Keywords

1 Introduction

The Proposal of the Central Committee of the Communist Party of China on the Formulation of the 14th Five-Year Plan for National Economic and Social Development and the Vision For 2035 (the “Recommendations”) put forward: “Priority should be given to the development of agricultural and rural areas and the overall promotion of rural revitalization”. One of the important foundations of rural revitalization is electric power construction. However, the network frame in rural areas is weak and the quality of power supply is prominent. The characteristics of low voltage, three-phase imbalance and high network loss are obvious, and the problem of heavy load and overload of power distribution transformer during peak load is very prominent, which affects the production and consumption of electricity by residents.

In addition, the Recommendations refer to “the development of a programme of action for the peak of carbon emissions by 2030”. “Carbon Peak” and “Carbon Neutrality” have become the strategic objectives of China’s energy industry development in the future [1]. Taking Guizhou as an example, the clean and efficient power industry represented by “roof photostatic” and “electricity substitution” has become one of the top ten industrial industries in Guizhou Province, and will also be an important support for the strategy of “village revitalization” during the 14th Five-Year Plan period. Considering the rapid growth trend of “roof photostatic” and “power substitution” poses a serious challenge to the current distribution network. The addition of electricity replacement at the lotus end will make the electricity consumption increase suddenly, increase the operating burden of the distribution and change, affect the reliability of power supply, and the incorporation of the source into distributed photostatic will lead to more serious problems such as reverse current and voltage overshoot, while its own volatility and randomness will affect the stability of the power grid and the quality of electricity produced and used by farmers. The superposition of the source-load end will lead to the load of “peak-on-peak”, aggravate the severity of the problem, easily lead to the distribution of burn-out, reduce the safety and economy of power grid operation, it is difficult to effectively support the “village revitalization” and “carbon peak, carbon neutral” two strategic objectives.

In recent years, the research on the coordination and control strategy of low voltage distribution network has attracted much attention. Based on the energy storage to achieve the trend of distribution network peak filling, but the required energy storage capacity is very large, high capital investment, but also cannot be widely used in the distribution network [2, 3]. Energy storage and photovoltaic inverter reactive collaborative control technology while ensuring voltage quality [4, 5], further reduce the low voltage distribution network for energy storage capacity demand, improve the economics of control, but it is difficult to solve the load peak and valley difference in the background of the distribution transformer overload and burn loss risk. In the context of power substitution, it has been studied that the use of regulator-conditioning and tuning technology is more effective to prevent the burning of power distribution transformers, improve the economics of transformer operation, but also to a certain extent to improve network losses, reduce the risk of voltage over-limits [6,7,8,9], but for large-scale distributed photovoltaic grid-connected three-phase imbalance, high volatility and randomness issues have not been fully considered [10,11,12,13]. In the practical experience of Guizhou power grid, it is also found that if the pressure conditioning technology does not consider to cooperate with the three-phase imbalance management, it will cause a lot of single-phase overload problems or the non-essential action of the tuning switch.

In view of the existing problems in the current research, this paper studies the adaptive control of the low voltage distribution network for distributed photovoltaic grid and power substitution, first of all, on the scale of the day, comprehensive consideration of network loss, three-phase imbalance, transformer overload and voltage overshoot and other key issues. A collaborative optimization control strategy is proposed to consider the tuning regulator transformer, energy storage, photovoltaic inverter and demand side response, and secondly, on the short-term control scale of day, a short-term response strategy of tuning switch and photovoltaic inverter is proposed. To prevent the overload of the weight of the distribution due to photovoltaic uncertainty and to suppress the voltage disturbance of the system, and improve the power supply quality of the distribution network.

2 Control Framework

This article proposes a—control architecture called Central—In Place. The central control and time scale of the optimization stage are one hour, and the in-place control and time scale of the daytime control stage are five minutes.

Because load fluctuation, high network loss and three-phase imbalance are global problems, all nodes need to run control overall planning. It is more appropriate to use centralized control with strong computing power to achieve global optimization control. Recently, the optimization stage, each node is directly connected with the central controller, before the control upload of the state information of the node, after control to accept the reference optimization results.

Given the high computing and communication requirements of centralized control and the long time required, centralized control alone is not sufficient to respond to photovoltaic and load fluctuations in a timely manner. In-place control with simple measurement computing power and rapid response is required. During the day-to-day control phase, each node relies on measurement values for rule-based correction control, enabling each node to respond quickly to power fluctuations.

The main purpose of designing the two-phase control framework for—control as shown in Fig. 1 is to calculate optimal current calculation optimization constraint variables based on hourly historical data (load and photovoltaic failure) and network loss, three-phase imbalance, and transformer loss as the target functions. In the inner-day control phase, the optimization results of the recent optimization are not fully adapted to the random fluctuations of the minutes of photovoltaics and loads, and rule-based correction control (photovoltaic reactive, tolerant taps) must be set to achieve rapid response to photovoltaic and load fluctuations and to suppress voltage overstaying of each node. Through the optimization of the day and the control phase in the hour optimization, minute level correction, to get better optimization control effect.

Fig. 1
Two-stage of three diagrams day and in day operation. Day has a graph of time versus power, a systematic model, and economic operation. The in-day operation has a graph of time versus power, short-term regulation within a one-day operation, and equipment security.

Two-stage control framework of day-ahead optimization and intra-day control

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The advantage of designing a two-stage control framework is that it takes into account the economics of the power grid and the security of the distribution. To ensure the economy and stability of power grid operation in the optimization phase. Ensure the safe operation of the distribution transformer during the daytime control phase. The proposed controls provide rapid response during the inner-day control phase. Significant fluctuations in photostatic are usually between a few seconds and 10 min, and load fluctuations are difficult to achieve high-accuracy predictions. According to the results of the recently optimized hourly optimization, it is too late to respond and adjust to the photovoltaic and load fluctuations, the network is likely to experience voltage overstays, voltage fluctuations, and counterweight overload. The proposed control can respond quickly to photovoltaic and load power fluctuations, suppress the voltage overstay of the network and reduce voltage fluctuations, in addition, the mating connection can also be adjusted to make the mating changes without heavy overload phenomenon, to ensure the safe operation of the matching.

3 Distribution Network Adaptive Control Model

Based on the optimal trend of three-phase four-wire system, the distribution network establishes an optimized control model, with the goal of network loss, transformer loss, three-phase imbalance and voltage overstay, and optimizes the power distribution network to regulate voltage switches, photovoltaic inverters, reactive and energy storage.

3.1 Day-Ahead Optimization

The target functions of the recent control layer mentioned in this article includes as follows:

  1. (1)

    Objective function

    $$\min F = F_{1}^{^{\prime}} + F_{2}^{^{\prime}} + F_{3}^{^{\prime}} = \frac{{F_{1} }}{{s_{1} }} + \frac{{F_{2} }}{{s_{2} }} + \frac{{F_{3} }}{{s_{3} }}$$
    (1)
    $$F = P_{loss.tot}$$
    (2)
    $$F_{1} = P_{loss.net}$$
    (3)
    $$F_{2} = P_{cu} + P_{Fe}$$
    (4)
    $$F_{3} = \sum\limits_{i \in \Re } {VUF_{i} } ,\varphi \in \Phi$$
    (5)
    $$P_{loss.net} = [I_{line}^{*} \otimes I_{line} ]^{^{\prime}} R$$
    (6)
    $$I_{line,t} = MU_{inj,t}$$
    (7)
    $$U_{inj,t} = Y_{ij}^{ - 1} I_{inj,t}$$
    (8)
    $$P_{loss.net} = [(MY_{ij}^{ - 1} I_{inj} )^{*} \otimes MY_{ij}^{ - 1} I_{inj} ]^{{\text{T}}} R$$
    (9)
    $$\left\{ {\begin{array}{*{20}c} {M_{i \to j} = Y_{ij} } \\ {M_{j \to i} = - Y_{ij} } \\ \end{array} } \right.$$
    (10)

In the form: the value of the target function; for the scale factor; For the total loss of the tuning regulator transformer; For network loss; Copper loss (line loss) for toleration of regulator change within one day; For one day to adjust the iron loss (empty load loss); set to fixed value; Three-phase imbalance for nodes; Represents a collection of nodes in the distribution network; Represents a collection of three phases.

Where represents the transpose of the matrix; is the line current,; represents the corresponding elements of the two matrices multiplied; /b116 > Phase resistance; A mapping matrix of node voltage and branch current, e.g. represents the association of branch current to node voltage between slave nodes; is the node /b131 > a conductive matrix between and; for the voltage of each node during the period; Inject current into each node during the time period.

$$P_{Cu} = I_{line}^{2} R$$
(11)
$$VUF_{i} = \frac{{U_{neg,i} }}{{U_{pos,i} }} = \frac{{U_{a,i} + \alpha^{2} U_{b,i} + \alpha U_{c,i} }}{{U_{a,i} + \alpha U_{b,i} + \alpha^{2} U_{c,i} }}$$
(12)

where and are the nodes with negative and positive voltages; /b117 > , phase voltage;

  1. (2)

    Constraints

The constraints of the control layer mentioned are in order to operate safely and steadily in the distribution network, and the constraints such as current, voltage, regulator tap, toning critical load, neutral line voltage and power need to be met.

$$\left\{ {\begin{array}{*{20}c} \begin{gathered} {\text{Re}} (U_{i} ) = ({\text{Re}} (Y_{ij} )^{ - 1} ){\text{Re}} (I_{inj} ) \hfill \\ - ({\text{Im}} (Y_{ij} )^{ - 1} ){\text{Im}} (I_{inj} ) \hfill \\ \end{gathered} \\ \begin{gathered} {\text{Im}} (U_{i} ) = ({\text{Im}} (Y_{ij} )^{ - 1} ){\text{Re}} (I_{inj} ) \hfill \\ + ({\text{Re}} (Y_{ij} )^{ - 1} ){\text{Im}} (I_{inj} ) \hfill \\ \end{gathered} \\ \end{array} } \right.$$
(13)
$$I_{ij} = Y_{ij} (U_{i} - U_{j} )$$
(14)
$$Y_{ij} = G_{ij} + jB_{ij}$$
(15)
$$\begin{gathered} {|}I_{ij} | = |Y_{ij} ||V_{ij} | = \sqrt {(G_{ij}^{2} + B_{ij}^{2} )} \hfill \\ \sqrt {({\text{Re}} (U_{i} ) - {\text{Re}} (U_{j} ))^{2} + ({\text{Im}} (U_{i} ) - {\text{Im}} (U_{j} ))^{2} } \hfill \\ \end{gathered}$$
(16)
$$G_{ij} = \left[ {\begin{array}{*{20}c} {G_{ia,ja} } & {G_{ia,jb} } & {G_{ia,ic} } & {G_{ia,jn} } \\ {G_{ib,ja} } & {G_{ib,jb} } & {G_{ib,ic} } & {G_{ib,jn} } \\ {G_{ic,ja} } & {G_{ic,jb} } & {G_{ic,jc} } & {G_{ic,jn} } \\ {G_{in,ja} } & {G_{in,jb} } & {G_{in,jc} } & {G_{in,jn} } \\ \end{array} } \right]$$
$$B_{ij} = \left[ {\begin{array}{*{20}c} {B_{ia,ja} } & {B_{ia,jb} } & {B_{ia,ic} } & {B_{ia,jn} } \\ {B_{ib,ja} } & {B_{ib,jb} } & {B_{ib,ic} } & {B_{ib,jn} } \\ {B_{ic,ja} } & {B_{ic,jb} } & {B_{ic,jc} } & {B_{ic,jn} } \\ {B_{in,ja} } & {B_{in,jb} } & {B_{in,jc} } & {B_{in,jn} } \\ \end{array} } \right]$$

The safe and stable operation of the distribution network needs to be met the balance of active and reactive power at the time-injection and outflow nodes, i.e.:

where and are expressed as matrix real and imaginary parts; and are phase conduction and induction between nodes and.

  1. (1)

    The node voltage constraint

In order to ensure the safe operation of the distribution network, the node voltage should be stable within the safe range [14], that is:

$$U_{\varphi ,i}^{min} \le U_{\varphi ,i,t} \le U_{\varphi ,i}^{max}$$
(17)

where and the lower and upper limits of the voltage amplitude of the phase node, respectively.

  1. (2)

    Neutral line voltage constraint

To ensure the stable operation of the line, the voltage amplitude at the moment needs to be less than the maximum allowable value of the neutral line voltage, i.e.:

$$\left| {U_{neu,i,t} } \right| \le U_{neu}$$
(18)

where is the voltage amplitude of the moment on the neutral line of the node; The maximum allowable value for the neutral line voltage.

  1. (3)

    Regulator tap constraints

The range of regulator with load-regulated pressure adjustment is limited, and its decomposition head gear cannot exceed the voltage-regulating range, i.e.:

$$T_{vol}^{min} \le T_{vol,t} \le T_{vol}^{max}$$
(19)

Type: for the split joint gear of the moment–time regulator transformer; and for the lower and upper limits of the on-load regulator transformer split joint gear.

  1. (4)

    Adjust critical load constraints

Considering the accuracy of the on-board tuning control strategy, the tuning critical load needs to be within the safe tuning range of i.e.:

$$P_{rate.cap}^{min} \le P_{real.cap,t} \le P_{rate.cap}^{max}$$
(20)
$$P_{real.cap} < \delta P_{rate.cap}$$
(21)
$$P_{rate.cap} = \left\{ {\begin{array}{*{20}c} {100,If\; T_{cap,t} = 0} \\ {300,If \;T_{cap,t} = 1} \\ \end{array} } \right.$$
(22)

In the formula: for the time period to adjust the actual capacity of the regulator transformer; and for the lower and upper limits of the capacity of the tuning regulator; Set the scale factor; Adjust the split joint gear for the time period.

  1. (5)

    Energy storage constraints

Considering the distributed photovoltaic grid-connected, there is a need for a power storage device for charge and discharge coordination, assuming that the energy storage is injected into the grid with positive power, i.e.:

$$P_{\varphi ,i}^{ESS} = \alpha_{1} P_{\varphi ,i}^{ESS,dis} + \alpha_{2} P_{\varphi ,i}^{ESS,cha}$$
(23)
$$\alpha_{1} + \alpha_{2} { = }1$$
(24)
$$\begin{aligned} SOC_{{\varphi ,i,t_{n} }}^{ESS} & = SOC_{{\varphi ,i,t_{0} }}^{ESS} - \frac{{\varepsilon_{in} \Delta t}}{{E_{ESS}^{cap} }}\sum\limits_{t^{\prime} = 1}^{t} {P_{\varphi ,i,t}^{cha} } - \frac{\Delta t}{{\varepsilon_{out} E_{ESS}^{cap} }}\sum\limits_{t^{\prime} = 1}^{t} {P_{\varphi ,i,t}^{dis} } \\ \end{aligned}$$
(25)

where for energy storage capacity; and for energy storage charge and discharge efficiency; for energy storage devices to the grid to inject total active power; b20 > / Phase nodes The initial charge state of energy storage; and the active power is absorbed/injected into the grid for energy storage.

There is an upper and lower limit on the SOC of the moment energy storage unit:

$$\forall t\left\{ {\begin{array}{*{20}c} { - P_{\varphi ,i}^{ESS,rated} < P_{\varphi ,i,t}^{ESS,cha} < 0} \\ {0 < P_{\varphi ,i,t}^{ESS,dis} < P_{\varphi ,i}^{ESS,rated} } \\ \end{array} } \right.$$
(26)
$$SOC_{\varphi ,i}^{ESS,min} < SOC_{\varphi ,i,t}^{ESS} < SOC_{\varphi ,i}^{ESS,max}$$
(27)
$$SOC_{{\varphi ,i,t_{0} }}^{ESS} = SOC_{{\varphi ,i,t_{n} }}^{ESS}$$
(28)

Medium: Rated power for the phase node energy storage unit; and is the maximum/small value of the energy storage state. The visual power output of the energy storage device needs to be less than the rated output visual power:

$${\text{S}}_{\varphi ,i,t}^{{{\text{ESS}}}} < S_{\varphi ,i}^{ESS,rated}$$
(29)
$$S_{\varphi ,i,t}^{ESS} = \sqrt {\left( {P_{\varphi ,i,t}^{ESS} } \right)^{2} + \left( {Q_{\varphi ,i,t}^{ESS} } \right)^{2} }$$
(30)

In: The energy storage device is the primary power of the phase node; the rating of the visual power of the energy storage device; The total reactive power injected into the power grid for the energy storage device.

  1. (6)

    Photovoltaic constraints

Considering the limited regulation of photovoltaic inelisity, it is necessary to constrain photovoltaic reactivity, i.e.:

$$Q_{\varphi ,i,t}^{PV} = \sqrt {(S_{\varphi ,i,t}^{PV} )^{2} - (P_{\varphi ,i,t}^{PV} )^{2} }$$
(31)
$$Q_{\varphi ,i,t}^{PV} < Q_{\varphi ,i}^{PV,rated}$$
(32)

In: the reactive power of the photovoltaic inverter for the first phase node of the moment; Active power for the photovoltaic inverter; Capacity for photovoltaic inverter; Is the first phase node /b116 > The maximum reactive power of the photovoltaic inverter.

  1. (7)

    Demand-side constraints

The demand-side response model is consistent with energy storage constraints. The amount of electricity used is equal to the amount of charge, and the movement of the electricity segment is the demand side response [15]. Don’t go into more detail here.

3.2 Control Within Days

The target of the inner-day control layer mentioned in this article is the gear of the reactive and tolerant disassoilation connector of the photovoltaic inverter.

  1. (1)

    Reactive power in PV systems

Photovoltaic reactive control uses the literature's variable slope sagging control model.

$$Q_{cor} = Q_{ref} + m_{i} (U_{no\_cor} - U_{ref} )$$
(33)
$$m_{i} { = }\frac{{2\sqrt {\left( {{\text{S}}^{PV.rate} } \right)^{2} - \left( {P^{PV.rate} } \right)^{2} } }}{{U_{upper} - U_{lower} }}$$
(34)

Type: for the day-to-day control phase of the modified photovoltaic reactive; for the uncorrected voltage; and for reactive and voltage optimization; For the sagging slope, rated capacity for photovoltaic inverters; Rated for photovoltaic inverters; and the maximum/small value for voltage scale values, generally 1.07 and 0.93.

According to the formula (33) and (34) the reactive control of the photovoltaic inverter is obtained, the control results of reactive control are obtained, and the new voltage amplitude change is measured.

  1. (2)

    Split joints in capacity regulating system

In order to ensure that the mating does not overload, the tuning dispensing connector must be modified in real time. And taking into account the infrequent action factors of the tuning switch, set: if the interval between two gear movements is less than 30 min do not act.

$$\sum\limits_{{t \in \mathfrak{I}}} {T_{cap,t} = 5} ,If T_{cap,t} + T_{cap,t + 6} = 2$$
(35)

where a collection of time for to. For example, the 25 min load is high, the tuning switch gear is in 1st gear, because the load fluctuates faster, the 26th min is offset by more photovoltaic force to offset some of the load, the load is lower, the switch gear action to 0th gear, and after 20 min, the switch moves again to 1st gear due to the increase in load. In this case, the set tuning switch does not move and remains in 1st gear from 25 min until the gear action after the next interval of 30 min.

According to the optimization results obtained by the optimization layer, the voltage change caused by photovoltaic fluctuations and load mutations is measured. As shown in Fig. 2.

Fig. 2
A flow chart flows from day ahead control to short-term regulation. It measures the voltage change caused by photovoltaic fluctuations.

Flow chart of day-ahead and intra-day control

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4 Control the Process and Solve the Method

Figure 2 is the distribution network day control—day control two-tier control flowchart. Before performing the optimization control, the distribution network parameters, load data and the net photovoltaic power need to be uploaded. After obtaining the distribution network information, the control layer has carried out the calculation of three-phase trend and optimal trend, and has been optimized to control the reference to the success. The reference values are then released to each control variable.

4.1 Control the Process

The specific steps of the control process are as follows:

S1: Upload distribution network parameters, load data and photovoltaic net power and so on;

S2: Get photovoltaic, load data;

S3: Formula (1) ~ (12) as the target function, formula (13) ~ (32) as a constraint, the optimal trend calculation of continuous variables;

S4: To carry out the optimization control of discrete variables, such as tuning the gear of the voltage-regulating dispenser;

S5: Output optimization variable results to each node;

S6: Measure real-time data;

S7: Photovoltaic reactive adjustment according to the formula;

S8: According to the formula for the tuning of the connector gear real-time correction;

S9: Measure new data;

S10: For each correction,. /b13 > When you restart measuring real-time data. Adaptive control strategies for variables.

4.2 Solution Methods

Through the embossed model, the non-convex nonlinear problem is converted into a simpler second-order cone planning problem. Since the ratio of positive to negative voltage is not a convex function, the pair(12)needs to be converted to:

In formula (16), the root number is removed after squared on both sides of the equation to further convex the formula. The resulting formula (16) can therefore be converted to:

$$\left| {I_{ij} (t)} \right|^{2} \le I_{ij}^{2}$$
(36)

The convexity of discrete variables differs from continuous variables, such as the 0–1 discrete variable switch for the tuning regulator, which requires binary expansion and large-M methods to maintain the convexity of the discrete variables [16, 17].

Finally, the convexity of the entire optimal trend calculation is guaranteed, and the optimal solution is obtained by solving using the CPLEX algorithm.

$$VUF_{i} = \frac{{U_{neg,i} }}{{U_{pos,i} }} \approx \frac{{U_{a,i} + \alpha^{2} U_{b,i} + \alpha U_{c,i} }}{{U_{\varphi } }}$$
(37)

5 Analysis

5.1 Background

This paper uses the actual model of a low-voltage distribution network in Bijie, Guizhou Province, to simulate the three-phase, four-wire network. Figure 3 is the network structure, and Fig. 4 represents the photovoltaic and load graph (Appendix A1). At the same time, after optimizing the control parameters through the established optimization model, the unnecessary reactive flow in the network can be avoided, thus reducing the network loss and ensuring the economy of the network operation. Rated at 380 V, line self-impedance and inter distorization parameters (Appendix A2). Distributed photovoltaic and energy storage access nodes (Appendix A3), single-phase photovoltaics are rated at 5 kW and photovoltaic inverters have a capacity of 1.1 times the active capacity of photovoltaics. A single energy storage unit is rated at 20 kWh with a maximum charge and discharge power of 4 kW per phase. This article uses a 315 kVA common transformer and a 100 (315) kVA tuning regulator transformer. To compare the effect of the—control strategy proposed in this article, control strategy is used to compare results.

Fig. 3
A low voltage distribution network for 21 nodes has users, a P V array, an energy storage system, and four phases with different colors, labeled from a to d.

21-node low-voltage distribution network

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Fig. 4
A graph has three lines, P V power, and equivalent load, original load, and P V power. It depicts time on the X-axis and P U on the Y-axis. All line exhibits downward trends.

PV and load unit value curves

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  1. (1)

    CS-1:Use the control methods proposed in the literature. The network frame structure model is consistent with this paper. The model simulation of three-phase four-wire system is carried out with network loss and three-phase unbalance as the target function. However, there is no tuning control technology, transformer overload on the economics of grid operation and intraday control strategy.

  2. (2)

    CS-2:That is, the two-stage control strategy of—control proposed in this paper. The control framework is shown in Fig. 3.

5.2 Power Substitution

In the actual operation of the power grid, the transformer operating power exceeds 80%of the rated power, and the transformer is determined to be overloaded. Figure 6a–d represent a graph of the voltage amplitude of 16 for the power and end nodes before and after the replacement of photovoltaics, electrical energy substitution.

As can be seen from Fig. 5, in the scene of no photovoltaic and power replacement, the transformer already has a long-term overload problem, which seriously affects the service life of the transformer and the safe operation of the power grid; In the photovoltaic, electrical energy replacement scene, due to photovoltaic grid-connected lead to reverse currents, transformer reverse overload and overload problems coexist, increasing the burden of distribution and transformation operation. Therefore, there is an urgent need for a low-voltage distribution network adaptive control strategy for distributed photovoltaics and power substitution.

Fig. 5
A set of four graphs depicts time on the X-axis. Graph a and b exhibits real power on the Y-axis and has four downward trend lines. Graph c and d depicts a voltage amplitude and has three upward trend lines.

Comparison chart of the outlet performance of a three-phase transformer

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Fig. 6
A graph has three lines, Phase a, b, and c, with time on the X-axis and voltage amplitude on the Y-axis. It depicts downtrends.

Voltage variation for node 16 under control strategy 1

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5.3 Optimization

This section mainly compares whether the three control methods in 4.1 can consider network loss, three-phase imbalance, transformer overload and voltage overstay in the context of power substitution and distributed photovoltaic grid, so as to ensure the economic operation of the power grid, the safe operation of the distribution transformer and the reliability of power supply.

Figure 5d is a voltage graph of 16 nodes without control, which is most prone to overvoltage and undervoltage because it is the last point of the network structure. In the noon period, the photovoltaic output power is significantly higher than the load power, there is a serious overvoltage problem in the network, in the evening period, there is no photovoltaic output, the load power reaches the peak of electricity consumption, so that the network has the problem of undervoltage. The three-phase imbalance is much higher than the 2%required by the grid. It is not economical and safe to operate the power grid, so control policies must be adopted to optimize control. Optimization control based on CS-1 gives a voltage graph of 16 nodes as shown in Fig. 6. There was no voltage oversizing problem, and the three-phase imbalance was much lower than 2%, but the heavy overload and loss of the distribution transformer was not considered. Using CS-1 makes it difficult to balance mismatch with load and optimal economic benefits.

Using the previous optimization control strategy proposed by CS-2, the problems of network loss, transformer loss, three-phase imbalance and voltage overshoot are considered, and the PV inverter is the control variable with no function, energy storage, and regulated voltage switch, and Figs. 7, 8 and 9 are used to get the optimization results according to the load curve. After the control, the grid loss and three-phase imbalance of the three control schemes are shown in Table 1.

Fig. 7
A graph has three lines, Phase a, b, and c, with time on the X-axis and voltage amplitude on the Y-axis. It depicts downward trends.

Voltage variation for node 16 under control strategy 2

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Fig. 8
A line graph depicts time on the X-axis, and the switch position on the Y-axis range from minus 1 to 1. The trends are increasing, decreasing, and stable.

Optimal day-ahead operation with switch control

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Fig. 9
A graph has two lines intra-day schedule and day ahead schedule with time on the X-axis and the switch position on the X-axis. The line has increasing, decreasing, and stable trends.

Short-term regulation with intra-day schedule

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Table 1 Target function indexes under different control schemes
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As can be seen from Table 1, CS-2 not only reduces system loss by 32.1% compared to CS-1, but also has a smaller three-phase imbalance. Explain that CS-2 guarantees good economic benefits while ensuring safe operation of the matching.

5.4 Daily Control Scheme

This section describes the intraday control strategy proposed by CS-2 to adjust switches, photovoltaic inactivity as control variables to prevent overweight and system voltage disturbances. Figure 9 is a real-time correction diagram of the tuning of the split joint gear. Recently optimize the consideration of operating economy, day control consider equipment safety. The intraday control tuning switch action threshold is higher than the previous optimization threshold, taking into account the non-essential action rules for tuning. Therefore, the daytime control phase switch does not necessarily move when the switch action is optimized.

As can be seen from Figs. 10 and 11, voltage overshoots and fluctuations can be suppressed and power distribution transformers can be prevented from overloading and burning accidents through photovoltaic reactive control and tuning of the dispenser gear correction. As can be seen from Figs. 12 and 13, the a-phase voltage of node 16(the very end) is more close to the a-phase voltage curve optimized for the day. And set the adjustment split joint action rules, reduce unnecessary switching action. Therefore, the in-day control strategy proposed in this paper, while ensuring that the matching does not overload, suppresses voltage fluctuations, reduces network operating losses, and extends the service life of the toned dispenser, as shown in Table 2 (the voltage deviation ratio is the percentage difference between the voltage before and after the correction and the previous optimized voltage).

$$U_{dev} = \sum {\left| {U_{ref} - U_{cor} } \right|} \times 100\%$$
(38)
$$U_{flu} = \sum {\left| {\frac{{U_{t} - U_{t + 1} }}{{U_{n} }}} \right|} \times 100\%$$
(39)
Fig. 10
A graph has three lines labeled a, b, and c with time on the X-axis and voltage amplitude on the Y-axis. It depicts downward trends.

Voltage variation for node 16 after regulation

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Fig. 11
A graph has three lines labeled a, b, and c with time on the X-axis and voltage amplitude on the Y-axis. It depicts fluctuating downward trends.

10 Voltage variation for node 16 before regulation

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Fig. 12
A graph has four lines labeled optimal values in the day-ahead schedule, values before and after regulation, and interference with time on the X-axis and voltage amplitude on the Y-axis. It exhibits fluctuating trends.

Voltage variation of phase a at node 16 under CS-2 (over 24 h)

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Fig. 13
A graph has four lines labeled day-ahead optimal value, before and after regulation, and interference, with time on the X-axis and voltage amplitude on the Y-axis. It exhibits downward trends.

Voltage variation of phase a at node 16 under CS-2 (from 11:00 to 13:00)

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Table 2 Parameters comparison of node 16 under CS-2
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In: for voltage deviation rate; for correction of voltage amplitude before and after control; for voltage volatility; For the voltage amplitude of the moment; Represents a voltage amplitude of 1.0.

6 Conclusions

This paper has proposed a two-stage control strategy by combing day-ahead and in-day control schemes. The main contributions of the study include three aspects as follows:

  1. (1)

    In the optimization stage, under the scenario of power substitution and distributed photovoltaic grid-connected, taking into account the key issues such as network loss, three-phase imbalance, voltage overstaying limit, transformer overload, a collaborative optimization control strategy is proposed to consider the corresponding co-optimization control strategy of tuning regulator transformer, energy storage, photovoltaic inverter and demand side, and proves that the control strategy proposed in this paper is more comprehensive, more effective and reliable. During the day-to-day control phase, the short-term correction strategy of tuning switch and photovoltaic inverter is adopted to deal with the problem of weight overload and voltage rapid disturbance caused by photovoltaic uncertainty and load fluctuation in time. The voltage fluctuates rapidly while ensuring that the match does not burn.

  2. (2)

    With the goal of reducing loss, three-phase imbalance and ensuring the safe operation of the matching, two-stage optimization control method is proposed. The proposed scheme loses 32.1% less power than the CS-1 control scheme.

  3. (3)

    Because the tuning regulator technology does not adapt to all the application scenarios, so in view of the weak network frame, long power supply radius, small wire diameter of the power supply scene, consider combining low voltage AC DC technology and tuning voltage control technology, to solve the end user low voltage, load fluctuations and high network loss problems.