# Impact of Local Emergency Demand Response Programs on the Operation of Electricity and Gas Systems

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

#### 2.1. PTDFs and ATC Formulation

#### 2.2. Economic Models of DR

#### 2.3. Modeling of the Economic Dispatch in the Power and Gas Networks

#### 2.4. Solution Methodology

## 3. Numerical Simulation and Results

#### 3.1. Test System and Scenarios

^{6}× m

^{3}) [29].

#### 3.2. Results and Discussion

#### 3.2.1. Computational Performance

#### 3.2.2. Operational Analysis

#### 3.2.3. Injection of Hydrogen through the Gas Infrastructure

^{6}× m

^{3}) in the gas network occurred. However, in Scenario 14, due to the flexibility provided by DRP (similar to Scenario 6), the supply–demand balance in both systems is maintained. It is worth mentioning that in the natural gas scenarios (Scenarios 1–12), the unserved demand is zero.

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Abbreviations | l | Transmission lines index | |

ATC | Available transmission capability | n | Node index |

CCS | carbon capture and storage | p | Pipeline index |

CM | Congestion management | s | Terminal nodes index |

DR | Demand response | t | Time index |

DRPs | demand response programs | q | Storage index |

EDRP | Emergency demand response program | Parameters | |

FACT | Flexible AC transmission | ${\mathrm{a}}_{g},{\mathrm{b}}_{g},{\mathrm{c}}_{g}$ | Cost coefficients for generation unit g |

GFPP | Gas-fired power plants | ${\mathrm{B}}_{l}$ | Susceptance of line l (℧) |

GTDF | Gas transfer distribution factor | ${\mathrm{cost}}^{\mathrm{gas}}$ | Cost of gas supply (USD/m^{3}) |

LEDRP | Local emergency demand response program | ${\mathrm{cost}}_{g}^{\mathrm{statup}/\mathrm{shutdown}}$ | Startup/Shutdown cost of generating unit g (USD) |

LF | Load factor | ${\mathrm{d}}_{{0}_{n,t}}^{\mathrm{gas}}$ | Initial demand of node n at time t in the gas network (10^{6} × m^{3}) |

PC | Peak reduction | ${\mathrm{Diameter}}_{p}$ | Diameter of pipe p (mm) |

PEM | Price elasticity matrix | ${\mathrm{d}}_{{0}_{i,t}}^{\mathrm{elec}}$ | Initial demand of i bus and t time at the power network (MW) |

P2H | Power to heating | ${\mathrm{d}}_{g}{,\mathrm{e}}_{g}$ | Point-valve effect coefficients for generation unit g |

P2G | Power to gas | ${\mathrm{GL}}_{q}^{\mathrm{min}/\mathrm{max}}$ | Maximum/Minimum gas storage level of facility q (m^{3}) |

PTDF | Power transfer distribution factor | ${\mathrm{H}}_{\mathrm{v}}$ | Gas heating value |

PTV | Peak to valley | ${\mathrm{Length}}_{p}$ | Length of pipe p (m) |

SCUC | Security-constrained unit commitment | ${\mathrm{LP}}_{p,t}^{0}$ | Initial gas stored in the pipe p and time t (10^{6} × m^{3}) |

TC | Total cost | ${\mathrm{n}}_{g}$ | Number of POZs for the generation unit g |

UC | Unit commitment | ${\mathrm{P}}_{l}^{\mathrm{max}/\mathrm{min}}$ | Thermal limitation for line l at time t (MW) |

Index | ${\mathrm{P}}_{g}^{\mathrm{max}/\mathrm{min}}$ | Maximum/Minimum output power for generation unit g (MW) | |

c | Compressor index | ${\mathrm{PW}}_{i,t}$ | Wind power at bus i and time t (MW) |

g | generation unit index | ${\mathrm{P}}_{g}^{{U}^{R}}$ | Upper limits for the Rth POZ (MW) |

i,j | Bus index | ${\mathrm{P}}_{g}^{{L}^{R}}$ | Lower limits for the Rth POZ (MW) |

${\mathrm{Pr}}_{n}^{\mathrm{min}/\mathrm{max}}$ | Maximum/Minimum pressure limits at node n (Pa) | $\mathsf{\sigma}$ | Thermal efficiency of gas-fired power plants |

${\mathrm{Pr}}_{c}^{\mathrm{comp}\text{}\mathrm{max}}$ | Maximum power consumption of compressor c (Pa) | ${\chi}^{\mathrm{normal}}$ | Gas density under standard condition (0.713 kg/m^{3}) |

${\mathrm{Q}}_{p}^{\mathrm{pipe}\text{}\mathrm{min}/\mathrm{max}}$ | Maximum/Minimum range for gas flow within pipeline p (m^{3}/h) | Variables | |

${\mathrm{Q}}_{\mathrm{c}}^{{\mathrm{comp}}_{}\mathrm{max}/\mathrm{min}}$ | Maximum/Minimum gas flow rate to compressor c (m^{3}/h) | $AT{C}_{l}$ | Available transfer capability of line l (MW) |

${\mathrm{Q}}_{q}^{{\mathrm{output}}_{}\mathrm{max}}\text{}$ | Maximum output of the q gas storage (m^{3}/h) | B(d(t)) | The benefit of consuming energy d(t) at time t (USD) |

${\mathrm{Q}}_{s}^{\mathrm{max}/\mathrm{min}}$ | Maximum/Minimum capacity of gas flow rate of terminal s (8.5 × 10^{6} × m^{3}/h) | $Cos{t}_{t}^{\mathrm{gas}}$ | Gas price at time t (USD/(10^{6} × m^{3})) |

${\mathrm{Q}}_{q}^{{\mathrm{input}}_{}\mathrm{max}}$ | Maximum input of the q gas storage (m^{3}/h) | ${\mathit{Cos}t}_{\mathit{EDRP}}^{\mathrm{elec}}$ | Cost of EDRP in the power network (USD) |

${\mathrm{RD}}_{g}$ | Ramp-down of the generation unit g (MW/h) | ${d}_{i,t}^{\mathrm{elec}}$ | Electricity demand at node i and time t (MW) |

${\mathrm{RP}}^{\mathrm{max}}$ | The maximum ratio of the inlet /outlet pressure in compressors (1.5) | ${d}_{n,t}^{\mathrm{gas}}\text{}$ | Gas demand at node n, time t (10^{6} × m^{3}) |

$\mathrm{R}$ | Gas constant for natural gas (518 J/(kg × K)) | d(t) | consumed energy at time t (MW) |

${\mathrm{RU}}_{g}$ | Ramp-up of the generation unit g (MW/h) | ${\mathit{GL}}_{q,t}$ | Gas storage level of storage facility q at time t (m^{3}) |

${\mathrm{SUR}}_{g}$ | Startup ramp of the generation unit g (MW/h) | ${\mathit{inc}}_{i,t}^{\mathrm{elec}}$ | Incentives applied to bus i of the power network at time t (USD/MW) |

${\mathrm{SDR}}_{g}$ | Shutdown ramp of the generation unit g (MW/h) | ${I}_{g,t}$ | Commitment status of generation unit g at time t (0 OR 1) |

${\mathrm{T}}^{\mathrm{normal}}$ | Gas temperature under standard condition (288 ‘degree’ K) | ${\mathit{inc}}_{n,t}^{\mathrm{gas}}$ | Incentives applied to node n of the gas network at time t (USD/(10^{6} × m^{3})) |

${\mathrm{T}}_{g}^{\mathrm{on}/\mathrm{off}}$ | Minimum up/down time of thermal generation unit g (h) | $INC\left(\Delta d\left(t\right)\right)$ | Total received incentives at time t from the network (USD) |

$\mathrm{Z}$ | Natural gas compressibility factor (0.95) | ${\mathit{LP}}_{p,t}$ | Linepack in pipeline p and time t (m^{3}/h) |

${\mathsf{\beta}}^{\mathrm{comp}}$ | Polytrophic exponent of a gas compressor | ${\mathit{Pr}}_{n,t}$ | Pressure at node n and time t (Pa) |

${\mathsf{\eta}}_{p}$ | Pipeline efficiency (80%) | $\mathit{pen}\left(t\right)$ | Non-execution penalty of DR at time t (USD) |

${\mathsf{\eta}}^{\mathrm{comp}}$ | Compressor efficiency (80%) | ${\mathit{Pr}}_{p,t}^{\mathrm{average}}$ | The average pressure inside the pipe p and time t (Pa) |

${\mathsf{\rho}}_{0}(t)$ | Initial electricity price at hour t (USD) | $PTDF{s}_{l,i}$ | The sensitivity coefficient of line l to the changing demand in the bus i |

${P}_{c,t}^{\mathrm{comp}}$ | Consumption power of c compressor at time t (MW) | ${Q}_{p,t}^{\mathrm{pipe}}$ | Gas flow of the pipeline p at time t (m^{3}/h) |

${Pr}_{c,t}^{\mathrm{in}}$ | Inlet gas pressure to compressor c at time t (Pa) | ${Q}_{p,t}^{\mathrm{out}.\mathrm{pipe}}$ | Outlet gas flow related to the pipeline p at time t (m^{3}/h) |

$P{r}_{c,t}^{\mathrm{out}}$ | Outlet gas pressure from compressor c at time t (Pa) | $SRP{T}_{t}$ | Essential spinning reserve at time t (MW) |

${PL}_{l,t}$ | Power flow of the line l at time t (MW) | ${\mathrm{TL}}_{l,i}$ | Transfer limitation associated with line l and bus i (MW) |

$PEN\left(\Delta d\left(t\right)\right)$ | Total paid fines at time t to the network (USD) | ${V}_{p,t}$ | Volume of gas related to pipeline p at time t (m^{3}) |

${P}_{g,t}$ | Produced power of the power plant g at the time t (MW) | ${\theta}_{l,t}$ | Voltage angle for line l at time t (rad) |

${Q}_{q,t}^{\mathrm{out}}$ | Outlet gas from the storage q at time t (m^{3}/h) | $\rho \left(t\right)$ | Electricity price at hour t (USD) |

${Q}_{g,t}^{\mathrm{gen}}$ | Gas consumption of gas-fired power plant g at time t (m^{3}/h) | ${\Delta P}_{i}$ | Power change in bus i (MW) |

${Q}_{q,t}^{\mathrm{in}}$ | Inlet gas from the storage q at time t (m^{3}/h) | ${\Delta P}_{l}$ | Power change in line l (MW) |

${Q}_{c,t}^{\mathrm{comp}}$ | Gas flow through c compressor at time t (m^{3}/h) | α | Optimal average power incentive (USD/MW) |

${Q}_{p,t}^{\mathrm{in}.\mathrm{pipe}}$ | Inlet gas flow to the pipeline p at time t (m^{3}/h) | γ | Optimal average gas incentive (USD/(10^{6} × m^{3})) |

${Q}_{s,t}^{\mathrm{sup}}$ | Gas flow rate related to terminal at node s and time t (m^{3}/h) |

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**Figure 2.**Studied integrated gas and power networks [29].

Valley (h) | Off-Peak (h) | Peak (h) | |
---|---|---|---|

Power network | 1 to 8 | (9 to 11) and (16 to 20) | (12 to 15) and (21 to 24) |

Gas network | 1 to 6 | (10 to 16) and (22 to 24) | (7 to 9) and (17 to 21) |

Scenario | System for LEDRP | Model of Basic LEDRP | Compared Model with Basic LEDRP | Injected Gas |
---|---|---|---|---|

1 | --------- | --------- | --------- | NG |

2 | Power | Linear | --------- | NG |

3 | Power | Power | --------- | NG |

4 | Power | Exp | --------- | NG |

5 | Power | Log | --------- | NG |

6 | Gas and Power | Linear | --------- | NG |

7 | Gas and Power | Power | --------- | NG |

8 | Gas and Power | Exp | --------- | NG |

9 | Gas and Power | Log | --------- | NG |

10 | Gas and Power | Linear | Power | NG |

11 | Gas and Power | Linear | Exp | NG |

12 | Gas and Power | Linear | Log | NG |

13 | --------- | -------- | ------ | H2 |

14 | Gas and Power | Linear | ------- | H2 |

Scenario | Number of Variables | Number of Non-Linear Variables | Number of Linear Variables | Number of Iteration | Running Time (Seconds) |
---|---|---|---|---|---|

1 | 41,828 | 14,078 | 27,750 | 1,104,252 | 877 |

2 | 42,981 | 14,078 | 28,903 | 1,126,421 | 902 |

3 | 42,981 | 14,678 | 28,303 | 1,739,217 | 1154 |

4 | 42,981 | 14,654 | 28,327 | 1,333,433 | 1001 |

5 | 42,981 | 14,654 | 28,327 | 1,230,979 | 982 |

6 | 43,725 | 14,322 | 29,403 | 1,432,400 | 1147 |

7 | 43,725 | 14,932 | 28,793 | 2,211,654 | 1467 |

8 | 43,725 | 14,908 | 28,817 | 1,695,643 | 1273 |

9 | 43,725 | 14,908 | 28,817 | 1,565,359 | 1249 |

Scenario | Optimal Elec. Incentive (USD/MWh) | Cost of DR Power network (USD 10 ^{3}) | Power Network Cost (USD 10 ^{3}) | Optimal Gas Incentive (USD/(10 ^{6} × m^{3})) | Cost of DR Gas System (USD 10 ^{3}) | Gas Network Cost (USD 10 ^{3}) | Total Cost (USD 10 ^{3}) | Power Loss (MW) |
---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 1161 | 0 | 0 | 2289 | 3449 | 1833 |

2 | 23.86 | 114.30 | 1092 | 0 | 0 | 2090 | 3182 | 1432 |

3 | 29.95 | 61.23 | 1129 | 0 | 0 | 2146 | 3275 | 1644 |

4 | 26.82 | 62.33 | 1116 | 0 | 0 | 2179 | 3295 | 1601 |

5 | 25.72 | 65.24 | 1120 | 0 | 0 | 2117 | 3237 | 1625 |

6 | 20.03 | 102.13 | 1060 | 278.40 | 47.98 | 2024 | 3083 | 1381 |

7 | 25.35 | 33.83 | 1086 | 230.03 | 23.18 | 2071 | 3157 | 1631 |

8 | 23.5 | 60.83 | 1108 | 255.73 | 34.90 | 2033 | 3141 | 1565 |

9 | 25.03 | 62.42 | 1093 | 242.88 | 27.91 | 2044 | 3137 | 1571 |

Scenario | Sum of Power Demand (GWh) | PTV (%) | Power Saving (%) | PC (%) | LF (%) |
---|---|---|---|---|---|

1 | 49.60 | 53.28 | 0 | 0 | 76.51 |

2 | 43.65 | 40.6 | 11.99 | 18.12 | 82.42 |

3 | 45.33 | 46.57 | 4.77 | 8.5 | 78.3 |

4 | 46.67 | 42.37 | 6.03 | 12.91 | 82.55 |

5 | 46.62 | 45.06 | 6.01 | 12.8 | 82.56 |

6 | 44.68 | 40.85 | 9.92 | 18.3 | 84.17 |

7 | 47.63 | 47.9 | 3.96 | 10.22 | 81.16 |

8 | 47.23 | 44.22 | 8.6 | 16.34 | 83.59 |

9 | 46.61 | 45.22 | 5.9 | 13.02 | 82.68 |

Scenario | Unsupplied Electricity (MW) | Unsupplied Gas (m^{3}) |
---|---|---|

13 | 50 | 16,583 |

14 | 0 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Davari, M.M.; Ameli, H.; Ameli, M.T.; Strbac, G. Impact of Local Emergency Demand Response Programs on the Operation of Electricity and Gas Systems. *Energies* **2022**, *15*, 2144.
https://doi.org/10.3390/en15062144

**AMA Style**

Davari MM, Ameli H, Ameli MT, Strbac G. Impact of Local Emergency Demand Response Programs on the Operation of Electricity and Gas Systems. *Energies*. 2022; 15(6):2144.
https://doi.org/10.3390/en15062144

**Chicago/Turabian Style**

Davari, Mohammad Mehdi, Hossein Ameli, Mohammad Taghi Ameli, and Goran Strbac. 2022. "Impact of Local Emergency Demand Response Programs on the Operation of Electricity and Gas Systems" *Energies* 15, no. 6: 2144.
https://doi.org/10.3390/en15062144