC. Since the binary variables are handled by exhaustive search, a series of MPEC problems will be generated by using various combination of binary variables. Then, multiple solutions will be obtained by solving these problems, and the best solution with minimal objective value is selected for the final execution. Fig. 4Open in figure viewerPowerPoint Computation procedures for multi-time scale application of the proposed VVC scheme Owing to the existed quadratic constraints and integer variables, the formulated MPEC constitutes a mixed-integer quadratic constraint programming problem. We solve it by Gurobi in a desktop equipped with Intel Core i5 processor and 8 GB RAM. The average computation time for each time interval is in 10 s, which is very fast for practical usage. 5 Case studies 5.1 System parameters The proposed VVC scheme is tested on a modified IEEE 33 nodes system [21] as shown in Fig. 5. In the test system, an OLTC with 20 tap positions is located at the substation, and tuning capacity for each tap position is 0.05 pu. Moreover, there are three SCs in the system. The SC1 has five steps, whereas the SC2 and SC3 have three steps. The tuning capacity is 0.1 MVAr per step for all the SCs. Furthermore, two wind turbine (WT) generators and two photovoltaic (PV) systems are connected to bus 14, 30, 25, and 8, respectively. The capacities of them are 2, 3, 1, and 1 MVA, respectively. Three hybrid AC/DC MGs are connected to buses 16, 21, and 32. The MGs' layouts are identical as shown in Fig. 3 and their parameters are listed in Table 1. In the MGs, the charging and discharging efficiencies are assumed identical for the ESSs, so and are equal as shown in Table 1. Fig. 5Open in figure viewerPowerPoint Modified IEEE 33 nodes system Table 1. Configurations of hybrid AC/DC MG AC subsystem fuel-based generator maximum generation 1 MW WT generation maximum generation 2 MW load maximum consumption 2 MW ESS maximum energy level 2 MWh minimum energy level 0.2 MWh maximum discharging/charging power 1 MW discharging/charging efficiency 0.77 DC subsystem fuel-based generator maximum generation 1 MW PV system maximum generation 1.5 MW load maximum consumption 1.5 MW ESS maximum energy level 2 MWh minimum energy level 0.2 MWh maximum discharging/charging power 1 MW discharging/charging efficiency 0.77 others interlinking converter capacity 1 MVA solid-state transformer capacity 2 MVA The original loads are timed by four in the modified system to accommodate the augmented generation and the multipliers as shown in Fig. 6 are used to make the loads and renewable generation changing over the 48 time intervals during the day. Fig. 6Open in figure viewerPowerPoint Multipliers for renewable generation and load 5.2 Assessment of VVC performance Fig. 7 shows the voltage profiles of some key buses with and without the proposed VVC functionality. The voltage profiles of these buses are out of the allowed ±5% range without the VVC functionality due to the heavy loads, the massive active power generation from DGs, and the various power injection from MGs determined by their local power management model. After functioning of the proposed VVC, the voltages of these buses are secured ranging from 0.97 to 1.01 pu, including the buses 18 and 33, which are the far-end buses in the HDN. Fig. 7Open in figure viewerPowerPoint Voltage profile of some key buses Fig. 8 illustrates the values of the two VVC objectives in (4) before and after the proposed VVC functionality. The two VVC objectives are named as active power loss and voltage deviation in this figure. It can be observed that the values of the two objectives are reduced significantly for each time interval after the proposed VVC functionality. The total active power loss in the system without the VVC is 37.103 MW during the day, whereas it is decreased to 7.788 MW by functioning the proposed VVC scheme. The aggregated voltage deviation value is decreased from 134.150 to 6.669 pu due to the proposed VVC functionality. Fig. 8Open in figure viewerPowerPoint Active power loss and voltage deviation in the distribution network The satisfied VVC objectives under the proposed VVC are achieved by coordinating the OLTC, SCs, DGs, and MGs. Fig. 9 shows the schedules of the OLTC and SCs during the day. The OLTC is operated at high tap positions during the daytime while it is at low tap positions at night to regulate system voltage considering varied load and renewable generation during the period. The three SCs are adjusted to compensate their local reactive power shortage, and their adjustment times are limited since the multi-time scale application is utilised. Fig. 9Open in figure viewerPowerPoint Set points of OLTC and SCs Four renewable DGs are operated to maximise their active power generation while their reactive power injections are adjusted to aid voltage control, as shown in Fig. 10. The coordination between the DGs and SCs can be seen from Figs. 9 and 10. For example, due to the significant amount of reactive power provided by WT2, the control burden of the nearest SC3 is relieved, and it remains deactivated until hour 7. Fig. 10Open in figure viewerPowerPoint Reactive power provided by renewable generators Figs. 11 and 12 show the active and reactive powers provided by the hybrid AC/DC MGs. Since the power management of these MGs is integrated into HDN's VVC, their active and reactive powers are controlled contributing to HDN's VVC task. Fig. 11Open in figure viewerPowerPoint Active power provided by MGs Fig. 12Open in figure viewerPowerPoint Reactive power provided by MGs 5.3 Power support from hybrid AC/DC MGs The power dispatches inside the hybrid AC/DC MGs are shown in Figs. 13–18. It is identified that three MGs show different energy schedules, although they have the same configurations. This is due to that they are controlled not only to achieve their own operational merits but also to coordinate with other voltage/var regulators to maintain the voltage in the HDN. Fig. 13Open in figure viewerPowerPoint Energy balance in AC subsystem of MG1 Fig. 14Open in figure viewerPowerPoint Energy balance in DC subsystem of MG1 Fig. 15Open in figure viewerPowerPoint Energy balance in AC subsystem of MG2 Fig. 16Open in figure viewerPowerPoint Energy balance in DC subsystem of MG2 Fig. 17Open in figure viewerPowerPoint Energy balance in AC subsystem of MG3 Fig. 18Open in figure viewerPowerPoint Energy balance in DC subsystem of MG3 Taking MG1 as an example, it can be observed in Figs. 13 and 14 that the renewable generation is always maximised while the usage of the fuel-based generators is limited over time. Since the AC subsystem and DC subsystem have imbalanced generation and load, the power exchange via the interlinking converter can be seen from these figures, and the ESSs are scheduled to compensate any power mismatch in the two subsystems. The MG1 is connected to bus 16, where the nearby loads are relatively heavy during the daytime. Therefore, it injects a significant amount of active power to the HDN from hour 3 to hour 15. In response to MG1's power injection, relatively high usage of fuel-based generators, ESSs, and power exchange from its DC subsystem to AC subsystem can be observed over the period. MG2 is connected to bus 21, which is close to the OLTC, and its neighbouring buses have relatively light loads. It is shown in Figs. 15 and 16 that its active power injection to the HDN is relatively low among three MGs, while it absorbs a certain amount of active power from hour 8 to hour 17 to avoid the neighbouring buses from overvoltage. In response to the less power injection, the fuel-based generators in MG2 are strictly dispatched. The power balance in the two subsystems of MG3 is shown in Figs. 17 and 18. The neighbour buses of MG3 are under heavy load during the day, so the usage of the local power sources including fuel-based generators and ESSs are heavy in response to its significant amount of active power injection. It can be observed from these figures that three grid-tied AC/DC MGs are scheduled to meet not only their local load changes but also the variations on loads and renewable generations in the HDN. Therefore, it can be validated that the coordination between MGs and other voltage regulators in the HDN can be ascertained under the proposed VVC scheme. 5.4 Comparative case study In this section, a comparative case study is performed to further demonstrate the superior performance of the proposed VVC over the traditional VVC as introduced in Section 2.1. In the traditional VVC, MGs' power management is separate with the HDN's VVC model, so the MGs' power management model introduced in Section 3.2 is performed first, and then the results are input to the HDN's VVC model in Section 3.1 to calculate the set points for all the VVC resources. Moreover, in order to show the advantages of the multi-time scale application as introduced in Section 4.2. The proposed VVC and the traditional VVC are performed by using single-time scale application and multi-time scale application, respectively. In the single-time scale application, all the control variables are free to be adjusted for any time interval. The voltage deviation factor (VDF) as given in (39) is introduced to compare the voltage control performance. Moreover, the adjustment times of the OLTC and SCs are also used for comparison purpose (39)Table 2 shows the comparative results obtained in four different cases. The proposed VVC (Case 3 and Case 4) yields lower VDF and active power loss compared with the traditional VVC (Case 3 and Case 4), which shows its superior performance in satisfying the VVC objectives. Table 2. Results of comparative case studies Traditional VVC with single-time scale application (Case 1) Traditional VVC with multi-time scale application (Case 2) Proposed VVC with single-time scale application (Case 3) Proposed VVC with multi-time scale application (Case 4; adopted in this paper) VDF 6.664 6.919 6.512 6.669 active power loss, MW 11.484 11.833 7.523 7.788 adjustment times of OLTC 18 10 14 8 adjustment times of SC1 8 2 5 0 adjustment times of SC2 0 0 0 0 adjustment times of SC3 5 3 1 1 It is also observed that Case 4 provides slightly higher VDF and active power loss compared with Case 3. However, the adjustment times of OLTC and SCs are reduced significantly in Case 4 because the multi-time scale application is used. The advantage of the multi-time scale application in reducing the usage of the OLTC and SCs can also be found by comparing Case 1 with Case 2. The largest values of VDF and active power loss are found in Case 2, which indicate that the VVC objectives are poorly achieved in Case 2, in which the traditional VVC is performed with multi-time scale application. It is worth noting that the traditional VVC utilises the OLTC, SCs as well as the reactive power provided by DGs and MGs to achieve the VVC objectives. However, it does not integrate the MGs' local power management but fixes the power exchange between the HDN and MGs. By contrast, the MGs' power management model and the HDN's VVC model are properly linked in the proposed VVC scheme, so that both active and reactive powers from MGs are coordinated with other VVC devices toward a better performance. 6 Conclusion This paper proposes a coordinated VVC scheme to regulate voltage in an HDN. The HDN's VVC model and the MG's power management model are built as two nested models under the theory of Stackelberg game. The two models are transformed into an integrated VVC model by using an approach called MPEC in order to coordinate MGs' power injections with other VVC resources in the HDN. Under the proposed scheme, the local power management of the hybrid AC/DC MGs is determined by not only the local loads but also the variations in the HDN. The OLTC, SCs, and DGs are adjusted in coordination with the MGs to maintain the system voltage within a secured range. Moreover, various VVC resources are timely coordinated in the proposed VVC scheme by adjusting them in multi-time scale. The lifetime of the mechanically controlled OLTC and SCs are saved as their adjustment times are reduced, while the electronically controlled DGs and MGs are adjusted more frequently to utilise their fast control speed. The control burden of OLTC and SCs is relieved by obtaining the support from DGs and MGs. Compared to the traditional VVC scheme, in which MGs' own power is separately managed and being unlinked to HDN's VVC, the performances on voltage control and power loss reduction are improved significantly by using the proposed VVC scheme. 8 References 1Lasseter, R.H.: ' Smart distribution: coupled microgrids', Proc. IEEE, 2011, 99, (6), pp. 1074– 1082CrossrefWeb of Science®Google Scholar 2Eid, B.M., Abd Rahim, N., Selvaraj, J., et al.: ' Control methods and objectives for electronically coupled distributed energy resources in microgrids: a review', IEEE Syst. J., 2016, 10, (2), pp. 446– 458CrossrefWeb of Science®Google Scholar 3Golsorkhi, M.S., Hill, D.J., Karshenas, H.R.: ' Distributed voltage control and power management of networked microgrids', IEEE J. Emerg. Sel. Top. Power Electron., 2018, 6, (4), pp. 1892– 1902CrossrefWeb of Science®Google Scholar 4Radwan, A.A.A., Mohamed, Y.A.R.I.: ' Networked control and power management of AC/DC hybrid microgrids', IEEE Syst. J., 2017, 11, (3), pp. 1662– 1673CrossrefWeb of Science®Google Scholar 5Turitsyn, K., Sulc, P., Backhaus, S., et al.: ' Options for control of reactive power by distributed photovoltaic generators', Proc. IEEE, 2011, 99, (6), pp. 1063– 1073CrossrefWeb of Science®Google Scholar 6Kim, Y.J., Kirtley, J.L., Norford, L.K.: ' Reactive power ancillary service of synchronous DGs in coordination with voltage control devices', IEEE Trans. Smart Grid, 2017, 8, (2), pp. 515– 527Web of Science®Google Scholar 7Xu, Y., Dong, Z.Y., Zhang, R., et al.: ' Multi-timescale coordinated voltage/var control of high renewable-penetrated distribution systems', IEEE Trans. Power Syst., 2017, 32, (6), pp. 4398– 4408CrossrefWeb of Science®Google Scholar 8Meirinhos, J.L., Rua, D.E., Carvalho, L.M., et al.: ' Multi-temporal optimal power flow for voltage control in MV networks using distributed energy resources', Electr. Power Syst. Res., 2017, 146, pp. 25– 32CrossrefWeb of Science®Google Scholar 9Zhang, L., Chen, Y., Shen, C., et al.: ' Coordinated voltage regulation of hybrid AC/DC medium-voltage distribution networks', J. Mod. Power Syst. Clean Energy, 2018, 6, (3), pp. 463– 472CrossrefWeb of Science®Google Scholar 10Marvasti, A.K., Fu, Y., Dor Mohammadi, S., et al.: ' Optimal operation of active distribution grids: a system of systems framework', IEEE Trans. Smart Grid, 2014, 5, (3), pp. 1228– 1237CrossrefWeb of Science®Google Scholar 11Nikmehr, N., Ravadanegh, S.N.: ' Optimal power dispatch of multi-microgrids at future smart distribution grids', IEEE Trans. Smart Grid, 2015, 6, (4), pp. 1648– 1657CrossrefWeb of Science®Google Scholar 12Tian, P.G., Xiao, X., Wang, K., et al.: ' A hierarchical energy management system based on hierarchical optimization for microgrid community economic operation', IEEE Trans. Smart Grid, 2016, 7, (5), pp. 2230– 2241CrossrefWeb of Science®Google Scholar 13Wang, Z.Y., Chen, B.K., Wang, J.H., et al.: ' Coordinated energy management of networked microgrids in distribution systems', IEEE Trans. Smart Grid, 2015, 6, (1), pp. 45– 53CrossrefWeb of Science®Google Scholar 14Madureira, A.G., Lopes, J.A.P.: ' Coordinated voltage support in distribution networks with distributed generation and microgrids', IET Renew. Power Gener., 2009, 3, (4), pp. 439– 454CrossrefWeb of Science®Google Scholar 15Wang, X., Wang, C., Xu, T., et al.: ' Decentralised voltage control with built-in incentives for participants in distribution networks', IET Gener. Transm. Distrib., 2017, 12, (3), pp. 790– 797Wiley Online LibraryWeb of Science®Google Scholar 16Dou, X., Xu, P., Hu, Q., et al.: ' A distributed voltage control strategy for multi-microgrid active distribution networks considering economy and response speed', IEEE Access, 2018, 6, pp. 31259– 31268CrossrefWeb of Science®Google Scholar 17Xiang, Y., Liu, J.Y., Liu, Y.L.: ' Robust energy management of microgrid with uncertain renewable generation and load', IEEE Trans. Smart Grid, 2016, 7, (2), pp. 1034– 1043Web of Science®Google Scholar 18Majzoobi, A., Khodaei, A.: ' Application of microgrids in supporting distribution grid flexibility', IEEE Trans. Power Syst., 2017, 32, (5), pp. 3660– 3669CrossrefWeb of Science®Google Scholar 19Liu, X., Wang, P., Loh, P.C.: ' A hybrid AC/DC microgrid and its coordination control', IEEE Trans. Smart Grid, 2011, 2, (2), pp. 278– 286CrossrefPubMedWeb of Science®Google Scholar 20Baboli, P.T., Shahparasti, M., Moghaddam, M.P., et al.: ' Energy management and operation modelling of hybrid AC–DC microgrid', IET Gener. Transm. Distrib., 2014, 8, (10), pp. 1700– 1711Wiley Online LibraryWeb of Science®Google Scholar 21Baran, M.E., Wu, F.F.: ' Network reconfiguration in distribution systems for loss reduction and load balancing', IEEE Trans. Power Deliv., 1989, 4, (2), pp. 1401– 1407CrossrefWeb of Science®Google Scholar 22Mazalov, V.: ' Mathematical game theory and applications' ( John Wiley & Sons, Inc., West Sussex, UK, 2014) Google Scholar 23Tu, C.M., Xiao, F., Lan, Z., et al.: ' Research of the high supply voltage quality control for solid-state transformer', IET Power Electron., 2018, 11, (11), pp. 1788– 1795Wiley Online LibraryWeb of Science®Google Scholar 24Miller, N.W., Zrebiec, R.S., Hunt, G., et al.: ' Design and commissioning of a 5 MVA, 2.5 MWH battery energy storage system'. 1996 IEEE Transmission and Distribution Conf. Proc., Los Angeles, CA, USA, 1996, pp. 339– 345Google Scholar 25Luo, Z.-Q., Pang, J.-S., Ralph, D.: ' Mathematical programs with equilibrium constraints' ( Cambridge University Press, Cambridge, UK, 1996) CrossrefGoogle Scholar 26Bard, J.F.: ' Practical bilevel optimization: algorithms and applications' ( Springer Science & Business Media, Boston, USA, 2013) Google Scholar Citing Literature Volume14, Issue11June 2020Pages 2129-2137 FiguresReferencesRelatedInformation
Referência(s)