In order to optimally coordinate and manage the operation of energy storage units in a typical distribution network, it is crucial to consider the aims and objectives of the asset owners. Given a normal operating condition (i.e., in the absence of network voltage and/or loading issues), the storage units are mainly dispatched in a way to improve the self-consumption and reduce the electricity bills if they are owned by “customers”. In this case, normally, a local control architecture is needed to meet the noted objectives. However, with utility as the storage owner, the aim will be to deal with the network problems in an efficient way, which in turn necessitates a coordinated control architecture. Therefore, efficient control of storage units greatly depends on the system’s objectives, related security/technical constraints, and operating modes.
This paper proposes an efficient cooperative control approach (which includes both local and distributed control approaches) to deal with over- and under-voltage issues in distribution network. As can be seen in
Figure 1, the local control approach uses the storage units at PCC bus voltages to determine the contribution of these units for a robust voltage control, while the distributed control approach determines the optimal contribution of storage units for voltage support.
2.1. Local Voltage Control Strategy
The local control approach uses the storage units at PCC bus voltages to determine the contribution of these units for a robust voltage control. In order to determine the triggering criteria for the local controllers, three control modes are defined for network operation, as given in
Figure 2.
If the voltages of all storage units are in the desirable range (between and ), the network control mode is normal. Therefore, storage units can be used for other purposes such as power buffering and so on. The second control mode engages when the voltage at any of the storage unit buses exceeds . In this case, storage units go to the over-voltage control mode and they start to collaborate with each other in coordinating their charging rate to achieve robust and efficient over-voltage prevention. This coordination continues until all the bus voltages go to the desirable range and the network goes to the normal mode.
Finally, under-voltage control mode is treated similar to the over-voltage control mode, where and determine the start and stop of this control mode. It should be noted that the aim of over- or under-voltage control is to avoid any bus violating the permissible limits (i.e., and ).
Each storage unit is supported by both local and distributed controllers. As soon as the voltage at a storage unit bus violates
or
, the local controller updates its reference power, as in (1).
where
Pl,i is the local contribution of storage unit, and
mi,o and
mi,u are the droop coefficients. As storage units should start to charge or discharge at critical limits and use their maximum capability in permissible limit, the droop coefficient is proposed as in Equations (2) and (3).
where
is the maximum available power in storage unit
i.
Additionally, to show that the network mode is changed, a local voltage control flag is used, as given in (4).
Based on this control structure, as soon as the voltage at any storage bus passes the critical limit, the storage unit starts to charge or discharge to deal with over- or under-voltage issues. Although this control can provide a robust over/under voltage control, it may not follow the optimal storage unit utilization. Therefore, a distributed control approach is used to guarantee the optimal utilization of storage units. Details of this control strategy are described in the following section.
2.2. Cooperative Voltage Control Strategy
A consensus algorithm is a distributed control that provides fair sharing among resources in a network. In this algorithm, the resources in a network are represented by a graph (
V,
E), where
V models graph vertices and
E models the graph edges, and pair (
i,
j) is member of
E if there is an edge between vertices
j and
i. An example of this graph model is shown in
Figure 3.
For each vertex, the set
Ni shows its neighbors, as given in (5).
Based on this technique, for each resource in node
i, a parameter named information state (
) is defined, which will be updated as in (6) to achieve a specific control objective [
1].
where
dij is a coefficient defined as in Equation (7) [
18].
where
cij models the communication link between resource
i and
j. In a discrete time domain, (7) can be shown in matrix format as given in (8).
This algorithm has been applied in applications which require fair sharing among resources [
19]. For example, in [
2], this approach is used to provide fair sharing of active power among storage units to perform load management in a power system; in [
20], this approach is adopted for load sharing among photovoltaic (PV)-storage system of a low-voltage network. In recent literature, this approach is also used to provide optimal utilization of resources [
21]. Based on the noted literatures, the proposed distributed control structure for a storage unit is implemented in this paper, as shown in
Figure 4.
The maximum and minimum power of a storage unit depends on the control mode of the network. Lflag is a local index of a network control mode. However, to extend the network mode to all storage units, is also defined. A value is assigned to this index based on the following arguments: Logic 1: is followed to charge all storage units during over-voltages and discharge during under-voltages; Logic 2: is followed to determine the maximum and minimum of a storage unit’s contributed power. These logics are formulated as follows:
Logic 1: if and all
if or any of
if or any of
In this paper, the aim is to use a consensus approach to provide an optimal utilization of storage units in voltage support. To achieve this objective, the utilization function of each storage unit is defined as (9).
where
Pd,i is the distributed contribution of storage unit, and
is the storage unit efficiency.
As noted in [
21], the efficiency of the storage unit reduces when its power increases. Therefore, the storage efficiency depends on its output power, as given in (10).
where
ai and
bi are coefficients that depend on the type of storage unit. These values can be different for charging or discharging. However, for the sake of simplicity, in this paper, fixed values are considered. So, the cost function for each storage unit can be shown as in (11).
In order to achieve an optimal utilization of energy storage units, the objective control function is defined as in (12).
where
n is the number of storage units. The optimal solution of this function can be written as in (13) [
21].
where
is the optimal incremental cost for each storage unit.
In this paper, to achieve the noted optimal point, the iterative process in [
21] is used to optimize the cost function for storage units, which includes the following distributed updating rules.
where
Pv,i is the difference between the current state of battery charge with respect to the value in the last time interval. This is the value shared by the neighbors to contribute, as set in the algorithm.
In matrix form, the noted equations can be shown in the forms given in (18)–(21).
where
based on [
21], these equations converge to:
by initiating
Pv and
Pd in (27) through (28):
We can rewrite (27) using (25), as in (29):
Therefore, (29) can be rewritten as:
So, the storage units’ incremental cost converges to the optimal point. The proposed mixed control approach can provide a robust and optimal over- and under-voltage control in a distribution network. To study the dynamic operation of this technique, the network internal states—such as voltage and current of PVs and storage units—are not considered, as these parameters have faster response times compared with storage unit output power [
2]. In other words, these parameters are stabilized faster than output power. Therefore, the proposed control approach determines the dynamic of the network, as given in
Figure 5, which illustrates the proposed approach with a flowchart.