Optimal Scheduling of Extreme Operating Conditions in Islanded Microgrid Based on Model Predictive Control

Abstract

To address the optimal scheduling of islanded microgrids under extreme operating conditions, this paper proposes a demand response (DR) economic optimization scheduling strategy based on model predictive control (MPC). The strategy improves the utilization of photovoltaic (PV) and energy storage systems while ensuring stable power supply to critical loads through a dynamic load shedding approach based on load priority and power system constraints. By incorporating time-of-use electricity pricing and load importance assessment, an innovative demand response incentive policy is designed to optimize consumer behavior and reduce grid load pressure. Experimental results demonstrate that the DR-MPC-based method reduces operating costs and increases renewable energy utilization compared to traditional methods. This approach is broadly applicable to pre-emptive load shedding and energy storage optimization in islanded microgrids during emergencies and is expected to be extended to the optimal scheduling of microgrid clusters in the future.

1. Introduction

Remote mountainous areas and villages are scattered, and far from the primary grid, with long transmission distances. They are prone to geological disasters such as landslides, leading to faults in the main grid transmission lines. In recent years, with the development and widespread application of renewable energy, microgrids have rapidly developed due to their flexible regulation capabilities, which can be independent of the main grid and form an island mode to achieve self-sufficiency [1,2,3].

Microgrid systems connected to the main grid for a long time do not need to be equipped with sufficient reserve capacity for the internal load, which can reduce system configuration costs. Once an extreme situation occurs, an independent islanded microgrid can be formed. However, insufficient configuration may lead to power shortages in the system, resulting in a decrease in frequency, and in severe cases, it may cause system crashes [4,5]. In August 2019, the super typhoon, “Lekima”, made landfall on the southeastern coast of China, causing over 4000 power line failures and leaving 6.7695 million users without electricity in provinces such as Zhejiang. To ensure the stability of system frequency and the operation of some important loads, it is particularly important to optimize the scheduling of islanded microgrids formed under extreme working conditions [6,7,8].

For systems that only contain new energy generation and energy storage equipment, there are two methods for optimizing scheduling: direct load control and energy storage charging and discharging plans. Direct load control is the process of directly cutting off user loads during power imbalance to maintain power balance and system stability. The traditional load reduction mode only reduces the load in stages, with low precision and errors between the actual system and scheduling strategies. The importance of the load has not been classified, resulting in low economic efficiency. Fixed unit load-cutting cost coefficients are commonly used for load reduction, or loss compensation is set for unit load-cutting cost coefficients in gradient intervals of load-cutting volume. Without considering the reduction period, reducing a large load during peak electricity consumption is easy, which is inconvenient for users [9,10,11,12,13] and affects their electricity comfort [14,15]. In this regard, this article proposes to combine time-of-use electricity prices with unit load shedding cost coefficients, which can minimize peak load shedding and improve load stability compared to traditional fixed coefficients.

Model predictive control utilizes current measurement data to optimize the predictive model in the rolling time domain, obtaining the optimal control sequence in the future control time domain and then implementing closed-loop optimal control through feedback correction to improve control accuracy [16]. Using the model predictive control (MPC) method for microgrid optimization scheduling and designing energy storage charging and discharging plans can improve the system’s anti-interference ability and enhance the system’s power supply stability [17,18].

In power systems, model predictive control technology has shown robustness in dealing with uncertain power sources such as wind power and photovoltaics (PVs) and has received increasing attention. Reference [19] provides a comprehensive overview of model predictive control (MPC) applications in building energy management, offering a unified framework for its implementation across various engineering disciplines. It critically discusses the outcomes of different MPC algorithms in thermal regulation, HVAC (Heating, Ventilation, and Air Conditioning) system optimization, and the management of energy storage and renewable sources, highlighting MPC’s potential to improve energy efficiency in buildings by considering constraints and multiple conflicting objectives such as thermal comfort and energy demand. Reference [20] introduces a model predictive control (MPC) strategy for energy management in a series hybrid electric tracked bulldozer (HETB), demonstrating a 6% improvement in fuel economy over rule-based methods and achieving 98% of the fuel optimality of dynamic programming, with proven robustness under large disturbances. Reference [21] proposes a risk-aware dynamic optimization method for independent microgrids, incorporating future operational risks and uncertainties in a CVaR-based day-ahead energy scheduling model. The method enhances long-period operational reliability by optimizing power scheduling strategies and reserve requirements for diesel generators, photovoltaic systems, energy storage, and flexible loads, reducing expected load losses and PV curtailment. Reference [22] introduces a novel dynamic power system scheduling approach to reduce generation costs in microgrids, utilizing a multi-vector energy model that integrates electricity, heating, and water generation sources. It evaluates the use of photovoltaic systems for partial load supply, incorporates a price-based demand response program to mitigate renewable energy source (RES) uncertainty, and minimizes system costs over a 24 h period. The above studies are all focused on scheduling in the grid-connected mode, with a greater emphasis on improving the economic efficiency of the system. In extreme operating conditions, an islanded microgrid focuses more on protecting essential loads.

In order to improve the economic, environmental, and necessary load supply operation of the islanded microgrid system, this paper proposes a rolling optimization economic dispatch strategy for an islanded microgrid under extreme working conditions: A load classification and dispatch framework model for each node of the high-proportion new energy-islanded microgrid is established. On the load side, the load is divided into three categories according to the importance level. The load is predicted through price-based demand response, and the load shedding cost coefficient is set based on the time of use, electricity price, and load importance. The charging and discharging strategy for grid-connected energy storage is obtained through recent optimization scheduling. The remaining power of grid-connected energy storage is considered on the power supply side through intra-day rolling optimization to obtain a load reduction plan. The optimization scheduling for charging and discharging of grid-connected energy storage is obtained through feedback correction. The model is solved using analytical methods and intelligent optimization algorithms. The contribution of this article is as follows:

(1)

This paper proposes a new load shedding optimization scheduling method, specifically designed for the operational characteristics of islanded microgrids. The method enhances the utilization of photovoltaic energy and energy storage systems through precise load shedding strategies, while ensuring the stability of power supply to critical loads. Specifically, the study designs a dynamic load shedding scheme based on load priorities and power system constraints, which can intelligently schedule power resources in response to sudden load fluctuations or energy shortages. This approach maximizes the absorption of renewable energy and ensures the continuous and stable operation of the system in the island mode.

(2)

This paper further explores the demand response (DR) mechanism and its operating modes at different time scales, and proposes a multi-level demand response optimization scheduling scheme to address the demand fluctuations and power supply–demand imbalances in islanded microgrids. In particular, this research not only considers conventional load management measures but also integrates time-of-use pricing mechanisms and load importance evaluation strategies. Targeted incentive and subsidy policies are designed to optimize consumer behavior. Through multi-stage optimization, this paper enables flexible adjustment of the demand response intensity at different time periods, effectively reducing grid load pressure and improving the economic and operational efficiency of the system.

2. Microgrid Demand Response Model

2.1. Differentiated Price-Based Demand Response

Differentiated price-based demand response refers to setting different prices based on market demand to guide consumers in adjusting their electricity consumption habits. This enables users to self-reduce and shift some of their loads and avoid concentrated peak electricity consumption. In 2014, PJM in the United States initiated demand-side response three times in response to a Polar Vortex, a large-scale cyclone occurring over the polar regions. Although electricity prices surged to USD 1.8 per kW/h at one point, the measure successfully ensured a stable power supply. Compared to traditional generation unit adjustments, demand-side response demonstrated higher reliability, faster response times, and more flexible regulation under extreme weather conditions. As a result, it can more effectively enhance the resilience of the power system while reducing operational costs. Reference [23] analyzes the self-elasticity and cross-elasticity coefficients of users’ electricity demand at different periods based on their actual electricity consumption situation, obtains the user demand response matrix, and then uses this matrix to predict the load changes of users after implementing electricity price-based demand-side management:

$$P^{PDR}=P_0+\lambda P_0$$

(1)

$$\lambda =\left[\begin{array}{cccc}{\lambda }_{1,1}& {\lambda }_{1,2}& \cdots & {\lambda }_{1,24}\\ {\lambda }_{2,1}& {\lambda }_{2,2}& \cdots & {\lambda }_{2,24}\\ ⋮& ⋮& ⋮& ⋮\\ {\lambda }_{24,1}& {\lambda }_{24,2}& \cdots & {\lambda }_{24,24}\end{array}\right]$$

(2)

$$P^{PDR}={[\begin{array}{cccc}{\mathrm{P}}_1^{\mathrm{PDR}}& {\mathrm{P}}_2^{\mathrm{PDR}}& \cdots & {\mathrm{P}}_{24}^{\mathrm{PDR}}\end{array}]}^{\mathsf{{\rm T}}}$$

(3)

$$P^0={[\begin{array}{cccc}{\mathrm{P}}_1^0& {\mathrm{P}}_2^0& \cdots & {\mathrm{P}}_{24}^0\end{array}]}^{\mathsf{{\rm T}}}$$

(4)

where $P^{PDR}$ is the predicted load that has undergone differentiated price demand response. $P_0$ is the initial electricity consumption of the load. Due to the varying impact of electricity prices on electricity consumption during different time periods, the elasticity coefficient of load during time period $i$ and $j$ will also differ. $\lambda$, the elasticity coefficient matrix for load, is provided in Appendix A for the specific calculation process.

2.2. Incentive Demand Response

Incentive demand response refers to the ability of users to flexibly adjust their demand for electricity based on market incentive mechanisms and compensation prices. The scheduling agency reduces the load on users based on the scheduling strategy and provides users with specific compensation according to the reduced load. This article categorizes loads into three types based on their importance level: (1) Essential loads include lighting, security, fire protection, communication, transportation, and administration, where power outages will affect social order stability. (2) Secondary essential loads include central air conditioning, water heaters, etc.; power outages of such equipment can affect daily life. (3) Nonessential loads, such as decorative landscapes, entertainment facilities, etc., can have their electricity interrupted at any time [24], and these three types of loads have varying regulating capabilities to some extent.

The traditional incentive demand response is a step-by-step reduction in load, which does not consider the type of node load and is not in line with actual electricity consumption. This article differentiates the loss of load shedding based on different load types in different periods, refines the loss cost, and makes the system scheduling more in line with the actual load shedding situation, which is more conducive to improving the comfort of user electricity consumption. The load reduction loss coefficient setting is adjusted according to the time-of-use-of-electricity price to improve economic efficiency. The incentive demand response cost formula for node load types is proposed as follows:

$$F_{IDR}\left(t\right)={{\displaystyle \sum }}_{i=1}^I{{\displaystyle \sum }}_{j=1}^J{K}_i\left(t\right){\sigma }_{i,j}\left(t\right)P_{i,j}\left(t\right),\left(J=1,2,3\right),\left({\sigma }_{i,j}=0,1\right)$$

(5)

where the incentive compensation cost is $F_{IDR}$ for the load reduction in the islanded microgrid during the $t$ period. $K_i$ is the load shedding loss coefficient of the i-th level load during time period t, adjusted according to the time-of-use electricity price. ${\sigma }_{i,j}$ is the direct load control strategy for node load, with values of 0 or 1, where 0 represents pruning and 1 represents retention. $J$ represents the importance level of the load, which is divided into three categories. $I$ represents the number of system nodes and $P_{i,j}$ is the electricity consumption of the $j$-th-type load of the $i$-th node in the microgrid that has undergone price-based demand response.

3. Rolling Optimization Scheduling of Isolated Microgrid Based on Differentiated Demand Response Comprehensive Incentive Mechanism

This article addresses the significant power errors in photovoltaic output under extreme working conditions and the power shortage caused by the inability of distributed energy storage within a microgrid to compensate for the power transfer of interconnection lines. Based on short-term photovoltaic and load forecasting, this article considers the charging and discharging process of grid-connected energy storage and the upper limit of energy supply for grid-connected energy storage. A day-ahead optimization scheduling model is constructed to minimize the comprehensive operating cost for the next 24 h. In the intra-day phase, the ultra-short-term photovoltaic output forecast is updated every hour. Based on the day-ahead scheduling scheme, the direct load control dispatching volume is adjusted to minimize the comprehensive operating cost in the rolling time domain. Based on the state of charge of the energy storage, a closed-loop feedback correction is formed. At the same time, essential loads that will be cut off are notified 2 h in advance, and secondary critical loads are notified 1 h in advance. The above DR-MPC (demand response–model predictive control)-based rolling optimization scheduling model framework is shown in Figure 1 (the same color represents the same instruction or status).

3.1. Pre-Optimization Scheduling

3.1.1. Day-Ahead Scheduling Optimization

In the day-ahead scheduling optimization, it will be determined that the time interval of each equipment’s future 24 h output plan is 1 h. In a high proportion of new energy power systems, the output of wind, solar, and photovoltaic systems accounts for a relatively high proportion, and their uncertainty needs to be considered in scheduling and operation. This article uses triangular fuzzy numbers to characterize wind and solar power output uncertainty. Based on the short-term photovoltaic forecast output values and load forecast values that have undergone differentiated price-based demand response, to minimize daily operating costs, a microgrid day-ahead optimization scheduling model is established.

$$minF={{\displaystyle \sum }}_{t=1}^{24}\left(F_t^{ESS1}+F_t^{ESS2}+F_t^{IDR}+F_t^{PV}\right)$$

(6)

$$F_t^{PV}=\xi \left(E\left({\tilde{P}}_t^{PV}\right)-P_{act,t}^{PV}\right)$$

(7)

$$F_t^{ESS1}=c_{ess1}\left(P_t^{ch1}-P_t^{dis1}\right)$$

(8)

$$F_t^{ESS2}=c_{ess2}\left(P_t^{ch2}-P_t^{dis2}\right)$$

(9)

$$F_t^{IDR}={{\displaystyle \sum }}_{i=1}^I{{\displaystyle \sum }}_{j=1}^J{K}_i\left(t\right)\left(1-{\sigma }_{i,j}\left(t\right)\right){\tilde{P}}_{i,j}\left(t\right),), ({\sigma }_{i,j}=0,1)$$

(10)

where $t$ is the current time period. $F_t^{IDR}$ is the IDR scheduling cost for period $t$, namely the load shedding cost. $F_t^{PV}$ is the cost of abandoned light during time period $t$, $\xi$ is the unit cost coefficient of the abandoned light amount, ${\tilde{P}}_t^{PV}$ and $P_{act,t}^{PV}$ are the fuzzy expression of the output power and actual consumption of the photovoltaic unit during time period $t$, and $E\left(\theta \right)$ represents the expected fuzzy number $\theta$. $F_t^{ESS1}$ represents the cost of grid-based energy storage scheduling, while $F_t^{ESS2}$ represents the cost of grid-based energy storage scheduling. $c_{ess1}$ and $c_{ess2}$ are the scheduling cost coefficients for grid-connected energy storage Ess1 and grid-connected energy storage Ess2, respectively. As the overcurrent capacity of grid-connected energy storage is greater than that of grid-connected energy storage, its cost increases significantly compared to grid-connected energy storage. ${\tilde{P}}_{i,j}$ is a fuzzy expression for the $j$-th class load of the $i$-th node in the microgrid. The triplet expression of photovoltaic and load output fuzzy numbers can be found in Appendix B.

3.1.2. Constraints

(1)

Power balance constraint

$${{\displaystyle \sum }}_{i=1}^m{{\displaystyle \sum }}_{j=1}^h{P}_{t,i,j}^{*}=P_t^{ESS1}+P_t^{ESS2}+{\tilde{P}}_t^{PV}$$

(11)

where $P_{t,i,j}^{*}$ is the load after load reduction; $P_t^{ESS1}$ and $P_t^{ESS2}$ are the charging and discharging power of grid-type energy storage Ess1 and grid-type energy storage Ess2.

(2)

Energy storage charging and discharging constraints

$$\left\{\begin{array}{c}0\le P_t^{ch1,2}\le P^{ch,max},0\le P_t^{d1,2}\le P^{d,max}\\ SO{C}_{min}\le SO{C}_t\le SO{C}_{max}\end{array}\right.$$

(12)

where $P^{ch,max}$ is the upper limit of energy storage charging power and $P^{d,max}$ is the upper limit of discharge power; $SO{C}_{min}$ and $SO{C}_{max}$ are the minimum and maximum states of charge for energy storage, respectively.

3.2. Intra-Day Scheduling Optimization

3.2.1. MPC-Based Intra-Day Scheduling Objective Function

Model predictive control consists of three main components: the predictive model, rolling optimization, and feedback regulation. At each prediction period, based on the current state of the system, that is, the remaining energy storage capacity, the optimal control sequence is generated through load forecasting and new energy generation forecasting. The first control instruction in the control time domain, the optimization result of load reduction, is applied to the next prediction time domain. At the same time, the actual measurement values are used to provide feedback and correct the output of the grid-type energy storage, accurately updating the remaining energy storage capacity and continuously rolling forward to optimize this process.

(1)

Prediction model

Based on the current state and future control variables of the system, the future state response of the system can be predicted, and the prediction model is as follows:

$$P_u\left(t+i\vee t\right)=P_{u0}\left(t\right)+{{\displaystyle \sum }}_{i=1}^N\Delta u\left(t+i\vee t\right),\left(i=1,2,\dots ,N\right),)$$

(13)

where $U$ is the total number of controllable units. $P_{u0}\left(t\right)$ is the initial output value of controllable unit $u$ during period $t$, obtained from the open-loop scheduling of the previous day. $u\left(t+i\vee t\right)$ is the output increment of controllable unit $u$ predicted for the future $\left[t,t+i\right]$ period in time $t$. $P_u\left(t+i\vee t\right)$ is the predicted output value of the controllable unit $u$ for the future $t+i$ period in time t; $N$ is the total number of predicted time periods in the time domain.

For this article, the control time domain is set to 1 h, and the rolling prediction scheduling time domain is set to 5 h. According to the actual system state and the required prediction accuracy, the rolling prediction and control time domains can be adjusted appropriately. The specific prediction model is expressed as follows:

$$\Delta u\left(t+i\vee t\right)=P^{load}\left(t+i\vee t\right)-P^{PV}\left(t+i\vee t\right)-P^{ESS1}\left(t+i\vee t\right)$$

(14)

$$W^{ESS2}\left(t+i\vee t\right)=W^{ESS2}\left(t\right)+P^{ESS2}\left(t+i\vee t\right)$$

(15)

where $P^{load}$ is the total value of all loads at the current time, and $W^{ESS2}$ is the remaining electricity of grid-type energy storage.

(2)

Rolling optimization

In the intra-day dispatching phase, the charging and discharging state of the grid following energy storage determined by the day-ahead dispatching is maintained. The control variables can be solved by optimizing the objective function of minimizing the comprehensive operating cost in the rolling prediction time domain. Then, the load reduction at all levels and the optimal output value of grid building energy storage in the future finite time can be obtained. The intra-day objective function is as follows:

$$minF={{\displaystyle \sum }}_{t=t_0}^{t_0+N}\left(F_t^{ESS1}+F_t^{ESS2}+F_t^{IDR}+F_t^{PV}\right)$$

(16)

$${\sigma }_{i,j}\left(t\right)=argminF$$

(17)

where $t_0$ is the current time period. N is the prediction time domain. ${\sigma }_{i,j}\left(t\right)$ is the direct load control strategy that minimizes the economic loss of the system within the prediction time domain.

(3)

Feedback correction

Although the output prediction of ultra-short-term photovoltaic power generation can achieve high accuracy, errors will continue to accumulate as the time scale expands, resulting in deviations between the state in the prediction model and the actual state. Therefore, it is necessary to introduce a feedback correction step to obtain the actual state results based on the rolling optimization strategy and use the actual state values as the starting values for the next round of optimization control, forming a closed-loop optimization control. By adjusting the system state in this way to eliminate errors caused by prediction accuracy, the feedback correction expression is as follows:

$$P_t^{ESS2*}=P_t^{L*}-\Delta P_t^{L*}-P_t^{PV*}$$

(18)

$$ESS{2}_{t+1}^{*}=ESS{2}_t^{*}-P_t^{ESS2*}$$

(19)

$$ESS{2}_{t+1}=ESS{2}_{t+1}^{*}$$

(20)

where $P_t^{ESS2*}$ represents the actual power change in grid-connected energy storage; $P_t^{L*}$ is the actual load capacity. $\Delta P_t^{L*}$ represents the actual load cut off. $P_t^{PV*}$ represents the actual photovoltaic output. $ESS{2}_{t+1}^{*}$ represents the actual energy storage of grid-connected energy storage at time t + 1. $ESS{2}_{t+1}^{*}$ assigned $ESS{2}_{t+1}$ for the calculation of the next prediction time domain.

3.2.2. Constraints

The intra-day rolling optimization scheduling constraints are consistent with day-ahead optimization scheduling.

3.3. Solution Process

The optimization scheduling process for extreme working conditions based on model predictive control includes three stages: pre-processing before the day, optimization operation within the day, and real-time feedback correction. In the pre-processing stage, the main purpose is to obtain the grid-connected energy storage output plan. Firstly, short-term load photovoltaic data are predicted based on annual historical data, and a unit combination model is established. The system unit combination model is usually a mixed integer linear programming model. The primary purpose of intra-day rolling optimization operation is to obtain a direct control strategy for the load, a 0–1-type dynamic programming problem for rolling periods. The system optimization operation model includes fuzzy constraints, which can be first transformed into a deterministic optimization problem through precise equivalence processing and then solved. The specific clarification equivalent processing procedure can be found in Appendix C. Real-time feedback correction eliminates prediction errors based on actual photovoltaic load values and intra-day optimization strategies to improve the accuracy of subsequent control strategies.

As mentioned earlier, this article requires solving a mixed 0–1 integer programming problem, which can be solved by combining heuristic algorithms and CPLEX A. Heuristic search algorithms are search methods based on experience and heuristic information. By evaluating the heuristic value of each search node, these algorithms guide the search direction, quickly generate high-quality initial solutions, and narrow the search space, providing a starting point for CPLEX to accelerate the solving process. The process of a heuristic search algorithm is as follows:

(1)

Initialize the search queue and add the starting node to the queue;

(2)

Select a node from the queue for expansion;

(3)

Evaluate the heuristic value of each extension node based on the heuristic function;

(4)

Add the node with the highest heuristic value to the queue;

(5)

Repeat steps 2–4 until the target node or queue is empty.

4. Example Calculation

4.1. Basic Data

To verify the effectiveness of the collaborative optimization scheduling method proposed in this article, a simulation example was conducted on an isolated microgrid, which includes five 25 kW photovoltaic units (PVs), three sets of 100 kW grids following energy storage (Ess1), and two sets of 150 kW grids forming energy storage (Ess2). The system structure is shown in Figure 2. The energy storage charging and discharging efficiency is 95%, and the maximum and minimum charging states are 0.9 and 0.2, respectively. The system has nine load nodes, each containing three types of loads, important, secondary necessary, and nonimportant, totaling 27 loads. This article uses the Gurobi solver on the MATLAB platform to solve the model. The calculator CPU is Inter (R) Core (TM) i5-9400F, 2.90 GHz, and 16 GB of memory.

The electricity situation at the load end is divided into three periods: peak and off-peak. The peak period is from 10 a.m. to 11 a.m. and 6 p.m. to 9 p.m. The off-peak period is from 7 a.m. to 10 a.m., 11 a.m. to 6 p.m., and 9 p.m. to 11 p.m. The off-peak period is from 0 a.m. to 7 a.m. and 11 p.m. to 12 p.m.

In the calculation example, the predicted power of PV is obtained by adding random prediction errors to the measured actual data. The actual value of PV and the predicted values of the short-term and ultra-short-term within the day are shown in Figure 3, and the classified load demand in each period is shown in Figure 4. The initial total power of grids following energy storage (Ess1) and grids forming energy storage (Ess2) is 180 kW. The loss coefficient of load importance is consistent with the proportion of time-of-use electricity price, and the load shedding loss coefficient of the third type of load is twice the valley time electricity price in the time-of-use electricity price. The simulation parameters are shown in Appendix D.

Figure 5 shows the comparison values of the load before and after the differentiated price demand response. The load between 10:00 and 13:00 and 17:00 and 20:00 belongs to the peak periods, where electricity demand is high. The load between 0:00 and 7:00 and 22:00 and 24:00 belongs to the off-peak periods, where electricity demand is low. After implementing demand response, the load demand during peak periods decreased, and the load during off-peak periods increased. This shows a clear effect of peak shaving and valley filling. The maximum fluctuation of the load change is 8.39%, and the curve before and after the response remains smooth, indicating that the demand response effect is stable.

4.2. Analysis of Scheduling Results

This article compares four different modes: Mode 1, referenced in [25], is the incentive subsidy policy scheduling based on time-of-use electricity price and load importance without considering model predictive control. Mode 2, referenced in [26], is the incentive subsidy policy scheduling based solely on load importance, considering MPC. Mode 3, referenced in [27], is the incentive subsidy policy scheduling based solely on time-of-use electricity price, considering MPC. Mode 4 is the incentive subsidy policy scheduling based on time-of-use electricity price and load importance, considering MPC. Figure 6 shows the optimized scheduling output under the four modes. Figure 6 shows that during periods without light, the photovoltaic output is 0, and the system load mainly relies on the energy storage discharge supply. During sufficient sunlight, there is a higher output of photovoltaic energy. In addition to supplying the load, energy storage can absorb excess electricity during peak load periods at night.

The comparison of optimization scheduling results under each mode is shown in

Table 1. Comparison of Optimization Scheduling Results.

Scheduling Mode	Comprehensive Operating Cost/CNY	Load Reduction/kW	Abandoned PV Rate/%
Mode 1	157.1410	106.7173	7.3995
Mode 2	122.9132	103.8846	7.1539
Mode 3	175.6449	103.7212	7.1500
Mode 4	122.3816	103.8304	7.1540

, and the reduction amounts of different types of loads in each mode are shown in

Table 2. Reduction amounts of different types of loads in each mode.

Scheduling Mode	Important Load	Secondary Load	Non-Critical Load
Mode 1	17.9064	33.4492	55.3616
Mode 2	0	1.5482	102.3364
Mode 3	32.5410	46.2099	24.9703
Mode 4	0	0	103.8304

. Since model predictive control is not considered in mode 1, it is impossible to cut off nonessential loads in advance to maintain essential loads, leading to energy storage depletion and total load cut-off at the last two moments. The total load cut-off is higher than other modes, and there is no day-ahead scheduling. PV load prediction error makes the light rejection rate higher than that of other modes. Mode 2 does not consider the time-of-use electricity price. From the perspective of the electricity sales economy, there will be a large amount of load shedding during peak electricity price periods, resulting in a decrease in electricity sales revenue and indirectly reducing the economy. Moreover, without considering the time-of-use electricity price, a large amount of load shedding at a single moment will occur, making it impossible to evenly distribute the disturbance among different moments and indirectly increasing the disturbance at a single moment. Mode 3 did not consider the importance of loads, resulting in the removal of many essential loads during the load reduction process. Compared to mode 4, the total load reduction was only reduced by 0.11%, but the overall operating cost increased by 42.9%. Mode 4 takes into account both time-of-use electricity prices and the importance of load, resulting in the lowest overall operating costs and minimum amount of wasted light. From an economic and environmental perspective, it improves system performance. It should be noted that the comprehensive operating cost calculation for all modes is the same; that is, only their respective strategies are used, and the cost calculation method and coefficients are consistent, which can reflect the fairness of the comparison.

Table 2 compares the amount of load shedding for three types of loads in different modes. Mode 1, due to the lack of consideration for model predictive control, resulted in a large amount of load shedding after energy storage consumption was complete. Mode 3, due to the lack of consideration for load importance, resulted in a large amount of necessary load shedding. Mode 2 and mode 4 did not remove essential loads due to the consideration of load importance, and the amount of load shedding for less essential loads in mode 4 was smaller than in mode 2. This indicates that incentive subsidy policies based on time-of-use electricity prices can reduce economic losses.

Table 3. Variance in Load Reduction Ratio.

	Mode 1	Mode 2	Mode 3	Mode 4
variance	0.0701	0.0145	0.0145	0.0098

shows the variance comparison of the load shedding ratio during load reduction. To ensure fairness in the comparison, only the variance calculation was performed for the load shedding ratio when the load needed shedding. Among them, the base for the cut-off load loss coefficient of mode 3, without considering the importance of load, is selected as the average 24 h of use electricity prices. Considering the impact of electricity prices, the load shedding loss coefficients for modes 1, 3, and 4 are the original base plus the time-of-use-of-electricity prices at each time point. From Table 3, it can be concluded that comparing mode 2 and mode 4, the variance in the load shedding ratio, considering the time-of-use-of-electricity pricing, is much smaller than that without considering it. This indicates that considering the time of use, electricity pricing can distribute the load reduction amount across different periods to reduce disturbances at each time and improve the stability and economy of the system.

In summary, mode 2 and mode 4 reduce nonessential loads in advance to ensure essential loads in the future. Compared with mode 1, they significantly improve the guarantee of essential loads in the future. Compared with mode 3, they consider the importance of loads and significantly improve the system’s economy. Compared with mode 2, mode 4 considers the impact of time-of-use electricity prices, reduces the variance in the load shedding ratio and comprehensive economic costs, and improves the stability and economy of the system’s load shedding strategy.

To determine the impact of penalty coefficients for load importance on optimal scheduling, we conducted the following data comparisons as shown in

Table 4. Comparison of total operational costs under different penalty coefficients.

The Ratio of Load Importance Coefficients	Comprehensive Operation
1.8:1.2:1	123.2914
2.0:1.2:1	122.4293
2.2:1.3:1	122.3971
2.3:1.4:1	122.3816
2.6:1.4:1	122.5085
2.6:1.5:1	122.7276
2.7:1.5:1	122.9667
3:2:1	122.9583
3.5:2.5:1	123.1885

, analyzing the effect of different penalty coefficients on the total operational cost. By gradually adjusting the penalty coefficients and recording the changes in total operational costs under each combination, the simulation results near the optimal point indicate that selecting penalty coefficients for the three types of load importance as 2.3:1.4:1 is the best choice.

4.3. Variable Analysis of Photovoltaic Output and Energy Storage Capacity

Under the method of mode 4, a variable analysis of photovoltaic output and energy storage capacity was conducted. First, the photovoltaic output was reduced to 85–70% of that in mode 4, while keeping the energy storage capacity unchanged. The scheduling results are shown in Figure 7, and the load shedding details are provided in

Table 5. Load shedding under changes in photovoltaic output.

PV	Important Load Reduction	Total Load Reduction
85%	0	184.2321
80%	0	240.0685
75%	1.3759	295.1434
70%	2.7760	349.9655

. The results indicate that when the energy storage capacity remains unchanged and photovoltaic output decreases below 80%, the system requires shedding important loads. In such cases, a power outage warning should be issued to critical loads two hours prior to the shedding.

Next, a variable analysis of energy storage capacity was conducted while keeping photovoltaic output unchanged. The energy storage capacity was increased by 10–40%. The scheduling results are shown in Figure 8, and the load shedding details are provided in

Table 6. Load shedding under changes in energy storage capacity.

ESS Increment	Total Load Reduction
10%	79.7122
20%	56.0228
30%	32.2590
40%	24.2915

. The results indicate that as the energy storage capacity increases, the amount of load shedding decreases. However, whether load shedding is necessary still mainly depends on the remaining energy within the system. Additionally, increasing the energy storage capacity will raise the system’s construction costs. When optimizing the configuration, the method proposed in this paper can be used as a reference to appropriately reduce the configuration of energy storage capacity, achieving economic optimization.

5. Conclusions

When long-term grid-connected microgrids experience connection failures due to natural disasters and operate in the extreme islanding mode, the reliability of their optimized scheduling is relatively poor due to the impact of insufficient self-configured capacity. This article establishes a rolling time-domain optimization scheduling model based on MPC for the operation mode of an islanded microgrid in extreme situations. The results show that

(1)

The DR-MPC-based method, compared to methods that do not consider time-of-use pricing and load importance, reduces the overall operating costs by 0.6% and 30%, respectively, while also improving the renewable energy absorption rate of the microgrid system.

(2)

This paper proposes a load classification scheduling framework for islanded microgrids with a high penetration of renewable energy, and based on this, designs a precise load shedding optimization scheduling strategy. By dynamically adjusting the output of the energy storage system, the method maximizes the utilization of renewable energy and ensures the stability of power supply to critical loads. Additionally, this study combines time-of-use pricing and load importance assessment to propose an innovative demand response incentive subsidy policy, effectively optimizing the scheduling of critical loads during peak load periods, ensuring the stability of power supply, and alleviating the power supply–demand imbalance.

This strategy can be applied to the emergency load shedding strategy optimization scheduling and energy storage capacity configuration calculation of an isolated microgrid. In the future, the proposed models and algorithms can be applied to optimize the scheduling of microgrid cluster systems. The method adopted in this study effectively improves system stability but still has certain limitations. First, rolling optimization increases the computational burden of the system and imposes higher requirements on hardware devices. While the MPC method reduces the inaccuracy of supply–demand balance, its ability to mitigate renewable energy curtailment is limited, requiring increased storage capacity to alleviate this issue. Moreover, the pre-shedding approach faces multiple challenges in practical applications, such as the complexity of load prioritization, low user acceptance, insufficient load forecasting accuracy, and inadequate support from energy storage systems. To overcome these limitations, future work should integrate advanced prediction and optimization techniques, enhance the reliability of energy storage and communication systems, and improve relevant policies and standards.