# Bilevel Optimal Economic Dispatch of CNG Main Station Considering Demand Response

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}. The number of natural gas vehicles (NGVs) in cities has continued to grow globally, especially in Asia. The average annual growth rate of NGV from 2002 to 2012 was as high as 35.1%, and the growth rate of China remained above 8% from 2010 to 2018 [9]. As of 2018, the number of NGVs in China exceeded 6760 × 10

^{3}[10], and about 9.6% of vehicles use natural gas to replace traditional vehicle fuels [11]. At the same time, the growing NGV filling demand has driven the rapid development of urban natural gas filling networks. As of 2019, the number of natural gas refueling stations reached 33,383. As of 2018, China had over 9000 natural gas fueling stations, including more than 5600 CNG refueling stations. From 2010 to 2018, the number of natural gas fueling stations in China grew consistently at a rate of over 5% [10]. Up to now, China has initially formed an urban natural gas filling network integrating CNG standard stations and main slave stations [12].

^{3}kWh, and the annual intake of natural gas was about 43,200 × 10

^{3}N·m

^{3}in 2020 [14]. The main process systems of the CNG main station include dehydration, compression, storage, and filling process systems. Among all the systems in the CNG main station, the dehydration and compression process systems consume most of the energy, accounting for about 92.48% of the total energy consumption. The compression process system accounts for 54.19%, and the dehydration process system accounts for 38.29% [15]. The CNG main station needs to process the imported natural gas into CNG in advance to meet the real-time NGV filling demand; therefore, it is generally equipped with a storage process system [16], which can temporarily store CNG, and the CNG main station production plan can be flexibly changed within the allowable range of the storage device pressure. The electricity–gas load of the production equipment can also be dispatched without affecting the NGV filling load in the station. The CNG main station is an important infrastructure for producing CNG and has a high level of electrification, making it a key player in the electricity market. Therefore, responding to DR price signals in order to reduce operating costs and improve market competitiveness is of great significance to CNG main station operators. Above all, CNG main stations have great potential and urgent practical needs for participating in DR.

## 2. General Framework of the Study

## 3. Dispatch Modeling and Problem Formulation

#### 3.1. Structure of CNG Main Station

#### 3.2. Equipment Modeling

_{n}is defined as 24 h, and the sampling time is defined as t

_{s}(h); then, the total number of samples N = 24/t

_{s}. W

_{d}(t) is the electrical energy of the dehydration device before time t (kWh). p

_{d1}is the dehydration power of a single adsorption tower (kW), and p

_{d2}is the regeneration and cold purging power of a single adsorption tower (kW). p

_{m}is the power of the Roots blower (kW), and p

_{w}is the power of the forced air cooler (kW). The heat medium heater is a kind of organic heat carrier heating furnace [30], which generally uses coal, oil, or combustible liquid as fuel; hence, it is not listed in the electricity–gas model of the dehydration progress system. m

_{d}(t) is the total processing gas volume of the dehydration device before the period t (kg), m

_{d1}(t) is the total processing gas volume of the adsorption tower A before the period t (kg), and m

_{d2}(t) is the total processing gas volume of the adsorption tower B before the period t (kg). m

_{dmp}is the outlet mass flow rate of the dehydration process of a single adsorption tower (kg/h). It can be calculated as follows:

_{std}is the compressed gas density under standard conditions (0 °C and 10

^{5}Pa). Mw

_{g}is the molecular weight of compressed gas, Mw

_{a}is the molecular weight of air, and ρ

_{std.a}is the density of air under standard conditions (kg/m

^{3}). Q

_{std.d}is the dehydration capacity of the single adsorption tower under standard conditions (N·m

^{3}/h).

_{c}(t) is the electrical energy of the compressor before the period t (kWh), and p

_{c}is the compressor power (kW). u

_{2}(i) is the switch state of the switch u

_{2}in the i-th sampling interval, and m

_{c}(t) is the total gas output of the compressor before the period t (kg); m

_{cmp}is the compressor outlet mass flow rate (kg/h), which can be calculated by

_{std.c}is the capacity of the compressor under standard conditions (N·m

^{3}/h).

_{b}is the dispenser device power (kW). The gas flow of the dispenser should be consistent with the CNG filling demand; thus, its gas model is omitted.

_{cp}(t) in buffer tank C at sampling time t can be calculated as follows:

_{cp}(0) is the initial gas volume of the buffer tank (kg). The pressure generated by the gas in the buffer tank during the dispatch period should not exceed the design working pressure range of the buffer tank. It can be described as

_{c}is the volume of the buffer tank (L). ${p}_{\mathrm{cp}}^{\mathrm{max}}$ and ${p}_{\mathrm{cp}}^{\mathrm{min}}$ represent the maximum and minimum pressure that the buffer tank can withstand (MPa); z is the gas compression coefficient, and R is the general gas constant (J/(mol·K)). T

_{max}and T

_{min}respectively represent the highest and lowest ambient temperatures of the buffer tank (K).

_{6}(i), u

_{7}(i), and u

_{8}(i) are the states of switches u

_{6}, u

_{7}, and u

_{8}in the i-th sampling time, respectively. The gas mass m

_{hp}(t), m

_{mp}(t), and m

_{lp}(t) of the high-pressure reservoir H, medium-pressure reservoir M, and low-pressure reservoir L in the t-th period should not exceed its reservoir design working pressure range. This can be expressed as follows [21]:

_{h}, V

_{m}, and V

_{l}, and pressure limits ${p}_{\mathrm{hp}}^{\mathrm{max}}$, ${p}_{\mathrm{mp}}^{\mathrm{max}}$, ${p}_{\mathrm{lp}}^{\mathrm{max}}$, ${p}_{\mathrm{hp}}^{\mathrm{min}}$, ${p}_{\mathrm{mp}}^{\mathrm{min}}$, and ${p}_{\mathrm{lp}}^{\mathrm{min}}$, as expressed in Equations (A1)–(A3) (Appendix A) [21].

#### 3.3. Objective Function

_{e}(t) is the electricity price during sampling time t. The electricity cost of the CNG main station also includes other constant cost components. These components do not participate in DR and should be discarded in the optimal economic model of the CNG main station [38].

#### 3.4. Constraints

_{a}, M

_{h}, M

_{m}, and M

_{l}are the terminal restriction margins of the buffer tank and the cascaded storage system. They generally take 10% of the initial gas mass of the corresponding storage device [21]. Furthermore, the decision switch variables u

_{j}are all binary, the constraints can be expressed as

_{1}(i) and u

_{11}(i), u

_{2}(i) and u

_{12}(i), u

_{3}(i) and u

_{9}(i), and u

_{4}(i) and u

_{10}(i) are kept in sync, and only one switch variable in each group needs to participate in the day-ahead scheduling. Meanwhile, the day-ahead economic optimal model of the CNG main station should meet the operating constraints of the equipment model in the station. All in all, Equations (4)–(7), (13), (15), (16)–(18), and (21)–(25) together constitute the constraints of the day-ahead economic optimal model of the CNG main station.

## 4. Algorithm Description

_{s}is small. Large-scale 0–1 variable programming is one of the current research focuses of evolutionary algorithms [39,40,41,42,43]. Having the advantages of better convergence, simpler calculation, and fewer parameter settings for 0–1 programming problems [44,45,46], the genetic algorithm (GA) has received more and more attention in this field. However, the massive variable dimension has become a bottleneck when decision variables are increasing.

#### 4.1. Bilevel Programming Model of CNG Main Station

_{1}. It can be expressed as

**A**

_{eq.c}

**x**

_{U}=

**b**

_{eq.c}), inequality constraints (

**b**

_{min.U}≤

**A**

_{U}

**x**

_{U}≤

**b**

_{max.U}), and the limits of decision variables (

**l**≤

**x**

_{U}≤

**u**). The decision variables u

_{5}(i), u

_{6}(i), u

_{7}(i), and u

_{8}(i) together form the decision variable vector

**x**

_{U}of the upper model. It can be expressed as

**A**

_{eq.c},

**A**

_{U}, and

**f**

_{2}and the vectors

**f**

_{1},

**b**

_{eq.c},

**b**

_{min.U},

**b**

_{max.U},

**l**, and

**u**are shown in Equations (A4)–(A18) (Appendix A).

_{2}. It can be expressed as

**A**

_{eq.d}

**x**

_{L}=

**b**

_{eq.d}, (

**A**

_{eq.m}

**x**

_{L})·(

**A**

_{eq.m}

**x**

_{L}) =

**b**

_{eq.m}, (

**A**

_{eq.n}

**x**

_{L})·(

**A**

_{eq.n}

**x**

_{L}) =

**b**

_{eq.n})), inequality constraints (

**b**

_{min.L}≤

**A**

_{L}

**x**

_{L}≤

**b**

_{max.L}), and the limits of decision variables (

**l**≤

**x**

_{L}≤

**u**). The decision variables u

_{1}(i), u

_{2}(i), u

_{3}(i), and u

_{4}(i) together form the decision variable vector

**x**

_{L}of the lower-level model. It can be expressed as

**A**

_{eq.d},

**A**

_{eq.m},

**A**

_{eq.n}, and

**A**

_{L}and the vector

**f**

_{3},

**b**

_{eq.d},

**b**

_{eq.m},

**b**

_{eq.n},

**b**

_{min.L}, and

**b**

_{max.L}are described in Equations (A19)–(A35) (Appendix A).

#### 4.2. The Process of Bilevel Programming Method Combined with GA

_{p}. The intermediate variable u

_{5}is selected individually. Each individual gene uses N-bit binary code, where u

_{5}= {u

_{5}(1), u

_{5}(2), …, u

_{5}(N)}.

_{5}as a known quantity into the upper model and introduces the SCIP solver to search the optimal combination of {u

_{6}, u

_{7}, u

_{8}} by the objective function J

_{1}. According to the optimal upper-level results, the optimal switches combination of {u

_{1}, u

_{2}, u

_{3}, u

_{4}} is solved by the SCIP solver with the smallest objective function J

_{2}.

_{h}is assigned to the infeasible individuals’ fitness generated in step 2. The infeasible individuals are eliminated in the selection process. The linear sorting method is used to allocate fitness, and stochastic universal selection is introduced to select high-fitness individuals in the selection process. The probability of an individual being selected is proportional to its fitness, and individuals with low fitness are not able to pass genes to their offspring through genetic processes. The value of J

_{h}is much larger than the optimized solution. Therefore, the probability of the infeasible individual being selected is the lowest in the entire population, and the infeasible individual is gradually eliminated.

_{c}. The discrete mutation operator is used in the mutation process with a mutation rate of p

_{m}.

## 5. Case Data

#### 5.1. CNG Main Station Data

#### 5.2. Critical Peak Pricing Mechanism

_{eHD}(t) and p

_{eLD}(t) respectively represent the CPP in the high-demand season (June to August) and the low-demand season. p

_{o}, p

_{s}, p

_{p}, and p

_{c}are the valley price, the standard price, the peak price, and the critical peak electricity price, respectively.

#### 5.3. CNG Filling Demand

## 6. Model Verification and Analysis

_{c}) in GA and the mutation rate (p

_{c}) were set to 0.6 and 0.01, respectively. The number of population individuals was set to 25, and the maximum number of iterations was 40. The sampling time of the CNG main station model (C) was 0.5 h. The initial gas volumes of the buffer tanks, high-pressure, medium-pressure, and low-pressure reservoirs were set to 150, 450, 350, and 250 kg, respectively. The weight factor (ξ) was set to 0.01 to make the penalty term the same order of magnitude as the CN. The inferior solution (J

_{h}) was set to 40.

#### 6.1. Solving Efficiency Comparison Experiment of Algorithms

#### 6.2. Economy Comparative Experiment of CNG Main Stations Dispatch Models Considering CPP

_{g}from the pressure limit of the gas storage device [9] considering real-time load requirements. M

_{g}was selected 25 kg; other parameter settings were consistent with the optimal dispatch model.

_{N}decreased from 1236.86 C to 976.65 C with a 21.04% reduction, and the compressor switching frequency f

_{N}decreased from nine times to five times with a 50.00% reduction. Different compressor operation times in scheduling schemes would lead to a difference in the processed CNG mass. If only the daily comprehensive power cost of the CNG main station is compared, it is difficult to judge the economy. To address this, the average comprehensive power cost of processing one unit of CNG (dC

_{N}) was introduced to compare the economy of the dispatching schemes. This can be expressed as follows:

#### 6.3. Economy Comparative Experiment of CNG Main Station Dispatch Model Considering TOU

#### 6.4. Control Performance Comparison Experiment of CNG Main Station Dispatch Model

^{3}of fuel gas per month in a typical CNG refueling station in theory [53]. In the pre-system model established in [13], the dehydration progress system was highly simplified to a single port element, and the regeneration and cold purging time was fixed at 12 h. This model cannot extend the switching cycle of the dual adsorption tower, making it difficult to meet the requirements of energy saving and cost reduction in the CNG main station. The proposed CNG main station model establishes a specific dehydration process model, which can specify the regeneration and cold blowing time T. Considering the optimal scheduling of the dehydration process system, the proposed model further deepens the CNG main station’s participation in DR and reduces the operating costs and energy consumption.

_{s}was set at 0.5 h, the m

_{dmp}was set 10 kg/h, and m

_{cmp}was 20 kg/h. The minimum CNG mass in the buffer tank was limited to 15 kg. During the actual CNG main station scheduling process, the original optimal model only considered the compression process system, and other process systems ran automatically according to the original strategy set in the PLC in the system. The low-pressure action margin in the buffer tank was M

_{g}= 20 × 0.5 = 10 kg. The scheduling schemes are shown in Figure 9. Only the gas quality and corresponding switching behavior of the buffer tank within a certain period are listed for illustration. Both schemes required the adsorption tower A to work in the regeneration state during [t − 2, t + 3], the adsorption tower B to work in the dehydration state during [t − 2, t + 3], and the compressor to keep running during [t − 1, t + 2]. In the original model, the PLC automatically opened u

_{10}at sampling time t to make the dehydration device run to prevent the pressure in the buffer tank from exceeding the pressure limit at the next sampling time t + 1. However, the continuous operation of the compressor still caused the buffer tank pressure to exceed the limit at sampling time t + 2. This could make the dispatching plan lose coordination with the station’s operating conditions and result in danger. Hence, it is necessary to incorporate the dehydration process system model into the economic dispatch model of the CNG main station. In the proposed model, the PLC opened the u

_{10}and filled gas to the buffer tank in advance in the low-electricity-price period [t − 2, t − 1] through the unified dispatch of the dehydration process system model and the compression process system. This ensured that the buffer tank pressure did not exceed the limit at sampling time t + 2 and reduced operating power costs.

#### 6.5. Continuous Operation Experiment of CNG Main Station Dispatch Model

## 7. Discussion and Conclusions

_{N}decreased from nine times to five times with a 50.00% reduction. Moreover, the average daily comprehensive electricity cost index of the CNG main station was 14.7082, with a 30.88% reduction compared to the original strategy scheduling scheme. The average electricity cost was 975.82 C with a 21.10% reduction, and the average processing unit CNG electricity cost was 0.77 C with a 21.10% reduction. This model considers the variable load in the dehydration process system and further deepens the CNG main station participation in the DR.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

J | Objective function | Q_{std.d} | Capacity of the dehydration device under standard conditions (N·m^{3}/h) |

Mw_{a} | Molecular weight of the air (g) | t_{s} | Sampling time (h) |

Mw_{g} | Molecular weight of the gas (g) | t_{n} | Day-ahead optimal dispatching time (h) |

${m}_{\mathrm{ap}}^{\mathrm{max}}\text{}$ | Maximum mass for buffer tank (kg) | u_{j} | State of switches |

${m}_{\mathrm{ap}}^{\mathrm{min}}\text{}$ | Minimum mass for buffer tank (kg) | M_{a} | Terminal restriction margins of the buffer tank (kg) |

m_{c} | Compressor total gas output (kg) | M_{h}, M_{m}, M_{l} | Terminal restriction margins of high-pressure, medium-pressure, and low-pressure reservoirs (kg) |

m_{d} | Dehydration device total gas output (kg) | V_{a} | Volume of buffer tanks (L) |

${m}_{\mathrm{hp}}^{\mathrm{max}}$ $,\text{}{m}_{\mathrm{mp}}^{\mathrm{max}}$ $,\text{}{m}_{\mathrm{lp}}^{\mathrm{max}}\text{}$ | Maximum mass for high-pressure, medium-pressure, and low-pressure reservoirs (kg) | V_{h}, V_{m}, V_{l} | Volume of high-pressure, medium-pressure, and low-pressure reservoirs (L) |

${m}_{\mathrm{hp}}^{\mathrm{min}}$ $,\text{}{m}_{\mathrm{mp}}^{\mathrm{min}}$ $,\text{}{m}_{\mathrm{lp}}^{\mathrm{min}}\text{}$ | Minimum mass for high-pressure, medium-pressure, and low-pressure reservoirs (kg) | W_{c} | Compressor electrical energy (kWh) |

m_{ohp}, m_{omp}, m_{olp} | Mass demand from high-pressure, medium-pressure, and low-pressure reservoirs (kg) | W_{f} | Pre-filter electrical energy (kWh) |

m_{cmp} | Compressor outlet mass flow rate (kg) | W_{d} | Dehydration device electrical energy (kWh) |

m_{dmp} | Dehydration device outlet mass flow rate (kg) | R | Universal gas constant (L·bar/K·mol) |

p_{c} | Compressor power rating (kW) | T | Regeneration and cold purging processes time (h) |

p_{d1} | Dehydration power rating (kW) | Tmax | Maximum ambient temperature (K) |

p_{d2} | Regeneration and cold purging power rating (kW) | Tmin | Minimum ambient temperature (K) |

p_{b} | Dispenser power rating (kW) | z | Compressibility factor of CNG |

Q_{std.c} | Capacity of the compressor under standard conditions (N·m^{3}/h) | ρ_{std.a} | Density of air under standard conditions (kg/m^{3}) |

## Appendix A

_{1}and f

_{2}in the upper model can be expressed as

_{U}, vectors b

_{max.U}, b

_{min.U}can be expressed as

_{eq.c}, with vector b

_{eq.c}, can be expressed as

_{3}in the lower model can be expressed as

_{L}, with vectors b

_{max.L}and b

_{min.L}, can be expressed as

**A**

_{eq.d},

**A**

_{eq.m}, and

**A**

_{eq.n}and the vectors

**b**

_{eq.d},

**b**

_{eq.m}, and

**b**

_{eq.n}can be expressed as

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**Figure 10.**Continuous operation experimental results of optimized dispatch strategy for CNG main station.

Symbol | Quantity | Value |
---|---|---|

pd1 | Dehydration power rating | 10 kW |

pm | Roots motor power rating | 7.5 kW |

pw | Forced air cooler power rating | 5 kW |

pc | Power rating of compressor | 132 kW |

Qstd.d | Capacity of dehydration device | 101 N·m^{3}/min |

Qstd.c | Capacity of the compressor | 76.67 N·m^{3}/min |

${p}_{\mathrm{ap}}^{\mathrm{max}}$ | Maximum pressure of buffer tank | 3.2 MPa |

${p}_{\mathrm{ap}}^{\mathrm{min}}$ | Minimum pressure of buffer tank | 0.1 MPa |

${p}_{\mathrm{hp}}^{\mathrm{max}}$ | Maximum pressure of high-pressure reservoir | 25.0 MPa |

${p}_{\mathrm{mp}}^{\mathrm{max}}$ | Maximum pressure of medium-pressure reservoir | 21.0 MPa |

${p}_{\mathrm{lp}}^{\mathrm{max}}$ | Maximum pressure of low-pressure reservoir | 15.0 MPa |

${p}_{\mathrm{hp}}^{\mathrm{min}}$ | Minimum pressure of high-pressure reservoir | 17.5 MPa |

${p}_{\mathrm{mp}}^{\mathrm{min}}$ | Minimum pressure of medium-pressure reservoir | 12.5 MPa |

${p}_{\mathrm{lp}}^{\mathrm{min}}$ | Minimum pressure of low-pressure reservoir | 7.5 MPa |

T | Regeneration and cold purging time of dehydration device | 8 h |

Tmax | Lowest ambient temperature | 304.15 K |

Tmin | Lowest ambient temperature | 284.15 K |

Va | Volume of buffer tank | 4000 × 3 L |

Vh (Vm, Vl) | Volume of the reservoirs | 4000 L |

Date | J | C_{N} | dC_{N} | f_{N} |
---|---|---|---|---|

Day 1 | 14.7165 | 976.65 | 0.77 | 5 |

Day 2 | 14.7165 | 976.65 | 0.77 | 5 |

Day 3 | 14.7165 | 976.65 | 0.77 | 5 |

Day 4 | 14.7020 | 975.20 | 0.77 | 5 |

Day 5 | 14.7020 | 975.20 | 0.77 | 5 |

Day 6 | 14.7020 | 975.20 | 0.77 | 5 |

Day 7 | 14.7020 | 975.20 | 0.77 | 5 |

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## Share and Cite

**MDPI and ACS Style**

Liang, Y.; Li, Z.; Li, Y.; Leng, S.; Cao, H.; Li, K. Bilevel Optimal Economic Dispatch of CNG Main Station Considering Demand Response. *Energies* **2023**, *16*, 3080.
https://doi.org/10.3390/en16073080

**AMA Style**

Liang Y, Li Z, Li Y, Leng S, Cao H, Li K. Bilevel Optimal Economic Dispatch of CNG Main Station Considering Demand Response. *Energies*. 2023; 16(7):3080.
https://doi.org/10.3390/en16073080

**Chicago/Turabian Style**

Liang, Yongliang, Zhiqi Li, Yuchuan Li, Shuwen Leng, Hongmei Cao, and Kejun Li. 2023. "Bilevel Optimal Economic Dispatch of CNG Main Station Considering Demand Response" *Energies* 16, no. 7: 3080.
https://doi.org/10.3390/en16073080