Distributed Voltage Reactive Power Control of Distribution Network Considering the Coordination Between DPV and SVC

With the increasing permeability rate of DPV in the distribution network, the safe and economic operation of the distribution network is faced with many challenges, among which the problem of voltage exceeding the limit must be solved urgently. A method for distributed voltage reactive power control, which involves coordinating DPV and SVC, is suggested to enhance the voltage regulation capacity in high-permeability distribution networks. Firstly, considering the limited reactive power regulation capacity of DPV, a coordinated control strategy is proposed to enable SVC when the reactive power capacity of DPV is insufficient. Secondly, a voltage-reactive power control model for distribution networks is established, with a focus on minimizing node voltage deviations and network losses. An adaptive penalty factor adjustment strategy, based on the alternating direction multiplier method, is introduced to achieve a comprehensive solution for this model. Finally, the enhanced IEEE 33-node system is utilized for verification and analysis. The outcomes demonstrate that the suggested coordination strategy involving DPV and SVC, alongside the distributed optimization control method, offers economic advantages and effectively achieves the safe and cost-effective operation of the distribution network.


Introduction
As the country actively promotes renewable energy development, particularly the widespread adoption of Distributed Photovoltaic (DPV) in distribution networks, challenges such as power flow backflow have become more prevalent.Among these challenges, the issue of grid voltage exceeding limits stands out, presenting a significant concern [1] .This problem not only jeopardizes the distribution network's safe operation but also impacts the economic interests of photovoltaic investors.Consequently, research on distribution network reactive power control is of utmost importance to ensure the safe and economically efficient operation of these networks.
At present, voltage reactive power control in our country to solve the problem of voltage over the limit is still mainly using the traditional voltage regulator equipment [2] such as on-load tap-changer (OLTC), shunt capacitors (SC), and so on.Although such equipment has mature technology and high reliability, the adjustment accuracy is poor and the response speed is slow.During grid-connected operation, distributed photovoltaic systems can enhance grid voltage quality and minimize active power loss by effectively adjusting voltage through reactive power control, thereby improving overall power system efficiency [3] .Dealing with voltage issues stemming from high photovoltaic penetration isn't adequately addressed by a single reactive power control device.Instead, it necessitates the comprehensive utilization of multiple devices and voltage control methods to effectively resolve the problem.Gao et al. [4] construct the optimal power flow model of the distribution network including OLTC, Distributed Generation (DG), Static Var Compensator (SVC), and other equipment, which is solved after transformation by second-order cone relaxation technology to ensure the safe and stable operation of distribution network.Yang et al. [5] propose a hierarchical voltage control approach for distribution networks, incorporating the involvement of DPV reactive power and energy storage active power.
Based on the communication mode between entities and voltage, reactive power control in distribution networks can be categorized into three types: local control [6] , centralized control [7] , and distributed control [8] .Because of the advantages of distributed control architecture, researchers have actively studied and discussed distributed optimal control methods and achieved remarkable research results.Distributed optimization algorithms can be divided into peer-to-peer control architecture and master-slave control architecture according to different communication structures.Among them, the distributed optimization algorithm of peer-to-peer control architecture has wider applicability, especially the Alternating Direction Method of Multipliers (ADMM).Because of its simple principle and wide application, it has become a key method for solving the distributed optimal control problem of power systems.Liu et al. [9] combined ADMM and branch and boundary methods to find out the optimal strategy to minimize the network loss and photovoltaic power generation loss in each region while ensuring the system voltage.Zhang et al. [10] propose a day-ahead two-stage distributed optimal scheduling strategy for active distribution networks based on ADMM.However, the traditional ADMM method used in the above literature has two main problems: slow calculation speed and too many iterations.Hence, enhancing the conventional ADMM algorithm is pivotal for improving the efficiency of reactive power control in distribution networks.
Considering the above problems, this paper presents a voltage and reactive power control method of distribution network considering the coordination between DPV and SVC.Firstly, due to the low control efficiency of a single device and the limited reactive power capacity of DPV, a coordinated control strategy is proposed to enable SVC when the reactive power capacity of DPV is insufficient.Secondly, the distribution network is divided into reasonable clusters, and the distribution network voltage reactive power control model aiming at the minimum node voltage deviation and network loss is constructed in the cluster.To enhance the convergence performance of the algorithm and achieve a holistic solution for the model, an adaptive penalty factor adjustment strategy is introduced between clusters using the ADMM as a foundation.Finally, the enhanced IEEE 33-node system serves for validation and analysis.

DPV and SVC coordinate control policies
At present, there is a wide range of research categories on voltage reactive power control of distribution networks at home and abroad, which can be divided into traditional reactive power control equipment and DPV from the perspective of participating control equipment.To avoid the situation that insufficient reactive power capacity of DPV can't solve the voltage over the limit problem, this section proposes the coordinated control strategy of DPV and SVC.

Reactive power control capability comparison
DPV reactive power control is an economical and efficient voltage regulation method, which is more popular than DPV photovoltaic reduction and traditional reactive power equipment.Recently, an increasing number of users have opted for inverters with reactive power regulation features when connecting to the grid.Leveraging DPV's reactive power control for voltage regulation is economically favorable, but it comes with limitations, particularly when facing high power demands or grid voltage fluctuations.Therefore, in some cases, it is necessary to work with other reactive power compensation devices to achieve more efficient reactive power control.
Although traditional reactive power control equipment such as OLTC and SC can reduce network loss and voltage deviation by controlling the reactive power compensation capacity and reactive power distribution, they are gradually replaced by modern reactive power control equipment due to their defects such as high price and limited adjustment times.Modern reactive power control equipment is the Mechanically Switched Capacitor (MSC), SVC, Static Var Generator (SVG), and other typical representatives.SVC is widely used because of its fast response and high-precision reactive power control.
Although SVC has demonstrated excellent performance in many aspects, its high cost and relatively complex maintenance and repair also need to be taken into consideration.In practical applications, choosing the right reactive power control equipment needs to weigh its advantages and disadvantages comprehensively to meet the needs of the power system and maintain economic benefits.

DPV and SVC coordinate control policies
In high-DPV penetration distribution networks characterized by high line impedance and lengthy lines, coordination control involving devices like DPV and OLTC is commonly employed to address voltage fluctuations.This section thus presents a control strategy that activates SVC when DPV's reactive power capacity is insufficient.
Here are the specific steps: (1) We calculate the distribution network's power flow to determine if the node voltage exceeds the limit.
(2) If the voltage exceeds the limit, we adjust the DPV's reactive power output based on power flow calculations to offset voltage deviations.
(3) If DPV's reactive power capacity is insufficient and voltage issues persist, we deploy SVC for swift voltage reactive power control in the distribution network.
This control sequence optimally utilizes DPV and SVC, enabling their synergistic cooperation in voltage control.It ensures their effective response to voltage irregularities while maintaining economic efficiency and robustly supporting power system stability.

Distributed voltage reactive power control strategy of distribution network
Based on the rational division of distribution network clusters, this section first constructs the voltage control model within the clusters, then proposes an adaptive penalty factor adjustment strategy and uses the improved ADMM algorithm to realize parallel optimal control among the clusters.

Voltage and reactive power control model in cluster
Based on the principle of decomposition and coordination, cluster boundary nodes can be copied into adjacent clusters to form independent new clusters and realize decoupling between adjacent clusters.

Objective function.
To minimize voltage deviation and active power loss, this paper adjusts the reactive power output of DPV and reactive power compensation equipment.So we create the following objective function: ( ) where bus N is a collection of nodes in the distribution network, j U is the node voltage amplitude, 1 U is the voltage reference value, : k j k → indicates the branch end node set with the node as the first node, jk r is the resistance of branch jk − , jk P and jk Q are the active and reactive power flowing through branch jk − from node j respectively, 1  and 2  are the minimized weight coefficients, 1  and 2  are correction factors greater than 0 to ensure that the two terms in the equation have similar values.i q are the active power and reactive power of injected node i respectively.The associated constraints can be expressed as: () ,, j j pv j load , , , j j pv j svc j load q q q q = + − (5) where , j pv p and , j pv q are the actual active power and reactive power output of the PV inverter on the node j respectively, , j load p and , j load q are the load active power and load reactive power on the node j respectively, and , j svc q is the discrete compensation power of SVC.Q are the maximum active and reactive power output power of PV respectively, and tan is the power factor angle tangent value of PV.
(4) SVC operation constraints ,,, j svc j svc j svc qqq  where , j svc q and , j svc q are the lower limit and upper limit of the output reactive power of SVC respectively.

Inter-cluster voltage reactive power control strategy
The ADMM algorithm's fundamental concept involves breaking down the initial problem into various sub-problems and incrementally approaching the optimal solution of the original problem by alternately solving these sub-problems.Thus, the reactive power control model for distribution networks based on ADMM is structured as follows: where  is the dual variable, 0   is a punishment factor, and cluster ' n is adjacent to cluster n .We take the specific iterative calculation process of two clusters n and ' n as an example: ( ) To enhance algorithm convergence speed, an adaptive penalty factor adjustment strategy is introduced to correct the iteration step size, as follows: According to the ADMM principle, the end condition of the iteration process is to stop the iteration when both the original and dual residuals reach the required convergence precision.That for a cluster is: In summary, the control strategy is detailed as follows: (1) We divide the distribution network into reasonable clusters, obtain the boundary variable n x and global variable ' nn y of each cluster after decoupling, and build the distributed voltage reactive power control model of the distribution network.
(2) We initialize the basic parameters and data, combine the reactive power control model, and build the Lagrange function as shown in Equation ( 14).
(3) We obtain independent solution and parallel optimization within each cluster, the interaction of boundary variables and global variables between adjacent clusters, iteration of cluster variable

Example setting
The enhanced IEEE 33-node system is shown in Figure 3.The system contains 32 normally closed branches, the voltage reference value is 12.66 kV, the reference capacity is 9 MVA, the total load is 3715 kW+j2300 kvar, and the safe operating range of the node voltage is [0.95, 1.05] pu.The installation positions and parameters of DPV and SVC are shown in Table 1

Impact of DPV and SVC coordination control policy on system running
This section further studies the influence of DPV and SVC coordination control strategy on system operation.The objective functions of this paper are voltage deviation and active power loss, but the economy of control is not well considered, and the control cost involves many factors such as equipment cost, operation, and maintenance cost.Therefore, the following schemes are set for comparative analysis: Case 1: On a sunny day, the reactive power capacity of DPV is insufficient, and the coordinated control strategy of DPV and SVC is not adopted.
Case 2: In sunny weather, the reactive power capacity of DPV is insufficient, and the coordinated control strategy of DPV and SVC is adopted.

SVC
-300 -100 In Figure 4, the voltage of nodes 7-18 and 28-33 exceeds 1.05 pu, and the voltage of nodes 12-18 exceeds 1.075 pu.Case 1 and Case 2 are used to optimize the control of the distribution network.Tables 2 and 3 show the reactive power output of DPV and SVC in the distribution network after Case 1 and Case 2 are used to optimize the control.
As shown in Figure 4, Case 1 and Case 2 can still realize the stable operation of the distribution network within the voltage safety range under the condition of insufficient reactive power capacity of DPV, and their voltage curves almost coincide.In Tables 2 and 3, the reactive power output power of 23 SVC SVC − in Case 1 has reached the upper limit, and other reactive power compensation devices also output capacitive reactive power suppression node voltage increase.In Case 2, each DPV reaches its reactive power output upper limit, and the SVC emits capacitive reactive power.Through analysis and comparison of the above schemes, it can be seen that Case 1 has no sequential coordination control strategy for DPV and SVC when a large area over the limit occurs in the distribution network.Because of SVC's fast control speed and high priority, SVC outputs too much reactive power regulating voltage.However, the adjustment cost and equipment maintenance cost of SVC are higher, resulting in the economy of Case 1 being slightly worse than Case 2.
Through the analysis and comparison of the above schemes, it can be seen when a large area over limit occurs in the distribution network, Case 1 results in excessive reactive power regulation voltage output by SVC due to its fast control speed and high priority.However, the adjustment cost and equipment maintenance cost of SVC are higher, resulting in the economy of Case 1 being slightly worse than Case 2.

Impact of DPV and SVC coordination control policy on system running
To verify the advantages of the adaptive penalty factor adjustment strategy adopted in this paper in terms of solving performance, the following three methods are adopted in this section to solve the reactive power control model: (1) traditional centralized optimization algorithm; (2) traditional ADMM algorithm; (3) adaptive step size ADMM algorithm.In Table 4, adopting control methods (1) to (3) for the distribution network optimization shows minimal disparities in the total voltage deviation and overall network loss.Notably, the distributed optimization algorithm outperforms the centralized optimization method in terms of computational efficiency.This suggests that the distributed optimization approach, facilitated by the exchange of boundary information, exhibits superior computational efficiency in coordinating the entire system.In Figure 5, control methods (2) and (3) are used to optimize the distribution network.After a finite number of iterations, the objective function converges with the centralized optimization results, demonstrating the effectiveness of the distributed optimization method in solving the reactive power control problem.Traditional ADMM convergence requires 45 iterations and takes 39.05 s to compute, while adaptive step size ADMM requires only 25 iterations and takes 21.75 s to compute.In conclusion,

4 u 5 u
indicates the voltage boundary variable retained by cluster 1, and '' indicates the voltage boundary variable replicated by cluster 1 to cluster 2. To achieve the global optimal solution to the global problem, we define the global variable 1 12 xy = , 2 12 xy = .

Figure 1 .Figure 2 .
Figure 1.Adjacent cluster decoupling legend.3.1.2.Constraint condition.(1) Disflow power flow constraints objective function of the cluster n model, ( nn hx ) is the equality constraint of the cluster n model, and ( ) nn gx is the inequality constraint of the cluster n model.The above model is converted to an augmented Lagrange function as follows: s are the primitive residuals and dual residuals respectively, residual convergence accuracy and dual residual convergence accuracy respectively.

4 )
According to Equation (17), the original residual k  and dual residual k s are calculated, and the convergence of the calculated results is judged.If both of them are less than the convergence threshold primal  and dual  , the iteration is stopped.Otherwise, we update the penalty factor according to Equation (16) and return to step (3).

Figure 4 .
Figure 4. Results of IEEE 33-node distribution network cluster division.

Table 2 .
Reactive power output of DPV in Case 1 and Case 2.

Table 3 .
Reactive power output of SVC in Case 1 and Case 2.