The subject of this study is a regional-level power system considering thermal constraints, depicted in Figure 1. The research accounts for load demand growth and the practicalities of electric-thermal coupling. Within the scope of long-term planning, expansions are made to the power and heat sources. The power component encompasses wind turbines, photovoltaic units, coal-fired power units, and energy storage systems. The heat sources involve heating boilers. CHP units serve as the coupling nodes in the studied system, fulfilling both electricity supply and heating tasks.

CHP units can both provide heating and participate in the power generation process. Based on the operational conditions of CHP units, they are mainly categorized into two types: back-pressure and extraction-condensing.

The power generation and heating output of back-pressure CHP units are approximately linearly related, as shown in (Eq. 1). H t = ρ P t + β (1) where, ρ is the electric-thermal ratio of back pressure CHP units, β is a constant related to the operating characteristics of CHP units, and can generally be approximated as 0.

The extraction-condensing CHP units can freely adjust their power output for both electricity generation and heat supply within a certain range. This adjustability in power output allows for flexible unit operation, as depicted in Figure 2, illustrating the range of electric-thermal output, and as shown in (Eq. 2). P t ≥ P min − σ v 1 H t − H m e d P t ≥ P min + σ m H t − H m e d P t ≤ P max − σ v 2 H t − H min (2) where, σ v 1 and σ v 2 represent the reduction in electric power resulting from an increase in unit heat power while maintaining constant steam inlet for CHP units, and σ m denotes the electric-thermal coefficient of CHP units under back-pressure conditions.

Additionally, heating boilers, functioning as supplemental heat sources on the thermal side, can decouple the electric-thermal coupling relationship of CHP units (Liu et al., 2021; Du et al., 2023).

The objective function of the multi-scenario planning model considering electric-thermal coupling is to minimize the total cost of the system during the planning period: as shown in (Eq. 3). min C t o t a l = C i n v + C m a i n + C o p + C c a r b o n + C d e l o a d + C d e o p (3) where, C t o t a l is the total cost of the system, C i n v is the investment cost, C m a i n is the maintenance cost, C o p is the operating cost, C c a r b o n is the cost for carbon emissions, C d e l o a d is the load shedding cost, and C d e o p is the decommissioning cost of coal-fired power units.

The units considered in the system mainly include wind turbines, photovoltaic units, coal-fired power units, CHP units, and heating boilers. Energy storage accounts for electrochemical energy storage systems. Among these, wind turbines encompass offshore and onshore wind power, while CHP units comprise back-pressure and extraction-condensing types. The construction and maintenance costs for each type of unit are as shown in (Eqs 4, 5). C i n v = C w i n d i n v + C p v i n v + C g i n v + C c h p i n v + C b o i l i n v + C e s s i n v = ∑ n ∈ Ω n R n ∑ s ∈ Ω s ∑ x ∈ Ω x a n , s , x P n , s , x N (4) C m a i n = C w i n d m a i n + C p v m a i n + C g m a i n + C c h p m a i n + C b o i l m a i n + C e s s m a i n = ∑ n ∈ Ω n R n ∑ s ∈ Ω s ∑ x ∈ Ω x b n , s , x P n , s , x N (5) where, a n , s , x and b n , s , x represent the unit capacity investment and maintenance costs of each type of generating unit, respectively; Ω n denotes the set of planning years, Ω s stands for the set of scenarios within a year, and Ω x signifies the set of various types of generating units. When calculating the costs incurred during the planning period, the costs generated in different years should be discounted to the equivalent present value at the beginning of the planning cycle using present value factors. Assuming the number of years between the occurrence of costs and the beginning of the planning period is represented by n, the formula for calculating the present value factor corresponding to that year is as shown in (Eq. 6). R n = 1 + i − n (6) where, i represents the discount rate.

The operating costs mainly comprise the generation cost and heat supply cost of fuel-based generating units, the curtailment penalty cost of new energy-based generating units, and the power operation cost of energy storage equipment: The operating costs are as shown in (Eqs 7, 8). C o p = C w i n d o p + C p v o p + C g o p + C c h p o p + C b o i l o p + C e s s o p (7) C w i n d o p = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s w i n d p n , s , t w i n d , i p r e − p n , s , t w i n d Δ t C p v o p = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s p v p n , s , t p v , i p r e − p n , s , t p v Δ t C g o p = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s g p n , s , t g Δ t C c h p o p = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s c h p , e p n , s , t c h p Δ t + c n , s c h p , h h n , s , t c h p Δ t C b o i l o p = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s b o i l h n , s , t b o i l Δ t C e s s o p = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s e s s p n , s , t e s s Δ t (8) where, c n , s w i n d and c n , s p v represent the curtailment penalty cost per unit of electricity for wind and photovoltaic units; c n , s g represents the unit electricity generation cost for coal-fired power units; c n , s c h p , e and c n , s c h p , h represent the unit electricity generation cost and the unit heat supply cost for CHP units; c n , s b o i l denotes the unit heat supply cost for heating boilers; c n , s e s s represents the unit operating cost for energy storage systems. p n , s , t w i n d , i p r e and p n , s , t p v , i p r e correspond to the predicted output of wind turbines and photovoltaic units; p n , s , t c h p and h n , s , t c h p denote the electric and thermal outputs of CHP units. Ω t represents the set of daily operational time slots.

The retirement planning of coal-fired power units should prioritize the decommissioning of units reaching the end of their service life. However, certain coal-fired power units with significant installed capacity and high efficiency may retain value as flexible resources even after reaching their designated lifespan. It is advisable to allow refurbishment and continued operation of these units.

During the planning period, for coal-fired power units that reach the end of their service life and are selected for decommissioning, their retirement costs should consider both disposal expenses and recovery revenue, as shown in (Eq. 9). C r t = R n c r e − c s P n , s r e (9) where, P n , s r e represents the capacity of coal-fired power units planned for retirement. c re and c re respectively denote the disposal cost and recovery revenue per unit capacity of retired coal-fired power units.

During the planning period, the refurbishment cost for the selected coal-fired power units earmarked for renovation is as shown in (Eq. 10). C r p = R n c ke P n , s k e (10) where, P n , s k e represents the capacity of coal-fired power units selected for continuation post-refurbishment, and c ke signifies the refurbishment cost per unit of coal-fired power capacity.

The total cost of planned decommissioning of coal-fired power units during the planning period is as shown in (Eq. 11). C d e o p = ∑ n ∈ Ω n ∑ s ∈ Ω s R n c r e − c s P n , s r e + R n c ke P n , s k e (11)

The penalty cost for load shedding and carbon emission cost of the system are as shown in (Eqs 12, 13). C d e l o a d = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n c n , s d e l o a d p n , s , t d e l o a d Δ t (12) C c a r b o n = C g c a r b o n + C c h p c a r b o n + C b o i l c a r b o n = ∑ n ∈ Ω n , s ∈ Ω s , t ∈ Ω t R n [ f n , s g p n , s , t g Δ t + f n , s b o i l h n , s , t b o i l Δ t + f n , s c h p , e p n , s , t c h p Δ t + f n , s c h p , h h n , s , t c h p Δ t (13) where, p n , s , t d e l o a d represents the system’s load shedding electricity and c n , s d e l o a d indicates the cost per unit of load shedding. f n , s g , f n , s c h p , e , f n , s c h p , h and f n , s b o i l stand for the penalty costs per unit of carbon emissions from coal-fired power generation, CHP generation, CHP heat supply, and heating boilers’ heat supply.

The constraint conditions mainly include planning-level constraints and operational-level constraints. Planning-level constraints consist of installed capacity constraints and preliminary screening constraints for unit capacity. Operational-level constraints encompass power balance constraints, transmission line power constraints, unit output characteristic constraints, energy storage system behavioral constraints, spinning reserve capacity demand constraints, and carbon emission limitations.

Installed capacity constraints is as shown in (Eq. 14). B n , x N ≤ P n , s , x N ≤ A n , x N (14) where, B n , x N and A n , x N represent the lower and upper limits of installed capacity for each type of generating unit. B n , x N depends on the initial installation situation of the system. A n , x N is contingent upon local resource endowments and government energy policies.

The total installed capacity of the system’s power and heat sources should meet the maximum electric and thermal loads with a certain margin, incorporating a confidence factor to further narrow down the constraints. It is evident that this constraint is not exhaustive and is used solely for preliminary screening of obviously inadequate unit installation capacity configurations. Preliminary screening constraints for unit capacity are as shown in (Eqs 15, 16). σ wind P n , s , w i n d N + σ p v P n , s , p v N + σ g P n , s , g N + σ c h p P n , s , c h p N ≥ P n , s , l o a d max 1 + R d , e (15) σ c h p H n , s , c h p N + σ b o i l H n , s , b o i l N ≥ H n , s , l o a d max 1 + R d , h (16) where, σ wind , σ p v , σ g and σ c h p are the confidence factors for the power supply unit, and σ b o i l is the confidence factor for heating boilers. Generally, the confidence factor for fuel units can be calculated at 100% confidence, while for the new energy unit, the confidence factor can be calculated based on the historical power generation data. P n , s , l o a d max and H n , s , l o a d max represent the maximum electric load and maximum thermal load in the current system planning level year; R d , e and R d , h represent the capacity reserve coefficient of electricity and heat, respectively.

The power balance constraints are as shown in (Eqs 17, 18). p n , s , t w i n d + p n , s , t p v + p n , s , t g + p n , s , t c h p + p n , s , t e s s = p n , s , t l o a d − p n , s , t d e l o a d (17) h n , s , t c h p + h n , s , t b o i l = h n , s , t l o a d (18) where, p n , s , t l o a d and h n , s , t l o a d are electric load demand and thermal load demand, respectively.

The transmission line power constraints is as shown in (Eq. 19). P n , s , k min ≤ p n , s , t , k ≤ P n , s , k max (19) where, p n , s , t , k represents the actual active power; P n , s , k max and P n , s , k min represent the maximum allowable power and the minimum allowable power of the transmission line, respectively.

The unit output characteristic constraints are as shown in (Eqs 20, 21). p n , s , t min ≤ p n , s , t ≤ p n , s , t max h n , s , t min ≤ h n , s , t ≤ h n , s , t max (20) p n , s , t + 1 − p n , s , t ≤ p n , s , t u p p n , s , t − p n , s , t + 1 ≤ p n , s , t d o w n h n , s , t + 1 − h n , s , t ≤ h n , s , t u p h n , s , t − h n , s , t + 1 ≤ h n , s , t d o w n (21) where, p n , s , t min and p n , s , t max are the minimum and maximum technical output of the power supply unit, respectively; h n , s , t min and h n , s , t max are the minimum and maximum technical output of the heating unit; p n , s , t u p and p n , s , t d o w n are the allowable power for uphill and downhill of the power supply unit; for the heating unit, h n , s , t u p and h n , s , t d o w n are the allowable power for uphill and downhill.

For energy storage systems, the electric energy level must remain consistent before and after scheduling cycle and must be maintained within a certain range. The energy storage system behavioral constraints are as shown in (Eqs 22, 23). p n , s , t e s s = p n , s , t d − p n , s , t c (22) 0 ≤ p n , s , t d , p n , s , t c ≤ P n , s , e s s N 0 ≤ p n , s , t d + p n , s , t c ≤ P n , s , e s s N E n , s , t e s s = E n , s , t − 1 e s s − η e s s p n , s , t e s s S O C n , s , ⁡ min ≤ E n , s , t e s s / E n , s , e s s N ≤ S O C n , s , ⁡ max E n , s , T e s s = E n , s , 0 e s s (23) where, P n , s , e s s N is the rated power capacity of the energy storage system; E n , s , e s s N is the rated energy capacity of the energy storage system; η e s s is the energy storage charging and discharging efficiency of the system; S O C n , s , ⁡ min and S O C n , s , ⁡ max are the minimum and maximum state of charge of the energy storage system; E n , s , 0 e s s is the energy storage capacity at the initial time of scheduling and E n , s , T e s s is the energy storage capacity at the end of the scheduling cycle.

Setting positive and negative rotating reserve capacity is an effective measure to improve the reliability of power system operation. Usually, the positive and negative rotating reserve capacity is borne by coal-fired power units, CHP units, and energy storage systems. The spinning reserve capacity demand constraints are as shown in (Eqs 24, 25). R g + R c h p + R e s s ≥ ∂ w i n d p n , s , t w i n d + ∂ p v p n , s , t p v + ∂ l o a d p n , s , t l o a d D g + D c h p + D e s s ≥ ∂ w i n d p n , s , t w i n d + ∂ p v p n , s , t p v + ∂ l o a d p n , s , t l o a d (24) where, ∂ l o a d , ∂ w i n d and ∂ p v represent the reserve capacity coefficients of load power, wind power, and photovoltaic power, and 0.12, 0.05, and 0.05 are taken in this paper. R g , R c h p and R e s s are the positive rotation reserve capacity provided for coal-fired power units, CHP units, and energy storage systems, as well as D g , D c h p and D e s s are the negative rotation reserve capacity provided for coal-fired power units, CHP units, and energy storage systems. R g = ⁡ min p n , s , ⁡ max g − p n , s , t g , p n , s , u p g D g = ⁡ min p n , s , t g − p n , s , ⁡ min g , p n , s , d o w n g R c h p = ⁡ min p n , s , ⁡ max c h p − p n , s , t c h p , p n , s , u p c h p D c h p = ⁡ min p n , s , t c h p − p n , s , ⁡ min c h p , p n , s , d o w n c h p R e s s = P n , s , e s s N − p n , s , t e s s D e s s = P n , s , e s s N + p n , s , t e s s (25)

To meet the dual carbon targets, limitations are imposed on the carbon emissions from fuel-based units in the system. Carbon emission limitations is as shown in (Eq. 26). ∑ s ∈ Ω s ∑ t ∈ Ω t c o n , s g p n , s , t g Δ t + c o n , s c h p , e p n , s , t c h p Δ t + c o n , s c h p , h h n , s , t c h p Δ t + c o n , s b o i l h n , s , t b o i l Δ t ≤ X n c o (26) where, p n , s , t g and p n , s , t c h p are the actual electric output of the fuel powered unit; h n , s , t c h p and h n , s , t b o i l are the actual thermal output of the fuel heating unit. c o n , s g , c o n , s c h p , e , c o n , s c h p , h and c o n , s b o i l are the carbon dioxide emission coefficient per unit output for the power supply part of thermal power units, CHP units, heating parts of CHP units, and heating boilers. X n c o is the upper limit of carbon dioxide emissions.

The planning model ensures the reliable supply of electric loads and thermal loads through constraint conditions while demanding compliance with carbon emission targets. The model can generate the installed capacities of power and heat sources annually under the most economically optimal strategy and provide operational insights for various scenarios.

This paper validates the planning model using an improved IEEE-39 bus power system (Gu et al., 2015). The selected planning horizon spans 15 years, divided into three phases within 5-year intervals. At the initial planning stage, the installed capacity of power supply units in the system totals 1940MW, and that of the heat supply units is 900 MW, with coal-fired power units capacity of 1000 MW. Considering the remaining lifespan of units and actual carbon emission requirements, the coal-fired power units should be phased out gradually. During the decommissioning decision, units may choose to exit directly or continue operating after renovation. In the first phase, 100 MW of coal-fired power units capacity is scheduled for retirement. In the second phase, 200 MW of coal-fired power units capacity is planned for retirement. In the third phase, 200 MW of coal-fired power units capacity is projected for retirement. By the end of the planning horizon, a total of 500 MW of coal-fired power units capacity is scheduled for retirement, accounting for 50% of the total coal-fired power units capacity.

The investment cost, maintenance cost, and operating cost of various types of units in the system are shown in Table 1. For wind turbines and photovoltaic units, only penalty costs for power abandonment are considered. In addition, the penalty cost coefficient for load shedding set by the system is 24,000 CNY/(MWh), the carbon tax price is 48 CNY/ton, and it increases at an annual growth rate of 20%. The annual growth rate of electricity and heat loads is 4.5%, and the annual discount rate is 8%.

The new energy output has strong seasonal characteristics. The planning year is divided into four seasons: spring, summer, autumn, and winter. The binary K-means clustering algorithm is used to cluster the new energy output, electric load and heat load of each season in each stage. Typical daily data is selected as the basic data input to solve the above planning model.

To validate the planning model considering carbon emission factors in this paper, four scenarios have been established for comparative analysis.

Scenario 1: The planning model does not consider carbon emission constraints or carbon tax.

Scenario 2: The planning model does not consider carbon emission constraints but considers carbon tax.

Scenario 3: The planning model does not consider carbon tax but considers carbon emission constraints.

Scenario 4: The planning model considers both carbon tax and carbon emission constraints.

1) Capacity allocation and economic analysis

In the aforementioned four scenarios, this paper conducts numerical simulations and solutions, analyzing the capacity allocation and the economic feasibility of the system individually.

The planning results of the fuel-based units are presented in Table 2. Scenario 4, verified by this model, involves coal-fired power units capacity of 500 MW constrained by carbon emissions. In Scenario 4, the planned retirement of coal-fired power units occurs as scheduled without choosing the option for renovation and continued operation. For Scenario 4, the installed capacity of CHP units reaches 1,334.17MW, with heating boilers capacity of 591.17 MW. In Scenario 1, orderly retirements of coal-fired power units occur in the first two phases. In the third phase, to meet the actual demands of both electric and heat loads, the coal-fired power units’ installed capacity is expanded to 999.05 MW. Simultaneously, the installed capacities of CHP units and heating boilers reach 1,341.09 and 455.12 MW, respectively. Scenarios 2 and 3 are affected by carbon emission constraints, resulting in the timely retirement of coal-fired power units, with CHP unit and heating boiler capacities similar to Scenario 4. In summary, carbon emission constraints drive the system toward cleaner and lower carbon operations, prompting the scheduled retirement of coal-fired power units. However, the large-scale retirement of these units may lead to insufficient system flexibility. The planning proposal addresses this by expanding CHP units and heating boilers to increase adjustment capabilities on the heat source side, thereby alleviating the adjustment pressure on the power system.

The installed capacities of wind power and photovoltaic units are shown in Table 3, and the planning results for energy storage capacities are presented in Table 4. The comparative economic costs across different scenarios are illustrated in Table 5. In Scenario 1, the installed capacity of new energy units remains at its original level, while the energy storage capacity is set at 451.19 MW to alleviate potential inadequacies in the system’s flexibility in later planning stages. Scenario 2 demonstrates a rise in the installed capacity of new energy units to 1,812.53 MW and an energy storage capacity of 604.08 MW. The limitations imposed by the carbon tax lead to increased operational costs for coal-fired power units, resulting in a substantial influx of new energy units. However, due to the stochastic and fluctuating nature of new energy sources, the system faces insufficient reserve capacity, necessitating further expansion in energy storage capacity. In Scenario 3, the installed capacity of new energy units reaches 1,863.72 MW, accompanied by an energy storage capacity of 604.88 MW, resulting in a total cost of 213,902 million CNY. Adhering to predefined standards for annual carbon emissions, there’s a sacrifice of economic efficiency to meet environmental requirements, leading to a cost increase of 19,215.5 million CNY compared to Scenario 1. Scenario 4 displays an installed capacity of new energy units reaching 1,868.79 MW, highlighting the growing trend in new energy unit capacity, as depicted in Figure 4. The planning model considers the evolving cost reduction in offshore wind power installations over time. During the first stage of the planning horizon, the capacity of new energy units remains unchanged due to ample installed capacity. In the second stage, onshore wind power proves more cost-effective than offshore wind power, becoming the preferred choice for new energy unit additions. In the final stage, the integrated cost of offshore wind power installations becomes lower than onshore wind power, making it the most economically viable option among new energy units. Moreover, Scenario 4 features an energy storage capacity of 679.7 MW, slightly increased compared to previous scenarios. These storage facilities contribute to peak shaving, reducing the curtailment of new energy and effectively minimizing carbon emissions during system operations. With a total cost of 299,147.3 million CNY, Scenario 4, having the most stringent carbon emission restrictions, exhibits the highest overall cost among the scenarios. In summary, the low-carbon evolution of the power system inevitably necessitates extensive expansion of new energy and energy storage systems. By judiciously selecting appropriate capacities for new energy and energy storage installations, the power system can economically develop while meeting load demands and ensuring operational stability.

According to the simulation examples in four scenarios, the planning results of installed capacity for each type of unit during the planning period are shown in Figure 5.

2) Comparison of carbon emissions

The carbon emissions for each scenario are illustrated in Figure 6. In Scenario 1, carbon emissions steadily rise year by year, with a total of 1.0873 million tons. Apart from the initial generation from new energy units, the remaining load is powered by fuel-based units. In Scenario 2, constrained by increasing carbon taxes, emissions slightly decrease in the initial phase due to lower carbon taxation costs. However, as carbon taxes surge, additional new energy generation is introduced to mitigate system emissions, resulting in a total of 0.8534 million tons. Scenario 3 abides by a unified standard for carbon emissions. Once the set limit is reached, carbon emissions stabilize, totaling 0.8218 million tons. In Scenario 4, total emissions amount to 0.8103 million tons, marking a reduction of 0.277 million tons compared to Scenario 1, constituting 25.48% of the total emissions in Scenario 1. Scenario 4 features the highest capacities for new energy units and energy storage. The primary power supply comes from new energy and CHP units, while the main heat supply is from CHP units, supplemented by heat supply boilers. In summary, the carbon emission constraints driven by economic incentives and policy regulations effectively enhance carbon reduction. Higher carbon tax prices and lower carbon emission limits lead to more substantial carbon reduction. However, a better carbon reduction performance increases the overall system cost, necessitating higher demands for new energy units and energy storage capacities, consequently elevating the proportion of new energy generation.

With the advancement of dual carbon targets, the paths to limit carbon emissions to achieve the target during the planning period can be categorized into uniform, front acceleration, and rear acceleration. Front acceleration refers to a relatively rapid increase or decrease in the early stage followed by a slowdown, while rear acceleration indicates a slower increase or decrease in the early stage followed by a faster rate later on. Uniform progression lies between the two, maintaining a steady increase or decrease throughout. Using the carbon emissions from the scenario not considering carbon emission constraints and carbon taxes as the baseline, within three 5-year planning phases, there are options to calculate carbon emission quotas based on the uniform, front acceleration, and rear acceleration paths, generating a total of 27 ERPs, as shown in Figure 7. Under these ERPs, the planning model considering carbon taxes is solved.

The economic costs under different ERPs are illustrated in Figure 8. Among these paths, the “Front Acceleration + Front Acceleration + Front Acceleration” trajectory exhibits the highest total cost, totaling 315.895 million CNY. Conversely, the “Rear Acceleration + Rear Acceleration + Rear Acceleration” trajectory reflects the lowest total cost at 306.471 million CNY, indicating a difference of 9.424 million CNY. The comparison of total costs across stages reveals that within the same phase, the rear acceleration pathway outperforms the uniform pathway, and the uniform pathway surpasses the front acceleration pathway. This trend is attributed to the higher carbon emission limits, enabling greater optimization scope for the output of various units within the system, resulting in superior optimization outcomes. Additionally, as the construction costs of offshore wind power units decrease over time, choosing to incorporate new offshore wind power units in the later stages of each phase evidently offers better economic viability.

The chosen comparative scenarios are: the “Uniform + Uniform + Uniform” path 1, representing the moderate economic feasibility, the “Front Acceleration + Front Acceleration + Front Acceleration” path 14, signifying the least economic viability, and the “Rear Acceleration + Rear Acceleration + Rear Acceleration” path 27, representing the most optimal economic performance. The planned capacities for new energy sources, energy storage, and the variations in carbon emissions are illustrated in Figure 9. In path 27, the carbon emissions during each phase of the planning period exhibit a rear acceleration trend, corresponding to the carbon emission constraints in this pathway. During this phase, the total carbon emissions amount to 722,600 tons. In contrast, in path 1 and path 14, the total carbon emissions amount to 690,800 and 660,300 tons, respectively. Notably, in the pathway showcasing the most optimal economic performance, the system exhibits relatively higher carbon emissions throughout the planning period. Furthermore, from an overall perspective, the trend in carbon emissions corresponds to the variations in new energy and energy storage capacities. Specifically, when selecting the rear acceleration pathway for carbon emission constraints, the capacities for new energy units and energy storage also follow the rear acceleration pathway.