# Coordinated voltage regulation of hybrid AC/DC medium voltage distribution networks

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## Abstract

In a hybrid AC/DC medium voltage distribution network, distributed generations (DGs), energy storage systems (ESSs), and the voltage source converters (VSCs) between AC and DC lines, have the ability to regulate node voltages in real-time. However, the voltage regulation abilities of above devices are limited by their ratings. And the voltage regulation efficiencies of these devices are also different. Besides, due to high *r*/*x* ratio, node voltages are influenced by both real and reactive power. In order to achieve the coordinated voltage regulation in a hybrid AC/DC distribution network, a priority-based real-time control strategy is proposed based on the voltage control effect of real and reactive power adjustment. The equivalence of real and reactive power adjustment on voltage control is considered in control area partition optimization, in which regulation efficiency and capability are taken as objectives. In order to accommodate more DGs, the coordination of controllable devices is achieved according to voltage sensitivities. Simulations studies are performed to verify the proposed method.

## Keywords

Hybrid AC/DC Distribution network Voltage control Partition Power system## 1 Introduction

Medium voltage distribution networks with high penetrations of distributed generations (DGs) are facing the challenge of nodal voltage regulations. Generally, in traditional AC distribution networks, voltage profiles are maintained through controlling on-load-tap-change transformers [1], shunt capacitors [2] and circuit breakers [3]. In a hybrid AC/DC distribution network, coordinated regulations of converter-based controllable devices are highly demanded for voltage control.

To mitigate probabilistic voltage violations, day-ahead dispatching methods have been presented in the literature [4, 5]. However, if unexpected fast variation of DG outputs and loads happen, day-ahead optimal schedules may fail to retain voltage profiles of all buses. In these circumstances, real time regulations of controllable devices should be applied to remain the voltage of important buses, which consequently also reduce undesirable DG curtailments and load shedding.

DGs and energy storage systems (ESSs) have been investigated to achieve real-time voltage regulation in distribution networks [6, 7, 8, 9, 10, 11, 12]. Moreover, in order to increase transfer capacities and DG accommodations, some AC lines can be converted into DC ones and forms a hybrid AC/DC distribution network by connecting existing AC lines through voltage source converters (VSCs) [13]. Then, real time regulations could be improved through utilizing flexible and fast control ability of VSCs. Ideally, controllable devices including ESSs, DGs, and the VSCs connecting AC and DC lines should be considered together to generate optimal real-time regulation strategies for the hybrid AC/DC distribution networks.

In distribution networks, nodal voltages are influenced by both real and reactive power flows due to high *r*/*x* ratio of lines [14]. Aforementioned controllable devices usually are connected to the distribution network through converter based interfaces. They have the ability of controlling their real power and reactive power independently. Thus, they can impact the system voltages through adjusting either output real power or reactive power. However, the power ratings of these converter-based devices are limited; their real and reactive power outputs are not fully decoupled. Therefore, during real time regulations, real and reactive power controls of various devices should be coordinated carefully.

Various methods of real-time regulations related to DGs and ESSs have been proposed in literatures. Reference [7] proposed a real-time voltage control method considering coordination of multiple battery ESSs. In [8], real-time market transactions, online dispatch of DGs and load curtailments are deployed in order to minimize expected operating costs. The reactive power capability of inverters and the technical requirement of DGs are analyzed in [9]. An Optimal control management of ESSs is proposed to mitigate the fluctuation and intermittence of renewable generations in [10]. The correlation between DGs is considered in a hybrid energy storage system in [11]. Reference [12] establishes an optimal economic operation mode for community microgrid incorporating temperature controlling devices with DGs and ESS. In [15], a centralized real-time control system is proposed to optimize the reactive power of DGs. Reference [16] leverages DC grid interconnections to enhance transfer capacities, and regulate voltages at AC feeder terminals. Reference [17] presents a centralized two-stage stochastic dispatch scheme, in which the day-ahead dispatch orders for controllable DG units are determined in the first stage, while appropriate corrective decisions are determined in the second stage.

In order to achieve an efficient local control, some papers proposed to use partition methods for voltage regulation [18, 19, 20]. A graph is introduced to represent a distribution network, in which controllable devices are connected to different nodes. A graph partition method is to divide the graph into a given number of sub-graphs, named control areas. Then, voltage regulation scheme can be designed and implemented separately for each control area. In [18], an analytical partition method based on capacitor reactive power is presented. Reference [19] divided the power system into regions based on a graph partition method and investigated a secondary voltage control for each region to prevent the propagation of disturbances. Reference [20] developed an approach for voltage and reactive power control in order to deal with the fluctuations caused by intermittent changes of renewable resources. However, in order to achieve local compensation of reactive power in AC system, existing references only considered reactive power, which does not exist in DC lines. Moreover, the control capability of both real and reactive power needs to be considered in a hybrid AC/DC medium voltage distribution network due to its flexible control capability and high *r*/*x*.

This paper proposes a coordinated real-time voltage regulation method for hybrid AC/DC medium distribution networks. This method makes full use of converter-based controllable devices, such as DGs, ESSs, and the VSCs between AC and DC lines. To eliminating possible conflicting controls, an optimal partition method is developed, which helps to determine suitable devices to retain node voltages against various uncertainties. This partition method commits to multiple objectives, in which both efficiency and capability of real and reactive power regulations are considered. Through a sensitivity analysis method, real and reactive power outputs of controllable devices can be adjusted to retain nodal voltages in real time operations. As power balances of both AC and DC grids are considered, these adjustments tend to be coordinated and help to minimize DG curtailments and load shedding. Finally, based on resultant network partition, priorities of control actions can be evaluated, according to which corresponding devices are controlled with special and temporal coordination.

## 2 Problem description

In particular, control areas are carefully defined with considerations of voltage regulation capability and efficiency of all controllable devices. Both real and reactive power outputs of VSCs, ESSs and DGs are utilized for nodal voltage regulation. Thus, to select suitable controllable devices for each important bus, a multi-objective optimal partition is formulated, and a priority-based coordination strategy is determined for the controllable devices in each control area.

Then, the coordination of real and reactive power controls of different controllable devices should be conducted. Power exchanges through the VSC2 (\( P_{VSC2}^{AC} \) and \( Q_{VSC2}^{AC} \)) can be adjusted flexibly, which helps to control power flow of the AC grid. Meanwhile, ESSs (\( P_{ESS} \) and \( Q_{ESS} \)) and DGs (\( P_{DG} \),\( Q_{DG} \)) can also be used to regulate node voltages, whose power outputs reshape the power flow of a control area directly. Adjustments of power outputs of these controllable devices should be determined regarding temporal sequence of their actions. Therefore, a voltage-sensitivity approach is used to determine the adjustments, based on which unnecessary curtailments of DGs could be avoided, while keeping nodal voltage acceptable.

## 3 Partition method of hybrid AC/DC distribution network considering both real and reactive power

### 3.1 Equivalent of real power to reactive power for node voltage regulation

*i*; \( S_{vp} \) and \( S_{vq} \) are the inverse Jacobian matrixes in Newton-Raphson algorithm [21]; \( \Delta P_{j} \) and \( \Delta Q_{j} \) are variations of injected real and reactive power of node

*j*.

For DC lines, \( \Delta Q_{j} \) is zero because there is no reactive power flowing in DC lines, and only real power can be used to regulate node voltages.

The regulation efficiency and capability of both real and reactive powers at node *j* to the voltage of node *i* can be represented by \( S_{vq} (i,j) \) and \( \Delta P_{j} \frac{{S_{vp} (i,j)}}{{S_{vq} (i,j)}} + \Delta Q_{j} \).

### 3.2 Multi-objective partition model of hybrid AC/DC distribution network

In order to achieve the coordination between \( P_{VSC2}^{AC} \), \( Q_{VSC2}^{AC} \), \( P_{ESS} \), \( Q_{ESS} \) and \( Q_{DG} \), a multi-objective partition method of hybrid AC/DC distribution network is proposed aiming at choosing a most efficient regulation device for each node. In the optimization, the connectivity of each partition should be ensured, so the number of branches is optimized as variables.

*i*; \( R_{i} \) is the power reserve of real and reactive power in partition

*i*; \( \overline{R} \) is the average power reserve of hybrid AC/DC distribution network. \( N_{par} \) is the number of partition.

*i*.

*k*and node

*n*in Fig. 1 can be calculated as [22]:

*k*and node

*n*.

*n*is the number of controllable devices in partition

*i*;

*m*is the number of nodes in partition

*i*; \( P_{L}^{j} \) and \( Q_{L}^{j} \) are real and reactive power load at node

*j*in partition

*i*; \( P_{CD,s}^{i} \) and \( Q_{CD,s}^{i} \) are real and reactive power capabilities of controllable devices in partition

*i*.

*i*. \( P_{CD,s}^{i} \) and \( Q_{CD,s}^{i} \) can be obtained from (11).

*m*and

*n*are node number of AC and DC lines respectively.

### 3.3 Optimization algorithm of multi-objective partition model

A Pareto-based NSGA-II algorithm [23] is used to solve the proposed multi-objective problem, and the set pair analysis (SPA) theory is used for decision-making [24].

*n*is the number of branches in hybrid AC/DC distribution network.

If the two nodes of branch *i* are within the same partition \( g_{i} \) is 0, or \( g_{i} \) is 1.

The elitist strategy is used in the algorithm in order to improve the convergence, and keep Pareto-optimal results to next generation.

## 4 Coordinated real time voltage control of hybrid AC/DC distribution networks

In order to regulate node voltages efficiently and flexibly, a novel coordinated voltage control strategy for hybrid AC/DC medium voltage distribution networks is proposed considering the controllable devices of VSC2 (\( P_{VSC2}^{AC} \) and \( Q_{VSC2}^{AC} \)), ESS (\( P_{ESS} \) and \( Q_{ESS} \)), and DG (\( P_{DG} \) and \( Q_{DG} \)). A priority-based coordination is carried out according to partition results, considering the regulation costs of each device.

### 4.1 Voltage-sensitivity approach

The coordinated voltage control strategy is triggered if a node voltage is above 1.05 p.u. or below 0.95 p.u.. The real-time voltage control will only switch back to the day-ahead optimal scheme if all node voltages are within [0.97, 1.03]. Hence, a linearized regulation can be formulated for remaining node voltages within a security operation range.

*i*and controllable devices. \( S_{Q} \) is only evaluated for AC lines.

It should be mentioned that the real and reactive power of VSC2 can be independently controlled by setting up the reference values of the real and reactive power, the hybrid AC/DC distribution network is decoupled by VSC2. Thus the sensitivity method can be used for AC and DC parts individually.

### 4.2 Priority-based coordination strategy

Firstly, if the voltage of an AC node is higher than 1.05 p.u., or lower than 0.95 p.u., the reactive power of the DG, \( Q_{DG} \), in the same partition is given priority to regulate the voltage when real power hasn’t used up all power rating of the DGs. Equation (18) is used to preliminarily calculate the adjustment of \( Q_{DG} \) based on the maximum voltage deviation of the measured nodes in \( [\Delta V] \).

Secondly, if the node voltage is still higher 1.05 p.u., or lower than 0.95 p.u. when \( Q_{DG} \) achieve its maximum value under the power rating limit of the DG, then the ESS or VSC2 in the same partition is considered to regulate the voltage because it is more efficient than other devices and has enough power reserve. For VSC2, the reactive power \( Q_{VSC2}^{AC} \), is firstly considered to regulate the voltage because DC lines are not affected by the reactive power regulation of the AC side. For ESSs, the real power \( P_{ESS} \), is firstly considered to regulate the voltage in order to reduce electricity purchase from the network.

Equations (17) and (18) are used to preliminarily calculate the adjustments of real and reactive power based on the maximum voltage deviation of the measured nodes in \( [\Delta V] \).

If \( Q_{VSC2}^{AC} \) and \( P_{ESS} \) cannot be achieved due to the power rating limit of converters, both real and reactive power will be used to regulate node voltages.

If \( S_{P} < S_{Q} \), the absolute value of ESSs or VSC2 real power will be reduced in order to release the ratings of converters for reactive power to regulate node voltages more effectively. In case \( S_{P} > S_{Q} \), the ratings of converters are used to meet real power, and the absolute value of reactive power will be reduced if real power is limited by current ratings.

Finally, if the node voltage is still higher 1.05 p.u., or lower than 0.95 p.u. after the adjustments of \( P_{VSC2}^{AC} \), \( Q_{VSC2}^{AC} \), \( P_{ESS} \), \( Q_{ESS} \). The curtailment of DG, \( P_{DG} \), in the same partition is considered to regulate node voltages. \( P_{DG} \) and \( Q_{DG} \) can be calculated through (20).

On the other hand, if a DC node voltage is higher than 1.05 p.u. or lower than 0.95 p.u., the real power of ESSs or VSC2 (\( P_{ESS} \) or \( P_{VSC2}^{AC} \)) in the same partition is used to regulate node voltages based on (17). Especially, the absolute value of \( Q_{VSC2}^{AC} \) will be reduced in order to release the rating of VSC2 for real power to regulate node voltages if real power is limited by current ratings of VSC2, and the \( P_{VSC2}^{AC} \) and \( Q_{VSC2}^{AC} \) can be calculated through (20).

## 5 Case studies

Case studies were conducted to demonstrate the superiority of proposed priority-based coordinated control strategy based on multi-objective partition considering the equivalence of real power to reactive power.

### 5.1 Simulation conditions

### 5.2 Study-1 benefits of considering equivalence of real power to reactive power during partition

In Case 1 the equivalence of real power to reactive power is considered in partition results, and in Case 2 only the capability of reactive power is considered.

Partition results of different solution methods

Solution method | Node number of partition |
---|---|

Case 1 | {1,2,3,4,5,25,26,27}{6,7,8,9}{10,11,12,13,14,15,16,17}{18,19,20,21}{22,23,24}{28,29,30,31,32}{33,34}{35,36,37,38} |

Case 2 | {1,2,3,4,5,6,25,26}{7,8,9,10,11,12}{13,14,15,16,17}{18,19,20,21}{22,23,24}{27,28,29,30,31,32}{33,34,35}{36,37,38} |

Node 10, 11, 12 belong to partition 2 in Case 2, instead of partition 3 in Case 1. That is because the regulation capacity increment of VSC2 is larger than ESS considering the capability of real power due to large rated capacity of VSC2.

In DC sides, node 35 belongs to partition 8 instead of partition 7 using the proposed method. That is because DC node voltages are not influenced by reactive power, and the real power of VSC2 is limited by both AC and DC lines.

### 5.3 Study-2 benefits of proposed priority-based coordinated control strategy

When the voltage of node 12 is above 1.05 p.u. at 120 s, the reactive power of DGs in partition 3 cannot control the voltage back to 1.03 p.u.. Thus, VSC2 change its reactive power output during 120-150 s, while in Case 2, the ESS in partition 2 change its real power according to (15).

## 6 Conclusion

By considering the equivalence of real power to reactive power in voltage regulation, a new partition method is proposed for hybrid AC/DC medium voltage distribution networks. In real-time, real and reactive power are coordinated to control the voltage in each partition obtained by the proposed method. The electrical distances and the available real and reactive power control capacity are used to optimally partition a hybrid AC/DC medium voltage distribution network. A priority-based control strategy, which coordinates different controllable devices in a partition, is proposed to achieve the voltage regulation while reducing curtailments of renewable energies.

When variations of DGs and loads happen and the reactive power of DGs are not able to regulate the voltages within [0.97, 1.03] due to the limited power ratings of the DGs, the VSC between AC and DC lines, or the ESS in the same partition will control node voltages.

Case studies indicate that through the proposed method 1.4 kWh more energy of DGs can be accommodated during 400 s in a 38-node hybrid AC/DC medium voltage distribution.

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