A Review of Optimization Scheduling for Active Distribution Networks with High-Penetration Distributed Generation Access

Abstract

The high-proportion integration of renewable energy sources, represented by wind power and photovoltaics, into active distribution networks (ADNs) can effectively alleviate the pressure associated with advancing China’s dual-carbon goals. However, the high uncertainty in renewable energy output leads to increased system voltage fluctuations and localized voltage violations, posing safety challenges. Consequently, research on optimal dispatch for ADNs with a high penetration of renewable energy has become a current focal point. This paper provides a comprehensive review of research in this domain over the past decade. Initially, it analyzes the voltage impact patterns and control principles in distribution networks under varying levels of renewable energy penetration. Subsequently, it introduces optimization dispatch models for ADNs that focus on three key objectives: safety, economy, and low carbon emissions. Furthermore, addressing the challenge of solving non-convex and nonlinear models, the paper highlights model reformulation strategies such as semidefinite relaxation, second-order cone relaxation, and convex inner approximation methods, along with summarizing relevant intelligent solution algorithms. Additionally, in response to the high uncertainty of renewable energy output, it reviews stochastic optimization dispatch strategies for ADNs, encompassing single-stage, two-stage, and multi-stage approaches. Meanwhile, given the promising prospects of large-scale deep reinforcement learning models in the power sector, their applications in ADN optimization dispatch are also reviewed. Finally, the paper outlines potential future research directions for ADN optimization dispatch.

1. Introduction

Large-scale combustion of fossil fuels is contributing to increasingly severe environmental pollution, with substantial carbon dioxide emissions accelerating the global warming trend [1,2,3]. The power sector, responsible for nearly half of total carbon emissions, has rendered the traditional energy development model unsustainable. Thus, an urgent transformation towards clean and low-carbon energy sources is imperative [4].

Under China’s dual-carbon policy goals, the nation’s total installed power capacity reached 3.35 billion kilowatts by the end of 2024, marking a 14.6% year-on-year increase. Renewable energy generation capacity exceeded 1.45 billion kilowatts, accounting for 52% of total capacity and surpassing thermal power for the first time, while power regulation capabilities continued to strengthen [5]. Future integration of renewable energy into the grid is expected at larger scales and higher ratios, with penetration projected to rise continuously. To achieve rational resource distribution, the penetration of distributed generation (DG) [6], energy storage systems (ESS), and static var compensation (SVC) technologies within distribution networks has progressively increased. These developments have enhanced the active regulation capabilities of traditional distribution networks, facilitating their evolution towards active distribution network (ADN) [7]. The challenges faced by active distribution networks (ADNs) with a high proportion of distributed generation (DG) integration primarily stem from intermittent renewable energy sources such as wind power and photovoltaics. Unless specifically distinguished otherwise in this paper, DG will be used as a collective term to refer to non-hydro renewable energy sources represented by wind power and photovoltaics. Research on ADN dispatch has undergone three major stages: centralized modeling, distributed collaborative breakthroughs, and artificial intelligence-based optimization, achieving a paradigm shift from single-device control to multi-source data-driven system coordination.

While high penetration levels of distributed power significantly enhance distribution network cleanliness and operational flexibility, several challenges remain significant. Renewable energy output exhibits strong coupling with complex stochastic meteorological factors [8,9,10], and the distributed grid characteristics of both renewables and new-type loads introduce greater randomness and complexity into active distribution network scheduling modes and power flow patterns. Simultaneously, spatiotemporal mismatches between generation sources and loads impede local photovoltaic resource utilization [11,12] and cause significant localized voltage deviations in high-penetration renewable distribution grids, even triggering voltage excursions that compromise grid security [13,14]. Consequently, optimized dispatch of diverse flexible grid resources is essential to meet the demands of future active distribution network development.

This paper synthesizes existing research in active distribution network optimization scheduling, outlining the fundamental structure and characteristics of ADN components. It examines voltage operation mechanisms in distribution networks under high distributed generation penetration conditions, classifies ADN optimization scheduling models, analyzes associated challenges, summarizes pertinent solution methodologies, and proposes future research trajectories.

2. Impact Analysis of Access at Different DG Penetration Rates

High penetration of distributed power induces bidirectional power flow, intensified voltage fluctuations, and dynamic power factor variations within distribution networks. These phenomena precipitate voltage regulation challenges, increased complexity in relay protection configuration, and heightened requirements for operational control flexibility [15,16].

Significant challenges include stability issues arising from source-load role switching, power balance pressures caused by intermittent generation, and the requisite compatibility of distribution network planning and operation with high renewable energy penetration—necessitating coordinated smart regulation technologies and novel market mechanisms. The fundamental structure of the active distribution network is illustrated in Figure 1.

2.1. Analysis of the Characteristics of Distribution Network Integration Under Varying Penetration Levels of Wind and Solar Power

DG penetration can be categorically defined into three types: capacity penetration (CP), energy penetration (EP), and power penetration (PP). Specifically, CP represents the percentage of installed DG capacity relative to the peak regional load; EP denotes the percentage of the total annual available electricity generation from DG compared to the annual electricity consumption of the system load; and PP indicates the maximum percentage of the total DG power generation at a certain moment throughout the year relative to the system load capacity. CP reflects the saturation level of photovoltaic installation capacity within the system; EP illustrates the distribution network’s capacity to absorb the total electricity generated by DG; PP demonstrates the optimal matching degree between DG power generation and load at a specific moment throughout the year, i.e., the maximum load-supporting capacity of DG during the year. Unless otherwise specified, the term “penetration” generally refers to CP by default.

DG penetration serves as a critical metric to evaluate the prevalence and influence of renewable energy in a specific region, acting as one of the key indicators for assessing DG market development. Existing studies have revealed the impacts of DG penetration on distribution networks from various dimensions. Reference [17] proposed that, compared to CP and EP, the PP indicator is significantly influenced by the temporal matching degree of source-load power. Reference [18], through simulation analysis, demonstrated that increasing DG integration ratios would exacerbate reverse power flow phenomena in the system, potentially leading to node voltage deviations beyond permissible limits and a surge in network losses. Reference [19], under the assumption of constant DG installed capacity, verified that the power consumption characteristics of different load types are a crucial factor contributing to variations in DG accommodation capacity. Reference [20], via security assessments, revealed that the integration location of DG has a pronounced impact on system stability, particularly at weak grid nodes where voltage violations may occur.

2.2. Laws of Influence of Different DG Penetration Rates on Node Voltage

This paper conducts an analysis based on the equivalent circuit model of a radial distribution network, as depicted in Figure 2, to establish the relationship between node voltage magnitude and DG penetration.

The impact of DG penetration on node voltage magnitudes, under the condition that the grid-connected nodes of DG remain constant, exhibits two distinct trends in voltage variation:

(1) When $P_{\mathrm{DG}}<\underset{x}{\min }\left\{{\displaystyle \frac{{\displaystyle \sum _{i=1}^x{e}_i}}{{\displaystyle \sum _{i=1}^x{h}_i}}}\right\}$., all nodes along the line will be uniformly elevated after DG accesses the trunk line tie-in node;

(2) when $P_{\mathrm{DG}}\ge \underset{x}{\max }\left\{{\displaystyle \frac{{\displaystyle \sum _{i=1}^x{e}_i}}{{\displaystyle \sum _{i=1}^x{h}_i}}}\right\}$, the DG access to the trunk line grid-connected nodes along the line will be uniformly lowered at all nodes.

This paper conducts simulation-based validation within the IEEE 33-node radial network to quantify the impact of DG penetration on distribution network node voltages. The topological structure, nodal load profiles, and branch impedance parameters of the IEEE 33-node system are adopted from Reference [21].

Qualitative analysis examines distributed generation operation within the distribution network at varying penetration levels, with integration sites specified at nodes 17, 22, 25, and 32. Five simulation scenarios comprise the study: baseline S2-1 contains no dis-tributed generation, while scenarios S2-2 through S2-5 feature successively increasing penetration levels of 20%, 40%, 60%, and 80% at these designated nodes. The computational results are summarized in

Table 1. Simulation results of example.

Take	Minimum Voltage/p.u.	Maximum Voltage Variation/p.u.	Number of Nodes with Voltage Deviations
S2-1	0.92250	-	9
S2-2	0.93621	0.01620	0
S2-3	0.95590	0.03136	0
S2-4	0.95601	0.04271	0
S2-5	0.96440	0.05985	0

.

Table 1 reveals that within the simulated scenarios, Scenario S2-1 exhibits the lowest system minimum voltage magnitude, with all other scenarios demonstrating elevated voltage levels. Regarding voltage deviation magnitude, Scenario S2-5 shows the most substantial node voltage fluctuations. Voltage limit violations remain negligible across Scenarios S2-2 through S2-5.

Figure 3 demonstrates that at varying penetration levels, maximum voltage deviations consistently occur near line terminals, specifically nodes 18 and 33. The 80% penetration scenario yields the optimal voltage profile throughout the distribution network. Without optimization measures, all node voltages proximal to DG connection points exhibit elevation with fundamentally similar variation patterns.

3. Optimal Scheduling Model Building and Solving

3.1. Development of an Optimal Dispatch Model for Distribution Networks

3.1.1. Control Variables

Four primary power output categories serve as decision variables for distribution network optimal dispatch: (1) Intermittent renewable distributed generation, exemplified by photovoltaic systems exhibiting significant stochastic volatility [22,23]; (2) stabilized distributed generation units, including gas microturbines with grid-connected inverters [24]; (3) integrated reactive compensation devices (Static Var Compensators and Switched Capacitor Banks) implementing dynamic switching strategies to provide coordinated grid voltage support and compensate for distributed generation fluctuations [25]; and (4) energy storage systems (ESS) utilizing peak-shaving and valley-filling operations to alleviate grid operational pressures while leveraging rapid response characteristics to mitigate intermittent renewable energy impacts [26].

3.1.2. Objective Function

To address the complex challenges arising from high-penetration distributed power integration in active distribution network, research has established an objective function framework encompassing security, economic efficiency, and low-carbon dimensions. This enables comprehensive operational enhancement through multi-objective synergistic optimization [27,28,29].

The inherent volatility, intermittency, and bidirectional power flow characteristics of distributed generation present significant safety challenges, prompting current research to focus on developing comprehensive security objective functions covering voltage stability [30,31], short-circuit current constraints [32], relay protection coordination, and islanded operation security [33]. In the realm of economic dispatch, Reference [34] focuses on minimizing generator operating costs, reserve expenses, and power transaction fees to achieve cost reduction and efficiency enhancement. Reference [35] proposes a dispatch strategy that limits the switching frequency of battery charging/discharging modes, effectively reducing system energy losses and operational costs. Reference [36] innovatively establishes an environmental–economic dispatch model, simultaneously enhancing economic benefits and significantly improving system environmental performance. Regarding low-carbon dispatch, references [37,38] optimize renewable energy station dispatch through carbon flow constraints and evaluate load-side carbon emissions. Reference [39] quantifies the carbon emission intensity of high-penetration wind systems, promoting the coordination of wind energy economic and environmental benefits. Reference [40] introduces a source-load bilateral carbon tax cost allocation method to enhance renewable energy penetration. References [41,42] coordinate demand response, renewable energy plants, and carbon capture stations to achieve low-carbon economic dispatch. Reference [43] integrates big data analytics to optimize generation-side dispatch through unit energy consumption and carbon emission intensity accounting. Finally, Reference [44] conducts multi-objective optimization targeting minimal voltage deviation, maximal distributed generation output, and minimal network losses, enabling secure, economic, and low-carbon operation of active distribution networks.

For multi-objective optimization problems, a linear weighting approach is employed to convert them into single-objective optimization problems.

$$\min F={\omega }_1{F}_1+{\omega }_2{F}_2+{\omega }_3(-F_3)$$

(1)

In the equation, $\omega$ represents the weighting coefficient, whose value can be determined through the empirical value method [45].

When addressing complex and conflicting objectives such as minimizing network losses and carbon emissions, the subjective nature of manually selecting weights necessitates careful consideration of computational trade-offs. Reference [46] introduced a novel voltage enhancement metric grounded in economic indicators to optimize voltage profiles, formulating a multi-objective optimization framework. This approach employed the Analytic Hierarchy Process (AHP) to determine objective weights before converting the problem into a single-objective programming task. In Reference [47], a hybrid weighting approach combining entropy weight method and AHP was adopted to assign weights to individual indicators.

3.1.3. The Power Flow Model for Distribution Networks

Optimal Power Flow (OPF) stands as a core technology for enhancing the security and economic efficiency of power grids. However, its non-convex quadratic power flow equality constraints have rendered the problem NP-hard, as demonstrated in previous studies [48,49]. The nonlinear power flow model for active distribution networks can be characterized as follows:

$$\left\{\begin{array}{l}{V}_j^2=V_i^2+2P_{ij}{r}_{ij}+2Q_{ij}{x}_{ij}-l_{ij}^2|Z_{ij}{|}^2\\ P_{ij}=P_j+{\displaystyle \sum _{h:h\to j}}\left(P_{jh}-r_{jh}{I}_{jh}^2\right.)\\ Q_{ij}=q_j+{\displaystyle \sum _{h:h\to j}}\left(Q_{jh}-x_{jh}{I}_{jh}^2\right.)\end{array}\right.$$

(2)

$$I_{ij}^2={\displaystyle \frac{P_{ij}^2+Q_{ij}^2}{V_j^2}},$$

(3)

where h denotes all nodes directly connected to node j except node i.

3.1.4. Operational Constraints

Distribution network optimization scheduling necessitates precise constraint definition to ensure feasible and secure solutions. The constraint framework encompasses equipment capacity limits, nodal voltage boundaries, line ampacity thresholds, and other operational boundaries while balancing economic, environmental, and demand-response considerations. Boundary specification constitutes both the foundation for stable grid operation and a prerequisite for achieving scheduling objectives.

Active distribution network optimization must therefore satisfy the following constraints [50]:

$$\left\{\begin{array}{l}{U}_{i\min }\le U_i\le U_{i\max }\\ 0\le P_{D,i}\le P_{D,i\max }\\ 0\le Q_{D,i}\le Q_{D,i\max }\\ P_{DSi\min }\le P_{DSi}\le P_{DSi\max }\\ Q_{SVCi\min }<Q_{SVCi}<Q_{SVCi\max }\end{array}\right.,$$

(4)

where $P_{DSi}$ is the charging and discharging power of the energy storage device, and $Q_{SVCi}$ is the reactive power of the reactive power compensator at node i.

In the optimal dispatch of active distribution networks with high penetration of distributed energy resources, strict adherence to power flow balance, nodal voltage limits, line capacity constraints, and distributed generator output boundaries is essential [51]. Constraints such as the state of charge for energy storage systems and radial network topology may exhibit greater operational flexibility in practical implementations. For instance, dynamic control strategies or flexible devices can enable scenario-specific simplifications of these constraints [52]. While the optimization model need not incorporate all equations compulsorily, preservation of critical safety constraints takes precedence. Secondary constraints may be adaptively modified based on system conditions and optimization objectives. Model development should strategically balance computational complexity with practical implement ability, prioritizing economic efficiency while maintaining operational safety to meet the evolving demands of active distribution networks under high distributed energy resource penetration.

3.2. Optimal Distribution Network Scheduling Model Solution

The nonconvex nonlinear nature of distribution network optimal scheduling models commonly results in convergence to locally optimal solutions [53,54], while the significant uncertainty inherent to distributed generation introduces additional operational complexity that compounds these nonconvex characteristics [55]. To address these computational challenges, research has primarily pursued two methodological approaches: (1) mathematical reformulation of nonconvex models into tractable convex counterparts solvable by commercial optimizers like CPLEX; and (2) direct solution via heuristic algorithms.

3.2.1. Mathematical Programming Methods

The integration of high-penetration renewable energy renders active distribution network optimization scheduling significantly complex, constituting a multivariable, multi-objective, multi-constraint nonconvex nonlinear programming problem. This formulation incorporates diverse control variables, including discrete parameters such as on-load tap-changing transformer positions and switched capacitor bank groupings alongside continuous variables including renewable generation outputs and reactive compensation device setpoints. Mathematical programming techniques [56,57] represent effective approaches for solving renewable-integrated distribution network reactive power optimization, deriving optimal solutions through mathematical modeling. The established methods include semidefinite programming (SDP) [58,59], second-order cone programming (SOCP) [60,61], and convex interior point approximations among others [62].

(1) Semi-definite relaxation

Semi-definite programming (SDP) addresses the standard form of the original optimization problem and is applied to solve tidal Optimal Power Flow (OPF) formulations. This approach employs a primal-dual interior-point method to obtain solutions for the OPF SDP model as defined in Equation (5):

$$\left\{\begin{array}{l}\min \mathit{F}={\mathit{A}}_0\mathit{X}\\ s.t.{\mathit{A}}_k\mathit{X}=b_k\hspace{1em}\hspace{1em}k=1,2,\cdots ,30\\ \mathit{X}\ge 0\end{array}\right.,$$

(5)

where $\mathit{F}$ is the target value; $\mathit{X}$ is the decision variable; ${\mathit{A}}_0$ is the coefficient matrix of the target function; ${\mathit{A}}_k$ is the coefficient matrix of the constraints; and ${\mathit{b}}_k$ consists of constants on the right-hand side of the constraints.

This conversion transforms the original mixed-integer nonlinear programming model into a mixed-integer semi-definite programming formulation, ensuring solution global optimality.

The mixed-integer SDP relaxation exhibits remarkable accuracy and enhanced applicability to AC-DC hybrid distribution network optimization problems. Following semi-definite relaxation, only the semi-definite matrix-variable constraints retain nonlinearity within the model; all other objectives and constraints become linear. This permits derivation of globally optimal solutions from the convex relaxation. Reference [63] validates relaxation accuracy by comparing SDP solutions with their mapped matrices; sufficiently small element-wise differences in the residual matrix indicate numerical proximity to a rank-1 solution, confirming relaxation adequacy. While achieving greater accuracy than linearized approximations, the semi-definite relaxation incurs elevated computational complexity.

(2) Second-order cone relaxation

In References [64,65], a branch flow model (BFM) for distribution networks was proposed, and its convexification was achieved through second-order cone programming (SOCP) techniques. This approach enables the representation of complex variable relationships within specially structured conic sets, thereby constraining the search space to a finite convex cone. Such formulation significantly simplifies the solution process of the original model, accelerates convergence, and enhances computational efficiency. Figure 4 illustrates the schematic diagram of second-order cone relaxation.

According to the branch circuit trend model, the optimal trend can be expressed as a nonlinear planning model, then we can make ${\tilde{I}}_{ij}$ = $I_{ij}^2$ and ${\tilde{V}}_j$ = $V_j^2$, and transform the trend model to get

$${\tilde{V}}_j={\tilde{V}}_i-2(P_{ij}{r}_{ij}+Q_{ij}{x}_{ij})+{\tilde{I}}_{ij}(r_{ij}^2+x_{ij}^2),\hspace{1em}\forall ij\in E,$$

(6)

$${‖\begin{array}{c}2P_{ij}\\ 2Q_{ij}\\ {\tilde{I}}_{ij}-{\tilde{V}}_j\end{array}‖}_2\le {\tilde{I}}_{ij}+{\tilde{V}}_j,\hspace{1em}\forall ij\in E,$$

(7)

$$I_{ij}^2\le {\tilde{I}}_{ij}\le {\overline{I}}_{ij}^2,\hspace{1em}\forall ij\in E,$$

(8)

$$V_j^2\le {\tilde{V}}_j\le {\overline{V}}_j^2,\hspace{1em}\forall j\in B^{+}.$$

(9)

To address the limitation of traditional optimal power flow (OPF) formulations in neglecting multi-period dynamic coupling, Reference [66] developed a mixed-integer second-order cone programming (MISOCP) framework for multi-period dynamic optimal power flow (DOPF) tailored for active distribution networks. This approach enhances the applicability of convex relaxation techniques in OPF analysis.

Sufficient conditions ensuring exact second-order cone relaxation exhibit practical restrictiveness and challenge fulfillment, categorizable into three classes by constraint boundary requirements: (1) theoretically unbounded nodal load power capacities [67], with only lower injected power limits constrained at select nodes [68,69]; (2) post-relaxation nodal voltage magnitudes remaining below upper bounds without reverse power flow—an a posteriori criterion [70,71]; and (3) identical pre/post-relaxation optimal solution sets occurring when inter-nodal voltage phase angles demonstrate sufficient proximity [72,73], similarly constituting an a posteriori criterion.

(3) Intra-convex approximation

Under certain conditions, solutions from relaxed convex problems can accurately represent globally optimal solutions to original nonconvex AC optimal power flow problems [74,75,76,77]. Practically, however, ensuring network admissibility proves more valuable than identifying global optima. Addressing this challenge, researchers have conducted substantial work on constructing inner feasible regions. Convex inner approximation (CIA) was initially proposed in Reference [78] to identify stability regions for finite families of chi-square affine polynomials. Accordingly, Reference [79] and Reference [80] applied CIA to distribution network optimization scheduling, achieving computational efficiency while guaranteeing operational feasibility.

Neglecting the transverse component of the voltage drop, the relationship between nodal voltage and power flow is obtained as follows:

$$\left\{\begin{array}{l}\mathit{V}={\mathit{V}}_0^2{1}_n+{\mathit{M}}_p\mathit{p}+{\mathit{M}}_q\mathit{q}-\mathit{H}\mathit{l}\\ \mathit{P}=\mathit{C}\mathit{p}-{\mathit{D}}_R\mathit{l}\\ \mathit{Q}=\mathit{C}\mathit{p}-{\mathit{D}}_X\mathit{l}\end{array}\right.,$$

(10)

where $\mathit{P}={[P_{ij}]}^{\mathit{T}}$, $\mathit{Q}={[Q_{ij}]}^{\mathit{T}}$, $\mathit{p}={[p_i]}^{\mathit{T}}$, $\mathit{q}={[q_i]}^{\mathit{T}}$, M_p = 2C^TRC, M_q = 2C^TXC, V = [v_i], ${\mathit{D}}_R={(\mathit{I}-\mathit{A})}^{-1}\mathit{A}\mathit{R}$, ${\mathit{D}}_X={(\mathit{I}-\mathit{A})}^{-1}\mathit{A}\mathit{X}$, $\mathit{H}={\mathit{C}}^{\mathit{T}}(2({\mathit{R}\mathit{D}}_R+{\mathit{X}\mathit{D}}_X)+{\mathit{Z}}^2)$, $\mathit{l}={[I_{ij}^2]}_n$, $\mathit{C}={(\mathit{I}-\mathit{A})}^{-1}$.

The variables $\mathit{P}$, $\mathit{Q}$, $\mathit{V}$, and $\mathit{l}$ are coupled to each other, and the rest of the variables except the branch circuit power flow are decision variables or state variables. The upper and lower bounds of each proxy variable can be obtained by using $\mathit{l}$ as an intermediate quantity to represent the other variables.

Convex inner approximation (CIA) presents a promising approach for balancing rigor and practicality, though its inherent conservatism may induce unnecessary restriction of the solution space at the expense of economic potential. To mitigate these limitations in distribution network dispatch optimization, recent research has shifted toward feasible solution recovery methodologies: Reference [81] recovers active dispatch using historical data but overlooks unit dynamic adaptability, thereby producing infeasible solutions; Reference [82] enhances feasibility through constraint tightening yet compromises economic efficiency while maintaining dependence on conventional models; and Reference [83] addresses active power bound violations but lacks integrated reactive-voltage coordination mechanisms.

To evaluate the dispatch performance of semidefinite programming (SDP), second-order cone programming (SOCP), and constraint interior-point algorithm (CIA) in active distribution networks under high-penetration distributed energy resources (DER) scenarios, this study employs the IEEE 33-bus system for simulation analysis. The test case configuration follows the methodology outlined in Reference [84]. Figure 5 presents a comparison of the voltage distribution across the entire power grid at 21:00; Figure 6 illustrates the active power losses in the active distribution network; and Figure 7 depicts the 24 h output curves of wind and solar power.

Table 2. A comparative analysis of different performance metrics across three methods.

Method	Average Value of Voltage Deviation/p.u.	Network Loss /kW	Utilization Rate of New Energy/%
SDP	0.4218	537.2	74.9
SOCP	0.4303	490.7	85.8
CIA	0.4403	545.0	89.4

presents a comparative analysis of three operational scenarios across key performance metrics. Examination of the data reveals distinct advantages among the evaluated methods. In terms of voltage regulation, the Second-Order Cone Programming (SOCP) approach demonstrates a 2.27% reduction in voltage deviation compared to the Convex Interior Point Algorithm (CIA). Notably, the Semi-Definite Programming (SDP) method achieves further improvement, reducing voltage fluctuations by an additional 1.98% relative to SOCP. Regarding power transmission efficiency, SOCP exhibits significantly lower network losses than both SDP and CIA methodologies. When evaluating renewable energy utilization, substantial disparities emerge: SDP achieves 74.9% efficiency, while SOCP increases this to 85.8%, marking a 10.9% improvement over SDP. The CIA method further elevates utilization to 89.4%, representing a 3.6% enhancement compared to SOCP. These findings underscore CIA’s particular effectiveness in optimizing distributed energy resource integration.

Overall, the SDP algorithm demonstrates optimal performance in voltage stability control, effectively reducing voltage deviations. Although the SOCP algorithm exhibits slightly weaker voltage control capabilities, it achieves the lowest network losses, reflecting a trade-off between stability and efficiency. The CIA method results in relatively larger voltage deviations and losses but significantly enhances the utilization rate of renewable energy sources. This study reveals that the choice of algorithm directly influences the capacity for integrating renewable energy, offering strategic insights for the coordinated realization of stability, efficiency, and low-carbon objectives in power grid optimization.

3.2.2. Scheduling Model Solving Algorithm

The optimal scheduling problem for renewable energy-integrated power distribution networks inherently represents a highly complex, nonlinear, multi-variable, and multi-constrained discrete optimization challenge. Modern heuristic AI algorithms—drawing inspiration from natural systems—have proliferated and demonstrate broad applicability in power system operational optimization [85,86]. These methods offer efficient, intelligent optimization by simulating natural processes or biological behaviors. Prominent heuristic approaches include particle swarm optimization [87,88], genetic algorithms [89], gray wolf optimization [90], and variable-space iterative contraction methodologies [91,92].

To enhance the solution capability of active distribution network scheduling models under large-scale decision variables, Reference [93] introduces a multi-objective hybrid population collaborative optimization algorithm, which is better suited for addressing non-convex and nonlinear optimization challenges inherent to distribution networks. References [94,95] employ the normalized plane constraint method to derive Pareto optimal solution sets, while Reference [96] utilizes an adaptive ε-constraint multi-objective particle swarm optimization algorithm to generate well-distributed Pareto fronts, with the TOPSIS decision-making approach applied for optimal solution selection. However, existing solution algorithms for active distribution network scheduling models frequently encounter challenges related to slow convergence rates and susceptibility to local optima.

In practical applications, optimization algorithms must meet stringent real-time requirements, particularly in dynamically evolving power systems. To enable real-time optimization, Reference [97] employs a receding horizon optimization approach, where the optimization problem is resolved at each time step to adapt to real-time system changes. Furthermore, Reference [98] enhances system performance through a multi-period scheduling framework that incorporates future system states and objective functions to develop long-term optimization strategies.

In addition, as the scale of the system expands, the complexity of the problem escalates exponentially, leading to prolonged computational time. To enhance scalability, Reference [99] employs parallel computing frameworks to decompose the problem into manageable subcomponents.

4. Study on Optimal Scheduling Strategies for High DG Penetration Rate

The high penetration of distributed generation in active distribution network introduces significant operational challenges to optimal scheduling due to DG output un-certainty. Addressing high-uncertainty distribution network optimization strategies is therefore critical for ensuring secure and economical system operation. This section presents systematic methodologies—including stochastic optimization, two-phase optimization, and multi-phase optimization—developed to meet challenges arising from ex-tensive distributed power integration.

4.1. Stochastic Optimization Methods

(1) Scenario optimization: Methods grounded in probability theory describe uncertain information through scenario generation or via random variables subject to specific probability distributions, establishing stochastic models to minimize expected costs [100,101]. Although scenario-based uncertainty optimization models offer simpler formulations and relatively tractable solutions, scenario scale determination presents implementation challenges. Reference [102] proposed a multi-stage distribution network market clearing model using scenario trees to characterize uncertainty, demonstrating superior performance of the stochastic framework. Reference [103] implemented Latin hypercube sampling for photovoltaic and wind power output scenarios, applied scenario reduction techniques to generate probability-weighted scenario sets, and established a scenario-based active-reactive power coordinated optimization model.

(2) Chance constrained optimization: It incorporates random variables to characterize uncertainties, permitting distribution network operational constraints to be probabilistically unsatisfied—a critical feature enabling flexible decision-making [104]. However, confidence level selection remains methodologically challenging. To address this, Reference [105] employs sample average approximation to convert the original chance-constrained planning model into a computationally tractable deterministic formulation.

(3) Robust optimization: The robust optimization method models the wind power by constructing an uncertainty set, which can obtain the optimization scheme under the worst scenario and ensure that the decisions under any scenario do not violate the security constraints, but the optimization results may be too conservative. Reference [106] proposes a two-stage robust optimization model for AC-DC hybrid distribution networks with the objectives of reducing operating cost and controlling reactive voltage, which can obtain the reactive voltage control scheme with the least operating cost under the worst renewable energy output scenario.

(4) Distributionally robust optimization (DRO): It synthesizes methodologies from robust and stochastic optimization, generating decisions under the worst-case probability distribution of random variables [107,108]. This approach mitigates solution conservatism while entailing significant computational complexity. In Reference [109], a data-driven DRO model for AC-DC hybrid distribution networks is proposed, employing jointly constrained ambiguity sets via 1-norm and ∞-norm to bound the probability distribution of stochastic information. Compared to conventional robust optimization models, this formulation exhibits reduced conservatism.

4.2. Two-Stage Stochastic Optimization Method

The traditional two-stage optimization model includes only two stages, day-ahead and real-time, and uses a stochastic scenario to describe the uncertain information of the wind and light outputs, and the mathematical model is shown in Equation (11) [110,111]:

$$\left\{\begin{array}{l}{K}_1{x}_{1,t}+{\displaystyle {\displaystyle \sum }_{s=1}^N}g(s)K_2{x}_{2,t,s}\\ s.t.A_t{x}_{1,t}+B_{t,s}{x}_{2,t,s}\le b_{t,s}\\ t=1,2,\cdots ,T\\ s=1,2,\cdots ,N\end{array}\right.,$$

(11)

where $K_1$ and $K_2$ are the constant coefficients for the day-ahead and real-time phases, respectively; $x_{1,t}$ is the discrete decision variable for the day-ahead phase; $x_{2,t,s}$ is the continuous decision variable for the real-time phase; $g(s)$ is the probability of each scenario; $A_t$ and $B_{t,s}$ are the coefficient matrices of the decision variables for the day-ahead and real-time phases, respectively; $b_{t,s}$ is the matrix of constants characterizing the parameters of the system; T is the scheduling period; and N is the total number of scenarios.

Conventional two-stage stochastic optimization models lack an intraday adjustment mechanism, characterized by fixed first-stage decision variables insensitive to evolving uncertain scenarios in the second stage, whereas second-stage variables exhibit dynamic responsiveness to real-time stochastic variations [112].

4.3. Multi-Stage Stochastic Optimization Approach

The absence of an intraday regulation phase in two-stage stochastic optimization typically elevates real-time balancing costs, diminishing overall economic efficiency in distribution network operations. To address this limitation, Reference [113] introduced a multi-stage stochastic optimal dispatch framework. In this model, photovoltaic output observations diverge across day-ahead, intraday, and real-time phases, causing purchased power from the main grid to fluctuate during operational decisions. The three-stage trading mechanism operates as follows: power deficits during intra-day/real-time phases trigger high-cost supplementary purchases, while surpluses enable low-revenue sales of excess energy.

The multi-stage stochastic optimization model structures the distribution network scheduling process across sequential phases, permitting stage-specific variable adjustments contingent on newly observed photovoltaic output uncertainties while ensuring decision consistency within each scenario. This mathematical formulation is expressed as follows:

$$\left\{\begin{array}{l}\min {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{s=1}^N}g(s)(K_1^{\prime }{\mathit{x}}_{1,t,s}^{\prime }+K_2^{\prime }{\mathit{x}}_{2,t,s}^{\prime }+K_3^{\prime }{\mathit{x}}_{3,t,s}^{\prime })\\ s.t.{\mathit{A}}_{t,s}^{\prime }{\mathit{x}}_{1,t,s}^{\prime }+{\mathit{B}}_{t,s}^{\prime }{\mathit{x}}_{2,t,s}^{\prime }+{\mathit{C}}_{t,s}^{\prime }{\mathit{x}}_{3,t,s}^{\prime }\le {\mathit{b}}_{t,s}^{\prime }\\ t=1,2,\cdots ,T\\ s=1,2,\cdots ,N\end{array}\right.,$$

(12)

where $K_1^{\prime }$, $K_2^{\prime }$, and $K_3^{\prime }$ are constant coefficients for the day-ahead, intraday and real-time phases, respectively; ${\mathit{x}}_{1,t,s}^{\prime }$ is the discrete decision variable for the day-ahead phase; ${\mathit{x}}_{2,t,s}^{\prime }$ and ${\mathit{x}}_{3,t,s}^{\prime }$ are the continuous decision variables for the intraday and real-time phases, respectively; ${\mathit{A}}_{t,s}^{\prime }$, ${\mathit{B}}_{t,s}^{\prime }$, and ${\mathit{C}}_{t,s}^{\prime }$ are the coefficient matrices of the decision variables for the day-ahead, intraday and real-time phases, respectively; and ${\mathit{b}}_{t,s}^{\prime }$ is the matrix of constants characterizing the system parameters.

5. Application of Artificial Intelligence Technology in Optimal Scheduling

Traditional distribution network optimization methods—including mathematical programming and heuristic algorithms—exhibit excessive dependence on accurate physical models. Operational uncertainties and observational constraints within distribution networks, however, render precise line parameters and system topology practically unobtainable. Consequently, artificial intelligence techniques [114,115,116] have gained widespread application in optimization scheduling, enabling extraction of latent patterns from extensive datasets without requiring precise physical models, thereby offering innovative frameworks for addressing complex scheduling challenges. Among the artificial intelligence methodologies, deep learning [117] and reinforcement learning [118,119] constitute two principal research branches.

5.1. Reinforcement Learning Methods

Reinforcement learning represents a machine learning paradigm wherein agents refine behavioral strategies through iterative environmental interactions and corresponding reward signals. Fundamentally operating within unsupervised learning frameworks [120], this approach dynamically adjusts decision policies to maximize cumulative rewards and demonstrates broad applicability across gaming applications, robotic control systems, and resource scheduling domains.

5.1.1. Markov Decision Process

Markov decision process (MDP) is often used to model reinforcement learning problems, Markov decision process contains the following four elements:

(1)

State set: S is the set of states of the environment, where the action of the intelligent body at moment t is $a_t\in A$;

(2)

Action set: A is the set of actions of an intelligent body, where the action of the intelligent body at moment t is $a_t\in A$;

(3)

State transfer process: The state transfer process $T(s_t,a_t,s_{t+1})\sim P_r(s_{t+1}|s_t,a_t)$ represents the probability that an intelligent body will perform an action in state and then transfer to the next moment state $s_{t+1}$;

(4)

Reward Function: The reward function $r_t$ is the immediate reward obtained by an intelligent body after performing the action $a_t$ in the state $s_t$;

At each turn, the intelligent body first observes the current state of the environment $s_t$ and makes a decision based on the state $a_t$, when the action is executed, the environment feeds back a reward value $r_t$ to the intelligent body, and then the environment shifts to the next state $s_{t+1}$, which is a Markov decision-making process, schematically shown in Figure 8.

5.1.2. Partially Observable Markov Decision Processes

Real-world problem-solving frequently encounters systems with partially observable states, compelling decision-making agents to infer system conditions exclusively through indirect observations, thereby determining appropriate actions. The partially observable Markov decision process (POMDP) framework was consequently developed to address such sequential decision challenges within environments of imperfect state information.

POMDP framework extends the standard MDP by formally incorporating a set of observations and an observation function. This model is fully specified by a six-tuple $〈S,A,T,R,\mathsf{\Omega },O〉$, wherein Ω represents the complete set of possible observations. The observation function, denoted as O: S × A → Π(Ω), characterizes the probabilistic relationship between states, actions, and observations; specifically, O (s’, a, o) provides the probability of an agent perceiving observation o after executing action a and transitioning to states.

5.2. Deep Reinforcement Learning Methods

Increasingly complex real-world scenarios challenge conventional machine learning methods to concurrently address environmental feature extraction and optimal decision-making. This limitation has motivated the development of DRL methodologies, which integrate deep learning’s representational capabilities with reinforcement learning’s sequential decision-making frameworks [121].

Deep learning leverages deep neural networks to autonomously extract high-level feature representations from extensive raw datasets, eliminating manual feature engineering—exemplified by precise target identification in image recognition. This capability facilitates environmental state comprehension in complex scenarios. Reinforcement learning optimizes behavioral policies through agent-environment interactions and environmental reward signals, such as performance maximization in gaming applications, enabling optimal decision-making based on current conditions. Deep reinforcement learning integrates perceptual and decision-making capacities, offering novel approaches to real-world problem-solving with considerable potential across autonomous driving, robotic control, gaming AI, and other domains. AlphaGo’s decisive victory over human counterparts demonstrates substantial capabilities, establishing this technology as a prominent research focus with anticipated breakthroughs in diverse fields.

5.3. Deep Reinforcement Learning-Based Optimal Scheduling Strategy for Distribution Networks

Deep reinforcement learning demonstrates superior control performance in numerous complex operational environments and has achieved successful deployment for optimization and control challenges in active distribution networks. A reinforcement learning-based online control framework for AC/DC hybrid microgrid energy storage systems was developed in [122], employing neural networks to dynamically model system behavior and using reinforcement learning algorithms to derive optimal control policies. Validation through software simulations and hardware experiments demonstrated its capacity for efficient system management under unknown model parameters. In [123], researchers presented a stochastic scheduling method for energy storage systems that integrated Monte Carlo tree search to estimate expected maximum Q-value, combined with embedded scheduling rules to constrain infeasible action exploration, effectively addressing multi-stage stochastic optimization with battery degradation considerations. A Double DQN-based scheduling strategy for energy storage devices was proposed in [124], incorporating future uncertainty into real-time charge/discharge decision-making to optimize sequential control problems. For electric vehicle scheduling, [125] formulated the optimization problem with state transition uncertainty as a Markov decision process, solved through deep deterministic policy gradient algorithms. Comparative experiments on IEEE 33-node systems in [126] revealed that proximal policy optimization (PPO)-based distribution network control outperformed DQN methods. Finally, [127] introduced a deep reinforcement learning approach for storage device scheduling that explicitly accounted for voltage impacts from distributed renewable energy integration in low-voltage distribution networks.

In active distribution network dispatching, key challenges persist including prolonged training duration, strong data dependency, and pronounced model uncertainty. Addressing these issues, study [128] proposed a multi-agent framework that extracts temporal characteristics of continuous dispatch strategies through offline interactions with distribution networks. By parallelizing physical model computations across system dispatch problems, this approach integrates deep reinforcement learning-based offline training with physics-informed online applications for joint decision-making. Concurrently, study [129] developed a hybrid deep reinforcement learning architecture supporting edge computing, which synergizes data-driven deep neural networks with physics-based online dispatch models. However, these methodologies face limitations in model integration complexity, high data coupling demands, and suboptimal training stability.

To eliminate dependence on physical models, Reference [130] employed interactive training between an agent and an actual system, enabling the trained agent to directly compute action values based on observed states and significantly reducing the demand for high-precision physical models. Reference [131] adopted a data-driven approach to train a distribution network simulator, which mimics the system state transition process. By leveraging this simulated process, the reinforcement learning agent can thoroughly explore the system state space. However, this method still relies on the topological structure of the distribution network, and the practical feasibility of actions is difficult to guarantee. Reference [132] utilized sampled data from the distribution network’s SCADA system to train a surrogate model that simulates the power flow calculation process of the distribution network. The trained surrogate model was then integrated into a deep reinforcement learning environment to provide reward signals. Through continuous interaction with the surrogate model, the deep reinforcement learning agent learns optimal strategies for distribution network optimization. To further enhance the accuracy of the trained model, Reference [133] proposed a distribution network optimization strategy based on adversarial reinforcement learning. This strategy combines reinforcement learning with adversarial training, improving the model’s adaptability and decision-making capabilities in complex environments through competition and collaboration among agents.

Through the above analysis, deep reinforcement learning has the following advantages in the application of power distribution networks:

(1)

Deep reinforcement learning employs Markov decision processes (MDPs) to formalize sequential decision-making optimization problems, leveraging Bellman’s equation to systematically deconstruct these problems and enable efficient solutions for sequential control challenges.

(2)

Through algorithmic refinement, deep reinforcement learning achieves model-free control capabilities, mitigating the influence of distribution network modeling inaccuracies on operational strategies.

(3)

Integration of deep reinforcement learning with multi-agent frameworks facilitates offline training and online optimization, enabling rapid system control via localized real-time information and minimal inter-agent communication while reducing reliance on continuous data exchange.

(4)

Hybrid approaches combining deep reinforcement learning with traditional optimization techniques enable coordinated control of heterogeneous devices, fully leveraging power-electronics-enabled devices’ rapid-response capacities to suppress dynamic voltage fluctuations in distribution networks.

However, the inherent “black-box” nature of artificial intelligence algorithms leads to inadequate robustness and interpretability, whereas power systems impose stringent security and reliability requirements. This disjunction contributes to a misalignment between theoretical research and engineering practice in deep reinforcement learning applications for distribution networks, with limited empirical validation in operational environments.

Meanwhile, the application of deep reinforcement learning (DRL) in active distribution network scheduling exhibits the following deficiencies:

(1)

DRL relies on time-consuming hyperparameter tuning to optimize performance. Manual experimental parameter adjustment is only feasible for small-scale models and is difficult to scale up to large-scale scenarios.

(2)

Most studies overlook actual physical constraints, relying solely on penalty terms in the reward function to guide solutions, which fails to ensure feasibility. Furthermore, the decision-making mechanism of neural networks remains opaque, making it difficult to trace the reasons behind the success or failure of the model.

(3)

Distribution networks are characterized by their time-varying and comprehensive nature. Changes in operational conditions can alter power flow distributions, diminishing the effectiveness of offline control strategies. Existing DRL methods have not fully accounted for these dynamic characteristics, resulting in insufficient adaptability.

(4)

DRL typically employs historical data for offline training of agents, which are then deployed online after training. However, extreme conditions that were not encountered during the agent’s training phase may arise during system operation, making it difficult to guarantee the feasibility of solutions provided by the agent under such circumstances.

6. Summary and Outlook

This review systematically examines the current state of research on optimal dispatch strategies for active distribution networks with high penetration of distributed energy resources. We survey domestic and international advancements in this field, identifying three promising frontiers for future exploration:

(1) Addressing computational challenges in active distribution network dispatch, future work may investigate adaptive relaxation strategies based on deep reinforcement learning. By integrating distributed optimization frameworks, these approaches could balance local precision with global coordination. Combining data-driven convex envelope approximation with physics-informed validation mechanisms would enable iterative error correction, ultimately delivering efficient and high-quality optimization solutions for distribution systems with substantial renewable integration.

(2) Next-generation dispatch frameworks could leverage advanced data acquisition and dynamic modeling technologies to establish multi-temporal coordination mechanisms across source-grid-load-storage systems. The development of flexible energy buffering networks incorporating emerging distribution technologies and storage devices, paired with decentralized adaptive control systems, would enhance system flexibility. Concurrently, power market reforms could introduce dynamic pricing models incorporating uncertainty costs, using market-based incentives to engage diverse stakeholders in system regulation. Wide-area measurement systems combined with distributed optimization algorithms would significantly improve cross-regional operational efficiency.

(3) Artificial intelligence technologies hold transformative potential for optimizing distribution networks with high distributed energy penetration. Minute-level forecasting accuracy could be achieved through spatiotemporal convolutional neural networks integrated with meteorological big data models. Multi-agent reinforcement learning frameworks would enable distributed collective intelligence decision-making systems, while digital twin platforms supported by edge computing would create real-time physical-digital mapping capabilities. The fusion of human expertise with machine intelligence would establish enhanced collaborative systems, culminating in AI-driven blockchain platforms that reconfigure energy market ecosystems. This paradigm shift from “load-following generation” to “source-load interaction” would provide critical technological support for the realization of zero-carbon power systems.