Synergistic Optimization of Coal Power and Renewable Energy Based on Generalized Adequacy

Abstract

As China accelerates its transition to a low-carbon society, its power system is facing growing challenges in terms of maintaining adequacy amid a rapidly evolving energy structure. The concept of adequacy, traditionally focused on power capacity and generation, has broadened to include dimensions like flexibility and inertia. Against this backdrop, optimizing the integration of coal power and renewable energy to meet the system’s needs for adequacy, flexibility, and frequency stability has become a critical research area. This paper introduces the concept of “Generalized Adequacy”, expanding the traditional understanding of adequacy, and proposes an optimization model for the coordinated development of coal power and renewable energy based on this concept. This study examines the effects of extreme weather, renewable energy penetration, wind–solar ratios, and generalized adequacy constraints using a case study from a central region of China. The findings reveal that extreme weather conditions drive an increase in photovoltaic installations, while higher renewable energy penetration leads to more wind power installations. Accounting for generalized adequacy constraints can moderate the retirement of coal-fired plants, reducing unnecessary inertia support in normal conditions and ensuring dynamic frequency stability during extreme weather events.

1. Introduction

The power production landscape is undergoing profound changes. Large-scale, intermittent renewable energy is gradually replacing controllable coal-fired units, leading to significant challenges in terms of energy absorption and curtailment of wind and solar power in some regions [1,2,3]. This issue primarily stems from insufficient system flexibility. The uncertainty of wind and solar power, combined with load-side uncertainties, can result in inadequate flexible capacity, impacting the system’s dynamic supply–demand balance [4,5]. Ensuring this balance requires not only meeting electricity demand but also having sufficient flexibility to accommodate dynamic changes in wind, solar, and load. Additionally, the extensive integration of converter-based resources has reduced the system inertia, making it more susceptible to disturbances [6]. For instance, the significant power outage in the UK in 2019 was due to high instantaneous shares of renewable energy lacking sufficient inertia support during large disturbances [7].

Furthermore, accelerating the decarbonization of the power sector is essential to meet low-carbon goals. Policies encourage the increase of renewable energy, with global projections indicating that renewable generation will constitute 45% of the total generation by 2030 [8,9]. China aims to establish a power system dominated by renewable energy. Ensuring an adequate and secure energy supply during this transition is crucial [10,11]. For example, Australia experienced a blackout due to the wind power output failing to meet the surging demand, and northeastern China faced power rationing in 2021 due to the insufficient coal supply [12]. Extreme weather significantly impacts renewable energy systems, as seen in Texas in 2021, where extreme cold led to power outages, and Sichuan, China, in 2022, where extreme heat increased the load and reduced the power output, resulting in power rationing [13,14]. Such conditions can severely affect the adequacy and safety of renewable energy-reliant power systems. To enhance the energy supply stability, many countries are exploring large-scale utilization of broader clean energy sources, such as hydrogen and methane, while also investigating their potential to reduce carbon dioxide and solid waste. For example, Imbayah et al. [15] identified hydrogen as a promising energy option for infrastructure-limited countries like Libya, after systematically analyzing hydrogen types, characteristics, production methods, and applications. Additionally, Alani et al. [16] presented a method to assess the potential of converting solid waste, such as paper cups, into methane and hydrogen. They demonstrate through practical application in Ghana that transforming solid waste into these gases could significantly reduce energy consumption and pollution. Despite the undeniable advantages, hydrogen and methane still face challenges like high costs and safety concerns compared to more mature resources like wind, solar, and hydropower. However, recent research on retrofitting coal-fired units with carbon capture, utilization, and storage (CCUS) technology shows significant potential. CCUS is increasingly viewed as an effective approach for reducing CO₂ emissions and converting them into valuable methane during the energy transition [17,18].

Given these technological and policy-driven requirements, the traditional concept of capacity adequacy is insufficient for new power systems. A “Generalized Adequacy” concept encompassing various dimensions, including traditional capacity adequacy, flexibility for dynamic balancing, and inertia for maintaining dynamic frequency safety, is urgently needed. In 2021, the Chinese Central Economic Work Conference emphasized that the gradual phase-out of traditional energy must be based on the secure and reliable substitution of renewable energy. This involves leveraging the country’s coal-based energy structure, ensuring clean and efficient coal utilization, increasing renewable energy absorption, and promoting the optimal combination of coal and renewable energy. Coal power and renewable energy generation play complementary roles in achieving the “dual carbon” goals, with renewable energy reducing carbon emissions and coal power providing reliable capacity support. Therefore, planning the synergy between coal power and renewable energy is crucial.

Recent research has focused on the planning of various resources in the future power system, including coal power, renewable energy, energy storage, demand response, etc. Meng et al. [19] proposed a dispatching strategy for park-level integrated energy systems that incorporates reward–punishment ladder-type carbon trading mechanisms and carbon capture equipment. Their strategy significantly improves the economic, flexibility, and low-carbon performance of the system. Similarly, Feng et al. [20] introduced a dynamic carbon incentive mechanism within a hierarchical two-stage robust planning model for demand-side energy storage. This model effectively reduces carbon emissions and enhances planning efficiency. Chen et al. [21] simultaneously considered the impact of regional carbon emission policies, renewable energy utilization constraints, storage technology, and other factors, proposing a capacity expansion model that optimizes investment decisions and the 8760 h power balance. The results indicate that when considering the limitation of grid access capacity, the investment in renewable energy will be more evenly geographically distributed. Liu et al. [22] introduced a bi-level collaborative optimization model—an innovative algorithmic framework specifically tailored for complex multi-energy systems. Peng et al. [23] proposed a multi-objective power expansion model considering renewable energy policy goals, and on this basis, a multi-objective evolutionary algorithm based on a distributed target search was used to solve the model. These studies collectively underscore the critical role of innovative dispatching strategies, robust planning models, and policy support in advancing the deployment and integration of renewable energy within electrical power systems. However, the aforementioned studies neglect the impact of extreme weather on power system planning. Given the increasing frequency of such weather events, this oversight makes it difficult for the planning methods to adequately meet the resource needs of power systems. Furthermore, their planning approaches consider only one aspect of generalized adequacy, failing to effectively address multiple dimensions.

As crucial components of the power system, effectively utilizing the existing thermal power capacity and achieving the coordinated development of thermal power with multiple types of resources are also a key focus of research. In the literature [24], a three-layer robust energy storage system (ESS) planning model considering wind power investment uncertainty and coal-fired unit retirement was proposed. The upper-layer model determines the ESS planning scheme, iteratively considering the worst-case scenarios of wind power investment and coal-fired unit retirement; the middle- and lower-layer models are used to achieve optimal daily economic dispatch under uncertain conditions in the worst-case scenarios. Carrión et al. [25] introduced primary frequency regulation-related constraints in the coordinated planning of thermal power and energy storage, ensuring system dynamic frequency safety through primary frequency regulation constraints and power distribution before and after accidents, but they did not consider the impact of the rate of change of frequency (ROCOF) constraint. To support the low-carbon transition, Yu et al. [26] have examined the role of energy storage and the decommissioning of coal power units, highlighting the supportive role of energy storage in renewable energy penetration. Comprehensive planning models have also been developed by Yuan et al. [27,28] to retain system flexibility while ensuring the decommissioning of coal power units and integrating renewable energy and storage. The retirement of coal-fired units and the development of new energy sources are inevitable trends, serving as the primary drivers for the planning of coal and new energy. While the above studies have somewhat addressed the flexibility needs arising from the volatility of new energy and the changes due to coal retirements, they have largely overlooked the diverse functional transformation methods of coal-fired units. This oversight hampers the proper guidance for the functional transformation of coal-fired units.

To address the gaps in the aforementioned studies, this paper conducts a systematic study on the coordinated planning method for coal-fired power units and renewable energy under the concept of generalized adequacy. This is the first time a planning method related to generalized adequacy has been proposed in this field, effectively meeting the resource-planning needs of power systems against the backdrop of the expanding scale of renewable energy. This paper proceeds from theory to application. Section 2 develops the concept of generalized adequacy, building on traditional adequacy. Section 3 presents an optimization model for the coordinated development of coal power and renewable energy that integrates generalized adequacy. Section 4 applies this model to a real-world system, analyzing how different factors influence power capacity optimization. The main contributions are as follows:

(1)

This paper expands the traditional concept of capacity adequacy to establish the “Generalized Adequacy” concept. It incorporates not only capacity adequacy but also flexibility and inertia adequacy, providing a comprehensive framework for the synergistic development of coal and renewable energy systems.

(2)

An advanced optimization planning model is developed to coordinate the development of coal and renewable energy. This model accounts for the seasonal capacity adequacy contributions of wind and solar power and enhances the computational efficiency by utilizing a cluster unit commitment model for coal units, ensuring the supply–demand balance on an hourly scale.

(3)

Various planning scenarios are analyzed under different conditions, focusing on the economic ratios of wind and solar power. This study also includes a comparative analysis of extreme weather scenarios to evaluate their impact on the performance and reliability of wind and solar power generation.

2. Generalized Adequacy Theory and Coal Power Transition Modeling

2.1. Expansion from Traditional Adequacy to Generalized Adequacy

Traditional power systems have numerous controllable power sources, with strong controllability on the supply side and high predictability on the demand side. Therefore, the focus has been primarily on generation capacity adequacy to meet users’ power and energy demands [29]. Ensuring sufficient generation capacity was typically sufficient to guarantee the power system’s supply capability. However, the rising proportion of renewable energy generation has altered some characteristics of the power system. Firstly, renewable energy generation is highly influenced by natural conditions, increasing the uncertainty and uncontrollability on the supply side. Secondly, the intermittency of renewable energy means it cannot provide the same load-bearing capacity as conventional coal-fired generation. Thirdly, the rapid fluctuations in renewable energy generation require other controllable units to quickly respond to meet load demands. Lastly, many renewable energy sources are inverter-based resources, which cannot provide the same rotational inertia as traditional synchronous units.

The concept of traditional generation capacity adequacy, established under a framework of very low renewable energy penetration, does not adequately reflect the needs of modern power systems. This necessitates the use of “generalized adequacy” to describe the new requirements. The term “generalized” reflects an expansion when describing the adequacy needs of modern power systems, also indicating the balance of energy within these systems.

Combining traditional adequacy with current conditions, this paper defines “generalized adequacy” on the supply side as the effective capacity, inertia, and ramping capabilities of various generation resources meeting the system’s needs, including power and energy, dynamic frequency security, and flexible resource ramping capability, over a given time period.

According to the concept defined in this paper, generalized adequacy includes three dimensions:

(1)

Traditional capacity adequacy, representing the ability to balance power and energy.

(2)

Flexibility adequacy, reflecting the flexible adjustment capabilities of different types of power sources and the system’s supply–demand flexibility.

(3)

Inertia adequacy, representing the ability of different power sources to support system inertia.

From the perspective of the energy balance, capacity adequacy ensures that the quantity of electrical energy is sufficient to meet user demands. Flexibility adequacy ensures timely responses to changes in energy. Inertia adequacy ensures the system’s ability to maintain its state during large disturbances and to resist rapid changes in energy, allowing enough time for the system to return to a normal state.

Building on the concept of ‘Generalized Adequacy’, a key challenge lies in achieving coordinated resource planning that incorporates this expanded adequacy framework. Figure 1 highlights the main differences between traditional coal and renewable energy (RE) planning frameworks and those that account for “Generalized Adequacy”. The traditional approach primarily bases resource needs on load growth, focusing on the supply–demand balance without fully considering the impacts of energy transition, carbon emissions, or coal power retirement and transformation.

In contrast, the “Generalized Adequacy” framework integrates the seasonal distribution characteristics of renewable energy (RE), the synergistic properties of diverse resources, and the diversification of thermal power transition, including technologies such as CCUS and Carnot batteries. The planning model under this framework considers the investment, retirement, and transformation costs of various resources, alongside the constraints related to “Generalized Adequacy”. This approach more comprehensively addresses the adequacy dimensions required for the development of current and future power systems, especially given the declining penetration of synchronous power sources and the increasing role of renewable energy generation.

2.2. Coal Power Transition Modeling

2.2.1. Carnot Battery Model

The principle of the Carnot battery is based on thermal energy storage technology. It involves retrofitting existing decommissioned units by replacing the coal-fired boiler with a thermal storage tank, allowing the system to absorb excess renewable energy. The Carnot battery provides not only flexibility in energy storage but also inertia support for the system. Essentially, the Carnot battery remains a system primarily used for storing electrical energy. During the charging process, electrical energy is used to transfer heat from a low-temperature storage container to a high-temperature one, which can be achieved using traditional heat pumps, electric heaters, or other heating technologies. During discharge, heat can be cycled back into the thermoelectric generator through thermodynamic cycles such as the Rankine or Brayton cycle. The operational model of the Carnot battery is detailed in Equations (1)–(9) [30,31].

$$P_{cb}^{\min }\le P_{cb}\le S_c-{\overline{S}}_c$$

(1)

$$0\le P_{cb,t}^{ch}\le P_{cb,t}^{ch,\max }$$

(2)

$$Q_{cb,t}^{ch}={\chi }_{cb}^{ch}\cdot P_{cb,t}^{ch}$$

(3)

$$Q_{cb,t}^{dis}={\displaystyle \frac{P_{cb,t}^{dis}}{{\chi }_{cb}^{dis}}}$$

(4)

$$Q_{cb,t+1}=Q_{cb,t}+{\eta }_{cb}^{ch}\cdot Q_{cb,t}^{ch}-{\displaystyle \frac{Q_{cb,t}^{dis}}{{\eta }_{cb}^{dis}}}-{\eta }_{cb}^{self}\cdot Q_{cb,t}$$

(5)

$$Q_{cb}^{plan}=b_{cb}\cdot Q_{cb}^{dis}$$

(6)

$$Q_{cb}^{\min }\le Q_{cb,t}\le Q_{cb}^{plan}$$

(7)

$${\lambda }_{cb}^{\min }\cdot P_{cb}\le P_{cb,t}^{dis}\le P_{cb}$$

(8)

$$-R_{cb}^{RD}\cdot \Delta t\le P_{cb,t}^{dis}-P_{cb,t-1}^{dis}\le R_{cb}^{RU}\cdot \Delta t$$

(9)

where $P_{cb}^{\min }$ represents the minimum transformation capacity of the Carnot battery, $S_c$ and ${\overline{S}}_c$ are the maximum installed capacities of coal-fired units before and during the planning stage, $P_{cb,t}^{ch}$ and $P_{cb,t}^{\mathit{dis}}$ represent the charging and discharging power of the Carnot battery at time $t$, $P_{\mathit{cb}}^{\mathit{ch},\max }$ and $P_{cb}$ represent the maximum charging and discharging power of the Carnot battery, ${\chi }_{\mathit{cb}}^{\mathit{ch}}$ and ${\chi }_{\mathit{cb}}^{\mathit{dis}}$ are the efficiencies of the electrical-to-thermal and thermal-to-electrical conversions in the Carnot battery, $Q_{\mathit{cb},t}^{\mathit{ch}}$, $Q_{\mathit{cb},t}^{\mathit{dis}}$ and $Q_{\mathit{cb},t}$ represent the thermal storage and discharge power and the current thermal storage at time $t$, ${\eta }_{\mathit{cb}}^{\mathit{ch}}$, ${\eta }_{\mathit{cb}}^{\mathit{dis}}$ and ${\eta }_{\mathit{cb}}^{\mathit{self}}$ represent the thermal storage, discharge efficiencies, and self-discharge rate of the Carnot battery, $Q_{\mathit{cb}}^{\mathit{dis}}$ and $Q_{\mathit{cb}}^{\mathit{plan}}$ represent the maximum thermal discharge capacity and the planned thermal storage capacity of the Carnot battery, $b_{\mathit{cb}}$ represents the maximum thermal discharge duration, ${\lambda }_{\mathit{cb}}^{\min }$ represents the minimum discharge coefficient of the Carnot battery, $R_{\mathit{cb}}^{\mathit{RD}}$ and $R_{\mathit{cb}}^{\mathit{RU}}$ represent the upward/downward ramp rates of the Carnot battery, and $∆t$ represents the time interval.

2.2.2. Carbon Capture and Reduction Model

Currently, coal-fired power generation remains dominant, and carbon reduction is imperative. However, it is not feasible to retire a large number of coal-fired plants in a short time, as they are still needed to ensure a reliable power supply for the safe operation of the power system. Therefore, technologies that help coal-fired power plants reduce carbon emissions have been developed. Carbon capture, utilization, and storage is a promising low-carbon technology crucial for the development of coal power. Additionally, captured high-concentration CO₂ can be processed and converted into methane for economic benefits. The operational model of the CCUS is detailed in Equations (10)–(16) [32].

$$r{t}^{CCUS,\min }\le r{t}^{CCUS}\le r{t}^{CCUS,\max }$$

(10)

where ${\mathit{rt}}^{\mathit{CCUS}}$ represents the proportion of coal-fired units equipped with carbon capture devices, and ${\mathit{rt}}^{\mathit{CCUS},\min }$ and ${\mathit{rt}}^{\mathit{CCUS},\max }$ represent the minimum and maximum proportions of carbon capture device installations during the planning stage, which can be determined based on regional development levels and policy requirements.

The maximum amount of CO₂ captured by the carbon capture device depends on the maximum capture capacity of the units equipped with carbon capture devices and the carbon emissions of coal-fired units in the system, which is expressed as:

$$K_{tan,t}^{CCUS,\max }={\theta }^{CCUS}\cdot \min \left\{P_{c,t}\right.\cdot k_c,r{t}^{CCUS}\cdot {\overline{S}}_c\cdot \left.k_c\right\}$$

(11)

$$0\le K_{tan,t}^{CCUS}\le K_{tan,t}^{CCUS,\max }$$

(12)

where $K_{\mathit{tan},t}^{\mathit{CCUS},\max }$ represents the maximum amount of CO₂ that can be captured by the carbon capture device, $K_{\mathit{tan},t}^{\mathit{CCU}}$ represents the amount of CO₂ captured by the carbon capture device at time $t$, ${\theta }^{\mathit{CCUS}}$ represents the maximum CO₂ capture rate of coal-fired units, $P_{c,t}$ represents the output of the cluster units at time $t$, and $k_c$ is the average carbon emission coefficient of the cluster units.

The energy consumption generated by installing carbon capture devices is as follows:

$$P_{CS,t}=P_{CS}+e\cdot K_{tan,t}^{CCUS}$$

(13)

where $P_{\mathit{CS},t}$ represents the power consumption of the carbon capture device at time $t$, $P_{\mathit{CS}}$ represents the fixed power consumption of the carbon capture device, and e represents the energy consumption per unit of captured CO₂.

The resulting modification costs are as follows:

$$C_{CCUS}=c_{CCUS}^{inv}\cdot r{t}^{CCUS}\cdot {\overline{S}}_c$$

(14)

where $c_{\mathit{CCUS}}^{\mathit{inv}}$ represents the unit investment price of the carbon capture, utilization, and storage device.

The CO₂ generated can be treated using power-to-gas (P2G) technology, which converts CO₂ into CH₄, thereby generating economic benefits.

$$K_{tan,t}^{P2G}={\psi }_{C{H}_4}{K}_{tan,t}^{CCUS}$$

(15)

$$C_{C{H}_4}=c_{C{H}_4}^{sale}\cdot {\displaystyle \sum _{t\in T}{K}_{tan,t}^{P2G}}$$

(16)

where $K_{\mathit{tan},t}^{P2G}$ denotes the amount of methane converted at time $t$, ${\psi }_{{\mathit{CH}}_4}$ represents the efficiency of the P2G technology in converting CO₂ to CH₄, $C_{{\mathit{CH}}_4}$ signifies the economic benefits of converting CO₂ to methane, and $c_{{\mathit{CH}}_4}^{\mathit{sale}}$ indicates the unit price of CH₄.

3. Coordinated Optimization Model of Coal Power and Renewable Energy

This section proposes a coordinated planning model for coal power and renewable energy, considering generalized adequacy constraints. The model primarily determines the planning capacities of coal power and renewable energy in a high-proportion renewable energy power system to ensure the economic, safe, and reliable operation of the new power system. It also considers the requirements for low-carbon policies and renewable energy generation to support the future low-carbon operation of the power system dominated by renewable energy.

3.1. Objective Function

In this model, the objective is to minimize the total system cost while ensuring the safe and reliable operation of the system. The total cost includes the investment, operation, maintenance, other startup and shutdown, and renewable energy costs, as well as the retirement and transformation costs of the units. The objective function can be expressed as follows:

$$\min C_{sys}=C_{inv}+C_{run}+C_{fix}+C_c+C_{retire}$$

(17)

where $C_{sys}$ represents the total system cost, $C_{inv}$ indicates the total investment cost, $C_{run}$ denotes the total operating cost, $C_{fix}$ signifies the maintenance cost of the units, $C_c$ includes other costs (such as the startup and shutdown costs of coal-fired units, carbon emission costs, excess carbon costs, and load-shedding costs), and $C_{retire}$ represents the retirement costs of coal-fired units. The calculation methods for each cost component are as follows:

$$\begin{array}{c}{C}_{inv}=CR{R}_G\cdot [ {\displaystyle \sum _{g\in G_g}{c}_{\mathrm{g}}^{inv}}\cdot S_g^{new}+{\displaystyle \sum _{w\in G^w}{c}_{w,y}^{inv}\cdot S_w^{new}}+{\displaystyle \sum _{PV\in G_{PV}}{c}_{PV}^{inv}\cdot S_{PV}^{new}}+\\ \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{\displaystyle \sum _{bat\in G_{bat}}(}{c}_{cap}^{inv}\cdot S_{bat}+c_{pow}^{inv}\cdot P_{bat}^{\max })+c_{CCUS}^{inv}\cdot r{t}^{CCUS}\cdot {\overline{S}}_c+\hfill \\ \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}(c_{cb}^{ch}\cdot P_{cb}^{ch,\max }+c_{cb}^Q\cdot Q_{cb}^{plan}+c_{cb}^{dis}\cdot P_{cb}\left.)\right]\hfill \end{array}$$

(18)

$$CR{R}_G={\displaystyle \frac{L_s\cdot {(1+L_s)}^{T_G^{life}}}{{(1+L_s)}^{T_G^{life}}-1}}$$

(19)

$$\begin{array}{c}{C}_{run}={\displaystyle \sum _{t\in T}({\displaystyle \sum _{g\in G_g}{P}_{g,t}}}\cdot c_g^{run}+{\displaystyle \sum _{w\in G_w}{P}_{w,t}}\cdot c_w^{run}+{\displaystyle \sum _{PV\in G_{PV}}{P}_{PV,t}}\cdot c_{PV}^{run}+\\ \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{\displaystyle \sum _{bat\in G_{bat}}(}{P}_{bat,t}^{dis}+P_{bat,t}^{ch})\cdot c_{bat}^{run})\hfill \end{array}$$

(20)

$$C_{fix}={\displaystyle \sum _{t\in T}({\displaystyle \sum _{g\in G}{\overline{S}}_g\cdot c_g^{fix}}}+{\displaystyle \sum _{w\in G_w}{\overline{S}}_w}\cdot c_w^{fix}+{\displaystyle \sum _{PV\in G_{PV}}{\overline{S}}_{PV}}\cdot c_{PV}^{fix}+{\displaystyle \sum _{bat\in G_{bat}}{S}_{bat}}\cdot c_{bat}^{fix})$$

(21)

$$C_c={\displaystyle \sum _{t\in T}({\displaystyle \sum _{g\in G_g}(S{U}_{g,t}\cdot c_g^{SU}}}+S{D}_{g,t}\cdot c_g^{SD}+P_{g,t}\cdot k_g\cdot c_{tan})+P_{loss,t}\cdot c_{loss}-K_{tan,t}^{CCUS}\cdot c_{tan})-C_{C{H}_4}$$

(22)

$$C_{retire}={\displaystyle \sum _{g\in G_g}{S}_g}\cdot ({\beta }_g-{\gamma }_g)\cdot {\alpha }_g^{retire}$$

(23)

where $G_g, G_w, G_{\mathit{PV}},G_{\mathit{bat}}$ represent the sets of coal-fired units, wind power units, photovoltaic units, and energy storage, respectively, $c_g^{\mathit{inv}},c_w^{\mathit{inv}},c_{\mathit{PV}}^{\mathit{inv}},c_{\mathit{cap}}^{\mathit{inv}}, c_{\mathit{pow}}^{\mathit{inv}}$ denote the investment costs for coal, wind, photovoltaic, energy storage capacity, and energy storage power, respectively, $c_{\mathit{cb}}^{\mathit{ch}},c_{\mathit{cb}}^Q,c_{\mathit{cb}}^{\mathit{dis}}$ represent the unit investment costs for the Carnot battery’s electricity-to-heat equipment, molten salt storage, and the steam generation system of the heat-to-electricity equipment, respectively, $S_g^{\mathit{new}},S_w^{\mathit{new}},S_{\mathit{PV}}^{\mathit{new}},S_{\mathit{bat}}$ represent the planned new investment capacities for coal, wind, photovoltaic, and energy storage, respectively, $P_{\mathit{bat}}^{\max }$ denotes the maximum power of the energy storage, ${\mathit{CCR}}_G$ represents the capital recovery factor for each type of unit, L_s is the discount rate, $T_G^{\mathit{life}}$ represents the maximum investment service life of each type of unit, $c_g^{\mathit{run}},c_w^{\mathit{run}},c_{\mathit{PV}}^{\mathit{run}},c_{\mathit{bat}}^{\mathit{run}}$ represent the running cost coefficients for coal, wind, photovoltaic, and energy storage, respectively (usually, wind and photovoltaic have no running costs, hence zero), $P_{g,t}$, $P_{w,t}$, $P_{\mathit{PV},t}$, $P_{\mathit{bat},t}^{\mathit{dis}}$, $P_{\mathit{bat},t}^{\mathit{ch}}$ represent the outputs at time $t$ for coal, wind, photovoltaic, energy storage discharging, and energy storage charging, respectively, $c_g^{\mathit{fix}}, c_w^{\mathit{fix}},c_{\mathit{PV}}^{\mathit{fix}}, c_{\mathit{bat}}^{\mathit{fix}}$ denote the maintenance costs for coal, wind, photovoltaic, and energy storage, respectively, ${\overline{S}}_g,{\overline{S}}_w, {\overline{S}}_{\mathit{PV}}$ represent the installed capacities of coal, wind, and photovoltaic at the planning stage, $c_g^{\mathit{SU}}, c_g^{\mathit{SD}},c_{\mathit{loss}},c_{\mathit{tan}}$ represent the startup cost, shutdown cost, system load-shedding cost, and carbon emission cost of coal-fired units, respectively, ${\mathit{SU}}_{g,t}, {\mathit{SD}}_{g,t},P_{\mathit{loss},t}$ represent the startup capacity, shutdown capacity, and system load-shedding capacity at time $t$, ${\beta }_g$, ${\gamma }_g$ represent the disposal cost per unit capacity and the equipment recovery revenue of coal-fired units, respectively, and ${\alpha }_g^{\mathit{retire}}$ denotes the retirement rate of coal-fired units.

3.2. Constraints

To meet the requirements of constructing a new power system under the “dual carbon” goals, this study considers not expanding coal-fired units. The retirement of units is performed directly based on existing installed capacities, and coal-fired units are clustered for decision-making on startup, shutdown, and output within the cluster. The following constraints are considered:

(1)

Coal Unit Retirement Constraints:

$${\alpha }_c^{retire}={\displaystyle \frac{S_c-{\overline{S}}_c}{S_c}}$$

(24)

$${\alpha }_c^{retire,\max }\ge {\alpha }_c^{retire}\ge {\alpha }_c^{retire,\min }$$

(25)

The retirement of coal units should proceed in an orderly fashion based on local development, with maximum and minimum retirement rates of ${\alpha }_c^{\mathit{retire},\max }$ and ${\alpha }_c^{\mathit{retire},\min }$.

(2)

Output and Installed Capacity Constraints of Different Units:

Due to the startup and shutdown costs, coal units cannot frequently start and stop, unlike wind and photovoltaic units, which can operate at their maximum output capacity.

$$0\le P_{c,t}\le {\overline{P}}_{c,t}\le {\overline{S}}_c,\forall t$$

(26)

$${\overline{P}}_{c,t}=n_{c,t}\times {\displaystyle \frac{S_c\times (1-{\alpha }_c^{retire})}{N_c}}=n_{c,t}\times {\displaystyle \frac{{\overline{S}}_c}{N_c}}$$

(27)

$${\lambda }_c^{\min }\cdot {\overline{P}}_{c,t}\le P_{c,t}\le {\lambda }_c^{\max }\cdot {\overline{P}}_{c,t},\forall t$$

(28)

$$P_{c,t}\le {\lambda }_c^{\max }\cdot ({\overline{P}}_{c,t}-S_{c,t}^{SU}-S_{c,t+1}^{SD})+S{U}_c\cdot S_{c,t}^{SU}+S{D}_c\cdot S_{c,t+1}^{SD},\forall t$$

(29)

$$0\le P_{w,t}\le {\overline{P}}_{w,t}={\sigma }_{w,t}{\overline{S}}_w,\forall t,\forall w\in G_w$$

(30)

$${\overline{S}}_w=S_w+S_w^{new},\forall w\in G_w$$

(31)

$$0\le P_{PV,t}\le {\overline{P}}_{PV,t}={\sigma }_{PV,t}\cdot {\overline{S}}_{PV},\forall t,\forall PV\in G_{PV}$$

(32)

$${\overline{S}}_{PV}=S_{PV}+S_{PV}^{new},\forall w\in G_w$$

(33)

where $P_{c,t}$ denotes the output of coal at time $t$, ${\overline{P}}_{c,t}$ denotes the online capacity of clustered units, $n_{c,t}$ represents the number of online coal units at time $t$, $N_c$ is the total number of clustered units, ${\lambda }_c^{\min }$ and ${\lambda }_c^{\max }$ are the minimum and maximum output levels of the units, respectively, ${\mathit{SU}}_c$ and ${\mathit{SD}}_c$ represent the ramping levels for startup and shutdown, ${\mathit{SU}}_{c,t}$, ${\mathit{SD}}_{c,t}$ represent the startup and shutdown capacity at time $t$, $P_{w,t},P_{\mathit{PV},t}$ are the wind and photovoltaic outputs at time $t$, ${\sigma }_{w,t},{\sigma }_{\mathit{PV},t}$ represent the hourly output factors for wind and photovoltaic, ${\overline{P}}_{w,t},{\overline{P}}_{\mathit{PV},t}$ represent the hourly online capacities for wind and photovoltaic, and $S_w$ and $S_{\mathit{PV}}$ represent the initial installed capacities of wind and photovoltaic units, respectively.

(3)

System Balance Constraint

$$\begin{array}{l}{P}_{c,t}+{\displaystyle \sum _{w\in G_w}{P}_{w,t}}+{\displaystyle \sum _{PV\in G_{PV}}{P}_{PV,t}}+{\displaystyle \sum _{bat\in G_{bat}}(}{P}_{bat,t}^{dis}-P_{bat,t}^{ch})+\\ \hspace{0.33em}{\displaystyle \sum _{cb\in G_{cb}}(}{P}_{cb,t}^{dis}-P_{cb,t}^{ch})+P_{loss,t}=D_t+P_{CS,t},\forall t\end{array}$$

(34)

where $D_t$ is the actual load demand of the system at time $t$.

(4)

Energy Storage Constraints

$$S_{bat}\ge 0,P_{bat}^{\max }\ge 0,\forall t,\forall bat\in G_{bat}$$

(35)

$$0\le P_{bat,t}^{dis}\le P_{bat}^{\max },\forall t,\forall bat\in G_{bat}$$

(36)

$$0\le P_{bat,t}^{ch}\le P_{bat}^{\max },\forall t,\forall bat\in G_{bat}$$

(37)

$$0\le P_{bat,t}^{dis}+P_{bat,t}^r\le P_{bat}^{\max },\forall t,\forall bat\in G_{bat}$$

(38)

$$0\le P_{bat,t}^r\le d_{bat}^r\cdot S_{bat},\forall t,\forall bat\in G_{bat}$$

(39)

$$E_{bat,t+1}=E_{bat,t}+{\eta }^{ch}\cdot P_{bat,t}^{ch}\cdot \Delta t-{\displaystyle \frac{P_{bat,t}^{dis}}{{\eta }^{dis}}}\cdot \Delta t-{\eta }^{self}\cdot E_{bat,t},\forall t,\forall bat\in G_{bat}$$

(40)

$${\lambda }_{bat}^{\min }\cdot S_{bat}\le E_{bat,t}\le {\lambda }_{bat}^{\max }\cdot S_{bat},\forall t,\forall bat\in G_{bat}$$

(41)

$$0\le E_{bat,t}-{\displaystyle \frac{P_{bat,t}^{dis}+P_{bat,t}^r}{{\eta }_{dis}}}\cdot \Delta t-{\eta }_{self}\cdot E_{bat,t},\forall t,\forall bat\in G_{bat}$$

(42)

$${\displaystyle \sum _{t\in T}(}{P}_{bat,t}^{dis}+P_{bat,t}^{ch})\cdot \Delta t\le S_{bat}\cdot W_{bat},\forall bat\in G_{bat}$$

(43)

$$E_{bat,0}=E_{bat,T_d},\forall bat\in G_{bat}$$

(44)

where $d_{\mathit{bat}}^r$ represents the backup rate of the energy storage output, $E_{\mathit{bat},t}$ represents the energy stored in the energy storage at time $t$, $P_{\mathit{bat},t}^r$ represents the backup output of the energy storage, ${\eta }^{\mathit{ch}},{\eta }^{\mathit{dis}}, {\eta }^{\mathit{self}}$ represent the charging, discharging and self-discharge efficiency, ${\lambda }_{\mathit{bat}}^{\min },{\lambda }_{\mathit{bat}}^{\max }$ denote the minimum and maximum state of charge coefficients, $W_{\mathit{bat}}$ represents the phased energy throughput in watt-hours for storage, and $T_d$ denotes the end of a typical day, meaning Equation (44) ensures that the initial state of charge for storage at the beginning of the day should match the state of charge at the end of the day.

(5)

Low-Carbon and Renewable Energy Constraints

To build an environmentally friendly power system, coal power carbon emissions and renewable energy generation must be controlled. Carbon emissions cannot exceed the carbon quota set by policies. This constraint is a response to the requirements of local low-carbon policies. These policies, on the one hand, promote the transition of the power system toward a new type of energy system, and on the other hand, encourage coal-fired units to enhance their efficiency and reduce carbon emissions through technological upgrades and changes in their positioning as energy sources. When there is a zero-carbon requirement solely for renewable energy generation, the carbon emission cap will be zero.

Some traditional coal-fired power provinces, due to their limited wind and solar resources, still maintain a high proportion of coal-fired units. In the short term, these provinces need to provide enough power to meet the demand. Considering the relatively stable output of coal-fired units and the requirements of carbon emission policies, there is a certain degree of flexibility in carbon emission limits, allowing for over-emissions. This excess can be viewed as a percentage of the annual carbon emission quota. However, the excess carbon emissions will incur penalties, which must be included in the cost calculations.

$${\displaystyle \sum _{t\in T}{P}_{c,t}}\cdot k_c\cdot \Delta t\le K_{\tan }$$

(45)

$${\displaystyle \sum _{t\in T}{P}_{c,t}}\cdot k_c\cdot \Delta t\le K_{tan}+Q_{tan}$$

(46)

where $K_{\mathit{tan}}$ is the carbon emission cap, and $Q_{\mathit{tan}}$ represents the allowance for excess carbon emissions as a percentage of the annual carbon emission, subject to penalties.

Units fitted with CCUS systems can capture a portion of their CO₂ emissions, thereby avoiding penalties for exceeding carbon emission limits. The exact calculation is shown below.

$${\displaystyle \sum _{t\in T}(P_{c,t}}\cdot k_c-K_{tan,t}^{CCUS})\le K_{tan}$$

(47)

As the renewable power system evolves, it is essential to progressively increase the role of renewable energy in power generation. Consequently, planning in various regions must align with the energy development strategy to establish the required proportion of renewable energy within the overall energy mix.

$${\displaystyle \sum _{t\in T}({\displaystyle \sum _{w\in G_w}{P}_{w,t}}+{\displaystyle \sum _{PV\in G_{PV}}{P}_{PV,t}})}\cdot \Delta t\ge I\cdot {\displaystyle \sum _{t\in T}(}{D}_t+{\zeta }_{bat,t}+{\zeta }_{cb,t})$$

(48)

$${\zeta }_{bat,t}=(P_{bat,t}^{ch}-P_{bat,t}^{dis})\cdot \Delta t,\forall t,\forall bat\in G_{bat}$$

(49)

$${\zeta }_{cb,t}=(P_{cb,t}^{ch}-P_{cb,t}^{dis})\cdot \Delta t,\forall t$$

(50)

where I is the renewable energy penetration rate, and ${\zeta }_{\mathit{bat},t}$ and ${\zeta }_{\mathit{cb},t}$ are related to the storage and Carnot battery capacity, respectively. In this model, the charging and discharging power of energy storage systems are both considered positive values. Despite some inevitable energy loss during operation, energy storage systems significantly enhance the absorption of renewable energy. Consequently, energy storage helps mitigate the effects of renewable energy penetration constraints. Each region has distinct policy requirements for renewable energy penetration. Regions rich in wind and solar resources can set a higher penetration target I, while regions with limited wind and solar resources can opt for a lower target or fulfill policy requirements by purchasing renewable energy generation from other regions.

(6)

Generalized Adequacy Constraints

To ensure system adequacy, the online capacity must include a certain reserve margin to meet the N − 1 contingency criterion. The largest online unit must be able to meet load demands even if it fails.

$$\begin{array}{l}{\overline{P}}_{c,t}+{\sigma }_{w,t}\cdot {\displaystyle \sum _{w\in G_w}{\overline{S}}_w}+{\sigma }_{PV,t}\cdot {\displaystyle \sum _{PV\in G_{PV}}{\overline{S}}_{PV}}+{\displaystyle \sum _{cb\in G_{cb}}(}{P}_{cb,t}^{dis}-P_{cb,t}^{ch})+\\ \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{\displaystyle \sum _{bat\in G_{bat}}(}{P}_{bat,t}^{dis}-P_{bat,t}^{ch}+P_{bat,t}^r)\ge (1+d)\cdot D_t,\forall t\end{array}$$

(51)

$$d=\max ({\displaystyle \frac{S_g^{\max }}{D^{\max }}},{\mu }_{load})$$

(52)

where $S_g^{\max }$ is the maximum capacity of the largest unit, $D^{\max }$ is the maximum system load, d is the load demand reserve ratio, and ${\mu }_{\mathit{load}}$ is the reserve load ratio. Considering the system’s adequacy and flexibility needs, a portion of the storage output is reserved as a backup due to its rapid and flexible response characteristics. This ensures quick responses to fluctuations on both the supply and demand sides.

Typically, the generation capacity adequacy of the system is evaluated using probabilistic indicators, which fundamentally assess the expectation of meeting the user load with the available generation capacity under operational conditions. Based on this, in power source planning, these reliability indicators are translated into capacity demand constraints under a certain level of adequacy. To ensure capacity reliability, renewable energy generation is represented by its capacity credit factor, which varies seasonally. Additionally, the forced outage rate of coal-fired units is also considered in the expressions. The specific expression is as follows:

$$(1-{\zeta }_c^{for})\cdot {\overline{S}}_c+{\mu }_{w,n}\cdot {\displaystyle \sum _{w\in G_w}{\overline{S}}_w}+{\mu }_{PV,n}\cdot {\displaystyle \sum _{PV\in G_{PV}}{\overline{S}}_{PV}}\ge D^{\max },\forall t$$

(53)

where ${\zeta }_c^{\mathit{for}}$ denotes the average forced outage rate of the unit, and ${\mu }_{w,n}$ and ${\mu }_{\mathit{PV},n}$ represent the capacity credit factors for wind power and photovoltaic power under different scenarios, with n = 1, 2, 3 representing spring/autumn, summer, and winter, respectively.

$$0\le P_{loss,t}\le D_t,\forall t$$

(54)

$${\displaystyle \sum _{t\in T}{P}_{loss,t}}\le I_{loss}\cdot {\displaystyle \sum _{t\in T}{D}_t}$$

(55)

where $I_{\mathit{loss},t}$ represents the proportion of load loss. During the system operation simulation, due to the variability in renewable energy output caused by weather conditions, a certain proportion of load loss is permissible. This allowance is determined based on indicators such as the expected energy not supplied (EENS) to ensure adequate planning margins.

Flexibility adequacy is primarily based on two aspects: first, the flexible response provided by controllable units, and second, the flexibility demand induced by fluctuations on the supply and demand sides. Therefore, flexibility adequacy indicators are translated into adequacy constraints in power planning. This ensures that the system can respond to supply and demand fluctuations with a certain level of margin based on its own flexible adjustment capabilities.

When load and renewable energy generation (wind and solar) fluctuate, the resulting flexibility demand requires coal-fired units to promptly increase or decrease the output. During output adjustments, these units are constrained by the ramp rates of the currently online units and the startup and the shutdown ramp rates of the offline units.

$$P_{c,t}-P_{c,t-1}\le ({\overline{P}}_{c,t}-S_{c,t}^{SU})\cdot R_c^{RU}+S_{uc}\cdot S_{c,t}^{SU}-{\lambda }_c^{\min }\cdot S_{c,t}^{SD},\forall t$$

(56)

$$P_{c,t-1}-P_{c,t}\le ({\overline{P}}_{c,t}-S_{c,t}^{SU})\cdot R_c^{RD}-{\lambda }_c^{\min }\cdot S_{c,t}^{SU}+S_{dc}\cdot S_{c,t}^{SD},\forall t$$

(57)

where $R_c^{\mathit{RD}}$ and $R_c^{\mathit{RU}}$ are the ramp-up and ramp-down rates, while $S_{\mathit{uc}}$ and $S_{\mathit{dc}}$ represent the ramping levels during startup and shutdown.

$${\overline{P}}_{c,t}={\overline{P}}_{c,t-1}+S_{c,t}^{SU}-S_{c,t}^{SD},\forall t$$

(58)

$$\left\{\begin{array}{l}0\le S_{c,t+1}^{SD}\le {\overline{P}}_{c,t}-{\displaystyle \sum _{\tau =0}^{t-1}}{S}_{c,t-\tau }^{SU},t=1,\dots ,T_c^{on}-1\\ 0\le S_{c,t+1}^{SD}\le {\overline{P}}_{c,t}-{\displaystyle \sum _{\tau =0}^{T_c^{on}-2}}{S}_{c,t-\tau }^{SU},t=T_c^{on},\dots ,T-1\end{array}\right.$$

(59)

$$\left\{\begin{array}{l}0\le S_{c,t+1}^{SU}\le {\overline{S}}_c-{\overline{P}}_{c,t}-{\displaystyle \sum _{\tau =0}^{t-1}}{S}_{c,t-\tau }^{SD},t=1,\dots ,T_c^{off}-1\\ 0\le S_{c,t+1}^{SU}\le {\overline{S}}_c-{\overline{P}}_{c,t}-{\displaystyle \sum _{\tau =0}^{T_c^{off}-2}}{S}_{c,t-\tau }^{SD},t=T_c^{off},\dots ,T-1\end{array}\right.$$

(60)

where $S_{c,t}^{\mathit{SU}}$ and $S_{c,t}^{\mathit{SD}}$ represent the capacity of units starting up and shutting down at time $t$, respectively, and $T_c^{\mathit{on}}$ and $T_c^{\mathit{off}}$ denote the minimum startup and shutdown times for the cluster of units. Equations (59) and (60) constrain the startup (or shutdown) capacity of coal-fired units within the time frame $\left[t-UT, t\right]$, preventing the units from being shut down (or started up) again at time t, thus avoiding frequent cycling.

The system’s flexibility demand arises from short-term fluctuations in the load and wind/solar power generation. Considering short-term responses, in addition to using energy storage resources, it is crucial to utilize the controllable ramp-up and ramp-down capabilities of coal-fired units. These units can quickly provide the necessary spinning reserve during different periods to meet flexibility requirements. To ensure sufficient flexibility adequacy, only the spinning reserve provided by coal-fired units is considered, without additional reliance on energy storage.

$$P_{c,t}^r={\overline{P}}_{c,t}-P_{c,t},\forall t$$

(61)

$$\min ({\displaystyle \frac{R_c^R\cdot {\overline{P}}_{c,t}}{h_n}},P_{c,t}^r)\ge r_{load}\cdot D_t+r_{vre}\cdot ({\displaystyle \sum _{w\in G_w}{P}_{w,t}}+{\displaystyle \sum _{PV\in G_{PV}}{P}_{PV,t}}),\forall t$$

(62)

where $P_{c,t}^r$ denotes the online thermal reserve capacity at time $t$, $R_c^R$ represents the ramp rate of the generating unit, and $r_{\mathit{load}}$ and $r_{\mathit{vre}}$ indicate the short-term fluctuation demand rates of the load and renewable energy sources, respectively.${ h}_n$ is shown as a constant, since the time intervals in this section are in hours, when ${ h}_n$ is 2, it indicates a response within 30 min, and when ${ h}_n$ is 4, it indicates a response within 15 min.

Inertia adequacy indicates that the inertia supply in the system meets the demand. The inertia demand level of the system load serves as the boundary constraint for the stable operation of the system. Considering the inertia support provided mainly by online coal-fired units and energy storage systems with fast response characteristics such as Carnot batteries, the specific expression is as follows:

$$E_{c,t}\ge E_0\cdot (D_t-P_{loss,t}),\forall t$$

(63)

$$E_{c,t}={\overline{P}}_{c,t}\cdot H_c+{\displaystyle \sum _{bat\in G_{bat}}{S}_{bat}}\cdot H_{bat}+P_{cb}\cdot H_{cb},\forall t$$

(64)

where $E_0$ is the minimum inertia requirement, while $H_c$, $H_{\mathit{bat}}$ and $H_{\mathit{cb}}$ are the inertia coefficients of coal units, storage, and Carnot batteries. All variables appearing in this manuscript, together with their meanings and units are listed in Appendix A.

3.3. Scenario Generation and Model Solution

The model in this paper optimizes the planning of coal-fired and renewable energy generation within the framework of generalized adequacy constraints. While using data for 8760 h in the planning model can enhance the computational accuracy, handling extensive data can reduce the solution efficiency. Figure 2 shows the scenario generation and application process used in this article. To balance computational efficiency with regional operational characteristics, and considering seasonal patterns, wind and solar generation data are processed using clustering to derive typical days representing different seasons. Additionally, to identify the influence of extreme weather scenarios, phenomena like heat wave conditions in summer and cold spell conditions in winter are added into the scenarios used by the planning model.

Additionally, to represent the capacity value of renewable energy generation in the system, different seasonal capacity factors for wind and solar, based on historical generation data and peak load ratios specific to the region, are utilized. Investment decisions and operational simulations in the model optimize the installation of coal-fired, renewable energy generation, and energy storage.

This section focuses on the horizontal planning of the electricity supply for a region in Central China, considering the actual conditions of wind, solar, and load within a planning horizon of one year. Figure 3 presents the load and wind/solar power curves generated based on historical data for typical scenarios. The planned generating units include coal-fired power plants, projecting the next-phase peak load of the region to reach 70,000 MW. The current installed capacities are 66,260 MW for coal, 18,500 MW for wind, and 15,560 MW for solar. A renewable energy penetration rate of 30% is targeted, requiring at least 30% of electricity generation from renewable sources. Considering the phased retirement of coal-fired units and local requirements, the maximum and minimum retirement rates are set at 20% and 2%, respectively. The retirement costs are referenced from [31], carbon capture and reduction parameters from [33], and other operational and cost parameters from [32,34]. In the model, wind and solar power generation do not include inertia support. MATLAB 2019a with the CPLEX 12.8.0 solver is used for the solving.

4. Results—Case Study

4.1. Impact of Extreme Weather Scenarios on Installed Capacity

To assess the impact of extreme weather scenarios on coal and renewable energy installations within a new power system, Figure 4 compares the system’s installed capacity under normal weather conditions with scenarios that include extreme weather events.

The findings in Figure 4 demonstrate that the retirement of coal-fired units slows down when extreme weather scenarios are factored in. Under these conditions, the support capability of renewable energy generation decreases, leading to increased system fluctuations. To ensure adequate supply from the source side, the system opts to install more easily constructed Carnot batteries while maintaining a larger number of coal-fired units to provide flexible support and stabilize renewable energy fluctuations. This outcome is due to two main reasons:

(1)

During extreme weather, the capacity for renewable energy generation is reduced, resulting in insufficient extra power for short-term energy storage charging.

(2)

There is a necessity to maintain adequate inertia support during extreme weather. While both Carnot batteries and traditional storage batteries can provide inertia response, Carnot batteries have the advantage of storing energy over longer periods, significantly reducing the need for short-term energy storage infrastructure.

This highlights Carnot batteries as a promising technology for future development, offering stronger environmental benefits and enhanced system support.

Additionally, this constraint aligns with local low-carbon policy requirements. These policies drive the transition of the power system to a new model, encouraging coal-fired units to enhance their generation efficiency, reduce carbon emissions, and undergo technological upgrades and repositioning. Under the zero-carbon requirements of renewable-only energy generation, the carbon emission cap would be zero.

4.2. Impact of Wind–Solar Ratio on Installed Capacity

In practical engineering applications, different ratios of wind and solar power generation can influence the installation of other types of power sources. Figure 5 compares various types of power installations under different wind–solar installation ratios. The optimal economic scenario does not restrict the wind–solar ratio to explore the system’s preferred ratio. The other three scenarios adjust the wind–solar ratio with economic goals in mind to compare the impacts on various power installations.

From an installation impact perspective, the region tends to favor a wind–solar installation ratio of approximately 3:2 due to wind power’s higher capacity value. Simulations reveal that as this ratio decreases, the system’s coal installation capacity significantly increases, which hinders the gradual retirement of coal units. This leads to a greater need for carbon capture devices, resulting in a higher proportion of such units. Additionally, a lower wind–solar ratio significantly reduces the system’s energy storage demand, highlighting that wind power necessitates more storage batteries for effective energy transfer and output smoothing.

4.3. Impact of Renewable Energy Penetration Rate on Installed Capacity

In this section, the renewable energy penetration rate is defined as the ratio of load borne by wind and solar power to the total load.

Table 1. Installed capacity of various sources under different shares of electricity from renewable sources.

Share of Electricity from Renewable Sources	0.3	0.325	0.35	0.375	0.4
Energy storage capacity (MWh)	15,996	35,891	35,699	38,211	40,048
Energy storage power (MW)	7522	16,878	16,787	17,966	18,832
Carnot battery scale (MW)	2873	3354	1695	1833	2225
Coal-fired units scale (MW)	61,452	60,130	60,482	61,248	60,978
Wind power scale (MW)	23,505	29,381	27,924	35,237	47,086
Photovoltaic scale (MW)	12,565	11,535	20,783	17,797	8491

presents the impact on coal and renewable energy installations under different penetration rates, focusing on the change from a 0.3 to 0.4 minimum penetration rate in recent development. As the renewable energy penetration rate requirement increases, the need for more wind and solar power installations to meet load demand rises, with the total additional installations of wind and solar power showing an upward trend. Wind power becomes the system’s preferred choice as penetration rates increase due to its higher capacity credibility compared to solar power, which lacks the day–night characteristics of solar but provides consistent power support. Consequently, the increase in wind installations reflects this preference.

As shown in Figure 6, the change in the cost and installed capacity of CCUS under different levels of renewable energy penetration highlights that increasing the proportion of renewable energy generation requires substantial investment and construction costs for new renewable energy generating units. The energy storage power and installed capacity also rise significantly with the increased installation of wind power generation.

Moreover, the increase in renewable energy generation reduces the demand for coal-fired power generation, as depicted in Figure 6. Combined with Table 1, it is clear that the decreased demand for coal-fired power generation does not substantially lower the installed capacity of these units. This is because coal-fired units provide not only power support but also flexible backup support. The high proportion of renewable energy generation integrated into the grid introduces significant volatility and uncertainty into the system. Therefore, there is a need for flexible power sources, such as coal-fired power generation and energy storage systems, to ensure adequate and responsive flexibility to address these fluctuations.

4.4. Impact of Considering General Adequacy Constraints on Planning

During power system planning and construction, adequacy has reached a new level of importance. To ensure flexibility and inertia adequacy in low-carbon transitions, the combined optimization planning model includes flexibility and inertia adequacy constraints.

Table 2. Case setting.

Case Number	Considering Factors
	Extreme Weather	Flexibility and Inertia Adequacy Constraints
1	×	√
2	×	×
3	√	×
4	√	√

sets out four cases, including normal and extreme weather conditions, to compare the impact of considering general adequacy constraints on coal and renewable energy planning.

Figure 7 illustrates that when the flexibility and inertia adequacy constraints are not taken into account, the capacity of retiring coal units increases, leading to their accelerated retirement. This helps balance the need to avoid excessive carbon emissions while keeping more coal units online. In Case 2, wind power installation increases while solar power installation decreases, necessitating more storage capacity to manage wind power fluctuations. Considering the flexibility and inertia constraints raises the system’s total cost by 0.0105% due to the need for increased investment in renewable installations and retaining more coal units for flexibility support.

Comparing Case 1 with Case 4, the system’s demand for flexibility and inertia support during extreme weather conditions requires higher output from coal-fired units. This results in increased carbon emissions, necessitating the installation of carbon capture units on a greater proportion of coal-fired plants to stay within the system’s carbon emission limits. Overall, the total installed capacity in the system increases under extreme scenarios, whether or not flexibility reserves and inertia constraints of generalized adequacy are considered.

From Figure 8, it is evident that in Case 1 and Case 2, the system’s inertia supply capability remains high due to the significant installed capacity of energy storage systems. Both energy storage and coal-fired units contribute to the inertia support, thereby maintaining high levels of inertia supply for the dynamic frequency support.

Comparing Case 1 with Case 2, considering the flexibility and inertia adequacy constraints shows a relative decline in the system’s inertia supply capability. This is due to a reduction in the energy storage capacity and the constraints preventing excessive online unit reserves, which avoids cost escalation and resource wastage. In Case 3 and Case 4, neglecting the constraints results in long-term inertia supply levels below the system’s requirements for dynamic frequency support, especially during extreme weather conditions. This makes it difficult to maintain frequency stability at the required inertia levels. The intensified load fluctuations during extreme weather cause coal-fired units to have longer startup and shutdown times, as indicated by the slower changes in the inertia levels during significant load variations in Figure 8. The results also demonstrate that considering the flexibility and inertia adequacy constraints in relation to generalized adequacy is beneficial for meeting flexibility demands and ensuring frequency stability during power disturbances.

5. Conclusions

The construction of a new low-carbon power system necessitates the gradual retirement of coal-fired units and an increased proportion of new energy generation. The traditional concept of adequacy no longer meets the needs of a new power system. Therefore, this paper expands it to generalized adequacy, which includes capacity adequacy, flexibility adequacy, and inertia adequacy. After considering various pathways for the retirement and transformation of coal-fired units, generalized adequacy is introduced into the optimized planning model for coal-fired and new energy.

Using actual data from a region in Central China, this paper conducts a case study analysis to make the system more applicable to real-world scenarios. The analysis focuses on the impacts of extreme weather, new energy penetration rates, wind–solar ratios, and generalized adequacy constraints on the installed capacity. Under extreme weather conditions, more photovoltaic installations are expected, while higher new energy penetration rates will lead to more wind power installations. Considering the generalized adequacy constraints will somewhat slow down the retirement process of coal-fired units, but it will reduce unnecessary inertia support during normal weather and maintain dynamic frequency security during extreme weather. Reasonable planning of coal-fired and new energy sources helps meet the development requirements of future power systems. Compared to similar studies, such as references [31,32], this research uniquely introduces the impact of extreme weather on power capacity requirements, offering a more accurate depiction of how renewable energy uncertainty affects the power supply over extended time scales. Additionally, this study builds on previous work by integrating the requirements for power capacity, flexibility, and inertia into the framework of generalized adequacy. This comprehensive approach better characterizes the resource needs during energy system transitions and provides more robust theoretical guidance for power planning. By avoiding the fragmentation of resources in planning and improving the resource utilization efficiency, this research supports the low-carbon transition of power systems.

Undeniably, as the future power system continues to evolve, there are areas in this study that require further refinement. Several key aspects warrant additional exploration:

This study primarily considers “Generalized Adequacy” from a system operation perspective. However, ensuring the operational supply–demand balance necessitates the support of diverse energy sources. Energy adequacy is influenced by economic, policy, and spatial distribution factors. Further research is needed to develop models that fully integrate operational adequacy with the adequacy of supporting energy resources.

In this study, the assessment of “Generalized Adequacy” assumes that system inertia is provided solely by conventional controllable coal-fired units. With the advancement of virtual inertia control technologies, renewable energy sources like wind and solar can simulate conventional units by offering virtual inertia support. This shift could accelerate changes in the power system’s energy mix. Future research should investigate how to incorporate the inertia contributions of various energy sources, including renewables, into adequacy assessments.

The emerging power system features multi-dimensional interactions between generation, grid, load, and storage, offering abundant flexibility resources. The network structure is also a critical aspect of adequacy planning. Further studies should focus on developing a “Generalized Adequacy”-based coordinated optimization method that encompasses all the aspects of generation, grid, load, and storage, leveraging the interactive potential of various resources.