A Multi-Source Multi-Timescale Cooperative Dispatch Optimization

Abstract

To address the power and energy balancing challenges faced by high-penetration renewable energy systems under long-term intermittent output conditions, this study proposes a multi-source, multi-timescale collaborative dispatch strategy (2MT-S) integrating wind, solar, hydro, thermal, and hydrogen energy resources. First, a long-term-to-day-ahead coupled scheduling framework is established based on intermittent output duration forecasts (3-day/10-day). By integrating seasonal hydrogen storage and pumped-storage hydroelectric plants, this framework achieves comprehensive coordination among electrochemical storage, thermal power, and other flexible resources. Second, a multi-time-horizon optimization model is developed to simultaneously minimize system operating costs and load curtailment costs. This model dynamically adjusts day-ahead scheduling boundary conditions based on long-term and short-term scheduling results, enabling cross-period resource complementarity during wind and photovoltaic generation troughs. Finally, comparative analysis on an enhanced IEEE 30-bus system demonstrates that compared to traditional day-ahead scheduling, this strategy significantly reduces renewable energy curtailment rates and load curtailment volumes during sustained low-generation periods, fully validating its significant advantages in enhancing power supply reliability and economic benefits.

1. Introduction

In recent years, driven by the national “dual carbon” strategic goals, the construction of new power systems has advanced rapidly. Their structure and operational characteristics have become increasingly complex, posing significant challenges to system resilience [1,2,3]. Both the supply and the demand sides of these new power systems exhibit high uncertainty, shifting the system balancing model from the traditional “deterministic generation tracking uncertain load” to “coordinated matching of dual uncertain sources” [4]. As renewable energy penetration continues to rise, grid dispatch faces unprecedented complexity [5,6,7]. Particularly across different time scales, the intermittent nature of renewable generation causes significant fluctuations in output, severely constraining the system’s power supply capacity and posing potential threats to grid security and stability [8]. Against this backdrop, there is an urgent need to develop new power system control technologies to effectively address increasingly complex power and energy balancing challenges and ensure safe and stable system operation.

A defining characteristic of new power systems is the “Dunkelflaute” phenomenon—a condition where overcast skies coincide with minimal wind conditions, causing both wind and solar power generation to plummet sharply and creating severe challenges for power and energy supply–demand balance. Therefore, the system must fully leverage the potential of various dispatchable resources, implement precise load management, and conduct coordinated optimization dispatch of generation, grid, load, and storage to enhance interaction levels [9].

Regarding dispatch challenges in high-penetration renewable energy systems, existing research primarily focuses on the day-ahead to intraday time scales. Reference [6] proposes a scheduling method for hybrid wind–solar power systems based on two-stage programming and sparse optimization, ensuring both safety and economic efficiency; reference [10] embeds an AGC fine-response model into opportunity-constrained economic dispatch to enhance short-term regulation capabilities; and reference [11] employs model predictive control to achieve reliable day-ahead and intraday optimization scheduling. Additionally, to address wind and solar uncertainty, reference [12] considers wind power ramping characteristics to optimize reserve allocation; and reference [13] proposed proposes a two-stage sample robust optimization model, improving system robustness and flexibility. However, existing research predominantly focuses on short-term time scales, with insufficient attention paid to scheduling issues involving long-duration intermittent output from renewable energy sources (e.g., the “Dunkelflaute” scenario), and it lacks dynamic coupling mechanisms between long-term and day-ahead dispatch [8]. For instance, studies have developed multi-timescale dispatch for integrated energy systems considering demand response and thermal inertia of pipelines to improve short-term flexibility and economy [14]. Nevertheless, such frameworks typically address intraday or day-ahead fluctuations and lack the mechanism necessary to couple with longer-term planning, which is crucial for managing persistent intermittency.

Regarding the coordination of flexible resources, pumped storage, electrochemical storage, and hydrogen energy are gradually being incorporated into scheduling models. The spectrum of energy storage systems (ESS) is broad, extending beyond pumped hydro and batteries to include thermal (e.g., sensible, latent), mechanical (e.g., compressed air, flywheel), and chemical (e.g., hydrogen, synthetic fuels) storage technologies, each with distinct characteristics suited for different duration and power applications. This technological diversity underpins the potential for multi-source complementarity within IES [15]. Reference [16] explores the coordinated development path of pumped storage and new energy storage; reference [17] proposes a two-tier energy management system to enhance the power scheduling of hydrogen energy storage; reference [18] investigates the dispatch potential of hydrogen energy storage from a multi-energy complementarity perspective; and reference [19] further considers the virtual inertia support role of hydrogen systems. Nevertheless, most existing studies fail to incorporate seasonal hydrogen storage into multi-timescale coordination frameworks and lack dynamic coupling mechanisms between long-term and day-ahead scheduling, hindering cross-period energy shifting and resource complementarity.

Distinct from existing approaches, this paper proposes a multi-source and multi-timescale scheduling (2MT-S) strategy for wind, solar, hydro, and thermal power systems. Focusing on the long-interval intermittency of renewable energy, this strategy establishes a coupled day-ahead scheduling framework for long-term (10 days) and short-term (3 days) planning. By incorporating flexible resources such as seasonal hydrogen storage and pumped storage, the strategy dynamically adjusts day-ahead scheduling boundaries based on long-term and short-term scheduling outcomes. This enables cross-period resource optimization, enhancing system reliability and economic efficiency during extreme weather events.

2. 2MT-S Optimized Scheduling Framework

Due to the long-term intermittency of wind and solar power generation [20], wind output drops significantly under windless conditions, while solar output decreases substantially during overcast weather. Furthermore, when intermittent generation persists for extended periods, all energy storage systems must adjust their operations based on the previous day’s energy status. Consequently, day-ahead scheduling alone proves inadequate for managing multi-day intermittent output from renewable sources.

To quantify and address the long-term intermittency of renewable energy output, this paper first defines intermittency events and their duration. The determination of an “intermittency day” is based on the daily total output level: First, define normal daily total output P_N based on the average value of typical historical daily output. For each day d in the forecast period, calculate its projected daily total output P_D. When the daily total output of renewable energy falls below σ times (typically, σ is 30%) of the normal daily total output, that day is classified as an intermittent output day. Identify the date range continuously marked as “Intermittent Output Days.” The start date of this range is d₁, and the end date is d₂. The duration D of an intermittent exertion event is the total number of days from the start date to the end date. The duration of intermittent output for renewable energy ranges from as short as 2–3 days to as long as 7–8 days. The time scale for extended scheduling cycles must be adjusted based on actual forecast conditions. The duration, D, is defined as follows:

$$\left\{\begin{array}{c}{P}_D{|}_{d_1\le d\le d_2}\le \sigma P_N\\ D=d_2-d_1\end{array}\right.$$

(1)

where P_D is the total output of intermittent renewable energy sources on a normal day, P_N is the total output of renewable energy sources on a normal day, d₁ is the start date of intermittent output, and d₂ is the end date of intermittent output.

The short-term scheduling threshold is 3 days, and the long-term scheduling threshold is 10 days. The 3-day threshold corresponds to the typical influence cycle of common weather systems and the usual duration of power supply from electrochemical energy storage; the 10-day threshold takes into account longer-term weather patterns and the scheduling needs of seasonal energy storage. This classification is based on power grid scheduling practices [8]. When the predicted duration of intermittent output is less than 3 days, short-term scheduling with a 3-day lead time shall be conducted. When the duration is greater than 3 days but less than 10 days, long-term scheduling with a 10-day lead time shall be conducted. Each day, based on the latest forecast data, D is reassessed to determine whether to activate the long-term or short-term scheduling model, rolling updates are applied to the schedule plan for the next 3 or 10 days. At the start of each scheduling cycle, the initial state of charge (SOC) for all energy storage systems (electrochemical, hydrogen, pumped storage) must match the SOC at the end of the previous day’s long-term/short-term scheduling cycle. The upper and lower limits of power generation output for thermal power units in day-ahead scheduling are determined by the set of output results from their long-term/short-term scheduling periods (such as minimum values, maximum values, or a specified confidence interval), with minor adjustments permitted based on more precise short-term forecasts. Both long-term and short-term scheduling are conducted while ensuring system economic efficiency and power supply–demand balance. Taking long-term scheduling as an example, each long-term scheduling cycle spans 10 days, with one day designated as the observation day. This observation day occurs in all 10 cycles. The final day of the first cycle is selected as the observation day, termed the scheduling day. This scheduling day also corresponds to the penultimate day of the second cycle. This pattern continues. The output of thermal power units and the state of energy storage after scheduling in each cycle are aggregated into the thermal power unit output set and the energy storage output set, respectively. Their upper and lower bounds are updated to the upper and lower bounds of the day-ahead schedule. Both long-term/short-term scheduling and day-ahead scheduling have a time granularity of 1 h, enabling multi-source, multi-timescale scheduling. The 2MT-S scheduling framework is shown in Figure 1.

Daily power system operation scheduling is conducted under the coordinated guidance of long-term/short-term scheduling and day-ahead scheduling. Long-term/short-term scheduling ensures overall power and energy balance at a larger timescale based on medium-to-long-term renewable generation and load forecasts. Day-ahead scheduling refines adjustments using more precise short-term forecasts within the long-term/short-term scheduling framework to achieve precise power and energy balance at the day-ahead timescale.

3. 2MT-S Model

3.1. Long-Term and Short-Term Optimization Model

The long-term and short-term optimization dispatch model proposed in this section incorporates the number of days of intermittent output from renewable energy sources into the dispatch strategy. This enables dynamic switching between long-term and short-term dispatch, enhancing the system’s ability to manage intermittent output through coordinated dispatch of wind, solar, hydro, thermal, and storage resources.

3.1.1. Objective Function

This paper proposes a long-term and short-term optimization model designed to achieve either long-term or short-term scheduling based on the number of consecutive days with intermittent output from renewable energy sources. During the scheduling period, the model coordinates the combined output of wind, solar, hydro, thermal, and storage resources. The storage components include electrochemical storage [21,22], seasonal hydrogen storage, and pumped storage [23]. The objective is to minimize system operating costs C. The objective function is as follows:

$$\min C=C_1+C_2+C_3+C_4$$

(2)

where C is the comprehensive operating cost of the power grid, C₁ is the operating cost of thermal power units, C₂ is the operating cost of energy storage, C₃ is the cost of curtailed energy, and C₄ is the cost of load shedding.

(1)

Operating Costs of Thermal Power Units

The operating costs of thermal power units [24] primarily encompass fuel expenses and startup/shutdown costs for each unit:

$$C_1={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^N\left[a_i{P}_{gi,t}^2+b_i{P}_{gi,t}+c_i+u_{gi,t}(1-u_{gi,t-1})S_{gi}\right]}}$$

(3)

where T is the scheduling cycle; N is the total number of thermal power units; a_i, b_i, and c_i are the consumption characteristic coefficients for the secondary, primary, and constant terms of thermal power unit i, respectively; u_gi,t is the start-up/shutdown status of thermal power unit I; and S_gi is the start-up/shutdown cost of thermal power unit i.

(2)

Energy Storage Operating Costs

Energy storage operating costs include depreciation costs for electrochemical storage, startup costs for hydrogen storage equipment, and startup costs for pumped storage power plants:

$$C_2={\displaystyle \sum _{t=1}^T[{\varsigma }_{\mathrm{soc}}(P_{\mathrm{soc},t}^{\mathrm{ch}}+P_{\mathrm{soc},t}^{\mathrm{dis}})+{\varsigma }_{\mathrm{ps}}(P_{\mathrm{ps},t}^{\mathrm{ch}}+P_{\mathrm{ps},t}^{\mathrm{dis}})]+}{\displaystyle \sum _{t=1}^{T_{\mathrm{H}}}{C}_{\mathrm{H},t}}$$

(4)

where ζ_soc is the operational cost coefficient for electrochemical energy storage, P^ch_soc,t and P^dis_soc,t are the charging and discharging power of electrochemical energy storage at time t, respectively, ζ_ps is the operational cost coefficient for pumped storage hydroelectric power plants, P^ch_ps,t and P^dis_ps,t are the charging and discharging power of pumped storage hydroelectric power plants at time t, respectively, T_H is the total startup time of electrolyzers within the dispatch cycle, and C_H,t is the startup cost of the electrolyzer at time t.

(3)

Curtailment Costs

Curtailment refers to the phenomenon where renewable energy generation is halted due to insufficient grid acceptance capacity and the inherent instability of renewable power generation [25]. In the new power system, renewable energy sources include wind power, photovoltaic power generation, and hydropower. To maximize the utilization of various renewable energy sources, penalty costs for the curtailment of each type of renewable energy are incorporated into the objective function:

$$C_3={\displaystyle \sum _{t=1}^T({\rho }_{WT}{P}_{WT,t}+{\rho }_{PV}{P}_{PV,t}+{\rho }_{HPP}{P}_{HPP,t})}$$

(5)

where ρ_WT, ρ_PV, and ρ_HPP are the curtailment penalty coefficients for wind power, photovoltaic power generation, and hydropower, respectively; and P_WT,t, P_PV,t, and P_HPP,t are the curtailed power output of wind power, photovoltaic power generation, and hydropower at time t, respectively.

(4)

Load Shedding Cost

When renewable energy sources exhibit prolonged intermittent output, the system incurs significant load shedding to maintain power supply–demand balance. To minimize load shedding and enhance system reliability, a load shedding penalty term is incorporated into the objective function as the load shedding cost:

$$C_4={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{n=1}^{N_o}{\rho }_{\mathrm{c}}{D}_{\mathrm{c},t}^n}}$$

(6)

where ρ_c is the load penalty coefficient, Dⁿ_c,t is the load at node n in the system at time t, and N_o is the total number of nodes in the system.

3.1.2. Constraints

The optimization dispatch model for the new power system must satisfy the following constraints during the solution process:

(1)

Node power balance constraint

$$P_{\mathrm{g},t}^n+P_{\mathrm{wt},t}^n+P_{\mathrm{pv},t}^n+P_{\mathrm{hpp},t}^n+P_{\mathrm{soc},t}^{n,\mathrm{dis}}-P_{\mathrm{soc},t}^{n,\mathrm{ch}}+P_{\mathrm{ps},t}^{n,\mathrm{dis}}-P_{\mathrm{ps},t}^{n,\mathrm{ch}}+P_{\mathrm{H},t}^{n,\mathrm{dis}}-P_{\mathrm{H},t}^{n,\mathrm{ch}}+{\displaystyle \sum _{l\in {\Omega }_n^{LT}}{P}_{\mathrm{l},t}^n-}{\displaystyle \sum _{l\in {\Omega }_n^{LF}}{P}_{\mathrm{l},t}^n}=D_t^n-D_{\mathrm{c},t}^n$$

(7)

where Pⁿ_g,t, Pⁿ_wt,t, Pⁿ_pv,t, and Pⁿ_hpp,t are the thermal power, wind power, photovoltaic power, and hydropower outputs at node n of the system at time t, respectively; P^n,dis_soc,t, P^n,dis_ps,t, and P^n,dis_H,t are the discharge power of electrochemical storage, pumped storage power plants, and seasonal hydrogen storage at node n of the system at time t, respectively; P^n,ch_soc,t, P^n,ch_ps,t, and P^n,ch_H,t are the charging power of electrochemical storage, pumped storage hydroelectric plants, and seasonal hydrogen storage at node n in the system at time t, respectively; Pⁿ_l,t is the transmission power of the lines connected to node n at time t; Ω^LT_n and Ω^LF_n are the sets of lines terminating at and originating from node n, respectively; and Dⁿ_t is the load at node n in the system at time t.

(2)

Operational Constraints of Thermal Power Units [26]

Thermal power units operate within upper and lower output limits, while the rate of output increase or decrease is also constrained by their inherent physical characteristics:

$$u_{gi,t}{P}_{gi}^{\min }\le P_{gi,t}\le u_{gi,t}{P}_{gi}^{\max }$$

(8)

$$\left\{\begin{array}{c}{u}_{gi,t}{P}_{gi,t}-u_{gi,t-1}{P}_{gi,t-1}\le r_{gi}^{\mathrm{up}}\\ u_{gi,t-1}{P}_{gi,t-1}-u_{gi,t}{P}_{gi,t}\le r_{gi}^{\mathrm{down}}\end{array}\right.$$

(9)

where P^min_gi and P^max_gi are the minimum and maximum power levels of the i-th thermal power unit, respectively, and r^up_gi and r^down_gi are the maximum ramp-up rate and maximum ramp-down rate of the i-th thermal power unit, respectively.

(3)

New Energy Output Constraints

The output of all new energy sources at time t shall not exceed their predicted values. In this paper, hydropower is treated as an energy source with a maximum technical output ceiling and uncontrollable output. Its actual output can be freely adjusted below the forecast value during optimization:

$$\left\{\begin{array}{c}0\le P_{\mathrm{wt},t}\le P_{\mathrm{wt},t}^{\mathrm{pre}}\\ 0\le P_{\mathrm{pv},t}\le P_{\mathrm{pv},t}^{\mathrm{pre}}\\ 0\le P_{\mathrm{hpp},t}\le P_{\mathrm{hpp},t}^{\mathrm{pre}}\end{array}\right.$$

(10)

where P^pre_wt,t, P^pre_pv,t and P^pre_hpp,t are the output prediction values for wind power, photovoltaic power, and hydropower at time t, respectively.

(4)

Operational Constraints of Electrochemical Energy Storage [27]

Constraints on electrochemical energy storage include power constraints during charging and discharging, as well as energy capacity constraints:

$$\left\{\begin{array}{c}0\le P_{\mathrm{soc},t}^{\mathrm{ch}}\le P_{\mathrm{soc},\max }^{\mathrm{ch}}{u}_{\mathrm{soc},t}^{\mathrm{ch}}\\ 0\le P_{\mathrm{soc},t}^{\mathrm{dis}}\le P_{\mathrm{soc},\max }^{\mathrm{dis}}{u}_{\mathrm{soc},t}^{\mathrm{dis}}\\ u_{\mathrm{soc},t}^{\mathrm{ch}}+u_{\mathrm{soc},t}^{\mathrm{dis}}\le 1\end{array}\right.$$

(11)

$$\left\{\begin{array}{c}{Q}_{\mathrm{soc},t}=Q_{\mathrm{soc},t-1}+P_{\mathrm{soc},t}^{\mathrm{ch}}{\eta }_{\mathrm{soc}}^{\mathrm{ch}}-P_{\mathrm{soc},t}^{\mathrm{dis}}/{\eta }_{\mathrm{soc}}^{\mathrm{dis}}\\ Q_{\mathrm{soc}}^{\min }\le Q_{\mathrm{soc},t}\le Q_{\mathrm{soc}}^{\max }\end{array}\right.$$

(12)

where P^ch_soc,max and P^dis_soc,max are the upper limits of the electrochemical energy storage charging and discharging power, respectively, u^ch_soc,t and u^dis_soc,t are the charging and discharging states of the electrochemical energy storage at time t, Q_soc,t is the stored energy of the electrochemical energy storage at time t, η^ch_soc and η^dis_soc are the charge and discharge efficiency of electrochemical energy storage, respectively, and Q^min_soc and Q^max_soc are the minimum and maximum stored energy capacities of the electrochemical energy storage system, respectively.

(5)

Seasonal Hydrogen Storage Operational Constraints

This study employs low-pressure hydrogen storage for seasonal applications. Due to the physical characteristics of the equipment, inherent energy losses occur during the energy release process. Therefore, define $ħ$ as the daily self-loss coefficient of hydrogen energy storage, which characterizes the natural energy decay rate during storage due to factors such as hydrogen leakage, permeation, or the energy loss required to maintain storage pressure.

$$\left\{\begin{array}{c}{\mu }_{\mathrm{H},t}^{\mathrm{ch}}+{\mu }_{\mathrm{H},t}^{\mathrm{dis}}\le 1\\ 0\le P_{\mathrm{H},t}^{\mathrm{ch}}\le {\mu }_{\mathrm{H},t}^{\mathrm{ch}}{S}_{\mathrm{H}}\\ 0\le P_{\mathrm{H},t}^{\mathrm{dis}}\le {\mu }_{\mathrm{H},t}^{\mathrm{dis}}{S}_{\mathrm{H}}\\ S_1=S_{\mathrm{end}}=ƛS_{\mathrm{H}}\\ S_{\mathrm{H},t}=(1-ħ)S_{\mathrm{H},t-1}+(P_{\mathrm{H},t}^{\mathrm{ch}}{\eta }_{\mathrm{H}}^{\mathrm{ch}}-P_{\mathrm{H},t}^{\mathrm{dis}}/{\eta }_{\mathrm{H}}^{\mathrm{dis}})\end{array}\right.$$

(13)

where μ^ch_H,t and μ^dis_H,t are the charge/discharge states of seasonal hydrogen storage at time t, P^ch_H,t and P^dis_H,t are the charge/discharge power of seasonal hydrogen storage at time t, S_H is the capacity of seasonal hydrogen storage, S₁ and S_end are the initial and final capacities of the seasonal hydrogen storage scheduling cycle, $ƛ$ is the proportional coefficient of the total capacity occupied by the initial and final states of seasonal hydrogen storage, S_H,t is the capacity of seasonal hydrogen storage at time t, $ħ$ is the self-loss coefficient, and η^ch_H and η^dis_H are the charging and discharging efficiencies of seasonal hydrogen storage, respectively.

(6)

Operational Constraints of Pumped Storage Power Plants

The operational constraints of pumped storage primarily include reservoir capacity constraints, power constraints, and functional conversion constraints. The basic model aligns with that in [28].

$$\left\{\begin{array}{c}{P}_{\mathrm{ps},t}^{n,\mathrm{ch}}=x_{\mathrm{ps},t}^{n,\mathrm{ch}}{P}_{\mathrm{ps},e}^n\\ x_{\mathrm{ps},t}^{n,\mathrm{dis}}{P}_{\mathrm{ps},t}^{n,\mathrm{dis},\min }\le P_{\mathrm{ps},t}^{n,\mathrm{dis}}\le x_{\mathrm{ps},t}^{n,\mathrm{dis}}{P}_{\mathrm{ps},t}^{n,\mathrm{dis},\max }\\ 0\le x_{\mathrm{ps},t}^{n,\mathrm{ch}}+x_{\mathrm{ps},t}^{n,\mathrm{dis}}\le 1\\ \begin{array}{c}{V}_i^{\min }\le V_{i,t}\le V_i^{\max }\\ V_{i,t+1}=V_{i,t}-(c_{\mathrm{dis}}{P}_{\mathrm{ps},t}^{n,\mathrm{dis}}+c_{\mathrm{ch}}{P}_{\mathrm{ps},t}^{n,\mathrm{ch}})\Delta t\end{array}\end{array}\right.$$

(14)

where x^n,ch_ps,t and x^n,dis_ps,t are the pumping and generating states of pumped storage unit i during time period t, respectively, P^n,ch_ps,t and P^n,dis_ps,t are the pumping power and generating power of pumped storage unit i during time period t, respectively, Pⁿ_ps,e is the rated installed capacity of pumped-storage unit I, P^n,dis,min_ps,t and P^n,dis,max_ps,t are the minimum pumping power and maximum pumping power of pumped storage unit i, respectively, V_i,t the reservoir capacity of pumped storage unit i at time t, V^min_i and V^max_i are the minimum reservoir capacity and maximum reservoir capacity of pumped storage unit I, c_dis and c_ch are the conversion coefficients between the generating power and pumping power versus flow rate for pumped-storage units, respectively, and Δt is the time step.

(7)

DC Power Flow Constraints [29]

To ensure safety, the system must satisfy line power flow constraints during normal operation, ensuring line power flows do not exceed safety limits. For simplification, this paper employs a direct current power flow model for network analysis, based on the following core assumptions: line resistance and ground admittance are neglected; the magnitude of voltage at each node is normalized to 1.0; only active power flow is considered; and the phase angle difference θ is small, satisfying sin θ ≈ θ:

$$\left\{\begin{array}{c}{P}_{L,t}=({\theta }_t^s-{\theta }_t^e)/X_L\\ -\overline{P_L}\le P_{L,t}\le \overline{P_L}\\ {\theta }_n^{\min }\le {\theta }_{n,t}\le {\theta }_n^{\max }\end{array}\right.$$

(15)

where P_L,t is the transmission power of line L at time t, θ_st and θ_et are the voltage phase angles at the start and end nodes of line L at time t, respectively, X_L is the reactance of line L, $\overline{P_L}$ is the upper limit of transmission power for line L, θ_n,t is the voltage phase angle at node n at time t, and θ^min_n and θ^max_n are the lower and upper limits of voltage phase angles at node n, respectively.

(8)

Load Shedding Constraints

During periods of intermittent output from renewable energy sources, the system may implement load shedding to maintain power supply–demand balance. Load shedding at any node must not exceed the node’s total load capacity. To ensure the effectiveness of the proposed method under extreme conditions and to focus on the study of long-term intermittency issues, this model assumes that during periods of normal (non-intermittent) renewable energy output, the system possesses sufficient regulation capacity. Therefore, no planned load shedding is scheduled:

$$\left\{\begin{array}{c}0\le D_{c,t}^n\le D_t^n\\ D_{c,\tau }^n=0\end{array}\right.$$

(16)

3.2. Recent Dispatch Model

During periods of intermittent output from renewable energy sources, thermal power units and energy storage play a critical role in ensuring overall system power supply–demand balance [30]. The daily energy states of thermal power units and storage are closely related to the previous day’s output. Therefore, by using the results of long-term and short-term optimization scheduling as boundary conditions and coupling the initial states of thermal power units and storage, the continuity and consistency of the scheduling strategy are achieved. The objective function and fundamental constraints of the day-ahead scheduling model are formally consistent with those in Section 3.1, differing only in scheduling horizon. Therefore, they are not repeated here. The newly added constraints are listed below:

(1)

Thermal Power Unit Coupling Constraints

Thermal power unit output in day-ahead scheduling is guided by long-term and short-term scheduling. Additionally, since renewable energy forecast errors differ between long-term/short-term and day-ahead stages, thermal power unit output is permitted to adjust within a specified range. σ_gi,t is set based on the uncertainty of the output forecast error between the long-term/short-term forecast and the current forecast. This article takes a value of 5%:

$$-{\sigma }_{gi,t}+P_{gi,{\gamma }_t}^{\min }\le P_{gi,t}\le P_{gi,{\gamma }_t}^{\max }+{\sigma }_{gi,t}$$

(17)

where γ_t is the corresponding time point t in both long-term/short-term scheduling and day-ahead scheduling, P^min_gi,γt and P^max_gi,γt are the lower and upper bounds of the output set for thermal power unit i at time point γt in long-term/short-term scheduling, respectively, and σ_gi,t is the output adjustment deviation of thermal power unit i at time point t caused by renewable energy forecasting errors.

(2)

Energy Storage State Coupling Constraints

The initial energy state of all energy storage devices shall match the energy state at the initial time of the final day in both long-term and short-term dispatch results. The output of all energy storage devices is constrained by long-term and short-term dispatch, with adjustments permitted within specified ranges:

$$\left\{\begin{array}{c}{Q}_{\mathrm{soc},1}=Q_{\mathrm{soc},{\gamma }_1}\\ S_{\mathrm{H},1}=S_{\mathrm{H},{\gamma }_1}\\ Q_{\mathrm{ps},1}=Q_{\mathrm{ps},{\gamma }_1}\\ P_{\mathrm{soc},{\gamma }_t}^{\mathrm{ch},\min }\le P_{\mathrm{soc},t}^{\mathrm{ch}}\le P_{\mathrm{soc},{\gamma }_t}^{\mathrm{ch},\max }\\ P_{\mathrm{soc},{\gamma }_t}^{\mathrm{dis},\min }\le P_{\mathrm{soc},t}^{\mathrm{dis}}\le P_{\mathrm{soc},{\gamma }_t}^{\mathrm{dis},\max }\\ P_{\mathrm{H},{\gamma }_t}^{\mathrm{ch},\min }\le P_{\mathrm{H},t}^{\mathrm{ch}}\le P_{\mathrm{H},{\gamma }_t}^{\mathrm{ch},\max }\\ P_{\mathrm{H},{\gamma }_t}^{\mathrm{dis},\min }\le P_{\mathrm{H},t}^{\mathrm{dis}}\le P_{\mathrm{H},{\gamma }_t}^{\mathrm{dis},\max }\\ P_{\mathrm{ps},{\gamma }_t}^{\mathrm{dis},\min }\le P_{\mathrm{ps},t}^{\mathrm{dis}}\le P_{\mathrm{ps},{\gamma }_t}^{\mathrm{dis},\max }\\ P_{\mathrm{ps},{\gamma }_t}^{\mathrm{ch},\min }\le P_{\mathrm{ps},t}^{\mathrm{ch}}\le P_{\mathrm{ps},{\gamma }_t}^{\mathrm{ch},\max }\end{array}\right.$$

(18)

where Q_soc,1, S_H,1, and Q_ps,1 are the energy states of electrochemical storage, seasonal hydrogen storage, and pumped storage power plants at the start time of the day-ahead scheduling; Q_{soc, γ1}, S_{H, γ1}, and Q_{ps, γ1} are the energy states of electrochemical storage, seasonal hydrogen storage, and pumped storage power plants at the start time of the final day of long-term and short-term scheduling; P^ch,min_soc,γt and P^ch,max_soc,γt are, respectively, the minimum and maximum values of the electrochemical energy storage charging power set during time γ_t in short-term and long-term scheduling; P^dis,min_soc,γt and P^dis,max_soc,γt are, respectively, the minimum and maximum values of the discharging power set for electrochemical storage at time γ_t during long-term and short-term scheduling; P^ch,min_H,γt and P^ch,max_H,γt are, respectively, the minimum and maximum values of the charging power set for seasonal hydrogen storage at time γ_t during long-term and short-term scheduling; P^dis,min_H,γt and P^dis,max_H,γt are, respectively, the minimum and maximum values of the discharging power set for seasonal hydrogen storage at time γ_t during long-term and short-term scheduling; P^dis,min_ps,γt and P^dis,max_ps,γt are the lower and upper bounds of the power generation set for pumped storage during short-term and long-term scheduling at time γ_t; P^ch,min_ps,γt and P^ch,max_ps,γt are the lower and upper bounds of the pumping power set for pumped storage during short-term and long-term scheduling at time γ_t; and P^dis_ps,t and P^ch_ps,t are the power output during generation and pumping states, respectively, for pumped storage.

3.3. Model Solving

The long-term/short-term dispatch model constructed in this paper and the day-ahead dispatch model both belong to mixed-integer linear programming problems. The core decision variables in the model comprise two categories: continuous variables, such as the output of each power generation unit (thermal, wind, solar PV, hydroelectric) and the charge/discharge power and energy status of various energy storage types (electrochemical, hydrogen, pumped storage); and critical binary integer variables representing discrete equipment states, such as the start/stop status of thermal units, the mutually exclusive charge/discharge state of electrochemical storage, and the operational state of hydrogen storage. Although the charging/discharging processes and efficiency constraints of energy storage systems contain product terms, they are successfully integrated into the linear framework by introducing binary variables for charging/discharging states and applying the large M method for linear modeling.

The models are constructed using the YALMIP modeling toolbox in MATLAB R2023a. The resulting MILP problems are solved using the Gurobi Optimizer 10.0.1. All simulations were conducted on a computer equipped with an Intel i9-13980HX processor which is manufactured by ASUS in Taiwan, China, and 24 GB of RAM. In this setting, all case study scenarios were solved to prove optimality within 3 to 4 min of computation time.

4. Case Study

4.1. System Parameters

The improved IEEE 30-bus system referenced in [31] was modified based on this case study for simulation analysis. The system topology is shown in Figure 2, where G is thermal power units, P is photovoltaic power plants, hpp is hydropower plants, W is wind power units, S is electrochemical energy storage, H is seasonal hydrogen storage, ps is pumped storage hydroelectric plants, the numbers represent node IDs, and the arrows indicate load. The system comprises five thermal power units with specific parameters listed in

Table 1. Parameters of thermal power units.

Thermal Power Unit	1	2	3	4	5
Pmax (MW)	200	200	250	250	250
Pmin (MW)	40	40	50	50	50
a (¥/(MW)2)	0.00048	0.00031	0.002	0.00211	0.00398
b (¥/(MW))	16.19	16.26	16.6	16.5	19.7
c (¥)	1000	970	700	680	450
rup, rdown (MW/h)	130.2	130.2	60	60	90
hg (s)	6.75	6.4	5.3	5.3	5.6
cpfr (¥/(MW))	21	21	18	18	17

. It includes a wind farm with a total capacity of 550 MW, a photovoltaic power station with a total capacity of 250 MW, and a hydropower station with a total capacity of 500 MW. The electrochemical energy storage has a total capacity of 230 MWh, with a maximum charging/discharging power of 50 MW and an efficiency of 95%. Electrolyzer start-up/shutdown costs are 500 ¥. Seasonal hydrogen storage power generation efficiency is 60%, with a maximum power output of 30 MW. $ƛ$ is set to 0.5, and $ħ$ is set to 0.15 [32]. The pumped storage power plant has a total capacity of 1000 MW, a maximum power output of 60 MW, and an efficiency of 85%. The curtailment penalty coefficient is 600 ¥/(MW·h), and the load shedding penalty coefficient is 1000 ¥/(MW·h). Both c_dis and c_ch are 90% in this paper. The long-term intermittent output and load curves for renewable energy are shown in Figure 3, while the short-term intermittent output and load curves are presented in Figure 4.

4.2. Analysis of Optimized Scheduling Results

To comprehensively verify the effectiveness of the model, this paper sets up eight comparative scenarios, which can be divided into three groups: (1) Scenarios 1–3 are used to validate the long-term advantages of pumped storage and seasonal hydrogen storage; (2) Scenarios 4–6 are used to compare the performance of the proposed method with traditional methods under different durations of intermittency; (3) Scenarios 7–8 are used to analyze the feasibility of the proposed method under normal renewable energy output:

• Scenario 1: Long-term dispatch of integrated wind, solar, hydro, and thermal power generation, considering only electrochemical energy storage.
• Scenario 2: Long-term dispatch of integrated wind, solar, hydro, and thermal power generation, considering electrochemical energy storage and pumped storage hydroelectric plants.
• Scenario 3: Long-term dispatch of integrated wind, solar, hydro, and thermal power generation, considering electrochemical storage, pumped storage hydroelectric plants, and seasonal hydrogen storage.
• Scenario 4: Traditional day-ahead economic dispatch during intermittent renewable energy output [31].
• Scenario 5: 2MT-S coupled economic dispatch (long-term intermittent output from renewable energy).
• Scenario 6: 2MT-S coupled economic dispatch (short-term intermittent output from renewable energy).
• Scenario 7: Traditional day-ahead economic dispatch during normal output from high-penetration renewable energy systems.
• Scenario 8: 2MT-S coupled economic dispatch during normal output from high-penetration renewable energy systems.

First, by comparing Scenarios 1, 2, and 3, we validate the advantages of pumped storage hydropower and seasonal hydrogen storage over the long term. The dispatch results for Scenarios 1–3 correspond to Figure 5, with detailed comparative analysis shown in

Table 2. Scenario comparison analysis table.

Comparison Scenario	Purpose of Comparison
1, 2, 3	Validating the Advantages of Pumped Storage Power Plants and Seasonal Hydrogen Storage
4, 5, 6	Comparing the Proposed Method with Traditional Methods Under Different Durations of Intermittent Output from New Energy Sources
7, 8	Feasibility Analysis of the Proposed Method under Normal Output Conditions of New Energy Sources

.

Analysis of the simulation results for Scenarios 1 and 2 via Figure 5, and

Table 3. Scheduling results.

Scenario	1	2	3
Thermal Power Output/MW	1.78 × 105	1.8 × 105	1.75 × 105
Power Curtailment Rate/%	16.6	16.0	15.8
Levelized Cost of Electricity/(¥/kW·h)	0.34	0.3394	0.3393
Electrochemical Energy Storage/MW	410.25	367.41	196.84
Seasonal Hydrogen Storage/MW	-	-	259.38
Pumped-storage Power Station/MW	-	3511.9	3509.80
Line Transmission Power/kW	3.3 × 105	3.36 × 105	3.37 × 105
Load shedding/MW	281.27	176.37	128.44
Maximum node Load shedding/MW	89.27	89.27	57.55
Maximum Duration of Load Shedding Event/h	3	3	2

reveals that under joint dispatch of wind, solar, hydro, and thermal power with only electrochemical energy storage integration, the renewable energy curtailment rate is 16.6%. The system levelized cost of electricity is 0.34 ¥/kWh, the total charge/discharge power of electrochemical energy storage is 410.25 MW, the total system load shedding was 281.27 MW, with a maximum instantaneous load shedding at any node reaching 89.27 MW. With pumped storage integration, the renewable energy curtailment rate decreased by 0.6 percentage points, and the system levelized cost of electricity [33] dropped to 0.3394 ¥/kWh, enhancing system economics. Concurrently, it alleviated the power supply pressure on electrochemical storage, reducing the overall system load shedding by 104.9 MW and significantly improving system supply reliability.

Analysis of simulation results for Scenarios 2 and 3 in Figure 5, and Table 3 shows that after further integrating seasonal hydrogen storage into the wind–solar-hydro-thermal dispatch system:

-

The renewable energy curtailment rate decreased by 0.2 percentage points;

-

The system levelized cost of electricity decreased to 0.3393 ¥/kWh;

-

The output of electrochemical energy storage decreased from 367.41 MW to 196.84 MW;

-

Seasonal hydrogen storage provided an output of 259.38 MW, significantly alleviating the pressure on electrochemical storage and further enhancing economic efficiency.

Concurrently, the overall system load shedding decreased by 47.93 MW, with the maximum load shedding at any single system node reduced by 31.72 MW, the maximum duration of load-shedding events has decreased by 1 h. Thereby improving grid resilience.

Overall, the introduction of flexible resources demonstrates significant synergistic effects, with seasonal hydrogen storage also playing a role in addressing the issue of prolonged low output from renewable energy sources.

4.3. Comparative Analysis

To further demonstrate the advantages of 2MT-S over traditional day-ahead economic dispatch, this paper sets up Scenarios 4, 5, and 6 for comparative analysis. The dispatch results for Scenarios 4–6 correspond to Figure 6. The detailed comparative analysis results are shown in

Table 4. Comparative analysis results for the intermittent output case.

Scenario	4	5	6
Thermal Power Output/MW	1.74 × 104	2.17 × 104	1.89 × 104
Levelized Cost of Electricity/(¥/kW·h)	0.452	0.476	0.455
Line Transmission Power/kW	4.43 × 104	4.96 × 104	4.67 × 104
Load shedding/MW	123.00	52.43	98.30
Maximum node Load shedding/MW	27.68	16.49	18.52
Maximum Duration of Load Shedding Event/h	2	1	1

.

The comparative analysis of Scenarios 4 and 5 addresses the long-term intermittent output characteristics of renewable energy sources, with results presented through Figure 6, and Table 4. As shown in Figure 6, relying solely on traditional day-ahead economic dispatch in the new power system leads to significant power and energy deficits. The system-wide load shedding reaches 123 MW, while total thermal power generation output drops to just 17,400 MW. When day-ahead scheduling is guided by the long-term 2MT-S scheduling results, the total system load shedding is reduced to only 52.43 MW, reduced by 70.57 MW, the maximum node load shedding is reduced by 11.19 MW, the maximum duration of load shedding event is reduced by 1h, and the system cost per kW·h increases by 0.024 ¥/kW·h. This significantly improves power supply reliability at the cost of a minor reduction in economic efficiency.

The comparative analysis of Scenarios 4 and 6 addresses the short-term intermittency of renewable energy output, with results presented in Figure 6 and Table 4. Under the guidance of the 2MT-S short-term dispatch results, the overall system load shedding was reduced to only 98.3 MW, reduced by 24.7 MW, the maximum node load shedding is reduced by 9.16 MW, the maximum Duration of Load Shedding Event is reduced by 1 h, with the system cost per kW·h increasing by 0.003 ¥/kWh. Similarly, while sacrificing a small amount of economic efficiency, this approach significantly enhanced power supply reliability.

Meanwhile, when renewable energy sources operate normally, the system’s power supply reliability is assured, and the 2MT-S coupled dispatch should not compromise the economic efficiency achieved through day-ahead dispatch. To further validate its effectiveness, Scenarios 7 and 8 were established for comparative analysis. The dispatch results for Scenarios 7 and 8 correspond to Figure 7, with detailed comparative analysis presented in

Table 5. Comparative analysis results under normal output.

Scenario	7	8
Thermal Power Output/MW	3.93 × 103	4.32 × 103
Levelized Cost of Electricity/(¥/kW·h)	0.230	0.231
Line Transmission Power/kW	5.65 × 104	5.83 × 104

.

As evident from Figure 7 and Table 5, when high-penetration renewable energy systems operate normally, traditional economic dispatch relies solely on one thermal power unit for generation. In contrast, 2MT-S coupled economic dispatch utilizes two units simultaneously, yet the overall thermal power output difference is minimal, increasing from 3.93 × 10³ MW to 4.32 × 10³ MW. The increase in the number of generating units and the total output leads to a rise in the overall transmission power of the lines. The system cost per kW·h remains virtually unchanged, increasing by only 0.001 ¥/kWh. The results indicate that when renewable energy is operating normally, the 2MT-S coupled economic dispatch does not compromise economic efficiency.

5. Conclusions

The proportion of renewable energy units in new power systems is increasing annually. To address the power and energy balancing challenges exacerbated by the long-term intermittency of renewable energy output in these systems, this paper proposes a 2MT-S scheduling strategy. Key findings are as follows:

(1)

The established long-term/short-term-to-day-ahead coupled scheduling framework dynamically switches between long-term and short-term scheduling modes by predicting the duration of intermittent output from renewable energy sources (3 days/10 days). It utilizes the results from long-term and short-term scheduling to refine the boundary conditions for day-ahead scheduling. Compared to conventional day-ahead scheduling, this framework reduces curtailment rates and load shedding during long-duration, low-output scenarios, significantly enhancing cross-time resource complementarity and system resilience.

(2)

After introducing seasonal hydrogen storage and pumped-storage hydroelectric plants, these two flexibility resources exhibit complementary characteristics in long-term scheduling: pumped storage mitigates short-term power gaps through rapid response, while seasonal hydrogen storage smooths long-term output fluctuations via cross-week energy storage. Case studies demonstrate that their synergy further reduces renewable curtailment by 0.8 percentage points and decreases system load shedding by 47.93 MW, validating hydrogen’s unique advantage as a long-duration energy storage medium.

(3)

Under intermittent renewable generation conditions, the framework dynamically adjusts the initial states of thermal power units and energy storage based on short- and long-term dispatch results, achieving spatiotemporal consistency in dispatch strategies. Compared to traditional methods, the 2MT-S approach reduces system load shedding from 123.00 MW to 52.43 MW at an economic cost of 0.024 ¥/kWh, providing an effective technical pathway to address supply–demand imbalances in extreme scenarios like “Dunkelflaute.”

Subsequent research will employ large-scale system models to further validate the feasibility of the proposed method.