1. Introduction

Under the trend of increasingly severe energy shortages and environmental pollution, renewable energy sources such as wind and solar power have experienced rapid development and expanding grid integration due to their abundant reserves and zero-emission, renewable advantages [1]. However, the inherent high volatility and intermittency of renewable energy exacerbate the peak-valley difference in the power system’s equivalent load when integrated at scale. This compresses the spinning reserve capacity of conventional power sources, reduces the accommodation space for renewable energy itself [2], and increases operational challenges, intensifying wind and solar curtailment. Consequently, there is an urgent need to deeply explore additional reserve resources within the grid without increasing carbon emissions [3,4]. Concentrating Solar Power (CSP), particularly thermal storage-equipped CSP plants, represents a promising solar technology with time-shifting and continuously adjustable capabilities, enabling it to provide spinning reserve for the system [5-6]. However, CSP operation is constrained by solar resource availability and thermal storage capacity. Thus, coordinating the allocation of spinning reserve capacities between CSP units and conventional units to maximize renewable energy utilization while ensuring power system stability and security has become a critical research priority.

Existing studies have investigated the coordinated dispatch of CSP plants with thermal power units, wind farms, and photovoltaic plants. Reference [7] established a joint dispatch system for CSP and thermal power units, demonstrating that rational utilization of CSP output significantly reduces system economic costs. Reference [8] developed an optimized operation model for wind-PV-CSP hybrid systems to address power imbalance during peak and off-peak periods, ensuring grid-connected power aligns with dispatch curves. These studies confirm the feasibility of CSP as a flexible power source for providing spinning reserves, offering theoretical foundations for further research. However, they lack effective solutions for constraints imposed by solar irradiation and thermal storage capacity on CSP dispatchability. Some scholars propose integrating electric heaters (EH) with CSP plants to enhance operational flexibility. Reference [9] combined EH-CSP with price-based demand response (PDR) in a wind- photovoltaic (PV) -CSP hybrid system, achieving cost reduction and improved dispatch capability. Reference [10] introduced incentive-based demand response into a wind-PV-EH-CSP co-generation model, enhancing renewable energy utilization while lowering operational costs. While these studies validate that EH-CSP integration promotes wind power accommodation and strengthens reserve capacity, most focus on economic benefits and inadequately address the efficient utilization challenges under high-penetration, large-scale renewable energy integration.

In summary, this paper focuses on coordinating the power outputs of thermal power, CSP plants, and EH with the dual objectives of reducing system operational costs and enhancing wind and solar energy utilization. The study is conducted under a framework of multi-timescale and multi-objective optimization. First, the fundamental generation principles and output models of EH-CSP plants are introduced. Building on this, a day-ahead and intra-day optimal dispatch model for a multi-source power generation system incorporating EH-CSP plants is proposed. The model is solved using the CIPSO algorithm. Finally, case study simulations verify the effectiveness of the proposed model.

2. Operational mechanism of EH-CSP plant

A CSP plant primarily consists of three components: the solar field (SF), thermal energy storage (TES), and power block (PB) [11]. The heat transfer fluid (HTF) facilitates energy transfer among these components. The solar field absorbs solar energy and uses thermal conversion equipment to heat the HTF, converting solar energy into thermal energy. A portion of this thermal energy is converted into electricity via steam turbine units, while the remainder is stored in the TES. The TES releases stored thermal energy to the power block via the HTF when needed [12]. An EH, which converts electrical energy into thermal energy, is typically implemented in three practical forms: electrode-based, electromagnetic induction-based, and resistive heaters [13]. This study employs a resistive molten salt electric heater as the EH device.

The system integrating EH and CSP plants is illustrated in Figure 1. Compared to conventional CSP plants, the heat-conducting molten salt in the thermal storage system absorbs not only thermal energy from the solar field’s photothermal conversion but also additional heat generated by the EH through electric heating during its flow from the low-temperature to high-temperature molten salt tanks. This integration reduces the dependency on solar irradiation for CSP generation capacity. Furthermore, the EH, functioning as an adjustable load, can provide reserve capacity for the system by modulating its power consumption.

The thermal power absorbed by the CSP plant is expressed as:

$$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}={\mathrm{\eta }}_{\mathrm{S}\mathrm{F}}{\mathrm{S}}_{\mathrm{S}\mathrm{F}}{\mathrm{D}}_{\mathrm{t}}$$(1)

Where:  $$ {\mathrm{\eta }}_{\mathrm{S}\mathrm{F}}$$  is the solar-to-thermal conversion efficiency of the solar field (unit: %);  $$ {\mathrm{S}}_{\mathrm{S}\mathrm{F}}$$  is the total area of the solar field (unit:  $$ {\mathrm{h}\mathrm{m}}^2$$ );  $$ {\mathrm{D}}_{\mathrm{t}}$$  is the direct normal irradiance (DNI) at time  $$ \mathrm{t}$$  (unit:  $$ {\mathrm{w}/\mathrm{m}}^2$$ );  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$$  represents the thermal power absorbed by the solar collector during time period  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ ).

The thermal energy absorbed by the solar collector is utilized to generate electricity during peak load periods, while during off-peak periods, it is transferred to the TES (Thermal Energy Storage) for storage. The stored thermal energy is then released during subsequent peak load periods to produce electricity.

$$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}={\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{H}-\mathrm{P}}+{\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{H}-\mathrm{T}}$$(2)

Where:  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{H}-\mathrm{P}}$$ : thermal power **directly utilized for electricity generation by the solar collector at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ );  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{H}-\mathrm{T}}$$ : thermal power supplied to the TES by the solar collector at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ ).

Thermal losses occur during both charging and discharging processes, and charging and discharging cannot be conducted simultaneously. The charge-discharge characteristics are thus defined as:

$$ \{\begin{array}{c}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{c}}={\mathrm{\eta }}_{\mathrm{c}}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{H}-\mathrm{T}}\\ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{d}}=\frac{{\mathrm{P}}_{\mathrm{t}}^{\mathrm{T}-\mathrm{H}}}{{\mathrm{\eta }}_{\mathrm{d}}}\\ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{c}}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{d}}=0\end{array}$$(3)

Where:  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{c}}$$  and  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{d}}$$ : charging and discharging thermal power at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ );  $$ {\mathrm{\eta }}_{\mathrm{c}}$$  and  $$ {\mathrm{\eta }}_{\mathrm{d}}$$ : charging and discharging efficiencies (unit: %);  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{T}-\mathrm{H}}$$ : thermal energy transferred from TES to HTF at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ ).

The thermal energy stored in the TES, accounting for energy dissipation, is expressed as:

$$ {\mathrm{E}}_{\mathrm{t}}={\mathrm{e}}^{-\mathrm{\delta }\mathrm{\Delta }\mathrm{t}}{\mathrm{E}}_{\mathrm{t}-1}+\left({\mathrm{P}}_{\mathrm{t}-1}^{\mathrm{c}}-{\mathrm{P}}_{\mathrm{t}-1}^{\mathrm{d}}\right)\mathrm{\Delta }\mathrm{t}$$(4)

Where:  $$ {\mathrm{E}}_{\mathrm{t}}$$ : thermal energy stored in the TES at time  $$ \mathrm{t}$$ ;  $$ \mathrm{ ;}$$ : dissipation coefficient;  $$ \mathrm{\Delta }\mathrm{t}$$ : time interval.

The electrical power output of the CSP plant is derived from thermal energy supplied by both the solar collector and thermal storage system, expressed as:

$$ {\mathrm{P}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}={\mathrm{\eta }}_{\mathrm{f}}\left({\mathrm{P}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}-\frac{{\mathrm{P}}_{\mathrm{t}}^{\mathrm{c}}}{{\mathrm{\eta }}_{\mathrm{c}}}+{\mathrm{P}}_{\mathrm{t}}^{\mathrm{d}}{\mathrm{\eta }}_{\mathrm{d}}+{\mathrm{E}}_{\mathrm{t},\mathrm{E}\mathrm{H}}\right)$$(5)

Where:  $$ {\mathrm{\eta }}_{\mathrm{f}}$$ : thermal-to-electric conversion efficiency of the CSP plant (unit:  $$ \mathrm{\%}$$ );  $$ {\mathrm{E}}_{\mathrm{t},\mathrm{E}\mathrm{H}}$$ : thermal power generated by the EH at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ );  $$ {\mathrm{P}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}$$ : electrical power output of the CSP plant at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ ).

The EH, as a critical electro-thermal conversion component in the CSP plant, achieves a conversion efficiency of nearly 100% [14]. Its thermal output is determined by the curtailed wind and solar power, modeled as:

$$ {\mathrm{E}}_{\mathrm{t},\mathrm{E}\mathrm{H}}={\mathrm{\eta }}_{\mathrm{E}\mathrm{H}}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{E}\mathrm{H}}$$(6)

Where:  $$ {\mathrm{P}}_{\mathrm{t}}^{\mathrm{E}\mathrm{H}}$$ : input electrical power to the EH at time  $$ \mathrm{t}$$ ;  $$ {\mathrm{\eta }}_{\mathrm{E}\mathrm{H}}$$ : electro-thermal conversion efficiency of the EH under steady-state operation.

The thermal output is constrained by:

$$ 0<;{\mathrm{E}}_{\mathrm{t},\mathrm{E}\mathrm{H}}<;{\mathrm{E}}_{\mathrm{E}\mathrm{H}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$$(7)

Where:  $$ {\mathrm{E}}_{\mathrm{E}\mathrm{H}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$$  denotes the maximum thermal power output limit of the EH.

3. Optimization of wireless charging system

This study proposes a day-ahead and intra-day optimal dispatch model for a multi-source power generation system incorporating EH-CSP plants, targeting maximization of daily renewable energy generation and minimization of system operational costs. The model comprises two components: a day-ahead dispatch plan and an intra-day dispatch plan, as illustrated in Figure 2.

The day-ahead dispatch plan operates with a time scale of 1 hour, formulated one day in advance. Based on the predicted load demand curve and renewable energy output forecast curves, it determines the start-up and shutdown schedules for thermal power units and the dispatch output plans for thermal power, wind power, PV and CSP plants. The day-ahead dispatch results serve as input variables for the intra-day dispatch plan.

The intra-day dispatch plan operates with a time scale of 15 minutes and an execution cycle of 4 hours. Without considering the start-up and shutdown costs of thermal power units, it prioritizes rolling optimization for the first 1-4 hours based on day-ahead dispatch data and ultra-short-term load demand and renewable energy output forecasts. Using the optimized load, PV, wind, and CSP data, the system predicts the next hour's load demand and renewable energy output, then rolling optimizes 2-5 hours. This process repeats 24 times to obtain dispatch output data for 96 time points across wind, PV, CSP, and thermal power units. Finally, by adjusting the output of all power sources, the dispatch output plans for each power source and the system spinning reserve plan are determined.

3.1. Day-ahead dispatch plan model

3.1.1. Day-ahead dispatch plan model objective function

(1) Maximization of Daily Power Output for CSP, PV, and Wind Power

$$ {\mathrm{f}}_1=\mathrm{m}\mathrm{a}\mathrm{x}\sum _{\mathrm{t}=1}^{\mathrm{T}}\left({\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}+{\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}+{\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}\right)$$(8)

Where:  $$ {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}$$ ,  $$ {\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}$$  and  $$ {\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}$$  represent the dispatch outputs of the CSP, PV, and wind power at time  $$ \mathrm{t}$$ , respectively;  $$ \mathrm{T}$$  is the dispatch duration of the scheduling day, with  $$ \mathrm{T}\mathrm{ ;}=24$$  hours.

(2) Minimization of Comprehensive Operational Cost

$$ \mathrm{m}\mathrm{i}\mathrm{n}{\mathrm{f}}_2=\left({\mathrm{C}}_{11}+{\mathrm{C}}_2+{\mathrm{C}}_3+{\mathrm{C}}_4\right)$$(9)

Where:  $$ {\mathrm{f}}_2$$ : total operational cost;  $$ {\mathrm{C}}_{11}$$ : generation cost of thermal power units in the day-ahead dispatch plan;  $$ {\mathrm{C}}_2$$ : operation and maintenance(O&;M) costs for wind, PV, and CSP generation;  $$ {\mathrm{C}}_3$$ : penalty costs for wind and solar curtailment;  $$ {\mathrm{C}}_4$$ : system spinning reserve capacity cost.

The generation cost of thermal power units in the day-ahead dispatch plan,  $$ {\mathrm{C}}_{11}$$ , is expressed as:

$$ {\mathrm{C}}_{11}={\mathrm{p}}_{\mathrm{i}\mathrm{t}}\sum _{\mathrm{t}=1}^{\mathrm{T}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[{\mathrm{a}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}\mathrm{t}}^2+{\mathrm{b}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}\mathrm{t}}+{\mathrm{c}}_{\mathrm{i}}\right]+{\mathrm{u}}_{\mathrm{i}\mathrm{t}}\sum _{\mathrm{t}=1}^{\mathrm{T}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[{\mathrm{u}}_{\mathrm{i}\mathrm{t}}\left(1-{\mathrm{u}}_{\mathrm{i}\left(\mathrm{t}-1\right)}\right){\mathrm{S}}_{\mathrm{i}}\right]$$(10)

Where:  $$ {\mathrm{p}}_{\mathrm{i}\mathrm{t}}$$ : electrical power output of thermal unit  $$ \mathrm{i}$$  at time  $$ \mathrm{t}$$  (unit:  $$ \mathrm{M}\mathrm{W}$$ );  $$ {\mathrm{u}}_{\mathrm{i}\mathrm{t}}$$ : operational status of thermal unit  $$ \mathrm{i}$$  at time  $$ \mathrm{t}$$  ( $$ {\mathrm{u}}_{\mathrm{i}\mathrm{t}}=1$$  for online,  $$ {\mathrm{u}}_{\mathrm{i}\mathrm{t}}=0$$  for offline);  $$ {\mathrm{a}}_{\mathrm{i}}$$ ,  $$ {\mathrm{b}}_{\mathrm{i}}$$ ,  $$ {\mathrm{c}}_{\mathrm{i}}$$ : fuel cost coefficients of thermal unit  $$ \mathrm{i}$$ ;  $$ \mathrm{n}$$ : total number of thermal units.

The operation and maintenance cost for wind, PV, and CSP generation,  $$ {\mathrm{C}}_2$$ , is expressed as:

$$ {\mathrm{C}}_2={\mathrm{k}}_{\mathrm{j}}{\mathrm{\eta }}_{\mathrm{d}}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{S}\mathrm{F},\mathrm{r}}+{\mathrm{k}}_{\mathrm{T}\mathrm{s}}\left(1-{\mathrm{\eta }}_{\mathrm{f}}\right){\mathrm{\eta }}_{\mathrm{d}}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{T}\mathrm{S},\mathrm{f}}+{\mathrm{k}}_{\mathrm{w}}{\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}+{\mathrm{k}}_{\mathrm{v}}{\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}$$(11)

Where:  $$ {\mathrm{p}}_{\mathrm{t}}^{\mathrm{S}\mathrm{F},\mathrm{r}}$$ : thermal power directly used for generation by the solar collector at time  $$ \mathrm{t}$$ ;  $$ {\mathrm{p}}_{\mathrm{t}}^{\mathrm{T}\mathrm{S},\mathrm{f}}$$ : thermal power supplied by TES discharge at time  $$ \mathrm{t}$$ ;  $$ {\mathrm{\eta }}_{\mathrm{d}}$$ : thermal-to-electric conversion efficiency;  $$ {\mathrm{\eta }}_{\mathrm{f}}$$ : heat loss rate of the TES;  $$ {\mathrm{k}}_{\mathrm{j}}$$ ,  $$ {\mathrm{k}}_{\mathrm{T}\mathrm{s}}$$ : O&;M cost coefficients for solar field-based and TES-based CSP generation;  $$ {\mathrm{k}}_{\mathrm{w}}$$ ,  $$ {\mathrm{k}}_{\mathrm{v}}$$ : O&;M cost coefficients for wind and PV generation;  $$ {\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}$$ ,  $$ {\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}$$ : power outputs of wind and PV at time  $$ \mathrm{t}$$ .

The penalty cost for wind and solar curtailment,  $$ {\mathrm{C}}_3$$ , is expressed as:

$$ {\mathrm{C}}_3={\mathrm{k}}_{\mathrm{w}\mathrm{c}}{\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}^{\mathrm{c}}+{\mathrm{k}}_{\mathrm{v}\mathrm{c}}{\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}^{\mathrm{c}}$$(12)

Where:  $$ {\mathrm{k}}_{\mathrm{w}\mathrm{c}}$$ ,  $$ {\mathrm{k}}_{\mathrm{v}\mathrm{c}}$$ : penalty coefficients for wind and solar curtailment;  $$ {\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}^{\mathrm{c}}$$ ,  $$ {\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}^{\mathrm{c}}$$ : curtailed wind and solar power at time  $$ \mathrm{t}$$ .

The system spinning reserve capacity cost,  $$ {\mathrm{C}}_4$$ , is expressed as:

$$ {\mathrm{C}}_4={\mathrm{k}}_{\mathrm{i}}\left({\mathrm{U}}_{\mathrm{i}\mathrm{t}}+{\mathrm{D}}_{\mathrm{i}\mathrm{t}}\right)+{\mathrm{k}}_{\mathrm{c}}\left({\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}^{\mathrm{U}\mathrm{p}}+{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}^{\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}}\right)+{\mathrm{k}}_{\mathrm{e}}\left({\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}^{\mathrm{U}\mathrm{p}}+{\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}^{\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}}\right)$$(13)

Where:  $$ {\mathrm{k}}_{\mathrm{i}}$$ ,  $$ {\mathrm{k}}_{\mathrm{c}}$$ ,  $$ {\mathrm{k}}_{\mathrm{e}}$$ : spinning reserve cost coefficients for thermal units, CSP plants, and EH;  $$ {\mathrm{U}}_{\mathrm{i}\mathrm{t}}$$ ,  $$ {\mathrm{D}}_{\mathrm{i}\mathrm{t}}$$ : upward/downward spinning reserve capacities of thermal unit  $$ \mathrm{i}$$  at time  $$ \mathrm{t}$$ ;  $$ {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}^{\mathrm{U}\mathrm{p}}$$ ,  $$ {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}^{\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}}$$ : upward/downward spinning reserves from the CSP plant;  $$ {\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}^{\mathrm{U}\mathrm{p}}$$ ,  $$ {\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}^{\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}}$$ : upward/downward spinning reserves from the EH.

3.1.2. Constraints

(1) The power balance constraint for the integrated system

$$ \sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{p}}_{\mathrm{i}\mathrm{t}}+{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}+{\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}+{\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}={\mathrm{p}}_{\mathrm{f}\_\mathrm{t}}$$(14)

Where:  $$ {\mathrm{p}}_{\mathrm{f}\_\mathrm{t}}$$ : forecasted load demand power at time  $$ \mathrm{t}$$ .

(2) Thermal Power Unit Operational Constraints

The upward and downward spinning reserve capacity constraints are formulated as:

$$ \{\begin{array}{c}{\mathrm{U}}_{\mathrm{i}\mathrm{t}}=\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{p}}_{\mathrm{i}\mathrm{t}},{\mathrm{r}}_{\mathrm{u}\mathrm{i}}\right)\ge {\mathrm{p}}_{\mathrm{c}\_\mathrm{t}}={\mathrm{p}}_{\mathrm{f}\_\mathrm{t}}\mathrm{L}\\ {\mathrm{D}}_{\mathrm{i}\mathrm{t}}=\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{p}}_{\mathrm{i}\mathrm{t}}-{\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{i}\mathrm{n}},{\mathrm{r}}_{\mathrm{d}\mathrm{i}}\right)\ge {\mathrm{p}}_{\mathrm{c}\_\mathrm{t}}={\mathrm{p}}_{\mathrm{f}\_\mathrm{t}}L\end{array}$$(15)

Where:  $$ {\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$ ,  $$ {\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{i}\mathrm{n}}$$ : upper and lower output limits of thermal unit  $$ \mathrm{i}$$ ;  $$ {\mathrm{r}}_{\mathrm{u}\mathrm{i}}$$ ,  $$ {\mathrm{r}}_{\mathrm{d}\mathrm{i}}$$ : maximum upward and downward ramping rates of unit  $$ \mathrm{i}$$ ;  $$ {\mathrm{p}}_{\mathrm{c}\_\mathrm{t}}$$ : forecast error of system load.

Power Output Constraints of Thermal Units

$$ {\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{p}}_{\mathrm{i}\mathrm{t}}\le {\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$(16)

Ramping Rate Constraints of Thermal Units

$$ {-\mathrm{r}}_{\mathrm{d}\mathrm{i}}\le {\mathrm{p}}_{\mathrm{i}\mathrm{t}}-{\mathrm{p}}_{\mathrm{i}\left(\mathrm{t}-1\right)}\le {\mathrm{r}}_{\mathrm{u}\mathrm{i}}$$(17)

Power Output Constraints During Start-Up/Shut-Down

$$ {\mathrm{p}}_{\mathrm{i}\mathrm{t}}={\mathrm{p}}_{\mathrm{i}\_\mathrm{m}\mathrm{i}\mathrm{n}}=\{\begin{array}{c}{\mathrm{u}}_{\mathrm{i}\left(\mathrm{t}-1\right)}=0,{\mathrm{u}}_{\mathrm{i}\mathrm{t}}=1\\ {\mathrm{u}}_{\mathrm{i}\mathrm{t}}=1,{\mathrm{u}}_{\mathrm{i}\left(\mathrm{t}+1\right)}=0\end{array}$$(18)

This equation indicates that when a thermal unit transitions from offline to online or online to offline, its power output during that interval is set to the minimum stable operating output.

(3) Operational Constraints of the CSP Plant

Thermal Storage Capacity Constraints

$$ {\mathrm{E}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{t}\mathrm{h}}\le {\mathrm{E}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h}}\le {\mathrm{E}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{t}\mathrm{h}}={\mathrm{m}}^{\mathrm{T}\mathrm{E}\mathrm{X}}{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$(19)

Where:  $$ {\mathrm{E}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{t}\mathrm{h}}$$ ,  $$ {\mathrm{E}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{t}\mathrm{h}}$$ : upper and lower limits of TES thermal storage capacity;  $$ {\mathrm{m}}^{\mathrm{T}\mathrm{E}\mathrm{X}}$$ : maximum TES capacity in full-load hours (FLH);  $$ {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$ : maximum power output of the CSP plant.

Thermal Charge/Discharge Power Constraints

$$ \{\begin{array}{c}0\le {\mathrm{p}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{c}}\le {\mathrm{p}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{t}\mathrm{h},\mathrm{c}}\\ 0\le {\mathrm{p}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{d}}\le {\mathrm{p}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{t}\mathrm{h},\mathrm{d}}\end{array}$$(20)

Where:  $$ {\mathrm{p}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{t}\mathrm{h},\mathrm{c}}$$ ,  $$ {\mathrm{p}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{t}\mathrm{h},\mathrm{d}}$$  are the maximum thermal charge and discharge power rates.

Mutual Exclusion of Charge/Discharge in the Same Interval

$$ {\mathrm{p}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{c}}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{t}\mathrm{h},\mathrm{d}}=0$$(21)

Power Output Constraints

$$ {{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}\le \mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$(22)

Where:  $$ {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{i}\mathrm{n}}$$  is the minimum power output of the CSP plant.

Ramping Rate Constraints

$$ {-\mathrm{r}}_{\mathrm{d}\_\mathrm{c}\mathrm{s}\mathrm{p}}\le {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}-{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\left(\mathrm{t}-1\right)}\le {\mathrm{r}}_{\mathrm{u}\_\mathrm{c}\mathrm{s}\mathrm{p}}$$(23)

Where:  $$ {\mathrm{r}}_{\mathrm{u}\_\mathrm{c}\mathrm{s}\mathrm{p}}$$ ,  $$ {-\mathrm{r}}_{\mathrm{d}\_\mathrm{c}\mathrm{s}\mathrm{p}}$$  are the maximum upward and downward ramping rates.

Spinning Reserve Capacity Constraints

$$ \{\begin{array}{c}{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}^{\mathrm{U}\mathrm{p}}\le {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}\\ {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}^{\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}}\le {\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}-{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{m}\mathrm{i}\mathrm{n}}\end{array}$$(24)

(4) EH Operational Constraints

Power Output Constraints

$0\le p_{e{h}_t}=k_{we}(P_{W_t}-P_{win{d}_t}-P_{win{d}_t}^c)+k_{ve}(P_{V_t}-P_{v_t}-P_{v_t}^c)\le p_{EH}$(25)

Where:  $$ {\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}$$ : power output of the EH at time  $$ \mathrm{t}$$ ;  $$ {\mathrm{p}}_{\mathrm{E}\mathrm{H}}$$ : rated power capacity of the EH;  $$ {\mathrm{P}}_{\mathrm{W}\_\mathrm{t}}$$ ,  $$ {\mathrm{P}}_{\mathrm{V}\_\mathrm{t}}$$ : forecasted wind and PV power outputs at time  $$ \mathrm{t}$$ ;  $$ {\mathrm{k}}_{\mathrm{w}\mathrm{e}}$$ ,  $$ {\mathrm{k}}_{\mathrm{v}\mathrm{e}}$$ : absorption coefficients of the EH for surplus wind and PV power.

(5) Spinning Reserve Capacity Constraints

$$ \{\begin{array}{c}{\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}^{\mathrm{U}\mathrm{p}}\le {\mathrm{p}}_{\mathrm{E}\mathrm{H}}-{\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}\\ {\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}^{\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}}\le {\mathrm{p}}_{\mathrm{e}\mathrm{h}\_\mathrm{t}}\end{array}$$(26)

Wind Farm Power Output Constraints

$$ 0\le {\mathrm{P}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}\le {\mathrm{P}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$(27)

(6) PV Power Plant Output Constraints

$$ 0\le {\mathrm{P}}_{\mathrm{v}\_\mathrm{t}}\le {\mathrm{P}}_{\mathrm{v}\_\mathrm{m}\mathrm{a}\mathrm{x}}$$(28)

3.2. Intra-day dispatch plan model

3.2.1. Objective function

(1) Maximization of Daily Power Output for CSP, PV, and Wind Power

$$ {\mathrm{f}}_3=\mathrm{m}\mathrm{a}\mathrm{x}\sum _{\mathrm{t}=1}^{\mathrm{T}}\left({\mathrm{p}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}\_\mathrm{t}}+{\mathrm{p}}_{\mathrm{v}\_\mathrm{t}}+{\mathrm{p}}_{\mathrm{c}\mathrm{s}\mathrm{p}\_\mathrm{t}}\right)$$(29)

(2) Minimization of Comprehensive Operational Cost

$$ \mathrm{m}\mathrm{i}\mathrm{n}{\mathrm{f}}_4=\left({\mathrm{C}}_{12}+{\mathrm{C}}_2+{\mathrm{C}}_3+{\mathrm{C}}_4\right)$$(30)

The generation cost of thermal power units in the intra-day dispatch plan,  $$ {\mathrm{C}}_{12}$$ , is expressed as:

$$ {\mathrm{C}}_{12}={\mathrm{p}}_{\mathrm{i}\mathrm{t}}\sum _{\mathrm{t}=1}^{\mathrm{T}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[{\mathrm{a}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}\mathrm{t}}^2+{\mathrm{b}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}\mathrm{t}}+{\mathrm{c}}_{\mathrm{i}}\right]$$(31)

3.2.2. Constraints

The intra-day dispatch plan model shares the same specific constraints as the day-ahead dispatch plan model and will not be reiterated here.

3.3. Model solution

3.3.1. Day-ahead dispatch plan model

The model proposed in this study is a multi-objective optimization problem. By assigning different weighting coefficients to each objective function, the multi-objective problem can be transformed into a single-objective problem for solution. In the day-ahead dispatch plan model, which includes two objective functions  $$ {\mathrm{f}}_1$$  and  $$ {\mathrm{f}}_2$$ , their coordination is addressed as:

$$ \mathrm{A}=\mathrm{m}\mathrm{i}\mathrm{n}({\mathrm{\lambda }}_1\frac{{\mathrm{f}}_{1\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_1}{{\mathrm{f}}_{1\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_{1\mathrm{m}\mathrm{i}\mathrm{n}}}+{\mathrm{\lambda }}_2\frac{{\mathrm{f}}_2-{\mathrm{f}}_{2\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{f}}_{2\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_{2\mathrm{m}\mathrm{i}\mathrm{n}}})$$(32)

Where:  $$ {\mathrm{\lambda }}_1$$ ,  $$ {\mathrm{\lambda }}_2$$ : linear weighting coefficients for  $$ {\mathrm{f}}_1$$  and  $$ {\mathrm{f}}_2$$ , respectively, with  $$ {\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2=1$$  and  $$ {\mathrm{\lambda }}_1$$ ,  $$ {\mathrm{\lambda }}_2\in \left[\mathrm{0,1}\right]$$ ;  $$ {\mathrm{f}}_{1\mathrm{m}\mathrm{a}\mathrm{x}}$$ ,  $$ {\mathrm{f}}_{2\mathrm{m}\mathrm{a}\mathrm{x}}$$ : optimal solutions (best values) for  $$ {\mathrm{f}}_1$$  and  $$ {\mathrm{f}}_2$$ ;  $$ {\mathrm{f}}_{1\mathrm{m}\mathrm{i}\mathrm{n}}$$ ,  $$ {\mathrm{f}}_{2\mathrm{m}\mathrm{i}\mathrm{n}}$$ : worst solutions (poorest values) for  $$ {\mathrm{f}}_1$$  and  $$ {\mathrm{f}}_2$$ .

The intra-day dispatch plan model follows a similar approach:

$$ \mathrm{B}=\mathrm{m}\mathrm{i}\mathrm{n}({\mathrm{\lambda }}_3\frac{{\mathrm{f}}_{3\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_3}{{\mathrm{f}}_{3\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_{3\mathrm{m}\mathrm{i}\mathrm{n}}}+{\mathrm{\lambda }}_4\frac{{\mathrm{f}}_4-{\mathrm{f}}_{4\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{f}}_{4\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{f}}_{4\mathrm{m}\mathrm{i}\mathrm{n}}})$$(33)

where:  $$ {\mathrm{\lambda }}_3$$ ,  $$ {\mathrm{\lambda }}_4$$ : linear weighting coefficients for  $$ {\mathrm{f}}_3$$  and  $$ {\mathrm{f}}_4$$ , respectively, with  $$ {\mathrm{\lambda }}_3+{\mathrm{\lambda }}_4=1$$  and  $$ {\mathrm{\lambda }}_3$$ ,  $$ {\mathrm{\lambda }}_4\in \left[\mathrm{0,1}\right]$$ ;  $$ {\mathrm{f}}_{3\mathrm{m}\mathrm{a}\mathrm{x}}$$ ,  $$ {\mathrm{f}}_{4\mathrm{m}\mathrm{a}\mathrm{x}}$$ : optimal solutions (best values) for  $$ {\mathrm{f}}_3$$  and  $$ {\mathrm{f}}_4$$ ;  $$ {\mathrm{f}}_{3\mathrm{m}\mathrm{i}\mathrm{n}}$$ ,  $$ {\mathrm{f}}_{4\mathrm{m}\mathrm{i}\mathrm{n}}$$ : worst solutions (poorest values) for  $$ {\mathrm{f}}_3$$  and  $$ {\mathrm{f}}_4$$ .

The focus of this study is to address the green and efficient absorption of renewable energy after large-scale grid integration. Therefore, we prioritize  $$ {\mathrm{f}}_1$$  over  $$ {\mathrm{f}}_2$$  and  $$ {\mathrm{f}}_3$$  over  $$ {\mathrm{f}}_4$$ . Accordingly, the weighting coefficients are set as:  $$ {\mathrm{\lambda }}_1$$  slightly larger than  $$ {\mathrm{\lambda }}_2$$ ;  $$ {\mathrm{\lambda }}_3$$  slightly larger than  $$ {\mathrm{\lambda }}_4$$ .

3.3.2. CIPSO algorithm

To address the limitations of the traditional Particle Swarm Optimization (PSO) algorithm, such as its sensitivity to the initial population's positional states, poor global search capability, significant reduction in population diversity, and premature convergence in later stages[15], this study employs the CIPSO algorithm for model solving. The workflow of the CIPSO algorithm for solving the model is illustrated in Figure 3.

4. Case study analysis

4.1. Case study overview

This paper adopts a modified IEEE 30-node system to validate the effectiveness of the proposed day-ahead and intra-day optimal scheduling method for a multi-source power generation system incorporating EH-CSP plants. The CSP plant equipped with EH devices are connected to Node 1, the Wind Turbine Generator Systems (WTGS) is connected to Node 2, the PV power plant is connected to Node 5, and thermal power units are connected to Nodes 8, 11, and 13. The modified network topology is shown in Figure 4.

The installed capacities of the wind farm and PV power plant participating in system dispatch are 480 MW and 150 MW, respectively. The rated capacity of the EH is  $$ {\mathrm{P}}_{\mathrm{E}\mathrm{H}}=50\mathrm{M}\mathrm{W}$$  and the system load forecast error rate is  $$ \mathrm{L}\mathrm{ ;}=0.05$$ . The operation and maintenance cost coefficients for wind and PV power are  $$ {\mathrm{k}}_{\mathrm{w}}=20\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$  and  $$ {\mathrm{k}}_{\mathrm{v}}=30\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$ respectively. The CSP plant’s operation and maintenance cost coefficients are  $$ {\mathrm{k}}_{\mathrm{i}}=20\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$  (for solar collector-based power generation) and  $$ {\mathrm{k}}_{\mathrm{T}\mathrm{s}}=40\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$  (for thermal storage-based power generation). The penalty cost coefficients for wind and PV curtailment are  $$ {\mathrm{k}}_{\mathrm{w}\mathrm{c}}=100$$  and  $$ {\mathrm{k}}_{\mathrm{v}\mathrm{c}}=100$$  respectively. The spinning reserve cost coefficients for thermal units, the CSP plant, and the EH are  $$ 130\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$ ,  $$ 50\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$  and  $$ 40\mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{M}\mathrm{W}$$  respectively.

The detailed operational parameters of the CSP plant are listed in Table 1, and the parameters of the three thermal units are provided in Table 2.

4.2. Case study results

To validate the effectiveness of the proposed dispatch method, three operational modes are defined:

Mode 1: No participation of CSP plants or EH. Optimal dispatch is performed only for the system composed of wind, PV, and thermal units.

Mode 2: Building upon Mode 1, CSP plants are incorporated into the system dispatch.

Mode 3: Further expanding on Mode 2, EH participation is added to the system dispatch.

The simulation of the three modes is conducted under the same typical day.

4.2.1. Unit output results under different modes

Figures 5, 6, and 7 show the power output results of thermal units, CSP plants, wind, and PV under the three operational modes, respectively.

Although the power output of thermal units in Mode 2 is smoother compared to Mode 3 and Mode 1, its total output is significantly higher than that of Mode 3, resulting in less pronounced advantages in terms of dispatch economy. In Mode 3, the power output of thermal units is only 69.2% of Mode 1 and 82.33% of Mode 2, demonstrating superior economic efficiency.

In Mode 1, the CSP plant does not participate in dispatch, and its power output is 0. Due to the joint participation of the EH and CSP plant in system dispatch, the power output of the CSP plant in Mode 3 is significantly greater than that in Mode 2, and the output is more stable. The power output of the CSP plant in Mode 2 is only 67.66% of that in Mode 3.

In the three dispatch modes, the grid-connected power of wind and PV increases sequentially. The wind power output in Mode 1 is 94.24% of that in Mode 3, and the PV power output is 98.62% of that in Mode 3. The wind power output in Mode 2 is 97.61% of that in Mode 3, and the PV power output is 98.10% of that in Mode 3.

4.2.2. System spinning reserve allocation results under different modes

Figures 8, 9, and 10 show the allocation plans for the upward spinning reserve capacity required by the system under the three modes, respectively.

In Mode 1, the system’s spinning reserve capacity is entirely provided by thermal units. In Mode 2, the CSP plant and thermal units jointly provide the spinning reserve capacity. In Mode 3, the EH is further added to participate. Therefore, in the optimized dispatch of Mode 3, compared to Modes 1 and 2, the reserve pressure on thermal units is significantly reduced, and the upward spinning reserve capacity decreases by 365.83 MW and 263.97 MW, respectively.

4.2.3. System wind and PV power absorption under different modes

Figure 11 shows the curtailed wind power and curtailed PV power of the system under the three modes.

Table 3 shows the actual wind and PV power absorption under the three modes.

In Mode 1, since CSP plants and EH are not considered, the forecast errors of wind and PV power outputs are compensated solely by adjusting the output of thermal units. Although Mode 2 incorporates CSP plants and thermal units to jointly compensate for wind and PV forecast errors, the actual absorption of wind power does not reach the expected level. In Mode 3, by coordinately regulating thermal units, CSP plants, and EH to compensate for wind and PV forecast errors, the absorption rates of wind and PV power are significantly increased.

4.2.4. Total dispatch cost under different modes

As shown in Table 3.3, Mode 3 achieves the lowest total dispatch cost. In the day-ahead dispatch, Mode 3 reduces the dispatch cost by 6.53% and 4.18% compared to Modes 1 and 2, respectively. In the intra-day dispatch, the cost reductions are 9.71% and 8.36% compared to Modes 1 and 2, respectively. Under the same mode, the intra-day dispatch cost of Mode 3 is 65,400 yuan lower than its day-ahead dispatch cost, demonstrating significant improvement in the system’s operational economy under Mode 3.

5. Conclusion

To address the intensified peak-valley difference in the equivalent load of power systems and the "wind/PV curtailment" phenomena caused by large-scale integration of renewable energy, this paper proposes a day-ahead and intra-day optimal dispatch method for a multi-source generation system incorporating EH-CSP plants. By leveraging the dispatchability of EH-CSP plants and the complementary characteristics of renewable energy outputs, the proposed method establishes a coordinated multi-timescale and multi-objective optimization strategy. This approach effectively enhances wind and PV power absorption while reducing system operational costs. The research findings provide valuable insights for the rational dispatch of power systems with high-penetration renewable energy integration.

​​Due to time constraints, this paper focuses only on the coordinated optimal scheduling across the day-ahead and intraday time scales. Additionally, the study emphasizes theoretical modeling, with limited exploration of solution algorithms. Future research could extend to multi-time-scale optimization (e.g., week-ahead, day-ahead, intraday, and real-time scheduling) and analyze the performance of various solution algorithms to identify more efficient solving approaches.