Optimal Design Parameters for Supercritical Steam Power Plants

Abstract

Steam thermal power plants represent important energy production systems. Within the energy mix, these could allow flexible generation and the use of hybrid systems by integrating renewables. The optimum design solution and parameters allow higher energy efficiency and lower environmental impact. This paper analyzes single reheat supercritical steam power plants design solutions using a genetic heuristic algorithm. A multi-objective optimization was made to find the Pareto frontier that allows the maximization of the thermal cycle net efficiency and minimization of the specific investment in the power plant equipment. The Pareto population was split and analyzed depending on the total number of preheaters. The mean values and the standard deviations were found for the objective functions and main parameters. For the thermal cycle schemes with eight preheaters, the average optimal thermal cycle efficiency is (48.09 ± 0.16)%. Adding a preheater increases the average optimal thermal cycle efficiency by 0.64%, but also increases the average optimum specific investments by 7%. It emphasized the importance of choosing a proper ratio between the reheating and the main steam pressure. Schemes with eight and nine preheaters have an average optimum value of 0.178 ± 0.021 and 0.220 ± 0.011, respectively. The results comply with data from the literature.

1. Introduction

Thermal power plants (TPPs) are expected to remain one of the most important components of the future power generation mix, at least until the shift towards clean energy renewable sources is made and international insecurity is reduced. The interest in TPPs is maintained by the improvements in the thermal cycle, which led to thermal efficiencies over 42% [1,2,3].

Several scientific papers analyze supercritical power plants’ design and operation. For 1000 MW single reheat ultra-supercritical coal-fired power plant systems, Lin et al. [4] analyzed the bypass flue thermal system with and without a steam–air heater, showing that the thermal efficiency may reach 43.89% if steam–air heaters are integrated. For a similar power plant, Liu et al. [1] achieved a power generation efficiency of 48.35% for a modified steam system that uses the flue gas from the economizer to partially heat the condensate, while the rest of the condensate is preheated by steam extractions from the turbine. Chen et al. [2] propose a cascade energy use, by the integration of an ultra-supercritical coal-fired power plant with solvent-based post-combustion carbon capture and molten-salt heat storage systems, for a 1000 MWe scheme. Additionally, for a 1000 MW unit, Li et al. [5] optimize the pressure drop of the main and reheat steam pipes. A multi-energy cascade system conducting cross heat exchange was analyzed and evaluated by Chi et al. [6], showing an increase in the power generation efficiency of up to 49.39%.

Different optimization methods of supercritical steam power plants are proposed in the literature [7], based on neural networks [8], fuzzy logic [9,10], statistical neural-based models [8], gradient-free methods [11,12], heuristic methods [13,14,15] or combinations of several methods. Considering the need to use thermal power plants to maintain power grid stability when renewables sources are not available, their operational efficiency is directly impacted. To study the impact of flexible operation on their efficiency, a digital twin model that integrates mechanism and data-driven methods was developed by [16]. Moreover, new control strategies of thermal power plants have been proposed [17,18,19].

Simulation software used to model supercritical power plants include SimuEngine [20], TRNSYS [21], Apros [22], IPSEpro [23], MATLAB [24], EBSILON [25], Modeliga [26], etc. A critical review of the techniques used for modeling and controlling supercritical power plants was conducted by Mohamed et al. [27].

Most of the studies published on supercritical steam power plants use specialized software to analyze an imposed scheme of the thermodynamic cycle. However, a more flexible approach is necessary to find the optimum from different scheme solutions and input parameters.

This paper is based on the methodology for the optimal design of single reheat thermodynamic steam cycles given by [28] to find the optimal design parameters for supercritical steam power plants by using a genetic algorithm. The multi-objective optimization results are detailed for different numbers of preheaters, obtaining the optimal variation domains for: the main steam temperature and pressure, reheat temperature and pressure, condenser pressure, deaerator pressure, feed water temperature into steam generator, steam quality at the exit of the turbine, net specific main mass steam flow rate, net specific energy and temperature increase on a preheater. Two objective functions are considered: the thermal cycle efficiency and the specific investments in the power plant’s equipment.

2. Materials and Methods

2.1. Thermodynamic Cycle Configurations

The single reheat supercritical steam thermal power plants’ thermodynamic cycle configuration was studied (Figure 1).

The turbine (T) contains the high-pressure turbine (HPT), the intermediate-pressure turbine (IPT) and the low-pressure turbine (LPT). The steam that exits from T is condensed within the condenser (C) and then pumped towards the preheating system (PH). While passing through PH, the feed water is preheated with steam extracted from T. PH includes three types of heaters to increase the temperature of the feedwater: several low-pressure (LPHs) and high-pressure (HPHs) heaters, and a deaerator (D). The number of LPHs and HPHs depend on the fluid parameters at the entrance and exit of T, and on the design constraints, being subject to technical optimization. Steam is supplied to D from IPT, to LPHs from lower pressure turbine steam extractions and to HPHs from higher pressure turbine steam extractions.

The condensate pump (CP) is used to cover the pressure loss on LPHs and to ensure the necessary pressure at the deaerator. The feed water pump (FWP) is used to cover the pressure loss on HPHs and SG and to ensure the required main steam pressure. Between HPT and IPT, the steam is reheated by SG (Figure 1).

The thermal cycle is calculated according to the methodology described in [14], with the best configuration of PH and T being defined. The main input parameters of the model include as follows:

• The main steam pressure (p_ms, in bar) and the main steam temperature (t_ms, in °C);
• The ratio between the reheating and the main steam pressure:

r_p = p_rh/p_ms,

(1)

where p_rh is the steam at the HPT exit, in bar;

• The reheat steam temperature (t_rh, in °C);
• The pressure at the condenser (p_c, in bar);
• The fuel heat flow rate (Q_fuel, in MW).

The main design hypothesis and constrains are as follows [14,28]:

• Equal temperature increase on each preheater (Δt, in °C);
• Maximum value for Δt (maximum 32 °C);
• Maximum value for the deaeration pressure (p_D, in bar), (maximum 12 bar);
• Limitation of the number of HPHs by the number of LPHs (the number of HPHs should not exceed the number of LPTs);
• Restriction of the exhaust steam quality (x_out, dimensionless) to avoid blades corrosion (minimum 0.88);
• The turbine is divided into several zones, defined between successive steam intakes and extractions of each cylinder, including between successive steam extractions from T;
• Variable internal isentropic efficiency through the turbine, depending on the volumetric flow rate and on the specific theoretical enthalpy reduction on the cylinder (for HPT and IPT); on the specific theoretical enthalpy reduction and on x_out (for LPT);
• Imposed constant values for the overall efficiency of FWP (0.85) and PC (0.8), including their electrical motors;
• Imposed SG efficiency (0.95).

The best configuration of the thermal cycle and its main parameters are defined within three main steps as follows [14]:

• Definition of the thermodynamic cycle configuration;
• Calculation of the thermodynamic cycle;
• Calculation of the thermodynamic cycle efficiency indicators and investment.

2.1.1. Definition of the Thermodynamic Cycle Configuration

The configuration of the thermodynamic cycle is defined within an iterative calculation, starting from the input data, a simplest configuration of the preheating system (PH) and the main design hypothesis and constraints (Figure 2).

Starting from the simplest configuration of the thermodynamic cycle configuration system with a minimum number of preheaters (three LPHs, the deaerator and one HPH), the temperature increase on each preheater (Δt) and the pressure at the deaerator (p_D) are calculated. The configuration of the cycle is adjusted and improved successively by adding a preheater and/or moving a preheater between HPTs and LPTs until Δt and p_D meet the requirements.

2.1.2. Calculation of the Thermodynamic Cycle

The main parameters for the chosen configuration of the thermodynamic cycle are also calculated within several iterations, until the error between the results of two successive iterations are below an acceptable error (Figure 3).

Through several iterations, the main components of the cycle (turbine, condenser, preheating system, pumps, steam generator) are calculated, until the parameters at the interface between the components of the system fit to one another [28].

2.1.3. Calculation of the Thermodynamic Cycle Efficiency Indicators and Investment

For the chosen cycle configuration, the following indicators are determined:

• The thermal cycle net efficiency, dimensionless [14]:

η_n = P_n/Q_fuel,

(2)

where P_n is the thermal cycle net power, in kW [29], and Q_fuel is the heat flow rate into SG, in kW. P_n is the difference between the power at the electrical generator and the electrical motor power of the pumps (CP and FWP) [28].

• The specific investment in power plant equipment, in USD/kW [11]:

I_sp = (C_m + C_e)·k_u/P_n,

(3)

where C_m and C_e are the costs of the main equipment and the electrical equipment, respectively, in USD/kW; k_u is a multiplying factor used to consider other costs.

• The specific net main steam flow rate, in kg/kWh:

d_sp = 3600·F_ms/P_n,

(4)

where F_ms is the main steam mass flow rate, in kg/s.

• The specific net energy, in kJ/kg:

e_sp = 3600/d_sp

(5)

2.2. Multi-Objective Optimization

Both technical and economical multi-objective optimizations of the steam cycle are performed by considering the thermal cycle net efficiency and the specific investment in equipment, respectively.

For the given cycle configuration (Figure 1), the optimization is conducted considering the variation in the main parameters within the domains given in

Table 1. Variation domain of the main parameters.

Parameter	Unit	Variation Domain
pms	bar	300–320
tms	°C	590–610
t rh	°C	590–630
rph	-	0.14–0.36
pc	bar	0.04–0.05

. The heat flow rate is imposed at Q_fuel = 2100 MW [14].

The objective function F aims at the maximization of the thermal cycle net efficiency (η_n) and the minimization of the specific investment in the power plant equipment (I_sp):

F = max(η_n) & min(I_sp),

(6)

subject to the design constraints mentioned prior.

The optimum values of the analyzed parameters are searched by using a Non-dominant Sorting Genetic Algorithm (NSGA). Thus, considering an initial set of solutions for different input values within the considered domain (an initial population), new improved generations are obtained iteratively. By mutation and crossover processes, only the solutions that best meet the requirements of the objective function are retained for further evolution and generate a new generation [30,31].

The Pareto solution to the multi-objective optimization is obtained from the last computed generation of possible cycle schemes, by retaining only the non-dominated solutions where neither solution is better than another one (the improvement of an optimization criterion leads to the worsening of the other one).

For each of the analyzed cases, the initial population consisted of 500 non-dominated Pareto solutions, which were improved along 500 generations.

The optimization model was developed under the Scilab software 6.1.0 [32], using the Niched Sharing Genetic Algorithm (optim_nsga2 function) and Pareto Filtering (pareto_filter function). The Pareto solution was found, consisting of a set of input and output parameters and chosen design schemes (Figure 4).

3. Results

The results of the heuristic multi-objective optimization of single reheat cycle configurations consist of the Pareto solution of the final population presented in Figure 5. The thermal cycle net efficiency (η_n) increases with the specific investment (I_sp). At the range ends, the curves tend to flatten; thus, at small I_sp, η_n decreases sharply and at high η_n, I_sp increases sharply. This emphasizes the importance of the multi-objective optimization and the choice of the best scheme.

In Figure 5, three intervals are highlighted as follows:

• z = 8: η_n ∈ (47.71–48.20)% and I_sp ∈ (1848–1949) USD/kW;
• z = 8, z = 9: η_n ∈ (48.20–48.35)% and I_sp ∈ (1949–2021) USD/kW;
• z = 9: η_n ∈ (48.35–48.54)% and I_sp ∈ (2021–2163) USD/kW.

In Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19, the Pareto population was sorted to highlight the two scheme solutions (z = 8 and z = 9) and the effects of η_n increases. Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19 and

Table 2. Optimum values (mean value and standard deviation) for single reheat supercritical steam power plant, for schemes with z = 8 and z = 9.

Parameters and Results		Units	Mean Value ± Standard Deviation (SD)
			z = 8	z = 9
Main steam pressure	pms	bar	312.1 ± 2.1	313.3 ± 1.4
Main steam temperature	tms	°C	591.1 ± 0.7	592.5 ± 0.8
Condenser pressure	pc	bar	0.049 ± 0.002	0.044 ± 0.002
Deaerator pressure	pD	bar	10.7 ± 1.1	8.6 ± 0.4
Reheat steam pressure	prh	bar	55.4 ± 6.5	68.8 ± 3.6
Reheat steam temperature	trh	°C	608.3 ± 1.8	611.2 ± 1.1
Ratio between prh and pms	rp	-	0.178 ± 0.021	0.220 ± 0.011
Number of HPHs	zHPH	-	3	4
Number of LPHs	zLPH	-	4	4
Temperature increase on each preheater	Δt	°C	30.1 ± 1.1	28.5 ± 0.5
Exhaust steam quality	xout	-	0.913 ± 0.004	0.903 ± 0.003
SG feedwater temperature	tinSG	°C	278.8 ± 7.9	293.0 ± 3.5
Specific main steam flow rate	dsp	kg/kWh	2.65 ± 0.06	2.75 ± 0.03
Net specific energy	esp	kJ/kg	1358 ± 28	1312 ± 13
Specific investment	Isp	USD/kW	1924 ± 44	2059 ± 52
Thermal cycle net efficiency	ηn	%	48.09 ± 0.16	48.40 ± 0.09

emphasize the chosen solutions. Considering a normal distribution of the results, the 68.2% confidence domain was highlighted in Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19 with dashed lines. This level of confidence corresponds to the mean value ± standard deviation.

Table 2 synthetizes the Pareto solutions, emphasizing the mean value and the standard deviation for each chosen number of preheaters (z = 8 and z = 9).

The steam expansion in the steam turbine is presented on the specific enthalpy–specific entropy diagram in Figure 20 (h-s diagram). For z = 8 (the red line) and z = 9 (the blue line), the mean values of p_ms, t_ms, p_c, t_rh, r_p, z_HPH, z_LPH from Table 2 were taken as input data for the h-s diagram.

The h-s diagram in Figure 20 illustrates the influence of r_p on the steam expansion in the steam turbine. The increase in r_p implies a decrease in the expansion within HPT (due to the increase of p_rh). Similar values of t_rh and the increase in p_rh lead to the shift of the steam expansion in IPT and LPT to the left in the h-s diagram. Moreover, given the similar p_c values, the steam quality at the LPT exhaust (x_out) worsens, but it still remains over the minimum imposed value.

Further, the analysis is expanded to consider lower values of the fuel heat flow rate (Q_fuel), between the reference value (2100 MW) and a quarter of it (525 MW). This leads to the decrease in the thermal cycle net power from about 1000 MW to about 200 MW (Figure 21). Figure 22 and Figure 23 show the variation in the objective functions with Q_fuel.

The increase in Q_fuel leads to the increase in η_n (and the decrease in I_sp, due to the scale effect). This trend is flattening towards higher Q_fuel.

The results of the model are analyzed and validated with data from the scientific literature in the next section.

4. Discussion

Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19 and Table 2 highlight the optimum solutions chosen for z = 8 and z = 9.

As shown in Figure 6, the optimum p_ms values have small variations, even if z is changed from 8 to 9. Thus, for z = 8, p_ms ∈ (310.0, 314.2) bar, and for z = 9, p_ms ∈ (310.6, 315.9) bar. However, according to Figure 8, the optimum p_rh values have important variations even for the same z. It can be observed that for z = 8, p_rh ∈ (48.9, 61.9) bar, and for z = 9, p_ms ∈ (65.3, 72.4) bar.

To obtain a dimensionless parameter that can be optimized, p_rh was linked on p_ms by dividing p_rh by p_ms (Equation (1)). From Figure 9’s results, the optimum dimensionless parameter r_p for the analyzed interval is as follows:

• For schemes with z = 8, r_p ∈ (0.140, 0.202) bar;
• For schemes with z = 9, r_p ∈ (0.202, 0.253) bar.

The significant variation in r_p is due to the variation in p_rh in the conditions in which p_ms values have a small standard deviation. For z = 8, p_ms = 312.1 ± 2.1 bar, and for z = 8, p_ms = 313.3 ± 1.4 bar (Table 2).

In the scientific literature, within simulations using typical parameters and z = 8, r_p was considered as follows: 0.165 in simulations with GSE software [33]; 0.166 [34]; 0.167 [35]; 0.170 in simulations with Aspen Plus software [36]; 0.173 [37]; 0.176 [20]; 0.181 in simulations with Gate Cycle software [38]; 0.183 when a typical 1000 MW plant was considered [39]; 0.187 in simulation with Aspen Plus software [40].

The configurations obtained within this paper are of interest mainly for the design of new power plants. There are in operation power units with supercritical parameters that use configurations and parameters highlighted in the paper. Thus, for the existing plant in Changchun, China [41], with supercritical parameters and z = 8: r_p = 0.180. These parameters are proposed for the retrofitting of the existing coal-fired power plants by integrating a CO₂ capture system. For a 600 MW existing supercritical steam power plant in China that is firing lignite, a configuration with z_HPH = 3, z_LPH = 4 and r_p = 0.157 is given [42]. Additionally, for the coal-fired Łagisza power plant operated in Poland [43], r_p = 0.183 was used at z = 8. For this existing supercritical power plant, in [43], a repowering solution was proposed. It can be observed that all the r_p values presented for z = 8 in the literature are within the confidence interval of the optimum r_p obtained in the paper for the same number of preheaters: (0.157, 0.199); that is, r_p = 0.178 ± 0.021, as shown in Figure 9 and Table 2.

In the literature, for z = 9, simulations that use typical parameters considered the following r_p values: 0.214 [44] and 0.217 for a typical 1000 MW plant [1]. The 600 MWe ultra-supercritical power plant with biomass co-combustion is analyzed [45] and uses r_p = 0.229. For a power unit that is currently under construction in Poland [46], r_p is about 0.21. Moreover, optimization models using ISPEpro and MATLAB software indicate for z = 9 the ratio r_p = 0.211 [24]. All the values presented in the literature for z = 9 are within the confidence interval of the optimum r_p obtained in the paper (0.209, 0.230): r_p = 0.220 ± 0.011 (Figure 9, Table 2).

The increases in p_rh lead to the increase in the pressure to the corresponding HPH and the steam condensation temperature at the corresponding preheater. Therefore, the water temperature at the exit of the preheater increases and the feed water temperature t_inGS also increases (Figure 15). On the other hand, the saturation temperature at the condenser pressure (t_c) has small variations because p_c also has small variations: for z = 8, p_c ∈ (0.044, 0.05) bar, and for z = 9, p_c ∈ (0.041, 0.048) bar (Figure 13). For z = 8 and z = 9, the steam condensation temperature (t_c) at the condenser varies only by 2.1 °C and 2.9 °C, respectively. Therefore, the temperature difference between t_inSG and t_c increases with p_rh and r_p, and for the same number of total preheaters (z). Moreover, Δt (increase in temperature on each preheater) increases (Figure 11).

For the same number of z and LPHs, if r_p increases, the deaerator pressure (p_D) increases (Figure 12) due to the increase in Δt (Figure 11). When an HPH is added and z jumps from 8 to 9, at a similar SG feedwater temperature (t_inSG), p_D decreases due to the decrease in Δt (Figure 11, Figure 12 and Figure 15). The values obtained in this paper for p_D are in concordance with the values specified in the scientific literature. For example, for z = 8, p_D ∈ (8.51, 12) bar and the average p_D = 10.7 ± 1.1 bar = 9.6–11.8 bar (Figure 12, Table 2). In the literature, for z = 8, p_D = 8.9 bar [38], 9.6 bar [35,37] and 11.1 bar [36].

The increasing of t_ms and t_rh (Figure 7 and Figure 10) and the decreasing of p_c (Figure 13) imply better thermodynamic performances of the steam cycle and the increase in η_n (Figure 18). On the other hand, the decreasing of p_c leads to the decreasing of the steam quality (x_out) at the low-pressure (LPT) turbine exit (Figure 14). Nevertheless, the x_out values are maintained at acceptable limits [43].

d_sp (Equation (4), Figure 16) and e_sp (Equation (5), Figure 17) are inversely proportional and depend on the mass steam flow rate (F_ms). The optimum values of d_sp and e_sp are also useful for estimating F_ms when P_n is known.

The thermal cycle net efficiency (η_n) (Equation (2), Figure 18) increases with the specific investment (I_sp) (Equation (3), Figure 19). The addition of one LPH (corresponding to the increase in z from 8 to 9), increases by 0.64% the optimum η_n average value, but also increases by 7% the optimum I_sp average value.

The configurations obtained within this paper can be implemented for the design of new power plants, considering different sites or economic contexts. The site influences the cooling water temperature, which directly affects the condenser pressure. Figure 13 and Table 2 show the Pareto solution for the p_c values, which are in accordance with values from the above-mentioned existing power plants. The site, along with the economic and political context, influences the type and the power of the power plants. A higher power can lead to lower specific investments and better efficiencies, as emphasized in Figure 21, Figure 22 and Figure 23.

In the methodology used in this paper, both the fuel composition and the fuel heat flow rate are imposed. Therefore, the quantity of CO₂ emitted into the atmosphere is the same. However, when the thermal cycle net efficiency increases, the CO₂ emission factor [47], in kg_CO2/kWh, decreases with the same percentage as thermal cycle net efficiency. Thus, the paper incorporates, indirectly, metrics that evaluate CO₂ emissions, through the thermal cycle net efficiency.

5. Conclusions

This paper analyzed the different design configurations of single reheat supercritical steam power plants. A genetic heuristic algorithm was used to optimize the steam cycle design considering two antagonistic objective functions: the thermal cycle net efficiency and the specific investment in the power plant equipment. The result of the multi-objective optimization consists of the Pareto solution.

Within the Pareto solution, the solutions with eight and nine preheaters were distinguished separately. For a better understanding of the interdependence between the parameters, the Pareto populations for each of the two scheme solutions (z = 8 and z = 9) were sorted according to the increase in the net cycle efficiency.

For the Pareto solutions of each chosen number of preheaters, the values of their corresponding main parameters were analyzed, based on the mean value and the standard deviation. The optimal variation domains for the main steam temperature and pressure, the reheat temperature and pressure, the condenser and the deaerator pressure, the feed water temperature into the steam generator, the steam quality at the exit of the turbine, the temperature increase on a preheater and the specific indicators were obtained.

The variation domains of the objective functions were as follows:

• For the thermal cycle efficiency, between (47.71 and 48.35)% at z = 8, and between (48.20 and 48.54)% at z = 9;
• For specific investments in the power plant’s equipment, between (1848 and 2021) USD/kW at z = 8, and between (1949 and 2163) USD/kW at z = 9.

The variation domain of the ratio between the reheating and the main steam pressure, which represents the main optimized parameter was: (0.14–0.202) at z = 8, and between (0.202 and 0.252) at z = 9.

The mean values and the standard deviation of the two objective functions were as follows:

• 48.09 ± 0.16 at z = 8, and 48.40 ± 0.09 at z = 9, for the thermal cycle efficiency;
• 1924 ± 44 USD/kW at z = 8, and 2059 ± 52 USD/kW at z = 9, for specific investments in the power plant’s equipment.

For the ratio between the reheating and the main steam pressure, the mean values and the standard deviation were: 0.178 ± 0.021 at z = 8, and 0.220 ± 0.011 at z = 9.

The mean values of the optimum ratios between the reheating and the main steam pressure obtained in the paper, and their confidence interval, are in very good agreement with the results from the scientific literature for the design and the existing power plants with supercritical main steam parameters.

To consider future possible schemes which could integrate renewable energy sources, the analysis was extended for lower powers, showing the decrease in the specific investment and the increase in the thermal cycle net efficiency with the increase in the thermal cycle net power. The variation in the objective functions has a flattening trend.

The analysis is limited to the study of design solutions for single reheat steam power plants with eight and nine preheaters. Future research directions may consider cogeneration, hybrid systems by the partial integration of renewable sources, the integration of CO₂ capture, etc. Additionally, for the optimum design solutions, their behavior under flexible operation conditions represents an important issue to be studied. Thus, for the optimal steady-state configurations given by the model, off-design operation could be analyzed to assess the performance of the power plant under partial load operation conditions. Moreover, the analysis could be expanded to consider alternative optimization methods.