Evaluation and Improvement of the Flexibility of Biomass Blended Burning Units in a Virtual Power Plant

Abstract

Aiming at the problems of small thermal power units and biomass mixed combustion units with small generation loads and insufficient primary frequency modulation capability, which cannot be connected to the virtual power plant, this paper adopts a variety of flexibility retrofit methods for the units and explores the peak load capability of the units. Then, multiple units are coupled, and the unit coupling scheme with better economy and environmental protection is screened using comprehensive evaluation indexes. While evaluating the peaking load space of multiple unit coupling, the units’ primary frequency regulation capability and new energy consumption capability are improved. According to the calculation results, the low-pressure cylinder zero-output retrofit has the largest peaking potential among different technical paths, in which unit #3 has 27.55 MW of peaking space. The compression heat pump decoupling retrofit has the best economy, in which the daily profit of unit #3 increases from 0.93 to 1.02 million CNY with an increase of 0.09 million CNY. After the unit has been retrofitted with steam extraction, the three units can be coupled to meet the national feed-in standards. The multiple unit coupling can accommodate up to 203.44 MW of other energy sources while meeting the standard.

1. Introduction

China has the largest power grid system in the world, and solving the problems of China’s power grid will help the world build a better energy system. Nowadays, China is vigorously developing renewable energy to cope with the global energy shortage. However, the volatility of renewable energy output leads to significant impacts on unit loads in time and space, challenging the security and reliability of the power grid [1,2,3].

In recent years, as China has continued to develop and its population has grown, the volume of waste has been increasing dramatically. In 2021, the sludge generation in China will be 72,883,000t, but the sludge disposal capacity will only account for one third of the total sludge generation [4]. In 2022, the generation of straw in China will be 977 million tons, and the utilization volume will only be 662 million tons with a utilization rate of 67.76% [5]. To solve the large amount of remaining waste products, China has retrofitted existing thermal power units (TPUs). A large number of waste is mixed with the coal and burned on the boilers of existing large TPUs, which can leverage the favorable conditions of higher boiler temperatures and sufficiently long residence time of fuels in the furnaces to leverage the calorific value of the waste, maximizing the use of energy and reducing treatment costs [6].

There is now a growing demand to build flexible power systems and improve energy management technologies and efficiency. However, the instability of renewable energy output has greatly influenced the power grid, posing challenges to power grid security and stability. Therefore, transforming power generation, establishing a flexible power system, and improving energy management technology and efficiency have gradually become new research directions.

Virtual power plant (VPP) technology has rapidly developed in recent years. VPP technology effectively integrates and rationally schedules multiple energy sources [7,8,9], including stored energy, wind power, photovoltaic et al. [7,8]. It also includes many small TPUs, which did not meet the grid connection condition.

Although the TPU, which is doped with the waste product, can consume a large number of waste products, the flexibility of the unit is reduced accordingly. The primary frequency modulation (PFR) load change capacity under the unit’s design condition cannot meet the grid’s PFR load change requirements, so it is difficult to integrate into the grid [9], enhancing the complexity of power grid peak shaving and dispatching. Therefore, the TPUs doped with waste products are incorporated into the VPP, and the coordination of TPU peak shaving has become the emerging research direction of the power grid. Mutual coupling between multiple units can significantly make up for the shortcomings of the units’ inflexibility, so that units can meet the conditions of a national power grid connection. Simultaneously, it can enhance the peak load capability and unit flexibility.

In this regard, some experts have carried out relevant research on the issue of flexibility transformation of thermal power units. Zhang et al. [10] carried out further research on thermal power unit PER flexibility transformation. They combined four traditional thermal power unit PFR flexibility control methods and proposed a new scheduling strategy on this basis. However, they only analyzed for a single large thermal power unit. In order to study the impact of decarbonization on thermal power units, Liu et al. [11] utilized the carbon capture modification of emerging thermal power units, but the carbon capture device leads to the reduction in unit output space. Therefore, they further proposed a low-pressure cylinder zero-output scheme to enhance the unit flexibility and compared the load space changes of the unit after different modifications. The carbon capture device caused the unit load space to be reduced from 87–300 MW to 147–217 MW, but the zero-output modification of the low-pressure cylinder changed the load space of the unit to 47–217 MW, which reduced the reduction in the unit load space. However, they discussed only one flexibility modification method for zero output of a low-pressure cylinder. Liu et al. [12] proposed a flexible retrofitting method for thermal-energy-storage-coupled thermal power units. The exergy flow Sankey diagram and efficiency of the three charging methods are analyzed in detail, and comparative data are provided. The new thermal energy storage mode coupled with steam ejectors was the optimal solution with a significantly higher round-trip efficiency than the published results. As the extraction of reheated steam decreases and the extraction of main steam increases, the minimum generation capacity of the unit decreases continuously, reaching a minimum of 40 MW (6.67%). In contrast, the maximum output of the unit at 100% turbine heat acceptance (THA) release can reach 682 MW, which caused the unit load to change from 26–100% to 6.67–113.67% before and after the retrofit.

Although the above experts have proposed a large number of unit flexibility transformation schemes, most of them only study one retrofit mode, and they do not take into account the primary frequency modulation load change needs of the unit. Therefore, in this paper, three typical small TPUs were selected for flexibility retrofit (i.e., the retrofit that can improve the unit’s variable load capacity and primary frequency modulation performance) based on the research in northern China. The peak load capacity of these units and the overall peak load capacity under multi-unit coupling were investigated.

The crucial and novel contribution of this study is as follows.

(1)

In this paper, based on the steam extraction retrofit of the unit, three flexibility retrofit methods are used to compare the impact of different flexibility retrofits on the peak load capacity and to summarize the characteristics of different flexibility retrofit methods.

(2)

The paper innovatively established a set of comprehensive evaluation indexes for each unit to quantify the unit’s peak load capacity and economy by using the comprehensive evaluation indexes so that VPP agencies can quickly and intuitively judge the unit’s performance potential.

(3)

The paper is coupling multiple units and utilizing flexibility retrofit and steam extraction retrofit, and it utilizes the VPP “multi-energy complementarity” at the same time, to explore the peaking capacity of the off-grid TPU and biomass blended burning units when the unit meets the national PFR regulation and power grid access conditions.

2. Case Units

After the research, it is concluded that there are still numerous small TPU and biomass blended burning units in China that cannot be connected to the power grid due to their low power output efficiency, low power output load, and the inability of the PFR load change to meet the requirements of the power grid’s PFR load change. In this paper, one off-grid TPU and two off-grid biomass blended burning units are selected as the research object, which are named #1, #2 and #3, respectively. A VPP project in northern China is proposed to plan these three units and new energy units to form a VPP with unified dispatching.

Unit #1’s design output is 300 MW. The fuel is the coal blended sludge with the sludge blended at 10% of the total mass fraction of the original design coal. The reheat system includes three high-pressure reheaters (HPRHs), one deaerator (DEA), and three low-pressure reheaters (LPRHs). A steam extraction port is provided at the third HPRH. Unit #2’s design output is 315 MW. The fuel is coal. The reheat system consists of three HPRHs, one DEA, and four LPRHs. A steam extraction port is provided at the third HPRH. Unit #3’s design output is 350 MW. The fuel is coal-blended straw pellet units with the straw pellet blended at 15% of the total mass fraction of the original design coal. The reheat system consists of three HPRHs, one DEA, and four LPRHs. A steam extraction port is provided at the third HPRH.

The thermal systems of the three case units are shown in Figure 1.

Table 1. Basic parameters of each case unit.

Item	Unit #1	Unit #2	Unit #3
Main steam temperature/°C	538.00	538.00	569.00
Main steam pressure/MPa	16.67	16.70	24.60
Main steam flow/(kg·s−1)	260.38	268.59	285.33
Rated back pressure/MPa	0.014	0.005	0.005
Feed water temperature/°C	325.30	277.50	292.30
Rated power/kW	300,234.00	315,000.00	350,000.00
Heat consumption/(kJ·kWh−1)	8182.40	7949.30	7679.80

lists the basic parameters of each case unit.

The paper uses Ebsilon software V14 (provided by Shanghai Feiyi Company, Shanghai, China) to build the unit model, which is shown in Figure 2, to simulate the parameters [13]. The simulation parameters of each unit modeling are then compared with the design thermal parameters for error calculation.

It is verified that the simulation parameters do not differ much from the design thermal parameters, and each error is less than 2%, which is within the controllable range. The error is so small that the study can be continued based on the modeled data. The data are shown in

Table 2. Simulation parameters of each case unit.

Item	Design	Simulation	Relative Error/%
#1
Main steam temperature/°C	538.00	538.00	0.00
Main steam pressure/MPa	16.67	16.67	0.00
Main steam flow rate/(kg·s−1)	937.35	937.35	0.00
Rated back pressure/kPa	0.014	0.014	0.00
Feed water temperature/°C	272.20	272.24	0.01
Rated power/MW	300.23	300.32	0.03
#2
Main steam temperature/°C	538.00	538.00	0.00
Main steam pressure/MPa	16.70	16.70	0.00
Main steam flow rate/(kg·s−1)	966.92	966.92	0.00
Rated back pressure/kPa	0.005	0.005	0.00
Feed water temperature/°C	277.50	277.54	0.01
Rated power/MW	315.00	315.06	0.02
#3
Main steam temperature/°C	569.00	569.00	0.00
Main steam pressure/MPa	24.60	24.60	0.00
Main steam flow rate/(kg·s−1)	1027.18	1027.18	0.00
Rated back pressure/kPa	0.005	0.005	0.00
Feed water temperature/°C	292.30	287.95	−1.49
Rated power/MW	350.00	349.96	−0.01

.

3. Methodology

TPUs within VPPs are often the important choice for peak shaving because of their stability and reliability [14]. The unit in the peak-shaving process should consider its peak load capability to coordinate peak shaving with other units. More importantly, we have to consider the grid connection condition that the unit must meet. Through the study of single-unit flexibility peak load capability, this paper innovatively considers the unit’s PFR load change capacity to meet the grid connection condition. Then, it derives its coupled peak shaving potential under the premise of the coupled multiple units peak shaving.

In this paper, three units are selected as the study object, and Ebsilon models the units. The principled thermodynamic system of each case unit is used as a benchmark to build the model [15]. The models are used for subsequent studies. Data simulation and comparative analysis with Ebsilon is performed to derive the changes in heat–power decoupling capacity, economics, and unit conclusions under different retrofit scenarios.

3.1. Peak-Shaving Potential Analysis under Different Flexibility Retrofit Methods for TPUs

3.1.1. Flexibility Retrofit Method and Its Boundary Conditions

To lessen the heat and power coupling degree of units, in the case of an HPRH extraction retrofit, the unit was remodeled by three options: low-pressure cylinder zero-output, high back pressure combined spent steam heating, and compression heat pump decoupling [13,16,17].

To evaluate the unit’s flexibility peak load capability, treat the unit’s minimum output load for a certain heating load as an indicator. Horizontally compare the thermoelectric characteristics of each unit to enhance the flexibility peak load capability of the TPU [18].

(1)

Low-pressure cylinder zero-output retrofit: The program uses a low-pressure cylinder zero-output retrofit to achieve a higher heating load [13,19,20]. In the program, the low-pressure cylinder is bypassed. Only a little steam goes into the low-pressure cylinder, which is used to cool the heat generated by the turbine rotor rotation. The medium-pressure cylinder exhaust steam enters the condenser to be condensed directly [13,21].

(2)

High back pressure combined spent steam heating retrofit: To achieve a higher heating load, the scheme uses preheating with spent steam at high back pressure [13]. Increasing the unit’s spent steam pressure can increase the spent steam temperature to preheat the hot network water [22].

(3)

Compression heat pump decoupling retrofit: The retrofit employs a compression heat pump to recover heat from the condenser cooling water, thereby achieving a higher heating load [23,24] and providing electricity for the pump to reduce power output [25,26].

To ensure the safe operation of the unit, the case unit has to be provided with the following safety thresholds. The boundary conditions are shown in

Table 3. Safety operational boundary conditions for units.

Item	Boundary Condition	Reference	Unit #1	Unit #2	Unit #3
Minimum low-pressure cylinder steam flow	15% of the main steam flow/(kg·s−1)	[13]	38.98	40.28	43.06
Maximum main steam flow	Main steam flow under VWO condition/(kg·s−1)	[13]	296.89	284.72	313.89

and

Table 4. Safety operational boundary conditions for different retrofits.

Retrofit	Boundary Condition	Reference	Unit #1	Unit #2	Unit #3
Zero-output	Minimum low-pressure cylinder steam flow/(kg·s−1)	[21]	6.20	8.32	9.23
High back pressure	Spent steam pressure/MPa	[27]	0.024	0.0074	0.008
Heat pump decoupling	Condenser circulating cooling water temperature/°C	[17]	27.55	27.52	28.58

.

3.1.2. Economic Analysis

In the paper, three different units are selected, and for the unit under three different flexibility retrofits, the economic index of the unit is calculated by the net profit of the unit’s power output, which is used as the index for evaluating the unit’s economy [28].

The unit’s fuel consumption is associated with its main steam flow rate, the specific enthalpy of the main steam, and the boiler efficiency, which is calculated by Equation (1).

$$B_u={\displaystyle \frac{D_o(H_o-H_{fw})}{1000\times Q_{net,ar}\times {\eta }_b}}$$

(1)

where $B_u$ is the unit coal consumption, kg/s; $D_o$ is the main steam flow rate, kg/s; $H_o$ is the main steam enthalpy, kJ/kg; $H_{fw}$ is the feedwater enthalpy, kJ/kg; $Q_{net,ar}$ is the low calorific value of coal, kJ/kg; ${\eta }_b$ is the boiler efficiency, and 94% is taken in the calculation [13,29]. The boiler efficiency is taken as 94% in the calculation.

The coal feed rate of the unit is calculated by Equation (2).

$$G_u={\displaystyle \frac{B_u\times 3.6}{W_e}}$$

(2)

where $G_u$ is the coal feed rate of the unit, kg/MWh; and $W_e$ is the unit’s power output, MW.

To test the final cost-effective performance of the units’ retrofits, we use the dynamic payback period (DPP) and the net present value (NPV) as economic evaluation indicators. Considering the time value of money, DPP represents the year that is required to recoup the entire capital expenditure, as shown in Equation (3) [30,31].

$${\displaystyle \sum _{y=1}^{\mathrm{DPP}}\frac{(C_{in}-C_{out})}{{(1+{\mathrm{r}}_{\mathrm{dis}})}^y}=0}$$

(3)

where y is the year in the life cycle of the project; $C_{in}$ and $C_{out}$ are the year cash inflows and year cash outflows during y years, respectively, k$; and ${\mathrm{r}}_{\mathrm{dis}}$ is the discount rate.

NPV stands for the cumulative present value, which is the net cash flow over the project’s lifespan. A higher NPV indicates better profitability and project viability, and the formula is shown in Equation (4) [32,33].

$${\displaystyle \sum _{y=1}^n\frac{(C_{in}-C_{out})}{{(1+r_{dis})}^y}=\mathrm{NPV}}$$

(4)

where n is the project’s lifespan in years.

3.2. Analysis of Coupling Peak Shaving Potential of Multiple Thermal Power Units under PFR Transformation

The paper constructs a set of unit flexibility peak load capability comprehensive evaluation indexes to make the subsequent multiple units coupling calculation more convenient and valuable. The paper set the comprehensive examination of peak load capability, energy utilization, economic efficiency, and other indexes before and after the retrofit of the unit and quantifies them to derive the combination of operating conditions with better comprehensive benefits after the coupling of the three case units and to screen and integrate the existing data. See Section 3.2.1, Section 3.2.2, Section 3.2.3 and Section 3.2.4 for the evaluation process.

The PFR load change in the unit is mainly used to adjust the load that changes frequently in a small area as well as to quickly adjust the generating unit output in the case of an accident in the power grid to inhibit the further deterioration of the frequency of the power grid. In VPPs, TPUs should make an excellent PFR response to compensate for the negative impact of new energy output fluctuations and ensure the power grid operates safely and stably [34,35,36,37]. This paper adopted the HPRH feedwater bypass retrofit method for unit PFR load change after examining various TPUs [36,38].

We used the national standard of the People’s Republic of China [39] Section 5.3.1. This paper identifies the following provisions: For TPUs connected to VPPs, the PFR load change variation shall be not less than ±8% of the rated power.

The paper uses the HPRH feedwater bypass method of the PFR load change combined with the flexibility retrofit of the steam extraction retrofit to make the unit meet the requirements of the PFR load change [40,41,42]. According to the retrofit, the unit can increase the amplitude of the PFR load change, reduce the power output, and increase the new energy consumption capacity [43]. We utilized the multi-source complementary nature of VPP and the “over-peaking” of other units to consume the unit’s peaking deficit under variable operating condition [44]. Similarly, the unit can be replaced by any units with poor peak load capability. The complementary nature of the VPPs dramatically enhances the power grid operating safely and stably [45,46]. It provides the possibility for more small units and new energy units to be connected to the grid.

3.2.1. Flexibility Comprehensive Evaluation Index Calculation Process

The paper evaluated the flexibility of TPUs from two aspects: economy and environmental protection. Firstly, a large number of existing unit data are integrated, and valuable data sets are selected; secondly, the data are fitted by polynomials to obtain the calculation formula of evaluation factors, and then through the weighted integral mean method based on the case unit, the numerical quantification is realized. Finally, each evaluation index is integrated to form the evaluation score of the unit operating condition and then realize the comprehensive index evaluation of the unit flexibility [47]. The evaluation process is shown in Figure 3.

3.2.2. Economic Index

TPUs are designed to operate under the standard operating conditions. When a TPU participates in peak shaving, its output must be adjusted frequently. The unit’s prolonged operation under non-standard operating condition will cause a unit’s economy decrease. The profit of the unit is also an aspect to be considered in the peaking work. The coal feed rate is an evaluation factor of the unit economic index. See Section 3.1.2 for the calculation procedure.

3.2.3. Environmental Friendliness Index

The unit has been running in non-standard operating condition for a long time, which will lead to the significant energy loss of the unit. To meet the environmental protection requirements of the unit, energy efficiency and exergy efficiency are also important aspects to consider. Energy efficiency and energy efficiency are used as the evaluation factors of the unit’s environmental friendliness index.

The energy efficiency of the unit is the ratio of the output energy to the input energy, as shown in Equation (5). Here, the output energy is mainly the unit power output and heat load, and the input energy is the chemical energy of the coal [47].

$${\eta }_{en}={\displaystyle \frac{W_e+W_s}{Q_{net,ar}\times B_u}}$$

(5)

where ${\eta }_{\mathrm{en}}$ is the unit’s energy efficiency, %; and $W_s$ is the unit’s heat load, MW.

The unit’s exergy efficiency is the ratio of the input exergy, which includes the electric and heat exergy, to the output exergy, which includes the chemical exergy of coal, which is calculated by Equation (6) [29].

$${\eta }_{ex}={\displaystyle \frac{E_e+E_s}{E_f}}$$

(6)

where ${\eta }_{\mathrm{ex}}$ is the unit’s exergy efficiency, %; $E_{\mathrm{e}}$ is the electric exergy, kJ; $E_s$ is the heat exergy, kJ; and $E_f$ is the chemical exergy, kJ [29].

The power exergy is calculated from Equation (7).

$$E_e=W_e$$

(7)

The heat exergy is calculated from Equation (8).

$$\begin{array}{c}{E}_s=E_h-E_c\\ E_h=D_h[H_h-H_0-T_0(S_h-S_0)]\\ E_c=D_h[H_c-H_0-T_0(S_c-S_0)]\end{array}$$

(8)

where $E_h$ is the energy of steam supplied to the heat network, kJ; $E_c$ is the energy of water that returns to the unit, kJ; $D_h$ is the heat network circulating water flow rate, kg/s; $H_h$ and $H_c$ are the enthalpy of the supply steam and return water, kJ/kg; $S_h$ and $S_c$ are the entropy of the supply steam and return water, kJ/(kg·K); $H_0$ represents the enthalpy of the water at the ambient temperature, kJ/kg; $S_0$ represents the entropy of the water at the ambient temperature, kJ/(kg·K); and $T_0$ represents the ambient temperature, K [28].

The chemical exergy is calculated from Equation (9).

$$E_f=B_u{Q}_{gr,ar}$$

(9)

where $Q_{gr,ar}$ is the high heat of coal, kJ/kg [28].

The unit’s efficiency is used to calculate the exergy efficiency index $I_{ex}$ and the energy efficiency index $I_{en}$. The index was weighted and averaged to obtain the index for evaluating the environmental friendliness of the unit at different heat loads.

3.2.4. Quantification of Evaluation Index

The unit data were obtained through Ebsilon simulation. Due to the large amount of data, obtaining the unit evaluation data intuitively is impossible. To correlate and analyze the multiple data, polynomial fitting and weighted integral mean methods were used to quantify the evaluation indexes [47]. The process involves the following steps:

• Polynomial fitting of the data obtained from the unit to obtain the relationship equation between the required quantities $\mathrm{y}=f(x)$

, the confidence interval of the evaluation indexes obtained from the characteristics of the data distribution and the required operating condition $\left[N_{in},N_{en}\right]$, and the evaluation indexes are calculated as in Equation (11).

$$\begin{array}{l}I=\mathrm{B}.{\displaystyle \underset{N_{in}}{\overset{N_{en}}{\int }}f(x)dx/(N_{en}-N_{in})}\\ ={\mathrm{b}}_1.{\displaystyle \underset{N_{in}}{\overset{N_1}{\int }}f(x)dx/(N_1-N_{in})}+{\mathrm{b}}_2.{\displaystyle \underset{N_1}{\overset{N_2}{\int }}f(x)dx/(N_2-N_1)}\\ +\dots \dots +{\mathrm{b}}_n.{\displaystyle \underset{N_{n-1}}{\overset{N_{en}}{\int }}f(x)dx/(N_{en}-N_{n-1})}\end{array}$$

(10)

where $\mathrm{B}=\left[b_1,b_2,\dots \dots ,b_n\right]$ is the set of weighting coefficients for each sub-interval, and ${\mathrm{b}}_i(i=1,2,\dots \dots ,\mathrm{n})$ is the sub-interval weighting coefficients.

(2)

The resulting evaluation index needs to be normalized to weigh and compare the different evaluation indexes [47]. The normalization process is shown in Equation (12).

$${\mathrm{r}}_{ji}=\left[x_{ji}-{\min }_j(x_{ji})\right]/\left[{\max }_j(x_{ji})-{\min }_j(x_{ji})\right]$$

(11)

$${\mathrm{r}}_{ji}=\left[{\max }_j(x_{ji})-x_{ji}\right]/\left[{\max }_j(x_{ji})-{\min }_j(x_{ji})\right]$$

(12)

where $x_{ji}(j=1,2,,\dots \dots ,m;i=1,2,,\dots \dots ,n)$ is the ith evaluation index of the jth object after quantization; ${\max }_j(x_{ji})$ and ${\min }_j(x_{ji})$ are the largest and smallest values of the evaluation indexes of the jth object; ${\mathrm{r}}_{ji}$ is the ith evaluation index of the jth object after demarcation; and m and n are the number of evaluation indexes, respectively. For the evaluation indexes that characterize the better performance of the unit with larger values, Equations (11) and (12) are used for processing.

4. The Results of TPU Peak Shaving Potential under Different Flexibility Retrofit Methods

4.1. Sensitivity Analysis

The unit under study in this paper is mainly designed to induce a change in the unit’s output by changing the unit’s pumping flow and main steam flow rate. Therefore, in the sensitivity analysis, the sensitivity of the pumping steam flow and the main steam flow rate to the output of the unit is analyzed separately by ensuring that the other thermal parameters of the unit remain unchanged. The results of the sensitivity analysis of the three units are shown in Figure 4, Figure 5 and Figure 6. It can be seen from the results that with the increase in the pumping steam flow rate, the unit output gradually decreases; when the pumping flow rate of unit #1 increases by 152.78 kg/s, the unit output decreases by 136.38 MW; when the pumping flow rate of unit #2 increases by 152.78 kg/s, the unit output decreases by 151.39 MW; when the pumping flow rate of unit #3 increases by 147.22 kg/s, the unit output decreases by 156.33 MW. As the main steam flow rate decreases, the unit output gradually decreases; when the main steam flow rate of unit #1 decreases by 130.19 kg/s, the unit output decreases by 151.96 MW; when the main steam flow rate of unit #2 decreases by 134.30 kg/s, the unit output decreases by 159.08 MW; when the main steam flow rate of unit #3 decreases by 142.68 kg/s, the unit output decreases by 178.05 MW. That is to say, it is feasible to change the unit pumping flow and main steam flow rate and then improve the unit peak shifting capability.

4.2. Variation in Units’ Thermoelectric Output

After the unit modification, some of the thermal parameters have been changed, and the specific parameter changes are shown in

Table 5. Changes in thermal parameters of the unit before and after retrofit.

Retrofit	Item		Case Unit	After Retrofit
#1
zero-output	fifth intermediate steam extraction	flow rate/(kg·s−1)	11.03	30.81
	intermediate pressure cylinder outlet	flow rate/(kg·s−1)	191.31	171.52
	condenser inlet	temperature/°C	52.55	290.22
		flow rate/(kg·s−1)	172.32	174.53
high back pressure	condenser inlet	temperature/°C	52.55	64.05
		pressure/kPa	14.00	24.00
heat pump decoupling	condenser condensate outlet	temperature/°C	47.55	47.07
		pressure/kPa	50.00	47.00
#2
zero-output	fifth intermediate steam extraction	flow rate/(kg·s−1)	11.23	31.99
	intermediate pressure cylinder outlet	flow rate/(kg·s−1)	184.26	163.50
	condenser inlet	temperature/°C	32.52	236.80
		flow rate/(kg·s−1)	160.79	163.50
high back pressure	condenser inlet	temperature/°C	32.52	64.05
		pressure/kPa	4.90	7.40
heat pump decoupling	condenser condensate outlet	temperature/°C	27.52	27.49
		pressure/kPa	50.00	47.00
#3
zero-output	fifth intermediate steam extraction	flow rate/(kg·s−1)	11.63	37.47
	intermediate pressure cylinder outlet	flow rate/(kg·s−1)	190.75	164.92
	condenser inlet	temperature/°C	33.58	270.09
		flow rate/(kg·s−1)	164.12	166.59
high back pressure	condenser inlet	temperature/°C	33.58	41.51
		pressure/kPa	5.20	8.00
heat pump decoupling	condenser condensate outlet	temperature/°C	28.58	28.26
		pressure/kPa	50.00	47.00

.

Next, we further investigate the peaking potential of unit flexibility retrofits. A comparison of the thermoelectric characteristics of unit #1 under the three flexibility retrofit is shown in Figure 7, which reflects the heat–power decoupling potential of unit #1. It can be seen that the unit’s power output after flexibility retrofit is much smaller than the original unit. When the heating load is 0–120 MW, because of the restriction of the minimum production load, the unit’s power output needs to be not less than 90 MW. The power output of the unit retrofitted remains unchanged. When the heat load is over 120 MW, the output of the unit rises.

After the retrofit, unit #1 was modified in three different methods to reduce the minimum electrical load for 25.87 MW, 0.05 MW, and 0 MW, respectively. At 50% heat load (220 MW), the minimum electrical load was reduced for 27.41 MW, 1.26 MW, and 2.1 MW, respectively. The largest heat load achieved by the modified unit is 474.32 MW, which is 22.75 MW more than the original unit.

Using the same method, the thermoelectric characteristic diagrams of unit #2 and unit #3 under three flexibility retrofit are obtained, the results of which are shown in Figure 8 and Figure 9.

After the retrofit, unit #2 was modified using three different methods to reduce the minimum electrical load for 9.22 MW, −0.25 MW, and 4.44 MW, respectively. At 50% heat load (200 MW), the minimum electrical load was reduced for 20.24 MW, 0.71 MW, and 4.13 MW, respectively. The largest heat load achieved by the modified unit is 427.03 MW, which is 16.84 MW more than the original unit.

After the retrofit, unit #3 was modified using three methods to reduce the minimum electrical load for 30.62 MW, 0.15 MW, and 5.38 MW, respectively. At 50% heat load (180 MW), the minimum electrical load was reduced by 27.55 MW, 0.73 MW, and 5.12 MW, respectively. The largest heat load achieved by the modified unit is 386.39 MW, which is 19.38 MW more than the original unit.

4.3. Comparative Analysis of Changes in Minimum Power Output between Units

For TPU retrofit, from the point of view of the minimum power output reduced after retrofit, the zero-output retrofit method is the most apparent, and high back pressure retrofit and heat pump decoupling retrofit potential is relatively small. To compare the effect of a flexibility retrofit between different units more effectually, the following discussion uses the analysis of the zero-output retrofit data.

To analyze the flexibility retrofit effect of different units, we adopt the gap between the minimum electrical output and the design power output as the intermediate quantity. The percentage point (pp) improvement of the difference value after retrofit compared to the case unit is used as the basis for comparison, and the situation of each unit is shown in Figure 10.

Figure 10 shows that unit #1 has a larger potential for flexibility retrofit, which can accommodate more electric loads and has an obvious advantage. At the maximum heat load, the flexibility retrofit potential is 21.50%, which can accommodate more electric loads; unit #3 is always in the middle level, and unit #2 has poorer flexibility retrofit potential.

During unit operation, with the change in heat load, the flexibility retrofit potential of unit #1 and unit #3 changed greatly with an apparent drastic increase trend, which is difficult to control; the overall trend of the flexibility retrofit potential of unit #2 changed gently, which is easier to control.

4.4. Comparative Analysis of Changes in Maximum Heat Load between Units

The flexibility retrofit unit will produce a certain amount of hot steam as a by-product, which is generally used to supply the user side of the heat supply and other purposes. By comparing different units, we can attain the maximum heat load to conclude what kind of flexibility retrofit between different units is the user-friendly type.

In the paper, the percentage increases after the retrofit compared to the original unit, which is used to evaluate the heat supply capacity of the retrofitted unit, are shown in Figure 11.

From Figure 11, it can be seen that for unit #1, the zero-output retrofit can obtain the largest heat load, which has been improved by 5.04 pp compared with the case unit; for unit #2, the heat pump decoupling retrofit can obtain the largest heat load, which has been improved by 4.10 pp compared with the case unit; for unit #3, the zero-output retrofit can obtain the largest heat load, which has been improved by 5.28 pp.

The maximum heat load that can be attained is unit #1, zero-output retrofit, which can achieve a maximum heat load of 474.32 MW, and it is 22.75 MW higher than the original unit.

4.5. Comparative Analysis of Unit Economics Analysis Results

The unit’s economy is calculated by the daily net profit of the unit through the unit coal feed rate. The coal type is selected as power coal with a low calorific value of 23,022.18 kJ/kg and a high calorific value of 26,098.79 kJ/kg. The selling price of the coal is 960 CNY/t. Straw’s low calorific value is 13,394.72 kJ/kg, straw treatment costs 350.00 CNY/t, there were 5.11 million tons of production in 2022, and the subsidy is 177.67 million CNY [5]. In 2022, the province in northern China calculated that each ton of straw disposal fee subsidy is 34.79 CNY/t. Sludge’s low calorific value is 11,366.68 kJ/kg, sludge treatment costs 500 CNY/t, and the sewage treatment subsidy is 0.2 CNY/t, according to each 10,000 t of water to produce 7 t of sludge with 80% water content. In 2022, the province in northern China calculated that each ton of sludge disposal fee subsidy 285.71 CNY/t [4]. In 2022, the feed-in tariff is 435.39 CNY/MWh and the heating price is 108 CNY per MWh. The province is a large province of sludge and straw production, and the price of each raw material is reasonable and has universal applicability. Data from the province could be used for the study.

Calculations lead to

Table 6. Daily profit of the unit.

Item		Case Unit	Zero-Output	High Back Pressure	Heat Pump Decoupling
Unit #1
Coal feed rate/(kg·kwh−1)	0 MW heating	317.80	503.09	329.91	317.80
	50% heating	413.59	569.79	424.17	413.59
	75% heating	494.93	614.19	502.45	494.93
	Maximum heating	605.64	661.45	606.48	605.64
Biomass feed rate/(kg·kwh−1)	0 MW heating	31.76	50.28	32.97	31.76
	50% heating	41.33	56.94	42.39	41.33
	75% heating	49.46	61.38	50.21	49.46
	Maximum heating	60.52	66.10	60.61	60.52
Daily net profit/million CNY	0 MW heating	1.02	−0.30	0.89	1.04
	50% heating	0.76	0.06	0.69	0.78
	75% heating	0.62	0.17	0.58	0.64
	Maximum heating	0.48	0.32	0.48	0.50
Unit #2
Coal feed rate/(kg·kwh−1)	0 MW heating	308.81	468.25	316.42	308.81
	50% heating	407.05	542.04	413.60	400.66
	75% heating	493.30	593.44	498.10	475.00
	Maximum heating	611.34	646.65	610.44	596.85
Biomass feed rate/(kg·kwh−1)	0 MW heating	—	—	—	—
	50% heating	—	—	—	—
	75% heating	—	—	—	—
	Maximum heating	—	—	—	—
Daily net profit/million CNY	0 MW heating	1.11	−0.07	1.04	1.16
	50% heating	0.79	0.13	0.75	0.85
	75% heating	0.61	0.24	0.59	0.69
	Maximum heating	0.45	0.34	0.45	0.51
Unit #3
Coal feed rate/(kg·kwh−1)	0 MW heating	280.59	433.29	284.43	277.94
	50% heating	361.44	492.78	364.03	352.41
	75% heating	421.76	528.36	422.76	410.15
	Maximum heating	514.27	574.45	509.80	490.52
Biomass feed rate/(kg·kwh−1)	0 MW heating	43.35	66.94	43.94	42.94
	50% heating	55.84	76.13	56.24	54.44
	75% heating	65.15	81.62	65.31	63.36
	Maximum heating	79.45	88.74	78.75	75.78
Daily net profit/million CNY	0 MW heating	1.41	−0.01	1.34	1.48
	50% heating	0.93	0.17	0.91	1.02
	75% heating	0.76	0.26	0.75	0.84
	Maximum heating	0.57	0.37	0.58	0.67

. The biomass feed rates in the table represent sludge feed rates for unit #1 and straw feed rates for unit #3.

For the daily profit of the unit, the heat pump decoupling retrofit of the three case units all led to a decrease in the coal feed rate, the biomass feed rate remained unchanged or decreased, and there was a growth in the daily profit: for the daily net profit of the units, the three units increased by 0.02, 0.06, and 0.09 million CNY, respectively. The retrofit of high back pressure led to an increase in the coal feed rate and the biomass feed rate, and there was a decrease in the daily profit: for the daily net profit of the units, the three units increased by −0.07, −0.04, and −0.02 million CNY, respectively. The zero-output retrofit led to a dramatic increase in the coal and biomass feed rate, a significant decrease in the daily profit, and even a loss: for the daily net profit of the units, the three units increased by −0.70, −0.66, and −0.76 million CNY, respectively.

Considering the unit’s economic efficiency, compression heat pump decoupling retrofit can make the unit’s daily net profit effectively increase and slightly reduce the coal feed rate; a low-zero retrofit drastically reduces the unit’s profit or even loses money; and a high-back retrofit makes the unit’s daily profit slightly decrease.

After calculating the daily profit of each unit with different retrofit methods, we calculated the NPV and DPP for each unit. The calculations in this paper assume that the lifetime of the project is 23, the construction period is 2 years, the spend in the first year is 40%, and the annual operating cost is 10% of the total capital cost. The zero-output retrofit costs 15 million CNY [48], high back pressure retrofit costs 50 million CNY [48], and heat pump decoupling retrofit costs 1.34 million CNY [49]; these calculations are based on 300 days of operation per year. In order to calculate the comparison intuitively, the units used are 50% heating condition daily profit. The results are shown in

Table 7. Economic comparison of the unit before and after retrofit.

Item	Retrofit
	Zero-Output	High Back Pressure	Heat Pump Decoupling
Unit #1
Annual income/million CNY	18.00	207.00	234.00
Total capital cost/million CNY	15.00	50.00	1.34
Annual operating cost/million CNY DPP/year	1.50	5.00	0.13
	3.04	2.28	2.01
Net gain over five years/million CNY	21.02	372.19	479.50
NPV/ million CNY	108.24	1440.01	1715.78
Unit #2
Annual income/million CNY	39.00	225.00	255.00
Total capital cost/million CNY	15.00	50.00	1.34
Annual operating cost/million CNY	1.50	5.00	0.13
DPP/year	2.25	2.25	2.01
Net gain over five years/million CNY	64.18	409.18	522.66
NPV/ million CNY	262.41	1572.15	1869.95
Unit #3
Annual income/million CNY	51.00	273.00	306.00
Total capital cost/million CNY	15.00	50.00	1.34
Annual operating cost/million CNY	1.50	5.00	0.13
DPP/year	2.34	2.21	2.01
Net gain over five years/million CNY	88.84	545.11	627.48
NPV/million CNY	350.51	1980.33	2244.36

.

From the table, it can be seen that for the zero-output retrofit, the initial cost of the three units can be recovered in 3.04, 2.25, and 2.34 years, respectively; for the high back pressure retrofit, the initial cost of the three units can be recovered in 2.28, 2.25, and 2.21 years, respectively; for the heat pump decoupling retrofit, the initial cost of the three units can be recovered in 2.01, 2.01, and 2.01 years, respectively.

5. The Results of Coupling Peak-Shaving Potential of Multiple Thermal Power Units under PFR Transformation

We simulated the change amplitude of PFR load change under the THA condition of the three case units. The calculation shows that under the THA condition of unit #1, the PFR load change potential is 16.62 MW, with a change of 5.53%, which is much smaller than the 8% change amplitude required by the standard. Under the THA condition of unit #2, the PFR load change potential is 19.78 MW, with a change of 6.28%, which is much smaller than the 8% change required by the standard. Under the THA condition of unit #3, the PFR load change potential is 18.57 MW, with a change of 5.31%, which is much smaller than the 8% change required by the standard. To summarize, all three units cannot meet grid connection standards under THA operating conditions.

5.1. The Calculation Result of Flexibility Comprehensive Evaluation Index

5.1.1. Example

As the example, the 50% operating condition of the #1 case unit is chosen as the evaluation object, and its comprehensive evaluation index is calculated.

(1)

Economic index

By fitting a polynomial to the unit’s heat load and daily profit, the relationship at the 50% operating condition of unit #1 is obtained, as shown in Figure 12.

Figure 12 shows that as the unit’s heat load increases, the daily profit decreases and then increases, and the unit usually operates at a lower heat load during the unit’s peaking process, which is conducive to obtaining higher stability.

This is based on the fact that the unit is operated chiefly at low heat load, b₁ = 1.6 in the span of heat load (0–33%) $W_s$ and b₂ = 0.4 in the span of heat load (33–100%) $W_s$.

Based on the calculations, unit #1’s 50% operating condition economic index ${\mathrm{r}}_{13}$ = 0.01.

(2)

Environmental friendliness index

The energy efficiency and exergy efficiency, which characterize the environmental friendliness index of the unit above, are calculated and normalized to obtain the exergy efficiency index $I_{\eta y}$ and energy efficiency index $I_{\eta n}$, and the weighted average of the energy efficiency index and exergy efficiency index is used as the evaluation parameter of environmental friendliness. After consideration, the weights of the energy and exergy efficiency indexes are 0.5 each.

The unit is mainly operated at low heat load, b₁ = 1.6 in the range of low heat load (0–33%) $W_s$ and b₂ = 0.2 in the range of high heat load (33–100%) $W_s$.

Based on the calculations, the environmental friendliness index for unit #1 is at 50% operating condition ${\mathrm{r}}_{23}=$ 0.24.

5.1.2. Flexibility Comprehensive Evaluation Index

According to the above calculation, the evaluation indexes of nine operating condition of the three units are obtained, and the economic indexes and environmental friendliness indexes are utilized to calculate the comprehensive indexes of flexibility for different operating condition of the units. The weighting coefficients of the economic and environmental friendliness index are ${\mathrm{q}}_{\mathrm{ec}}=$0.50 and ${\mathrm{q}}_{\mathrm{pt}}=$0.50, respectively. The weighted summation results are shown in

Table 8. Evaluation index of unit operating condition.

Operating Condition		THA	75%	50%
Unit #1	Economic index	0.62	0.15	0.01
	Environmental index	0.42	0.42	0.24
	Flexibility comprehensive index	0.52	0.29	0.13
Unit #2	Economic index	1.00	0.26	−0.66
	Environmental index	0.73	0.47	0.46
	Flexibility comprehensive index	0.86	0.37	−0.10
Unit #3	Economic index	1.07	0.29	0.14
	Environmental index	0.84	0.50	0.43
	Flexibility comprehensive index	0.54	0.39	0.29

.

Next, we judged whether this kind of coupling scheme meets the demand according to the sum of the flexibility comprehensive indexes of each operating condition of the unit. The evaluation results are shown in

Table 9. Evaluation index for the case unit coupling program.

Unit	Operating Condition
#1	THA	THA	THA	THA	THA	THA	THA	THA	THA
#2	THA	THA	THA	75%	75%	75%	50%	50%	50%
#3	THA	75%	50%	THA	75%	50%	THA	75%	50%
Comprehensive index	1.92	1.77	1.67	1.43	1.28	1.18	0.96	0.81	0.71
Unit	Operating condition
#1	75%	75%	75%	75%	75%	75%	75%	75%	75%
#2	THA	THA	THA	75%	75%	75%	50%	50%	50%
#3	THA	75%	50%	THA	75%	50%	THA	75%	50%
Comprehensive index	1.69	1.54	1.44	1.20	1.05	0.95	0.73	0.58	0.48
Unit	Operating condition
#1	50%	50%	50%	50%	50%	50%	50%	50%	50%
#2	THA	THA	THA	75%	75%	75%	50%	50%	50%
#3	THA	75%	50%	THA	75%	50%	THA	75%	50%
Comprehensive index	1.53	1.38	1.28	1.07	0.89	0.79	0.57	0.42	0.32

.

In three cases of unit coupling, the comprehensive index, which is higher than 1.68, is efficient and has better flexibility. A total of three coupling scenarios are calculated to have better flexibility.

5.2. Results of Unit PFR Load Change Thermal Parameters

5.2.1. Unit #1 PFR Load Change Thermal Parameters

Figure 13 shows the unit THA operating condition load curve, the PFR load curve, and the folded line of load change for unit #1 fitted using Python V3.8 (https://www.python.org/). The shaded area is the difference between the unit THA operating condition load and the PFR load.

From Figure 13, there is a slight increase in the load of unit #1 after PFR retrofit. At the same time, with the heat load increase, the load change rate always shows an upward trend. When the extract heat steam flow of the unit is 105.06–166.14 kg/s, the load change rate of the unit is more than 8%. Currently, the unit meets the grid connection condition and has excess load to absorb other unit loads.

When the unit extract heat steam flow is 166.14 kg/s, unit #1 has the largest load change of 10.93%, significantly exceeding the national regulation of 8% PFR load change to meet the grid connection condition.

After the retrofit of the unit #1 load under THA operating condition without steam extraction, the change in the PFR load is 16.62 MW, with a load change rate of 5.53%; under the 84.83 kg/s steam extraction, the change in the PFR load is 16.61 MW, with a load change rate of 7.52%; under the 166.14 kg/s steam extraction, the change in the PFR load is 16.60 MW, with a load change rate of 10.93%.

The load variability of the modified unit has improved significantly.

5.2.2. Other Units PFR Load Change Thermal Parameters

According to the method shown in Section 5.2.1, the thermal parameters of other units with different operating condition are analyzed, and the load curves before and after the sub-frequency adjustment are obtained, as shown in Figure 14, Figure 15, Figure 16 and Figure 17.

5.3. Results of Unit Coupling

In the paper, Python combines the different operating conditions of the three units that meet the evaluation index criteria to obtain and analyze the coupling data of the three units in more cases. MATLAB is used to plot the range of values of x1, x2, and x3 that meet the condition in the three-dimensional coordinate system. Where x1 represents the extraction flow rate of unit #1; x2 represents the extraction flow rate of unit #2; x3 represents the extraction flow rate of unit #3.

5.3.1. Coupling of Unit #1 THA Condition, Unit #2 THA Condition and Unit #3 THA Condition

The value range of x1, x2, and x3 is shown in Figure 18.

After calculation, it can be obtained that when the three units are coupled with each other, the total output of the units can reach a maximum of 686.99 MW and a minimum of 483.55 MW under grid connection conditions. In other words, under grid connection conditions, the three units can absorb 203.44 MW of fluctuating load from other energy sources, such as new energy plants.

Flexibility retrofit brings not only the change in output but also the heat load. The heat load variation range of unit #1 when the three units are coupled is 0–411.1 MW; the heat load variation range of unit #2 is 0–395.0 MW; the heat load variation range of unit #3 is 0–402.1 MW. When the total unit output reaches the maximum output of 686.99 MW, a total of 696.60 MW of heat load is supplied to the heat network; when the total unit output reaches the minimum of 483.55 MW, a total of 1208.20 MW of heat load is supplied to the heat network.

5.3.2. Coupling of Unit #1 THA Condition, Unit #2 THA Condition and Unit #3 75% Condition

The value range of x1, x2, and x3 is shown in Figure 19.

After calculation, it can be obtained that when the three units are coupled with each other, the total output of the units can reach a maximum of 569.90 MW and a minimum of 506.61 MW under grid connection conditions. In other words, under grid connection conditions, the three units can absorb 63.29 MW of fluctuating load from other energy sources, such as new energy plants.

Flexibility retrofit brings not only the change in output but also the heat load. The heat load variation range of unit #1 when the three units are coupled is 269.5–411.1 MW; the heat load variation range of unit #2 is 268.4–395.0 MW; and the heat load variation range of unit #3 is 17.0–216.6 MW. When the total unit output reaches the maximum output of 569.90 MW, a total of 820.3 MW of heat load is supplied to the heat network; when the total unit output reaches the minimum of 506.61 MW, a total of 1,022.7 MW of heat load is supplied to the heat network.

5.3.3. Coupling of Unit #1 75% Operating Condition, Unit #2 THA Operating Condition, and Unit #3 THA Operating Condition

The value range of x1, x2, and x3 is shown in Figure 20.

After calculation, it can be obtained that when the three units are coupled with each other, the total output of the units can reach a maximum of 586.75 MW and a minimum of 509.51 MW under grid connection conditions. In other words, under grid connection conditions, the three units can absorb 77.24 MW of fluctuating load from other energy sources, such as new energy plants.

Flexibility retrofit brings not only the change in output but also the heat load. The heat load variation range of unit #1 when the three units are coupled is 0–197.4 MW; the heat load variation range of unit #2 is 225–395 MW; the heat load variation range of unit #3 is 243.5–402.1 MW. When the total unit output reaches the maximum output of 586.75 MW, a total of 763.8 MW of heat load is supplied to the heat network; when the total unit output reaches the minimum of 509.51 MW, a total of 994.5 MW of heat load is supplied to the heat network.

6. Conclusions

The space for unit peak shaving adjustment under flexibility retrofit for several units was analyzed using flexibility retrofit for different units. The changes in the values of minimum power output and maximum heat load before and after the retrofit were compared, and the conclusions reached were as follows:

• For unit retrofit, from the viewpoint of the minimum power output reduced after retrofit, the zero-output retrofit method is the most apparent. The high back pressure retrofit and heat pump decoupling retrofit potential are smaller. Unit #3’s flexibility retrofit potential is larger, can absorb more external electric load, and has obvious advantages, such as the largest reduction in the minimum electrical load for 27.55 MW at the 50% heat load. Unit #1 is always in the middle level, and the reduction in the minimum electrical load is 27.41 MW. Unit #2 has poorer flexibility retrofit potential: the reduction in the minimum electrical load is 20.24 MW. The zero-output retrofit can also obtain the largest heat load.
• Considering from the point of view of the unit’s flexibility retrofit economics, the heat pump decoupling retrofit effectively increases each unit’s daily net profit by 0.02, 0.06, and 0.09 million CNY, and the initial cost of the three units can be recovered in 2.01, 2.01, and 2.01 years; the low-zero retrofit reduces the unit’s profit or even loses money of the units by −0.70, −0.66, and −0.76 million CNY, and the initial cost of the three units can be recovered in 3.04, 2.25, and 2.34 years; and the high back pressure retrofit makes each unit’s daily profit decrease by −0.07, −0.04, and −0.02 million CNY, and the initial cost of the three units can be recovered in 2.28, 2.25, and 2.21 years.
• According to the comprehensive evaluation index of flexibility, three coupling cases have better flexibility. When the three units are coupled with different operating conditions, the total output of the unit still has a better heat–power decoupling effect under the condition of meeting the grid access. The PFR load change capability of the three units increases with the change in the extract heat steam flow after the units have been modified. When the units are all in THA condition, the three units have the best overall energy consumption capacity, with the highest output being 686.99 MW and the lowest output being 483.55 MW. The maximum output change is 203.44 MW. The total combined output load of the units after the steam extraction retrofit is negatively correlated with the heat supply of the heat network.

Currently, the multiple retrofit methods and multi-unit coupling adopted in this paper only consider the changes on the steady state of the unit and do not consider the problem on the time scale, and the number of quantitative indicators in the comprehensive evaluation index constructed in this paper is small. Future research will add the influence factor of time on the basis of the current one and continue to improve the comprehensive evaluation index and add more evaluation items.