A new voltage control scheme for active medium-voltage (MV) networks

The main objective of this paper is the effective voltage regulation in radial medium-voltage (MV) distribution networks with high distributed generation (DG) penetration, ensuring near-minimum active power losses. For this purpose, a new control strategy with low computational complexity is proposed. The method exploits the reactive power capability of DG units to mitigate overvoltages in coordination with the on-load tap changer of the high/medium-voltage transformer to achieve power losses reduction. This is attained by introducing a time delay allocation method based on the graph theory to prioritise the response of DG units. The control scheme is further enhanced by the active participation of MV loads in the voltage regulation process, contributing to the reactive power control of DG units. To evaluate the performance of the proposed control strategy, time-domain and time-series simulations are performed in an extended radial MV network. The former demonstrates the robustness and fast response of the proposed control scheme, while the latter highlights its improved power system performance over existing centralised as well as decentralised control methods.


Introduction
Sustainable energy is considered as one of the most challenging targets, set by local administrations and international organisations, to reduce the carbon footprint and the fossil fuel dependence [1]. This is achieved by providing incentives -in terms of feed-in tariffs or quota obligations -to install distributed generation (DG) units, mainly consisting 5 of renewable energy sources [2]. Nevertheless, the rapid deployment of DG units over the last decade has invoked voltage rise issues in the distribution grid, limiting the further penetration of DG [3].
Traditionally, medium-voltage (MV) networks have been designed by the distribution system operators (DSOs) on the assumption of passive grid operation. As a result, the 10 voltage regulation process was mainly performed by the on-load tap changer (OLTC) of the high-/medium-voltage (HV/MV) transformer and by the feeder capacitors or series voltage regulators [4]. However, these techniques fail to mitigate overvoltages in active networks with high DG penetration. The main reason lies in the fact that overvoltage is a local problem of the network [5], whereas the OLTC control concurrently manages all network nodes. 15 Furthermore, the activation of feeder capacitors has an adverse effect on the mitigation of overvoltages. Another alternative involves reinforcing the grid, which, however, is an expensive solution for DSOs.
The distinctive feature of the decentralised control schemes is that control actions are individually performed by each DG unit, based only on local measurements. The authors in [6] employ the reactive power capability of DG units to fully compensate the voltage 25 rise caused by the active power injections. Nevertheless, unnecessarily high reactive power consumption may be observed. A decentralised method is proposed in [7] to tackle a twoobjective problem, i.e. the overvoltage mitigation and the loss minimisation. Although this method is valid, conflicts between these objectives may appear in cases of high DG penetration. This problem has been partially addressed in [8], but the applicability of 30 the developed method is limited to active feeders where only DG units are connected. In [9], an on-line optimisation-based voltage regulation method has been developed, which, however, may introduce inaccuracies in the presence of multiple DG units. The integration of the Q(P ) and Q(V ) droop control characteristics into the DG units has been thoroughly investigated in [10], while an offline coordination procedure has been proposed in [11] and voltage thresholds for the activation of the RPC in each DG unit. Nevertheless, all of these methods are characterised by the uncoordinated real-time operation of DG units, leading to increased network losses.
To address the issues posed by the decentralised control, a distributed control strategy is 40 proposed in [14]. According to this approach, the operational settings of each DG unit are determined based on local measurements and on the information acquired by the neighboring units. Additionally, a hybrid approach of the RPC is proposed in [15], combining both the decentralised and distributed control schemes. However, the main drawbacks of these methods include slow convergence rates and possible local minimum solutions.

45
In the centralized control scheme, a central controller monitors the network and determines the set-points for all DG units at each time instant. This controller is usually located at the DSO level. The relevant research works can be classified into two main categories based on whether they use optimisation techniques or not. Considering the first category, the introduction of optimisation techniques in the distribution grids forms a mixed-integer 50 nonlinear optimisation problem characterised by increased computational complexity and local minimum solutions [16]. On the other hand, in the second category, the proposed solutions lack of optimisation procedures, focusing only on the secure and reliable network operation within permissible limits. More specifically, the authors in [17] and [18] use an analytical and approximate calculation of the sensitivity matrix to dispatch the reactive 55 power among the DG units. In [19], OLTC and DG units are combined in a cooperative framework to address only voltage rise issues. Additionally, a centralised solution with no optimisation techniques is presented in [20], where an updated version of the distribution management system (DMS) is proposed, taking into account the reactive power capability of DG units. The off-line coordination of the OLTC and the network capacitors is proposed 60 in [21], neglecting the participation of the DG units in the voltage regulation process.
In [22], a hybrid centralised-decentralised control strategy is proposed, in which the central controller is activated to optimise the network operation in case the decentralised voltage regulation control fails. An enhancement of [7] is proposed in [23], employing a central controller to decide the most appropriate objective at each time instant. In [24], the droop characteristics of all DG units are recalculated in a regular basis by solving an optimisation problem. However, these hybrid methods present the same disadvantages as those observed in the centralised control schemes.
In this paper, a hybrid centralised-decentralised voltage regulation strategy for radial MV networks is proposed, aiming at the minimisation of network losses by properly co-70 ordinating the response of the DG units, the MV loads, and the OLTC of the HV/MV transformer. Its distinct features include: 1) near optimal solutions compared to the decentralised approaches, 2) fast convergence against the distributed control schemes, and 3) low computational complexity compared to the centralised control strategies. The proposed method uses a time delay allocation procedure based on the graph theory to distribute the 75 reactive power among the DG units, while the inherent inductive behaviour of the loads is exploited for the first time as a supplementary means for the overvoltage mitigation. Furthermore, the OLTC control acts in coordination with DG units and MV loads to further reduce network losses.

80
The voltage regulation in conjunction with the minimisation of network losses constitutes an optimisation problem. To solve this problem, three different types of network elements are involved, namely the DG units, the MV loads, and the OLTC of the HV/MV transformer.
The DG units provide reactive power locally, since this is considered an effective voltage regulation method in MV distribution networks due to the relatively low R/X ratio of the 85 lines [6]. On the other hand, MV loads generally consist of commercial and industrial loads, as well as low-voltage (LV) networks, connected to the MV level via MV/LV transformers.
These loads are equipped with reactive power compensation devices, e.g. capacitor banks, to compensate their inherent inductive behaviour. Therefore, they can be exploited, similarly to the DG units, as controllable reactive power sources by switching on/off capacitor banks.

90
The combined operation of these network elements forms a mixed-integer nonlinear optimisation problem, where the objective function is the minimisation of network losses as follows: where N denotes the set of branches and of network nodes omitting the slack bus, while P loss,i is the active power loss of the i-th branch.
The equality constraints of the optimisation problem include the power flow equations and the OLTC operation. Assuming the HV/MV transformer is modelled as a series impedance referred to the MV side, the power flow equations can be expressed mathematically by: Eq.
(2) is used for the calculation of the network voltages, while (3) and (4) calculate the active (P loss,i ) and reactive (Q loss,i ) power losses of the i-th branch, respectively. V i and V pr(i) denote the voltage magnitudes of the i-th node and of the previous adjacent node, respectively, whereas R i and X i are the resistance and the reactance of the i-th branch. A i and B i are the active and reactive power flowing through the i-th branch and are calculated according to N d,i is the set of nodes located downstream of the i-th node, while P j and Q j denote the active and reactive power injections of the j-th node, respectively. n(i) are the nodes located right after the i-th node. Furthermore, the OLTC operation is modelled by discretely varying the voltage magnitude (V 0 ) of the slack bus as follows: where V hv is the voltage magnitude of the HV grid, m is the voltage transformation ratio, tap stands for the tap position of the OLTC, and δ is the percentage variation of the transformation ratio per tap position change.

95
To maintain the network voltages within permissible limits and to avoid congestion issues, the following inequality constraints are introduced: Here, V min and V max are the minimum and the maximum permissible voltage limits determined by the DSO, while I i and I max,i are the current magnitude and the thermal limit of the i-th branch, respectively. Additionally, (10)-(11) represent the boundary limits of the control variables: where N dg and N load are the set of network nodes in which the DG units and the loads are connected. Q i is the reactive power produced by either the DG unit or the load connected to the i-th node, whereas Q min,i and Q max,i are the corresponding permissible limits. The reactive power of loads is treated as a continuous variable in the optimisation problem. This can be justified by the fact that, in industrial loads, capacitors are switched on/off at a 100 resolution of 6-12 kVAr which is very small compared to the reactive power exchanged in the MV feeder. Finally, D is the discrete set of the available tap positions.
The optimisation problem of (1)-(11) presents an increased computational complexity which is mainly caused by three factors. The first corresponds to the inherent network nonlinearities. The second is the use of a discrete control variable to model the OLTC operation, 105 and finally the third one is the extensive size of MV networks. Consequently, conventional optimisation approaches are rather ineffective, since they suffer from local minimum solu-tions. On the contrary, heuristic or metaheuristic techniques can overcome this burden, but they are considerably time-consuming and thus cannot be applied in real field conditions.

Proposed voltage regulation strategy 110
Scope of the proposed method is to solve the optimisation problem following a rulebased approach. For this purpose, a generic and straightforward procedure is introduced to coordinate the operation of the network elements participating in the voltage regulation process. In this way, the computational complexity is reduced and near-optimal solutions can be achieved. An analytical description of the developed control strategy is carried out 115 in the next subsections, where the proposed operation for each network element type is presented including also their coordinated operation.

Reactive power control of DG units
Initially, a mathematical analysis is performed to investigate the impact of the DG selection on the network losses, regarding the voltage regulation of a specific node. More 120 specifically, according to the LinDistFlow equations of [7], for a given voltage regulation at node v (∆V v ), the necessary reactive power change of the DG unit connected to node q (∆Q q ) is approximately calculated by: where V is the nominal voltage of the network and P ath q denotes the set of nodes belonging to the path from the slack bus to node q. The corresponding network losses are estimated whereÃ i andB i are calculated using (5) and (6), respectively, neglecting the terms related to losses, since they constitute a small portion of the actual power flowing through the i-th 125 branch [7].
Depending on the relative position of node q with respect to node v, the following three cases are considered: 1) P ath q = P ath v . This is the reference case, in which the DG unit is connected to the regulated node v. 130 2) P ath q ⊃ P ath v , i.e. the DG unit is located downstream of the node v. In such a case, the same amount of reactive power as in the reference case is needed, which is verified by (12). Nevertheless, the network losses of (13) are increased, since a more distant node is used compared to the reference case.
3) (P ath q ∩ P ath v ) ⊂ P ath v . The DG unit is connected to the upstream nodes, resulting 135 in an increased amount of reactive power compared to the reference case. Furthermore, it can be proved that network losses are also increased, assuming a constant R/X ratio along the feeder, which is the normal case for a typical MV feeder.
Consequently, the main outcome of the above analysis can be summarized in the following statement: Assuming the voltage regulation of a specific node, the network losses are 140 minimized if the reactive power control is allocated only to the DG unit connected to this node.
The proposed reactive power allocation method is based on the above important outcome to tackle overvoltages in radial MV networks, minimizing the power losses at the same time.
More specifically, for a given loading condition of the network, the node with the maximum 145 voltage is the target node for the voltage regulation process.Furthermore, according to [25], the maximum network voltage is more likely to appear at the nodes where DG units are connected. As a result, the DG unit connected to the target node will absorb reactive power to mitigate overvoltage with minimum losses. Nevertheless, as the DG unit absorbs reactive power, the voltage profile along the network changes and a different network node downstream DG unit.
To implement this control concept, a coordinated control scheme is proposed. According to this, the DG unit connected to the i-th node is assigned to monitor and keep the PCC voltage (V pcc,i ) at acceptable levels, following the procedure described in Fig. 1. This procedure describes the dynamic operation of each DG unit participating in the voltage 160 regulation process and consists of two operation modes separated by a small deadband (db), where no actions occur in order to prevent oscillations and repeated activation-deactivation cycles.
The first operation mode corresponds to the overvoltage mitigation and is activated in case V pcc,i exceeds V max . Prior to the activation of this process, a time delay (d up,i ) is 165 introduced to attain a near-optimal reactive power allocation among the DG units, following the above-mentioned control concept. This time delay differs among the DG units and is determined by the central controller, considering the PCC voltage and the location of each DG unit. Afterwards, the DG unit starts absorbing reactive power by employing a proportional-integral (PI) controller to eliminate the error between V pcc,i and the target 170 voltage (V max − 0.5db). This process continues up to the reactive power capability limit of the DG unit unless either the voltage is successfully regulated or the network section power factor (NSPF) of the i-th node, i.e., the overall power factor (pf i ) seen from the i-th node and downstream, reaches the minimum one (pf min,i ). In the latter two cases, the PI controller attempts to maintain a constant NSPF, resulting in a constant voltage drop at 175 the i-th branch.
The constraint of minimum NSPF poses an upper limit to the reactive power flowing through the branch, which is calculated by This value depends only on the line characteristics and derives from the LinDistFlow equations of [7], assuming a zero voltage drop between the associated nodes. The zero voltage drop indicates that there exist upstream nodes with voltages equal to or greater than that of the i-th node. Thus, this constraint is introduced to avoid the excessive and unnecessary 180 reactive power consumption of this DG unit.
The second operation mode includes the reverse process of properly reducing the reactive power consumption. This is activated when V pcc,i falls below the voltage threshold (V max −db).
After a predefined time delay (d down,i ), the DG unit reduces the reactive power till zero or till the voltage regulation is accomplished. In the latter case, the constant NSPF operation 185 is activated.
It is evident that the DG units participating in the proposed control scheme should be overdimensioned to absorb reactive power, even at rated conditions. More specifically, a sufficient amount of reactive power must be always available to ensure the applicability of the above-mentioned control concept and thus the overvoltage mitigation with near-minimum active power losses. This amount is time-varying and can be approximately calculated by employing the LinDistFlow equations, assuming a zero voltage drop between two adjacent DG units: where Q av,i is the required available reactive power of the DG unit located at the i-th node, pd(i) is the node of the previous adjacent DG unit, and B pd(i),j is the set of branches between the pd(i) and the j-th node. It is worth mentioning that the oversizing factor can be estimated by employing (15) with generation and consumption forecasts. Nevertheless,190 this is considered beyond the scope of this paper.

Reactive power control of loads
In cases of smaller than required dimensioning of the DG units, their available reactive power may be inadequate for the effective voltage regulation. This usually occurs during high generation periods, where the DG units operate close to the rated active power and 195 present a limited reactive power capability [13]. Therefore, the reactive power capability of DG units is potentially a limiting factor of the overall DG penetration. Additionally, there exists the possibility that the maximum network voltage will appear at nodes where only loads are connected.
To overcome these issues, the RPC of loads is proposed as a supplementary method to

OLTC operation
Within the framework of the proposed method, the OLTC operation fulfills two objectives. The primary objective is the regulation of network voltages within permissible limits.
Since overvoltages can be fully tackled by the proposed RPC strategy based on the combined operation of DG units and loads, the OLTC control is employed for the mitigation of undervoltages that may occur in passive feeders. Although the Standard EN 50160 poses a maximum voltage variation of ±10% of the nominal voltage [26], many DSOs adopt stricter limits in MV networks. In this paper, the permissible voltage variation is considered equal to ±5%. The secondary objective is the reduction of network losses during high generation periods. This can be attained by decreasing the voltage magnitude of the MV busbar (V mv ) and thus of the network voltages to reduce the reactive power consumption of DG units and loads. The proposed OLTC operation can be expressed mathematically as follows: where

Operation of the central controller
The principal objective of the central controller is twofold: To monitor the network and 220 to ensure its near-optimal operation by means of minimising active power losses. This can be attained by coordinating the network elements, i.e. the DG units, the loads, and the OLTC, following the procedure described in the flowchart of Fig. 2. The operation of the central controller consists of four main steps, as presented in detail below: Step 1: Acquisition of network voltages. Step 2: Coordination of the DG units operation. Afterwards, the central controller coor-

Acquire network voltages (V )
Determine the time delay pairs (t up , t down ) Send the time delay pairs to the DG units Calculate the new OLTC settings Step 1 Step 2 Step 3 Step 4   in the second operation mode, high priority is given to the DG unit with the lowest voltage.

Communication requirements
According to above-mentioned analysis, it is evident that a communication infrastructure

Dynamic simulations
Considering the examined network of Fig. 3, only the feeder comprising PV units is modelled at the PSIM software that is widely used for time-domain simulations. It is worth mentioning that in these simulations, a detailed modelling of all network elements is used to   Prior to the activation of the RPC, the allocation of the time delays among the PV 315 units is carried out following the procedure described in Section 3.4. In particular, the tree of Fig. 4a, comprising the initial network voltages, is simplified to the tree of Fig. 4b to form a strictly increasing voltage profile in each path between the root and a leaf node.
Considering the first operation mode of overvoltage mitigation, the highest priority, i.e. instant reaction on voltage changes, is given to PV25, whereas the lowest is given to PV14 320 and PV6. PV23 and PV24 belong to the same level nodes and thus the same time delay is applied to simultaneously activate the RPC and achieve a proportional reactive power sharing. The time delays between sequential level nodes, depend on the response of the PV units, which is very small for typical grid-interfaced inverters. In these simulations, it is considered equal to 0.2 s.   After a time delay of 0.2 s, PV20 zeroes its reactive power consumption and finally at 2.2 s, In this way, an near-optimal reactive power allocation among the PV units is achieved.

Long-term evaluation
In   Fig. 7c, while the power losses and the daily energy losses of the network are presented in Fig. 8 and Table 5.

370
The decentralised method results in an increased reactive power consumption and thus increased energy losses, due to two main reasons. The first is related with the reactive power consumption of the PV units which is activated in lower voltages than the maximum permissible limit due to the existence of the droop characteristic. The second reason is the AVR operation, which maintains a constant voltage at the MV busbar close to 1.05 p.u. even 375 during high generation periods, leading the PV units to absorb more reactive power. This can be also observed in Fig. 7c where the tap position of the decentralised method follows a different pattern compared to the proposed and optimisation-based methods.
The proposed control strategy regulates effectively the network voltages as shown in Figs. 7b and 7d, while, according to Fig. 7a, the reactive power consumption is reduced com-380 pared to the decentralised method. As a result, the energy losses are reduced, as presented in Table 5. In comparison with the optimisation method, the proposed method presents a similar performance, indicating that the proposed method can ensure near-optimal solutions with reduced computational complexity. Furthermore, in case of communication loss or failure of the central controller, overvoltages may occur in the optimisation-based method, since 385 the network operation is strongly dependent on the central controller. On the other hand, in the proposed method, the PV units operate autonomously, but in a coordinated way, thus ensuring the overvoltage mitigation regardless the state of the central controller.

Conclusions
In this paper, the problem of optimal voltage regulation is addressed by developing a 390 generalised and straightforward control strategy. The proposed technique implements a distinct time delay allocation feature, based on the graph theory, which ensures the nearoptimal reactive power allocation among the DG units. The proposed method is further enhanced with the active participation of specific MV loads in the voltage regulation process, contributing in the reactive power consumption.

395
The validity of the proposed method is tested on a radial MV network by performing timedomain and time-series simulations. The proposed coordinated voltage regulation strategy presents a superior performance compared to the decentralised methods, regarding energy losses and the overall reactive power consumption. On the other hand, it presents a similar performance to the optimisation-based method, with reduced computational complexity and 400 communication needs. Therefore, it can be readily used to efficiently tackle overvoltages in the MV distribution networks.