Voltage Optimization Method for Port Power Supply Networks

Abstract

Increasing renewable energy penetration exacerbates voltage violation in integrated port power supply networks (IPPSNs). The technique of flexible connectivity based on soft open points (SOPs) could improve the controllability and voltage stability of the network. However, the generally used voltage control of SOPs may be too sluggish to accommodate the frequent voltage fluctuations and requires further investigation. This chapter proposes a real-time model predictive control (MPC)-based voltage optimization method for SOPs in IPPSNs. Combining the sensitivity analysis and the operational constraints of the network with SOPs, a localized real-time optimization model is established. With the rolling of the control horizon, the SOPs regulate the voltage and optimize the power flow at a time scale of seconds. Using simply the voltage at the connected node of the SOPs, the proposed method can significantly enhance the voltage stability of the IPPSNs and decrease power losses under the rapid fluctuations of the network voltage. To further improve the performance of voltage control, the optimization model is modified through feedback correction. The case studies demonstrate the effectiveness of the proposed method under different scenarios.

6.1 Introduction

Increasing penetration of renewable energy and electrification of logistics transport in port can reduce carbon emissions in integrated port power supply networks (IPPSNs) but exacerbating overvoltage issues [1,2,3]. A sharp fluctuation of feeder power and severe voltage violation frequently happens due to the constantly changing distributed power supply and the random access of electric vehicle charging [4]. The overvoltage problems of IPPSNs are more serious when extreme weather events or faults happen [5, 6]. To enhance the voltage stability of IPPSNs and ensure power supply to critical loads, it is of great significance to optimize the voltage of IPPSNs.

Port distribution networks could regulate conventional primary devices such as capacitor banks (CBs), series voltage regulators (SVRs), and on-load tap changers (OLTCs) to reduce voltage violation. It is difficult for conventional regulation methods to cope with rapid power flow changes in IPPSNs due to the slow response and discrete output [7, 8]. Most researches focus on managing the distributed generations or electric vehicles to make full use of their high controllability. Bai [9] and John [10] introduced a voltage regulation method to keep the nodal voltages within the limit with the controlled DG power curtailment. Ma [11] developed a decentralized voltage regulation method by adjusting the active and reactive power of each photovoltaic plant. Gusrialdi [12] and Hou [13] proposed scheduling algorithm to coordinate the charging behavior of electric vehicles and improve the utilization of charging resources on highways. However, the above studies are limited in that they do not modify the power flow distribution throughout the IPPSNs.

Soft open points (SOPs) are power electronic devices that interconnect two feeders as a replacement for normally-open points and can realize the flexible connection between feeders. Recently, SOPs are widely used in active distribution networks to optimize the power flow [14]. The voltage profiles of IPPSNs can be significantly improved using the voltage control strategy of SOPs. Ji [15] and I. Sarantakos [16] have studied the capacity support and optimization method of SOPs to improve the robustness and reliability of the distribution network. Literature [17] proposes a two-layer control strategy for SOPs in low-voltage distribution networks considering both the system layer and the equipment layer. According to the time scale, voltage optimization approaches for SOPs involvement in distribution networks are separated into long-time optimization methods and real-time optimization methods. The long-time optimization approach usually utilizes global system information for modeling and calculation. Literature [18] applies semidefinite programming (SDP) relaxation to the optimization model to realize rapid three-phase imbalance mitigation in distribution systems. The long-time optimization result is close to the theoretical global optimum but the optimization interval is too long to accommodate the frequent voltage fluctuations. Real-time optimization methods can regulate the power transmission of SOPs within a short time scale. Literature [19] proposes a coordinated scheduling method including fast-timescale scheduling which optimally coordinates the active and reactive power of SOPs. The real-time control for SOPs is usually implemented based on local information such as the bus voltage at each port of SOPs. Literature [20] and [21] use droop control methods to realize real-time local control of SOPs.

Model predictive control (MPC) based on rolling optimization can actively adjust the control strategy when voltage fluctuations occur to maintain the optimization effect [22]. Literature [23] proposes an MPC-based voltage control strategy for DGs that regularly tunes the parameter of local Q–V control curves to achieve better response to frequent voltage fluctuations. Literature [24] proposes a double-time-scale voltage control scheme using MPC to regulate the voltage profile across a network. MPC can effectively cope with the voltage violation problems in IPPSNs and improve real-time control performance.

Combining port grid topology with long-term measurement data to obtain port grid voltage and line loss sensitivity, a model for predicting distribution network voltage and line loss is developed. A real-time optimal control model is proposed, which aims to minimize the voltage deviation as well as the power losses. The active and reactive power transmission of the SOPs is optimized by the MPC approach and the predictive model is corrected through timely feedback.

The main contribution of this chapter is to propose an MPC-based real-time voltage optimization method for SOPs that does not rely on the global information of IPPSNs to reduce the impact of the distributed generation output uncertainty and load fluctuations on the node voltage. SOPs are optimally controlled considering both the voltage level and line loss, thus increasing operational efficiency during the normal situation and ensuring voltage levels under abnormal conditions.

6.2 Power Supply Networks with SOPs

6.2.1 IPPSNs Structure

IPPSNs provide electricity to the port logistics system and surrounding customers with a radial structure. In IPPSNs, more distributed generators (DGs) and charge stations for electric vehicles are installed to meet the demands of the economy and reduce carbon emissions. Meanwhile, increased energy storage and power electronics components have been introduced to the power supply networks in order to enable accurate voltage control. The grid topology of IPPSNs is usually operated in a radial configuration which is similar to that of the traditional distribution networks. Certain loads such as toll gates and charging infrastructures, are highly crucial and require superior power quality. The DGs are sometimes located far away from the heavy load, making it difficult for them to achieve a partial power balance between generation and loads. This would cause more severe overvoltage issues in certain regions. Furthermore, the power quality of these substantial loads cannot be guaranteed under certain extreme situations, posing a threat to IPPSNs.

The voltage violation at the end of the feeder tends to be severe considering the distance to the source node of IPPSNs. By integrating SOPs, the distribution network can transfer power between different feeders and realize fast and continuous power flow control to mitigate voltage deviation and reduce power losses of whole networks. The SOPs could be installed close to the important loads or DGs to achieve a better optimization effect. It can effectively balance out the power variations caused by renewable energy and lessen the effect on the distribution network’s voltage. A typical structure of IPPSNs with SOPs is shown in Fig. 6.1.

Fig. 6.1

Typical structure of IPPSN with SOPs

IPPSNs can flexibly control various equipment to realize synergistic interaction between distributed power and dynamic loads. However, simply employing the global optimization strategy cannot be sufficient to prevent voltage violation due to the high uncertainty of distributed generators and electric vehicle charging. The localized real-time control method with SOPs is necessary to enhance the voltage opt imitation effect and ensure power quality.

6.2.2 Structure and Operating Principle of the SOPs

SOPs can regulate the power flow of connected feeders within a microsecond time scale. The typical structure of SOPs is shown in Fig. 6.2.

Fig. 6.2

Typical structure and application of SOPs

By utilizing SOPs, IPPSNs are able to create a flexible connection between feeders with SOPs while the active and reactive power flow is fully controlled with fast adjustment capability. The transmission power of SOPs may be determined by the control center or computed utilizing local control techniques.

Considering the operating principle of SOPs, the power transmission constraint for each port of SOPs can be expressed as:

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\sqrt {P_{m}^{2} + Q_{m}^{2} } \le S_{{{\text{sop}}}}^{2} } \\ {\sqrt {P_{n}^{2} + Q_{n}^{2} } \le S_{{{\text{sop}}}}^{2} } \\ \end{array} } \right.} \\ \end{array}$$

(6.1)

The active and reactive power transmissions of SOPs can be controlled separately. To accomplish timely optimization for IPPSNs, a localized real-time control technique is proposed in this chapter. The performance of real-time control of SOPs is constrained by capacity limitations. By simultaneously adjusting the active and reactive power transmission of SOPs, the potential benefits of SOPs are further explored.

The switching loss of SOPs cannot be ignored though the loss is small relative to the transmission power. Note that the SOPs are connected between node m and node n. For convenience, the active power transmission of SOPs could be marked as $P = P_{m} = - P_{n}$ ignoring the transmit losses. The switching loss is related to the transmission capacity and can be written as Eq. (6.2).

$$\begin{array}{*{20}c} {P_{{{\text{sloss}}}} = k_{{{\text{sloss}}}} \left( {\sqrt {P^{2} + Q_{m}^{2} } + \sqrt {P^{2} + Q_{n}^{2} } } \right)} \\ \end{array}$$

(6.2)

6.3 The MPC-Based Voltage Optimization Method

6.3.1 Voltage and Power Losses Model

A sensitivity matrix is introduced to develop a prediction model for the distribution network’s voltage and power losses. A linear prediction model is developed for voltage and line loss changes arising from node power injection alterations. When the injected power of the distribution network line changes slightly, it will only affect the voltage distribution on this branch ignoring the higher-order error term [25, 26].

The power losses of the distribution network are shown in Eq. (6.3).

$$\begin{array}{*{20}c} {P_{{{\text{loss}}}} = \mathop \sum \limits_{j \in L} R_{j} \left( {\frac{{\left( {P_{j}^{2} + Q_{j}^{2} } \right)}}{{U_{j}^{2} }}} \right)} \\ \end{array}$$

(6.3)

Using (6.3) and first-order Taylor expansion, we have the power loss variation shown as (6.4).

$$\begin{array}{*{20}c} {\Delta P_{{{\text{loss}}}} = \mathop \sum \limits_{{j \in L_{i}^{path} }} \frac{{R_{j} \left( {2\Delta P \cdot P_{j} + \Delta P^{2} + 2\Delta Q \cdot Q_{j} + \Delta Q^{2} } \right)}}{{U_{j}^{2} }}} \\ \end{array}$$

(6.4)

The sensitivity of line losses to active power and reactive power $\frac{{\partial P_{{{\text{loss}}}} }}{\partial P}$ and $\frac{{\partial P_{{{\text{loss}}}} }}{\partial Q}$ can be written as (6.5) and (6.6).

$$\begin{array}{*{20}c} {\frac{{\partial P_{{{\text{loss}}}} }}{\partial P} = 2\Delta P\mathop \sum \limits_{{j \in L_{i}^{path} }} \frac{{R_{j} }}{{U_{j}^{2} }} + 2\mathop \sum \limits_{{j \in L_{i}^{path} }} \frac{{P_{j} \cdot R_{j} }}{{U_{j}^{2} }}} \\ \end{array}$$

(6.5)

$$\begin{array}{*{20}c} {\frac{{\partial P_{{{\text{loss}}}} }}{\partial Q} = 2\Delta Q\mathop \sum \limits_{{j \in L_{i}^{path} }} \frac{{R_{j} }}{{U_{j}^{2} }} + 2\mathop \sum \limits_{{j \in L_{i}^{path} }} \frac{{Q_{j} \cdot R_{j} }}{{U_{j}^{2} }}} \\ \end{array}$$

(6.6)

Assuming that the node voltage is the rated voltage $V_{0}$, , the node voltage variation can be written as (6.7).

$$\begin{array}{*{20}c} {\Delta V_{i} = \frac{{\Delta P\mathop \sum \nolimits_{{j \in L_{i}^{p} }} R_{j} + \Delta Q\mathop \sum \nolimits_{{j \in L_{i}^{p} }} X_{j} }}{{V_{0} }}} \\ \end{array}$$

(6.7)

The node voltage’s sensitivity to injected power changes can be determined using only the feeder voltage and the distribution network impedance. Sensitivity of node voltage to active power and reactive power can be written as (6.8) and (6.9).

$$\begin{array}{*{20}c} {\frac{{\partial V_{i} }}{\partial P} = \mathop \sum \limits_{{j \in L_{i}^{p} }} \frac{{R_{j} }}{{V_{0} }}} \\ \end{array}$$

(6.8)

$$\begin{array}{*{20}c} {\frac{{\partial V_{i} }}{\partial Q} = \mathop \sum \limits_{{j \in L_{i}^{p} }} \frac{{X_{j} }}{{V_{0} }}} \\ \end{array}$$

(6.9)

The sensitivity matrix is dependent on the operational state of the distribution network, and changes are not discernible in the presence of local disturbances. The voltage and line loss prediction models are established as the foundation of real-time model prediction control, and the sensitivity matrix is calculated using the electrical quantities of the distribution network at a specific time section and does not require frequent updates.

The control variables of the voltage and loss prediction model at time $t_{0}$ are denoted as (6.10). The prediction model of voltage and line loss can be written as (6.11) and (6.12).

$$\begin{array}{*{20}c} {\Delta u\left( {t_{0} } \right) = \left[ {\Delta P\left( {t_{0} } \right),\Delta Q_{n} \left( {t_{0} } \right),\Delta Q_{m} \left( {t_{0} } \right)} \right]} \\ \end{array}$$

(6.10)

$$\begin{array}{*{20}c} {V\left( {t_{0} + t{|}t_{0} } \right) = V\left( {t_{0} + t - 1{|}t_{0} } \right) + \frac{\partial V}{{\partial u}}\Delta u\left( {t_{0} + t - 1} \right)} \\ \end{array}$$

(6.11)

$$\begin{array}{*{20}c} {P_{loss} \left( {t_{0} + t|t_{0} } \right) = P_{loss} \left( {t_{0} + t - 1|t_{0} } \right) + \frac{{\partial P_{loss} }}{\partial u}\Delta u\left( {t_{0} + t - 1} \right)} \\ \end{array}$$

(6.12)

6.3.2 IPPSNs Voltage Optimization Model

The proposed real-time voltage optimization method in this chapter is a local control method that only uses the information from the connected node of the SOPs. The real-time voltage control method proposed in this chapter is a local control method that is based on the operating state of the SOPs for rolling horizon optimization (Fig. 6.3).

Fig. 6.3

Real-time voltage optimization method in IPPSNs

To assure the correctness of the prediction model, the optimization process predicts the changes in node voltage and network losses. The active and reactive power transmitted by the SOPs are controlled simultaneously and the prediction model is corrected via feedback correction.

The voltage control method proposed in this chapter is a local control method, which is based on the real-time voltage of the nodes at both ends of the SOPs and the working state of the SOPs for rolling optimization. The real-time optimization objective function is shown as follows.

$$\begin{array}{*{20}c} {\min :f = \mathop \sum \limits_{t = 1}^{{N_{p} }} \left[ {\Delta C_{{\text{ope,i}}} + \alpha \Delta C_{{\text{loss,t}}} } \right]} \\ \end{array}$$

(6.13)

$$\begin{array}{*{20}c} {\Delta C_{{{\text{ope}},t}} = P_{p} \Delta P_{t}^{2} + P_{q} \Delta Q_{m,t}^{2} + P_{q} \Delta Q_{n,t}^{2} } \\ \end{array}$$

(6.14)

$$\begin{array}{*{20}c} {\Delta C_{{{\text{loss}},t}} = P_{l} \left( {\frac{{\partial P_{{{\text{loss}}}} }}{{\partial P_{m} }}\Delta P_{t} - \frac{{\partial P_{{{\text{loss}}}} }}{{\partial P_{n} }}\Delta P_{t} + \frac{{\partial P_{{{\text{loss}}}} }}{{\partial Q_{m} }}\Delta Q_{m,t} + \frac{{\partial P_{{{\text{loss}}}} }}{{\partial Q_{n} }}\Delta Q_{n,t} } \right)} \\ \end{array}$$

(6.15)

The line loss coefficient will be reduced when the voltage deviation $V_{dev}$ is larger by controlling the value of the line loss coefficient α. By adjusting the line loss coefficient value in the objective function, the optimal function is modified to ensure that the node voltages at both ends of the SOPs operate within the ideal range.

$$\begin{array}{*{20}c} {\alpha = e^{{ - k_{v} V_{{{\text{dev}}}} }} } \\ \end{array}$$

(6.16)

Using voltage restrictions as Eq. (6.17), the node voltage at both ends of the SOPs is constrained:

$$\begin{array}{*{20}c} {V^{\min } \left( {k + i} \right) \le V\left( {k + i|k} \right) \le V^{\max } \left( {k + i} \right)} \\ \end{array}$$

(6.17)

In order to guarantee that the optimization model has a solution, a voltage asymptotic constraint is implemented when the voltage fluctuation is too large to be adjusted to the target range in a single interval.

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {V^{\min } \left( {k + i} \right) = \left( {1 - \frac{N - i}{{\rho N}}V^{\min } } \right)} \\ {V^{\max } \left( {k + i} \right) = \left( {1 + \frac{N - i}{{\rho N}}V^{\max } } \right)} \\ \end{array} } \right.} \\ \end{array}$$

(6.18)

Considering the operating limit, the power transmission constraint for SOPs of each time step can be written as:

$$\begin{array}{*{20}c} {\Delta P_{i} \le \Delta P_{\max } } \\ \end{array}$$

(6.19)

$$\begin{array}{*{20}c} {\Delta Q_{i} \le \Delta Q_{\max } } \\ \end{array}$$

(6.20)

To boost the predictive accuracy of the grid voltage and line loss prediction model, the real-time control must adjust the prediction model for the current round based on the previous round’s prediction control deviation. This is due to the ever-changing operational status of the distribution network.

If the operation state of the distribution network is stable, the deviation caused by the change in the working state of other nodes of the distribution network is disregarded. And the network loss sensitivity is corrected according to the change in SOPs’ working state, as shown in Eqs. (6.21) and (6.22).

$$\begin{array}{*{20}c} {\frac{{\partial \Delta P_{{{\text{loss}}}} }}{\partial \Delta P}\left( {t_{0} + 1} \right) = \frac{{\partial \Delta P_{{{\text{loss}}}} }}{\partial \Delta P}\left( {t_{0} } \right) + \frac{{\Delta P\left( {t_{0} } \right) \cdot R_{b} }}{{U_{0}^{2} }}} \\ \end{array}$$

(6.21)

$$\begin{array}{*{20}c} {\frac{{\partial \Delta P_{{{\text{loss}}}} }}{\partial \Delta Q}\left( {t_{0} + 1} \right) = \frac{{\partial \Delta P_{{{\text{loss}}}} }}{\partial \Delta Q}\left( {t_{0} } \right) + \frac{{\Delta Q\left( {t_{0} } \right) \cdot R_{b} }}{{U_{0}^{2} }}} \\ \end{array}$$

(6.22)

In the actual control process, a feedback correction is introduced in the voltage prediction control while the actual voltage of the distribution network is used as the initial value for a new round of rolling optimal scheduling, constituting a closed-loop voltage control, and the prediction model is corrected according to the control deviation of the previous round to improve the prediction accuracy of the voltage prediction model, as shown in Eqs. (6.23) and (6.24).

$$\begin{array}{*{20}c} {\Delta V_{{{\text{err}}}} \left( {t_{0} + 1} \right) = V\left( {t_{0} + 1} \right) - V\left( {t_{0} + 1|t_{0} } \right)} \\ \end{array}$$

(6.23)

$$\begin{array}{*{20}c} {V^{\prime}\left( {t_{0} + 1 + t{|}t_{0} + 1} \right) = V\left( {t_{0} + t{|}t_{0} + 1} \right) + \frac{\partial V}{{\partial u}}\Delta u\left( {t_{0} + t} \right) + \rho_{v} V_{{{\text{err}}}} \left( {t_{0} + 1} \right)} \\ \end{array}$$

(6.24)

At this point, the proposed optimization method can be solved quickly by commercial software.

6.4 Implementation of MPC-Based Voltage Optimization Method with SOPs

To cope with the constantly changing distributed power supply and the random access of electric vehicle charging, a real-time voltage optimization control method employing MPC is proposed in this chapter. The flow chart of the MPC-based real-time voltage optimization method is shown in Fig. 6.4.

Fig. 6.4

The flowchart of MPC-based voltage optimization method

The voltage and power losses sensitivity matrix are calculated and the prediction model is established using long-time information of IPPSNs. The initial value of the optimization model is set as the actual active and reactive power transmission of the SOPs. The objective function aims to minimize the operating costs of SOPs and power losses of IPPSNs. In the phase of real-time voltage optimization, the active and reactive power transmission of the SOPs is continuously modified to meet the voltage limit. A sequence of control variables in the next Np intervals is solved and the first command of the control variable sequence is issued as the active and reactive power transmission command of the SOPs.

The prediction model is corrected during the optimization process. The SOPs could measure the voltage from the connected node and the prediction error is considered as the correction amount. Thus, the MPC-based voltage optimization method can perform better on voltage improvement and power loss reduction.

The distribution network optimization level is evaluated by the network voltage deviation after completing the voltage optimization as shown in Eq. (6.25).

$$\begin{array}{*{20}c} {V_{dev} = \mathop \sum \limits_{t = 1}^{N} \left| {V_{i} - 1} \right|:\left( {V_{t} \ge \overline{V}_{{{\text{thr}}}} \parallel V_{t} \le \underline {V}_{{{\text{thr}}}} } \right)} \\ \end{array}$$

(6.25)

6.5 Case Studies

In this section, the case study of the proposed voltage optimization strategy is verified on a port power network in Zhejiang, China. The structure of the case is shown in Fig. 6.5. The simulation is performed in MATLAB software and the optimization solution is performed using YALMIP [27]. The numerical experiments were carried out on a computer with an Intel Core i5-13600 K running at 3.50 GHz and 32 GB of RAM.

Fig. 6.5

Structure of the modified IPPSNs system

The port power supply network system is a typical IPPSN that has a large installed DG capacity and frequent low-voltage phenomena at the end nodes. The IPPSN system includes a substation and 34 branches, of which the rated voltage level is 10 kV. The system contains 5 PV plants with 350 kVA capacity and 4 charging points with 200 kVA installed. An SOP with 500 kVA capacity is installed between nodes 14 and 35 to replace the existing switch. Several toll stations and other electrical loads are located separately in the network.

The loss factor of SOPs is set to 0.02 [28]. The ideal voltage operating range is [0.98 p.u., 1.02 p.u.] and the safe voltage operating range is [0.90 p.u., 1.10 p.u.] [29]. Set each time interval $t$ to 30 s and the total number of time intervals in the solving horizon $N_{p}$ to 3 rounds. The sampling time interval of voltage measurement is set as 30 s.

6.5.1 Analysis of All-Day Operation Scenario

Considering the fluctuating distributed power supply and random access of electric vehicles, a case of a typical day of IPPSN is studied in this section. Figure 6.6 shows the daily DG and load operation curves.

Fig. 6.6

Operation curves of DG and load

Figures 6.7 and 6.8 depict the voltage profiles of IPPSN before and after optimization, respectively. High-penetration PV units lead to frequent voltage fluctuations and voltage deviations. When the load reaches its peak, there is a considerable drop in network voltage. SOP could supply reactive power to support voltage and decrease the active power transmission when the node voltage is less than the lower limit. Noting that the PV power output peak coincides with the load power drop at 12:00 a.m. and causes voltage rise in some areas, the optimization strategy could reduce the reactive power injected into the bus. The nodes connected to SOP could basically remain at ideal voltage during the day while the proposed voltage optimization method is applied to the IPPSN.

Fig. 6.7

Voltage profiles of all nodes before optimization

Fig. 6.8

Voltage profiles of all nodes after optimization

Figure 6.9 shows the maximum and minimum system voltages before and after optimization. By voltage optimization, the proposed MPC-based real-time SOP control method has significant improvement effects on the voltage profile (Table 6.1).

Fig. 6.9

Maximum and minimum system voltages

Table 6.1 Optimization results before and after optimization

When the distributed power supply and electric vehicle charging fluctuates in the distribution network, the real-time optimization control method changes the transmitted active power and reactive power simultaneously through SOP to ensure the voltage of the distribution network operates within the acceptable range. The voltage deviation of the IPPSN is reduced by 38.92% and the network power losses are reduced by 4.09%.

6.5.2 Analysis of Comparison Study Under Abnormal Scenarios

In order to evaluate the effectiveness of the suggested strategy, the optimization of SOP is realized by 4 different methods in this section.

Method 1: IPPSN contains no SOP.

Method 2: A long-time scale optimization method with no real-time control strategy is conducted on SOP. M1’s purpose is to reduce the voltage deviation and line loss of the IPPSN while SOP operates in a centralized control mode. Every 30 min, the power transmission command of SOP is optimized.

Method 3: Utilizing long-term scale optimization and droop control to modify SOP’s reactive power transfer. Method 2 is a modified version of Method 1 that applies real-time droop control to the reactive power of the SOP as a supplement. Every 30 min, the active power transmission command of SOP is optimized, whereas the reactive power transmission command of SOP is updated every 30 s.

Method 4: The MPC-based optimization method proposed in this chapter. Method 4 is a modified control method based on Method 1 and the active and reactive power transmission command of SOP is optimized every 30 s.

In this case, the PV unit connected to bus 10 appears to be unscheduled offline and re-connects to the system after a few minutes (Figs. 6.10, 6.11 and 6.12).

Fig. 6.10

Voltage profiles of all nodes with Method 4

Fig. 6.11

Voltage curves of node 14 during the optimization

Fig. 6.12

Transmission power curves of SOP of Method 4

When the distributed power supply and electric vehicle charging fluctuates in IPPSN, the real-time optimization control technique simultaneously modifies the transmitted active power and reactive power via SOP to maintain the distribution network’s voltage within an acceptable range. Table 6.2 presents the optimization results of 4 different methods with unplanned PV off-grid.

Table 6.2 Optimization Results of Different Methods with unplanned PV off-grid

The optimization results show that Method 2 using centralized optimization can reduce the power losses and voltage deviations of the distribution network during normal operation, but cannot reduce the voltage deviation when a fault occurs. Method 3 applies droop control to SOP for real-time control and the node voltage deviation is larger and out of the ideal range. The optimization results of Method 2 and Method 3 show that Method 3 has a certain ability to maintain the node voltage during line faults, but cannot guarantee that the voltage is maintained near the ideal operating range. Method 4 introduces real-time optimization based on MPC and enables a rapid response when a fault occurs and supports the node voltage to return to normal levels. The node 14 voltage optimized by Method 4 rises rapidly after the PV is off-grid and is closer to the ideal voltage range [0.98 p.u., 1.02 p.u.] during the off-grid process. The voltage deviation under the control of Method 3 is 5.9267 p.u. while the voltage deviation of Method 4 is 4.6772 p.u.

After the PV is reconnected to the grid, the node voltages at both ends of the SOP optimized by Method 4 basically operate within the ideal voltage range, and the node voltages quickly recover to the optimal level with the optimization objective of minimizing network losses.

To verify the effect to the randomness of PV units’ power output, a case with PV power fluctuation at node 4 and node 13 due to cloud cover within 60 min is studied. The optimization results of 4 different methods are listed in Table 6.3.

Table 6.3 Optimization results of different methods

Comparing the optimization results of Method 1 and Method 2, it can be seen that after the centralized optimization control, the active power loss and voltage deviation of the IPPSN system can be effectively reduced. The comparison between the optimization results of Method 2 and Method 3 shows that the voltage deviation and the power losses of the IPPSN system are reduced while the droop control is introduced. Method 4 could further reduce the voltage deviation of the distribution network by 34.7% compared to Method 3, but the power loss of IPPSN increases slightly.

6.5.3 Analysis of Multiple SOPs Installed

A case study is conducted on an IPPSN with two SOPs to further explore the scalability and performance of the proposed MPC-based voltage optimization approach. The IPPSN structure is similar to Fig. 6.5 while an additional SOP with 500 kVA capacity is installed between bus 25 and bus 31. The daily DG and load operation curves are given in Fig. 6.13.

Fig. 6.13

Voltage profiles of all nodes after optimization with multiple SOPs

The optimization results of the IPPSN system with multiple SOPs are given in Table 6.4. This case demonstrates the scalability and effectiveness of the proposed voltage optimization method with multiple SOPs. When the distributed power supply and electric vehicle charging fluctuates in the distribution network, the real-time optimization control with two SOPs could significantly improve the efficiency and voltage stability of the IPPSN. The voltage deviation of the IPPSN is reduced by 60.79% and the network power losses are reduced by 5.39% compared to no optimization. The network losses are reduced by 35.79% and the network power losses are reduced by 1.35% compared to one SOP installed in STPSN.

Table 6.4 Optimization results before and after optimization with multiple SOPs installed

The reasons for efficiency increase mainly include: (1) Multiple SOPs having much more active power transmit and reactive power supply ability when needed. (2) The proposed voltage optimization method could work without cooperation between different SOPs. However, the bound voltage improvement of installing two SOPs to IPPSN is not apparent compared to a single SOP installed. The possible reasons are: (1) The SOPs are not installed in the same area thus there is no additional power supplement for the focus area. (2) The interaction between different SOPs has an effect on the optimization.

6.6 Conclusion

An MPC-based voltage optimization approach for port power supply networks with SOPs is proposed to address the problem of voltage overrun. It only requires the collection of electrical information from the nodes connected to the SOPs throughout the optimization process. The proposed method could actively change the control strategy when voltage variations occur, effectively lowering the amplitude of voltage fluctuations. By simultaneously regulating the active and reactive power transmitted by the SOPs, the proposed method maximizes the SOP’s ability meanwhile ensuring the system voltage runs within the desired range. Different case results demonstrate that the proposed method efficiently eliminates voltage deviations and reduces power losses when PV output power fluctuates or unplanned off-grid operation occurs. It can significantly minimize the voltage deviations of distribution network nodes compared with conventional optimization techniques and regulate the DG volatility in IPPSNs. By simultaneously modifying the active and reactive power transmission of SOPs, the potential advantages of SOPs are investigated further.