A New Framework for Mitigating Voltage Regulation Issue in Active Distribution Systems Considering Local Responsive Resources

Recently, renewable energy sources (RESs) have increasingly being integrated into the power grids as a result of environmental and governmental perspectives. In this regard, installation of RESs as potential power resources in distribution systems would benefit the grid by decreasing the power losses, as well as addressing the fossil fuel shortages, and their environmental aspects. Nevertheless, the high-level integration of RESs as well as the development of distributed structures in local systems could challenge the reliable operation of the grid. In this context, conventional approaches could not optimally regulate the voltage in the grid; therefore, utilities have to exploit the scheduling of local responsive resources to address the voltage regulation issue in systems with high penetration of RESs. Consequently, the proposed scheme in this paper enables the distribution system operator (DSO) to activate flexibility service from local responsive resources with the aim of addressing the voltage regulation issue in the grid. Respectively, DSO as the leader provides incentive control signals to ensure collaboration of the independent agents in voltage regulation procedure. Finally, the developed framework is applied on the 37-bus IEEE test network to investigate its application in mitigating the voltage issue in the active distribution systems with multi-agent structures.


I. INTRODUCTION
Active distribution systems are developed by the introduction of small-scale power generation units as well as storage units and responsive load demands in power networks. In this regard, integration of distributed energy resources (DERs) in power distribution systems has resulted in changing the conventional operational procedures in the grid [1]. In this context, renewable energy sources (RESs) would play a key role in supply the load demands in distribution systems. Respectively, installation of RESs, i.e. photovoltaic (PV) and wind power units, in distribution systems is supported based on reducing the fossil fuel consumption and environmental aspects as well as decreasing the power loss in the grid. Nevertheless, the high penetration of RESs could cause operational issues in the system. In this regard, over-power generation by RESs could result in voltage regulation issues in the distribution grid. Consequently, a new management scheme should be developed in order to enable the distribution system operator (DSO) to address the potential voltage regulation issues in active distribution networks.
In recent years, several research works have focused on optimizing the scheduling of local resources in distribution systems in order to address the voltage regulation issue in the grid. Respectively, a hierarchical management scheme is proposed in [2] in order to ensure the coordinated operational scheduling of storage units, which would finally facilitate regulation of the voltage in distribution networks with the high installation of PV units. In this context, independent aggregators optimize the scheduling of storage units in the lower level; while, the upper level aims to coordinate the operation of aggregators in order to ensure the voltage regulation in the grid. Moreover, authors in [3] have conducted a thorough review over the effects of the distributed generation units on the operation of the system This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2021.3127240, IEEE Access 2 from the protection and voltage regulation point of view. Furthermore, in [4], a chance-constrained centralized optimization model is proposed to address the over-voltages in distribution networks with the high-level integration of PV units. In addition, M. Aryanezhad in [5] has developed a scheme for management and coordination of scheduling of local resources to regulate the voltage as well as minimizing the power loss in distribution grids, which indicates the application of storage units in improving the voltage profile of the grid. Moreover, a coordination framework is proposed in [6] in order to optimize the scheduling of storage units with the aim of regulating the voltage in distribution networks with the high-level integration of PV units. Based on the above discussions, DSOs as entities responsible for the reliable operation of distribution grids have to exploit the scheduling of local resources to address the voltage regulation issue in systems with high levels of RESs. In other words, the outcome of the day-ahead market in power grids may not be associated with the limitation of distribution grids. In other words, the constraints of local grids are not taken into account in the current day-ahead market models such as the European zonal market, which could result in the over-voltage in distribution grids with high-level integration of RESs. As a result, DSO would rely on the re-scheduling of local responsive resources in order to regulate the voltage in the system without causing RESs/demands curtailment. Nevertheless, the distributed structure of modern distribution systems, which is developed as a result of privatization and restructuring would impede the direct access of the DSO over the scheduling of the local resources. In other words, while the multi-agent structure of modern distribution systems facilitates the integration of independently operated resources into the power grids; system operators could not directly change their scheduling to regulate the voltage in the grid. In multi-agent systems, local resources would be operated by independent agents, which could provide system operators with the flexibility service to efficiently operate the distribution grid. Consequently, novel management schemes should be developed to enable the DSOs to activate flexibility service from the local responsive resources in order to regulate the voltage in the grid. Respectively, system operators could provide incentive control signals for independent agents in order to exploit their power scheduling. In this context, authors in [7] have developed a scheme, in which the system operator provides incentives for energy storage systems to manage the variable power flows in the power grids. Furthermore, a case study for activation of residential flexibility in distribution systems in exchange of a reward in order to manage the peak power in the system is investigated in [8].
As mentioned, DSO would be able to employ a bonusbased model in order to incentivize the contribution of independent agents in voltage regulation procedure in the distribution grid, which would finally mitigate the potential RESs curtailment due to the over-voltage in systems with high-level integration of RESs. In this context, hierarchical structures based on the Stackelberg game concept could be employed to enable the DSO to exploit the operational scheduling of independently operated responsive resources. Correspondingly, Stackelberg game is taken into account in [9] to activate the demand response flexibility to address the variability of the wind power agent while participating in the power market model. Nevertheless, the proposed model has not investigated the network modeling and overlooked the voltage regulation in the grid. Moreover, a review over the application of the Stackelbeg game model as well as the cooperative and non-cooperative games for managing the integrated energy systems is conducted in [10]. Furthermore, authors in [11] have studied the application of the hierarchical Stackelberg game in modeling the incentive demand response in energy systems.
Taking into account the above discussions regarding the necessity of considering the re-scheduling of responsive resources in systems with the high-level integration of RESs to address the voltage regulation issue, this paper aims to develop a hierarchical management model based on the Stackelberg game concept to facilitate the contribution of the independent agents in the voltage regulation procedure in multi-agent distribution networks with high penetration of RESs. In this regard, while the conventional methods for regulating the voltage in the grid are not effective, the DSO would offer bonuses to the system agents in order to incentivize their collaboration in regulating the voltage in the grid. It is noteworthy that traditional voltage regulation techniques may hardly adapt to the new operational condition of the system and could not regulate the voltage without exploiting the active power transactions of the agents. Respectively, DSO as the leader strives to resolve the voltage regulation issue in the grid by exploiting the scheduling of independently operated flexible resources, which would finally minimize the potential RESs curtailment in the system. Furthermore, each agent as a follower aims to maximize its profit while providing operational service for the DSO. Note that the DSO, as the entity responsible for the operation of the grid, would prefer to address the voltage regulation issue with the minimum bonus payment. Based on the proposed approach, while most of the previous research works have merely considered the operational scheduling of storage units in a central manner to address the voltage regulation issue in the grid, the proposed scheme in this paper strives to investigate the role of different types of responsive resources as well as considering the multi-agent structure of the system. In this regard, the information exchange between the DSO and agents is limited to the bonus signals and the changes in the accumulated power requests to cope with the multi-agent structure of the system.
In this paper, a bonus-based operational management scheme is developed in order to activate flexibility service from local responsive resources to address the voltage This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2021.3127240, IEEE Access 3 regulation issue in the grid. In this regard, modeling of the distribution system with a multi-agent structure is illustrated in Section. II.A. Moreover, the proposed framework for managing the voltage regulation issue in the grid by rescheduling the local responsive resources in the distribution system is explained in Section. II.B. In this regard, the mathematical formulations of the optimization problems employed by the independent agents of the system as well as the DSO to respectively maximize/minimize their profit/cost are presented in Section. II.C. Furthermore, the derived onelevel optimization formulation for determining the optimal bonuses as well as re-scheduling of agents is presented in Section. II.D. Note that the iterative algorithm for mitigating the voltage regulation issue in the grid considering the rebound effects of the energy-limited resources is presented in Section II.D. Finally, simulation results associated with employing the proposed scheme for mitigating the voltage issue in the IEEE-37 bus test network are presented and discussed in Section. III, followed by the conclusion in Section IV.

A. Modeling of Multi-agent Distribution Systems
Privatization in distribution systems which is introduced to facilitate the integration of DERs has resulted in the development of multi-agent structures. In this structure, DSO would not have direct access to the operational scheduling of each of the local resources to address the privacy concerns of the independent prosumers. Respectively, this paper conceives active distribution systems with multi-agent structure as shown in Fig. 1, in order to facilitate the high-level integration of RESs and responsive resources into the grid. As a result, as presented in Fig. 1, without loss of generality, it is conceived that each agent of the system would merely operate a type of local resources (i.e. flexible demands, storage units, conventional distributed generation units, and RESs) to completely investigate the role of each responsive resources in regulating the voltage in the grid. In this context, R-Agent i, DG-Agent i, D-Agent i, and ESS-Agent i present the agents responsible for scheduling of RESs, conventional distributed generation, flexible demands, and storage units in node i of the network, respectively.

B. Hierarchical Bonus-based Voltage Regulation Framework
In multi-agent distribution systems, DSO would act as the responsible entity for operating the grid in a reliable manner; while, each agent schedules their resources independently. As mentioned, conventional voltage regulation procedures may not adapt to the new operational condition in active distribution networks with the high-level integration of RESs. Respectively, DSO aims to acquire operational service from local responsive resources in order to regulate the voltage in the grid. DSO should therefore exploit the scheduling of local responsive resources after clearing the day-ahead market to ensure that the system would not confront the over-voltage problem. Consequently, a bonus-based mechanism is developed in this paper in order to enable the DSO to incentivize the contribution of flexible resources in mitigating the voltage regulation issue in the grid to ensure the reliable operation of the grid. As a result, a hierarchical structure based on the Stackelberg game model is developed to determine the optimal re-scheduling of independent agents as well as their received bonuses from the DSO. In this context, DSO has the leader role in the proposed scheme, while agents as followers re-schedule their resources based upon the received bonuses. Furthermore, the strong duality concept is taken into account in order to recast the bi-level operational optimization model into a one-level optimization, which would determine the optimal outcomes of the model for regulating the voltage in the grid. In addition, considering the rebound effect in the rescheduling of energy-limited flexible resources, an iterative algorithm is proposed to apply the one-level optimization model for addressing the voltage regulation issue in the grid. Finally, it is noteworthy that the operational service provided by flexible resources would mitigate the overvoltage issue caused by the over-power generation of RESs in the system, which would facilitate the high-level integration of RESs in distribution systems without compromising the reliability of the system. A simplified model of the interaction between entities in the system is presented in Fig. 2. In this regard, the information exchange between the DSO and agents is limited to the bonus signals and to the changes in the accumulated power requests, which copes with the multi-agent structure of the system.

C. Mathematical Modeling of the Proposed Scheme
Based on the proposed bi-level scheme for regulating the voltage in a multi-agent distribution system, DSO strives to induce re-scheduling of independent agents by offering bonuses (i.e. Agent Agent P   ) to them. In this respect, independent agents as followers in the developed model reschedule their flexible resources with the aim of maximizing their profits while providing the DSO with operational service for mitigating the voltage regulation issue in the grid. In this regard, the following sub-sections illustrate the optimization model from each entity's perspective, as well as the one-level optimization model to determine the optimal re-scheduling of the agents as well as the offered bonuses by the DSO. In this context, as the developed scheme conducts after clearing the day-ahead market,  models the offered bonus to incentivize the decrease in the power request of the agent. Furthermore, the agents would be able to participate in the power market while conducting the proposed scheme. In this regard, as the developed scheme would be conducted after clearing the day-ahead market to address the voltage regulation issues raised by the market outcome, without loss of generality, it is conceived that the agents would be able to participate in the intra-day market. In this regard, buy t  shows the price of the power purchase from the market, while sell t  models the price of selling power to the upper-level network. Note that the proposed model could be conducted at any time interval to address the voltage regulation issue, and therefore the power prices would be associated with the power market at the respective time interval.

1) RE-SCHEDULING OF FLEXIBLE DEMANDS:
Flexible demands could provide the operational service to the DSO in case of receiving the bonus offers that compensate their loss of profit. In this regard, the optimization model associated with the re-scheduling of flexible demands operating by the demand agent at node i could be formulated as follows:

2) RE-SCHEDULING OF ENERGY STORAGE SYSTEMS:
The optimization associated with agents, operating the energy storage systems (ESSs), in order to maximize their profits while providing the flexibility service to the grid for regulating the voltage is formulated as follows:     This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

3) RE-SCHEDULING OF CONVENTIONAL DISTRIBUTED GENERATION UNITS:
Conventional distributed generation (CDG) units could benefit the grid by providing operational services for system operators to address operational issues in the grid. In this regard, the optimization model employed by agents, responsible for the operation of the conventional distributed generation units, based on the received bonus offers from the DSO is formulated as follows: show the increase and decrease in the power production by the CDG units as well as their respective maximum limitations. In the proposed formulation, the objective function in (3a) strives to maximize the profits of the agent at node i, while the constraints over the changes in the power production by the conventional-DG units are represented in (3b) -(3c).

4) DSO OPTIMIZATION MODELLING:
As discussed in previous sections, it is conceived that the conventional procedures such as reactive power injections and the tap changers could not completely mitigate the voltage regulation issue in the distribution grids with the high penetration of RESs. As a result, DSO would rely on exploiting the scheduling of local responsive resources in order to improve the voltage profile in the grid. Respectively, the optimization model conducted by the DSO considering the convex-form of DistFlow model [12][13][14] to avoid the curtailment of RESs in the system due to the high-voltage issue is formulated in (5). It is noteworthy that the DSO would provide the bonus to incentivize re-scheduling of responsive resources for regulating the voltage in the grid; which would finally minimize the RESs curtailment and power losses. , , , Where, , C RES it , and Dloss present the cost of alleviating the voltage issue in the network by exploiting the scheduling of local resources as well as the cost associated with the changes in the network power losses. In the developed optimization formulation, the objective function in (5a) strives to minimize the cost associated with the re-scheduling of local resources for regulating the voltage in the grid. In this respect, the cost associated with the offered bonuses to agents and the curtailment of RESs, as well as the cost associated with the changes in the power losses are modeled in the objective function. Moreover, the change in the power injection of each node of the system at each time interval is presented in (5b), while, the operational modeling of the grid is presented in (5c). Finally, the limitations over the voltage magnitudes in the grid are enforced by (5d), whereas, the bounds associated with the curtailment of RESs are indicated by (5e).
In the proposed optimization model for voltage regulation in a multi-agent distribution system, the DSO would offer bonuses to the agents in case of their contribution to improve the voltage profile of the grid. In this respect, the cost of bonuses as well as the cost 6 associated with the changes in the network power losses due to the re-scheduling of agents are taken into account by DSO; while each agent considers the price of power exchange with the upper-network as well as the received bonus offers from the DSO in its optimization model. In this regard, agents are responsible for the cost associated with the rescheduling of their resources. Respectively, the developed optimization model complies with the multiagent structure of future distribution systems. The proposed hierarchical structure is developed based on the Stackelberg game concept, where DSO acts as the leader and agents are conceived as followers. In this regard, to resolve the model with the efficient computation, the Strong duality theory is taken into account in the following section to recast the proposed bi-level model into a one-level optimization problem [10,15]. In other words, the developed one-level optimization model would converge to the optimal solution of the problem by determining the optimal bonus signals as well as the re-scheduling of local resources in the system.

D. Development of the One-level Optimization Model
As mentioned, for efficient computation, the developed bi-level model is recast into a one-level optimization model to determine the optimum bonuses as well as the rescheduling of the system agents. In this regard, the constraints of the lower optimization models (i.e optimization models of the agents), as well as the constraints of their dual formulations, are added to the optimization model of the DSO to ensure that the developed one-level optimization model would converge to the optimal outcome of the bi-level problem. Respectively, the obtained one-level optimization model could be formulated as follows:   (6i)   , ,  ,  , ,  ,,   , ,  ,  , ,  ,,   ,  ,  ,  ,  ,  ,,   , ,   This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2021.3127240, IEEE Access 7 time intervals that the grid confronts with the voltage regulation issue may cause the violation of the voltage regulation limitations at other time intervals. As a result, an iterative algorithm is developed in this paper to ensure the rebound effects associated with the re-scheduling of energy-limited resources would not cause voltage regulation issues at other time intervals in the grid. In this regard, as shown in Fig. 3, the time intervals that the grid confronts with the voltage regulation issue are included in the one-level optimization model in an iterative manner to ensure the optimum results would not violate the grid's voltage regulation at other time intervals. Respectively, the proposed iterative algorithm would continue until the step that the outcome of the optimization copes with the voltage regulation limitations at all time intervals.
It is noteworthy that the information exchange between the agents and the DSO in the proposed model is limited to the accumulated possible changes in the power injection of each agent as well as the offered bonus signals. In this respect, the developed algorithm for improving the voltage profile of the grid in multi-agent distribution systems copes with the distributed structure of the system. Finally, the non-linear terms (i.e.

III. Case Study
The proposed algorithm for regulating the voltage in the grid considering the re-scheduling of the responsive resources is implemented on the IEEE-37 bus test network [16,17], which is shown in Fig. 4, to investigate its application for improving the voltage profile of the systems with highintegration of RESs. Note that the system is considered to be structured as a multi-agent network represented in Fig. 1. As discussed, in the conceived multi-agent system, each agent would optimize its scheduling, while DSO offers bonuses to incentivize their contribution in mitigating the voltage regulation issue in the grid. As a result, the agents operating the conventional distributed generation units, demands, as well as storage units would re-schedule their resources to maximize their profits. Note that the operational characteristics of the test system as well as the local resources are presented in [18]. As mentioned, it is conceived that as the conventional methods have failed to address the voltage regulation issue in the grid; therefore, DSO has to exploit the operational scheduling of flexible resources to avoid curtailment of RESs. In other words, the grid is confronting with the overvoltage issue due to the high penetration of RESs in the multi-agent system. Respectively, the voltage magnitude of the grid at nodes 15, 25, 30, and 35 before and after employing the proposed algorithm for improving the voltage profile is presented in Fig. 5. In this regard, the proposed algorithm addresses the high voltage issue in the grid at hours 9 -16. Moreover, the voltage profile of the grid before and after the implementation of the proposed scheme at hour 12 is shown in Fig. 6. Based on the obtained results, the developed approach enables the DSO to incentivize the contribution of local flexible resources to address the high voltage issue in the grid, which is occurred due to the highlevel integration of RESs in modern distribution systems. Note that, based on the proposed algorithm in Fig. 3, the algorithm is conducted for two iterations to resolve the voltage regulation issue in the grid. In other words, due to the rebound effects of energy-limited resources, the obtained results in the first step violates the voltage regulation in nodes 34, 35, and 36 at hour 16. Nevertheless, the results of the developed one-level optimization in the second iteration considering the high voltage issue at hours 9 -16 address the voltage constraints of the grid at all time intervals. Based on the obtained results, the changes in the power scheduling of agents operating the flexible demands, conventional distributed generation units, and storage units are shown in Figs. 7 -10. In this context, the power request of storage units and load demands are increased at hours 9 -16 to address the high power production by RESs; while, their power request is increased at other time intervals in order to ensure their energy requests would be addressed. Furthermore, to decrease the power injection at each node of the grid, the power generation by conventional distributed generation units is decreased at hours 9 -16 that the DSO offered bonuses to incentivize their contribution of independent agents in mitigating the voltage regulation issue in the grid. In addition, the bonuses received by the agents operating the flexible demands, storage units, and conventional distributed generation units are represented in Figs. 11 -13. Respectively, the bonuses offered by the DSO would incentivize the increase in power requests of storage units and flexible demands in the system to alleviate the voltage regulation issue. In this regard, as shown in Figs. 5 and 6, the voltage regulation issue is more severe at nodes far from the common coupling point of the distribution and transmission systems (i.e. node 0), therefore, the over power production by RESs is tried to be compensated locally by the flexible resources in these nodes to address the over-voltage issue in the network. Furthermore, the bonuses associated with the agents operating the conventional distributed generation units incentivize their collaboration in addressing the voltage regulation issue in the grid by decreasing their power generation. Finally, the proportional increase in the overall offered bonuses to system agents compared with the current condition, in the case of increasing the installed capacity of RESs in the system is presented in Fig. 14. Based on the obtained results, the proposed algorithm for activation of local flexibility service to address the voltage regulation issue in the grid would facilitate the high integration of RESs. In other words, the proposed model enables the implementation of multi-agent structures with the high-level installation of RESs in distribution systems without compromising the reliability of the grid. This approach would finally facilitate efficient management of flexibility resources, which plays a key role in facilitating the development of smart energy systems with high penetration of RESs [19].

IV. Conclusion
In this paper, a hierarchical model is developed in order to enable the system operators of the distribution system to address the voltage regulation issue in the grid. Note that the conventional methods for regulating the voltage in the grid may not be able to address the voltage regulation issue in systems with the high penetration of RESs. Respectively, DSO should exploit the scheduling of local responsive resources to efficiently mitigate the voltage regulation issues without curtailment of RESs. In this regard, the proposed framework enables the DSO to incentivize the contribution of local responsive resources in mitigating the voltage regulation issue in the grid. Consequently, DSO, as the leader, offers bonuses to system agents to compensate their contribution in providing operational services for regulating the voltage in the grid. Furthermore, the preliminary hierarchical model is re-cast into a one-level optimization model, which is implemented in the system based on an iterative algorithm to determine the optimal rescheduling of the power requests by each agent as well as the offered bonuses by the DSO.
The developed algorithm is applied on the IEEE-37 bus test network in order to study its effectiveness in the activation of flexibility service from local responsive resources to address the voltage regulation in the grid. Finally, the obtained results show the application of the proposed scheme for incentivizing the contribution of local responsive resources for mitigating the voltage regulation in the grid; which, without compromising the reliability of the system, decreases the potential curtailment of RESs for managing the voltage profile of the grid.