Optimal operation of soft open points in medium voltage electrical distribution networks with distributed generation q

(cid:1) A sensitivity method was developed to visualize an SOP operating region in a graphical manner. (cid:1) Time series of SOP set-points were provided considering various load and generation conditions. (cid:1) A framework was developed to quantify the SOP operational beneﬁt with different objectives. (cid:1) This framework is able to facilitate the network operators to select SOP control schemes.

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Introduction
With the ambitions of reducing carbon emissions and enhancing energy security and affordability, the integration of distributed generators (DGs) into electrical power systems is being widely promoted by countries across the globe. Medium voltage (MV) distribution networks, to which DGs are connected directly (e.g., wind farms) or through the aggregation of installations in low voltage networks (e.g., residential-scale photovoltaic systems), are already facing technical challenges in areas where clusters of DG exist. Voltage excursions and thermal overloading are among the dominant issues that limit the ability of MV networks to host large volumes of DG.
Traditionally voltage and reactive power control in distribution networks was achieved by on-load tap changers (OLTCs) and shunt capacitors. In [1,2], in order to increase the penetration of DG in an MV network, OLTCs, and shunt capacitors were coordinated by the time delays of their operation, where shorter time delays were set for capacitors at mid-points of feeders, and longer delays for capacitors at the substation and OLTCs. In [3], the coordination between OLTCs and capacitors was achieved by multi-stage control. In the first stage, an optimal schedule for capacitors was determined using a genetic algorithm. In the second stage, the OLTCs were controlled in real time with varying set-points considering the differences between forecast and actual loads. In [4], Static Var Compensator (SVC) devices were also applied to improve voltage profiles in distribution networks with photovoltaic (PV) systems and wind power plants. Moreover, control strategies can also be applied to DG units to mitigate their adverse impacts [5].I n [6], reactive power control of DG was used to compensate the effect of the active power when voltage excursions occur. Similarly, a droop control of DG was proposed in [7] to manage power curtailment and prevent overvoltages in the network.
Network reconfiguration has also been used to mitigate voltage excursions and/or manage power flows in distribution networks with DG [8][9][10]. Depending on the operating time frame, network reconfiguration can be classified as static or dynamic. Static reconfiguration considers all switches (manually or remotely controlled), and looks for an improved fixed topology at the planning stage (e.g., on a yearly or seasonal basis). Dynamic reconfiguration manages these remotely controlled switches by a centralized control scheme to remove voltage constraints or grid congestion in real time [10].
In this work, a soft open point (SOP) was used to replace the mechanical switch at a previously normally open point of an MV network. An SOP is a power electronic device, usually using back-to-back voltage source converters (VSCs). Such device has also been called ''SIPLINK" [11], ''DC-link" [12][13][14], and ''SNOP" [15] in the literature.
Compared with network reconfiguration, the use of SOPs has the following advantages of: (1) regulating power flows in a continuous manner; (2) flexible and accurate controllability of active and reactive power. In particular, the control of reactive power at each terminal is independent; (3) short-circuit currents are not increased when using SOPs, due to the almost instantaneous control of current; and (4) SOPs can be used to connect any group of feeders, e.g., supplied from different substations or at unequal rated voltages [13].
SOP devices have been made commercially available [11], but the control strategies and their impact on power networks have not been thoroughly investigated. The benefits of using SOPs in power networks were analyzed in [13,16,17]. These studies, however, were limited to only a few snapshots, rather than considering SOP operation under different load and generation conditions and over a period of time. A few initiative pilot projects have been trialled using SOPs in MV distribution networks in the UK, such as [18,19], but they are in their early stage of development. As an Ofgem Low Carbon Networks Fund (LCNF) project, Flexible Urban Networks Low Voltage (FUN-LV) (initiated by UK Power Networks Ltd) has explored the use of SOP in LV networks [20]. Dual-or multi-terminal SOPs have been trialled across 36 networks. Different control modes, i.e. transformer equalization, voltage support, power factor support, and unbalance support, were applied to different networks adopting a hysteresis method. They did not consider the sensitivity of these control features, i.e. transformer loading, voltage, power factor, and network unbalance, to the SOP's active and reactive power injection. Moreover, there were no detailed models investigating the different effects of active and reactive power from an SOP on the networks. A VSC interconnected with an AC grid, is a nonlinear coupled double-input double-output control object [21].In [22] a PID (proportional-integral-derivative) controller was adopted to design the transfer function where the active and reactive power were de-coupled and active power was to manage voltage angle and reactive power was to regulate the magnitude. Therefore, to obtain a model and subsequent design of controllers, a mathematical analysis which simultaneously considers the active and reactive power injection from VSCs is required. On the other hand, the model needs to be general to be constant coefficient for the sensitivity between voltage angle (d i ) and the reactive power injection at node j (Q j ) C V i P j t constant coefficient for the sensitivity between voltage magnitude at node i (V i ) and the active power injection at node j (P j ) C V i Q j t constant coefficient for the sensitivity between voltage magnitude at node i (V i ) and reactive power injection at node j (Q j ) I k actual current at branch k I k rate rated current of branch k J Jacobian matrix n l total number of branches N total number of nodes P active power injection at a node P 1 active power that VSC1 provides to Feeder 1 P 2 active power that VSC2 provides to Feeder 2 P loss power losses of an SOP P T loss power losses of the transformers Q reactive power injection at a node Q 1 reactive power that VSC1 provides to Feeder 1 Q 2 reactive power that VSC2 provides to Feeder 2 r k resistance of the network branch k S 1 maximum apparent power of VSC1 S 2 maximum apparent power of VSC2 T time span of the period of interest V vector of nodal voltage jV i j SOPt voltage magnitude at node i with the SOP jV nom j target voltage for all nodes of the network for voltage profile improvement d voltage angle Dd it change of voltage angle at node i due to SOP's active and reactive power injection DjV i j t change of voltage magnitude at node i due to SOP's active and reactive power injection d i SOP t voltage angle at node i with the SOP Y ij admittance between nodes i and j applicable to networks with different topologies. In [23,24],a n optimization framework, so-called Intervals of Secure Power Injection method, was developed to maximize admissible sets of power injections for secure network operation under marginal changes in network topology. In this paper, a Jacobian matrix -based sensitivity method, which considers the correlation of the power injections of the SOP with the nodal voltages and line currents of the network, was used to define the operating region of an SOP when the grids/feeders at the two terminals of the SOP have various load and generation conditions. The exact operating set-points of the SOP were determined by using a non-linear optimization where three objectives, i.e. voltage profile improvement, line utilization balancing and energy loss minimization, were considered. The main contributions include: (1) representing the operating region of an SOP in a graphical manner by using a Jacobian matrix -based sensitivity method; (2) providing time series of set-points for an SOP when the grids/feeders at the two terminals of the SOP have various load and generation conditions; and (3) quantifying benefits and shortcomings of different optimization objectives, which will help Distribution Network Operators (DNOs) to select SOP control schemes. Fig. 1 shows a one line diagram of an MV distribution network with an SOP connected at the remote ends of two feeders. The two VSCs (i.e.VSC1 and VSC2) are connected via a common DC bus. P 1 and Q 1 represent the active and reactive power that VSC1 provides to Feeder 1, and P 2 and Q 2 are the active and reactive power that VSC2 provides to Feeder 2.

Modelling of Soft Open Point (SOP)
In a general case, n (n P 2) feeders can be connected through an SOP composed of n VSCs sharing the same DC bus. The AC terminal of each VSC is normally connected to an AC network via a coupling transformer. An SOP with two-or multi-VSCs introduces additional degrees of flexibility for network operation, and the power flow through the SOP can be adjusted within operating limits.
In this work, an SOP with two VSCs (i.e. two AC terminals) is considered. The power provided by an SOP can be modulated in the four quadrants of the power chart, and each VSC can operate in any region of the four quadrants. Fig. 2 shows an example of an SOP's operating point where two VSCs operate in region I and II, respectively. The two axes in Fig. 2 are for the active and reactive power. Positive values represent the VSC providing power and negative values represent the VSC absorbing power. The circles represent the size (i.e. maximum apparent power, S 1 , S 2 ) of the corresponding VSC. The power provided by the VSCs cannot exceed their ratings, as shown in With appropriate control, both VSCs produce their individual voltage waveforms with the desired amplitude and phase angle. This provides full (four-quadrant) control of the active and reactive power at both AC terminals. The reactive powers provided, or absorbed, by the two terminals, i.e. Q 1 , Q 2 , are independent; whilst the active powers, i.e. P 1 and P 2 , are not independent variables, as the sum of the active powers should be equal to zero, as shown in where P loss is the power losses of the SOP, including losses in the converters (conduction and switching losses), the DC link capacitor, the filter and the coupling transformers.
With the use of the modular multi-level converter (MMC) technology, the operating loss of a VSC is relatively low, approximately 1% per converter [25]. Therefore, for simplicity, the losses of the SOP are neglected, and Eq. (3) reduces to X j¼1;2 The SOP adopted is based on the MMC VSC technology at a commercially available size [11]. The SOP is capable of providing the required power within its operational constraint. The detailed control principle of the VSCs can be found in [26].

Jacobian matrix based sensitivity analysis
The sensitivity of voltages and currents in a network to the SOP's active and reactive power injections was analyzed using the Jacobian matrix [27]. For all the PQ buses, the voltage sensitivity to the bus injection of active and reactive power is calculated from where V is the vector of the nodal voltage, and d is the voltage angle; P and Q are the injection of active and reactive power at a node; J is the Jacobian matrix. The Jacobian matrix changes over time as the network configuration and load and generation conditions vary. For a given time instant, t, the Jacobian matrix is considered constant, and the corresponding inverse matrix is expressed by where N is the total number of nodes. C d i P j t is a constant coefficient for the sensitivity between voltage angle, d i , and the active power injection at node j. C d i Q j t is a constant coefficient for the sensitivity between d i and the reactive power injection at node j. C V i P j t is a constant coefficient for the sensitivity between voltage magnitude at node i, V i and P j . C V i Q j t is a constant coefficient for the sensitivity between V i and Q j . i ¼ 2; 3; 4; ......N, j =2 ; 3; 4; ......N. Note that node 1 is a ''slack" or ''infinite" bus, where the voltage magnitude is specified and phase angle is assumed to be zero. Therefore it is not included in the Jacobian matrix. At time instant t, the sensitivity of voltage angle and magnitude at node i are calculated by It is assumed that, at time instant t, apart from the SOP's active and reactive power injections, the change in active and reactive power at all nodes is zero. Despite the variations in demand and generation, the control of the SOP is able to be made as fast as milliseconds when using the power electronic devices [26]. There might be delays in data measurement and communications which will result in delay of the SOP control and require a sophisticated control algorithm design, but this is out of the scope of this work.
The assumption made here allows the impact of the SOP on the network to be analyzed, and more rigorous studies on real-time control of the SOP will be carried out in the future. Hence, the voltage angle and magnitude at node i are presented as where Dd it and DV it only consider SOP's active and reactive power injections.

Optimization formulation
Three optimization formulations were considered, each with a different objective. For each optimization formulation, the voltage angle and magnitude at node i (i.e. d i SOP t , jV i j SOP t ) were calculated by Eqs. (7)-(10), and the active and reactive power provided by the two VSCs were the decision variables.

Voltage Profile Improvement (VPI)
When improving the voltage profile of the network is desired, the objective function is where jV nom j is a target voltage for all nodes of the network. This objective function leads to an optimal dispatch of the SOP's active and reactive power values to bring all nodal voltages as close as possible to the target value. The nominal voltage, i.e. 1 p.u., was taken as the target voltage, because this is considered as a midpoint of the future scenarios, given that the integration of DG results in voltage rise and the electrification of transport and heating leads to low voltages.

Line Utilization Balancing (LUB)
When the line utilization of the network is to be balanced, the objective function is min where n l is the total number of branches, and I k and I k rate are the actual and rated current of branch k. Assuming that the node numbers of the two terminals of the branch k are i and j, and Y ij is the admittance between nodes i and j, the actual current in the branch k can be expressed by This objective function leads to an optimal dispatch of the SOP's active and reactive power values to achieve balancing of line utilization.

Energy Loss Minimization (ELM)
When the energy losses of the network are to be minimized, the objective function is where P T loss is the power losses of the transformers, r k is the resistance of the network branch k, and T is the time span of the period of interest. This objective function leads to an optimal dispatch of the SOP's active and reactive power values to achieve the lowest line and transformer energy losses.

Constraints
Together with the constraints shown in (1), (2) and (4), the operation of the network cannot breach the voltage and thermal limits, as shown in

Visualization of the SOP operating region
Considering the voltage constraints, the SOP's active and reactive power operating region is visualized in the four quadrants of the power chart. For illustration purposes, the charts for four different scenarios are presented. ''Undervoltage", ''overvoltage", and ''voltage within limit" are used to define the feeder voltage status without considering the SOP's power injection. ''Undervoltage" in a feeder means that the feeder is relatively heavily loaded, and undervoltage occurs when there is no power injection from the VSC. ''Overvoltage" means that the feeder has more distributed generation, and overvoltage occurs when there is no power injection from the VSC. ''Voltage within limit" means that the voltages in the feeder is within the limits when there is no power injection from the VSC. Fig. 3 shows two overlaid circles representing the active and reactive power limits for the two VSCs of the SOP, assuming the two VSCs are the same size. The circle for VSC2 (connected to Feeder 2) was mirrored in the y-axis so that the allowable operating region can be visualized. This is done because the active power of the two SOP terminals must be symmetric (see Eq. (4)). As a consequence, for any operating point in Fig. 3, Eq. (4) is met.
In In a general case, the SOP's active and reactive power operating region varies depending on the actual voltages and the sensitivity of the voltages to the active and reactive power injections of the SOP (i.e. slope of the constant voltage loci) of the two feeders. ''Undervoltage", ''overvoltage", and ''voltage within limit" were in a way to reflect a feeder's load and generation conditions. The graphical method provides a general idea of active and reactive power regions at which an SOP operates when the two feeders are under various load and generation scenarios, see Table 1.A qualitative analysis with a graphical visualization not only helps network operators to understand an SOP's operating status, but also provides high level operational decision support, such as choosing control schemes, and restraining operational boundaries.

MV distribution network model
An example distribution network obtained from [28] was used with some modifications. As shown in Fig. 7, the 11 kV network consists of four radial feeders (three-phase underground cables) with different lengths (each segment is 1 km) and load types. The rated capacity of the 33/11 kV transformer is 20 MVA. An SOP is connected at the remote ends of Feeder 2 and Feeder 3, with a rated capacity of 3 MVA for each VSC. Various DGs are installed at different locations to represent the expected load/generation distribution between feeders. Table 2 shows a summary of the load  I, II  I, II, III  II, III  Voltage within limit I, II, IV  -II, III, IV  Overvoltage  I, IV  I, III, IV  III,  and generation data. The impedance of the first half of the feeder (close to the substation) is 0.164 + j0.08 X/km, and the rated current is 335 A per phase, and the second half is 0.320 + j0.087 X/km, with a rated current of 230 A per phase. Fig. 8 shows the profiles for residential, commercial and industrial loads for two days (a weekend day and a weekday), with power factors of 0.98, 0.95, and 0.90. Fig. 9 shows the generation profiles for wind and PV systems for the two days under study, and all wind and PV generations are considered to operate at unity power factor. These load data was obtained from [29] and wind and PV generation data was obtained from [28], and these data are presented in the Appendix of this paper. These load and generation profiles are all normalized to their own peak values, and the corresponding peak load of a feeder and the peak of a DG unit are shown in Table 2.
Power flow calculations of the network were carried out in MATLAB using the Newton-Raphson method, and the tolerance of iteration was considered as 0.001 per unit. Jacobian matrix was obtained when the power flow solution reached convergence. Then the non-linear programming optimization with non-linear constraints was also carried out in MATLAB, where an Interior-Point algorithm and Hessian matrix were used to find the optimal solutions. The power flow calculations and optimizations were run at each time step, i.e. every 30 min, for the proposed three objective functions. The relevant computation experiments were performed on a desktop machine, Intel (R) Core (TM) i7-4790 CPU @ 3.6 GHz, 16 GB RAM and MATLAB version R2014a, and the optimization process for each time step is approximately 450 milliseconds.

DG penetration level
DG penetration level is defined as the total of the rating of each individual DG in the network in relation to the 33/11 kV transformer rated capacity, as shown in Various penetration scenarios were considered by scaling up/down the rating of each DG. For instance, the DG rating (MW) values shown in Table 2 represent a DG penetration level of 60%.
With these DG rating (MW) values halved, the penetration level is 30%. With 1.5 times of these DG rating (MW) values, the penetration level is 90%. Fig. 10 shows the performance of the network with the SOP and a 90% DG penetration. ±3% of nominal was considered as the voltage limit [16,30]. Note that, without an SOP, overvoltages occurred in Feeder 2 and Feeder 3. These overvoltages did not occur when using an SOP, irrespective of the objective function used. When using the VPI objective, the voltage profiles were better (i.e. closer to the 1 pu target value) than when using the LUB or ELM objective. In    Fig. 7. One line diagram of a radial MV network (the cable diameters of the first half of the feeders, i.e. closer to the substation, are bigger than the second half, therefore they are shown in thicker lines).

Two-day performance with a 90% DG penetration -full observability of the network
terms of dispatched active and reactive power values from the SOP, the active values were similar when adopting the three objective functions. However, more reactive power from SOP was dispatched when using the VPI objective than when using the LUB or ELM objective.
The dispatched active and reactive power values (i.e. set-points) of the SOP are shown in the four quadrant power chart in Fig. 11. As shown, more operating points were close to, or on, the edge of the circle using the VPI objective than using the LUB or the ELM objective, and this also illustrates more reactive power from  SOP was dispatched using the VPI objective. The objectives to achieve line balancing LUB and energy loss minimization ELM mainly relied on real power exchange.

Overall performance -full observability of the network
The network performance was examined by investigating the maximum and minimum voltages, the maximum line utilization and the energy losses of the network with DG penetration from 0 to 90% (10% per step), and they are presented in Figs. 12-14. Without using an SOP, overvoltages were present from 60% DG penetration, see Fig. 12. When using an SOP and disregarding the objective function used, the network reached 90% DG penetration without violating the voltage limits. The maximum voltages were kept lower when optimizing the voltage profile using the VPI objective than when using the line balance LUB or energy loss ELM objective, along all DG penetrations.
As shown in Fig. 13, for DG penetrations from 10% to 60%, the maximum line utilization was always larger when adopting the VPI objective than the case without an SOP. This was because the increased reactive power injection from the SOP resulted in an increase in the currents of some circuits. However, a slight decrease was shown when the penetration was more than 70%. This was because with higher penetrations of DG, the VSCs of the SOP began to consume reactive power reducing currents of some parts of the network. When using the LUB or the ELM objective, the maximum line utilization was always smaller than the case without an SOP, for all DG penetrations.
In Fig. 14, it is shown that, by using the VPI objective, the total energy losses were approximately twice those without an SOP. Considering only the loads (i.e. 0% DG penetration), the total energy losses for the two days were 2.55 MWh, which corresponds to approximately 1% of the total energy consumption. With a 90% DG penetration, and without an SOP, the total energy losses were 7.28 MWh (i.e. $2.9% of the total energy consumption). Also, due to the increased dispatch of reactive power, adopting the VPI objective resulted in a significant increase in losses, where the total energy losses were 15.1 MWh (i.e. $5.9% of the total energy consumption). In contrast, a reduction of energy losses was shown throughout all penetration levels when adopting LUB or ELM as the objective. For a 90% DG penetration, the energy losses when using the LUB were 6.13 MWh, and using the ELM the energy losses were 6.12 MWh, and both showed a slight reduction compared to the case without an SOP.

Overall performance -limited & no observability of the network
In reality, the control system will not have full network observability. A case in which loads were 20% smaller than the optimization input data was considered, assuming all DGs were correctly measured. The reduction rate for each load was randomly selected from a range of 10-30%, and the overall load reduction was 20%. This was a simple assumption made here to represent a global measurement error, when a network has limited measurements. The overall performance of the network is shown in Table 3. In this table, voltages above the limit are marked in red. It is seen that, when using the LUB and ELM objectives, overvoltages were present from 70% DG penetration; whilst, when using the VPI objective, the voltages were within the limits until the DG penetration reached 90%. For the network without an SOP, as the DG penetration increased, voltage excursions were encountered before thermal overloading. Therefore, the method optimizing voltage profiles, VPI, performed better than the line utilization balancing or loss   At minimal network observability, only the voltages at the SOP terminals are known by the SOP control system. In this case, the optimization formation with the voltage improvement VPI as the objective was used, and Eq. (11) only considered the voltages at the two terminals rather than all the nodes. It is found that, by using an SOP, the network's DG hosting capacity was increased from 50% to 80%.

Discussion
For the visualization of an SOP's operating region, the voltage limit boundaries (shown in Figs. 3-6) represent the most sensitive or the worst node voltage in a feeder. This node is most likely to be the remote end for a one-line MV feeder and might be another node for a grid/feeder with different topologies. However, Jacobian matrix based sensitivity method is able to provide the relation of voltage at any point of a network with the power injection of an SOP, irrespective of the network topology, therefore the methodology is applicable to different topologies, e.g. feeders with many laterals/branches.
An SOP with a given rating and location was considered. This research can be a framework for higher level studies, including finding the optimal number and size of SOPs with different network topologies and configurations. When a network is equipped with multiple SOPs, Eqs. (9) and (10) should include all the terminals of all SOPs. When the two feeders, to which an SOP is connected, are supplied by different substations, one Jacobian matrix is calculated for each substation, and two sets of Equations similar to (9) and (10) are created in order to include both terminals of the SOP.
Balanced three-phase load and generation were considered. Through adequate control of VSCs, the SOP is able to provide three-phase unbalanced power injections. The method used in this research to quantify the benefit of using an SOP could be applied to a three-phase unbalanced system.
Harmonics brought by VSCs and losses of VSCs, and their impact on the performance of the control schemes were out of the scope of this paper.
In this work, a data set of 30-min granularity with different load and generation conditions was taken. This is because this work is mainly for planning purposes, to provide distribution network operators with high level decision support, e.g. selecting control schemes and restraining SOP operation boundaries. However, given that the optimization calculation for each run took approximately 450 ms, the optimization is able to be run in real time, and the methodology is able to be used for real-time operation purposes.
This work did not consider active control devices, such as battery storage, OLTC, and capacitor banks. The control time frame of these active control devices is normally minutes or hours. Although some electronic interfaced battery storage is able to change control settings on a millisecond timeframe, due to the battery life time concern, battery banks normally operate in a steady state time frame. In the contrast, SOPs are not constrained by mechanical wear or life time concern therefore are able to change operating points more frequently. On the other hand, this work focuses on the performances of SOP control schemes, and provides decision supports of selecting control schemes. Hence, these active control devices were not considered. Future work can be undertaken investigating the real-time operation of SOP with battery storage systems, OLTC, and capacitor banks.

Conclusions
A non-linear programming optimization, to set the real and reactive power operating set-points for an SOP on an 11 kV network, was developed. Through a Jacobian matrix based sensitivity analysis, the SOP's operating region was defined within its voltage-limit bounds, and visualized in a graphical manner for different load and generation conditions at the grids or feeders at the two terminals of the SOP. The exact operating point was determined using three optimization objectives: voltage profile improvement, line utilization balancing and energy loss minimization.
Results showed that the use of an SOP significantly increases the network's DG hosting capacity. The control scheme using the objective for voltage profile improvement increased the headroom of the voltage limits by the largest margin. This control scheme dispatched increased reactive power, and, hence, was at the expense of increased energy losses.
The control schemes using the objectives to achieve line utilization balance and energy losses minimization showed the most improvement in circuit utilization and in limiting energy losses, mainly relying on the real power exchange between feeders.
This work does not make a suggestion on which optimization objective is better than others, but presents the performance of each and leaving the selecting options to network operators based on their needs. Defining a unifying cost function is difficult, because the cost of breaching voltage and thermal limits, and cost of energy losses may vary from network to network. According to a network's characteristics, network operators are able to devise the control scheme using one or multi-objective functions. The proposed methodology provides a potential framework/solution for electricity network operators, allowing them to choose appropriate control schemes more effectively. This selection requires the network operators to attribute value to the increase in hosting capacity, mitigation in voltage issues, the reduction in the maximum line utilization and the reduction in energy losses.