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This paper addresses the problem of reducing CO_{2} emissions by applying convex optimal power flow model to the combined economic and emission dispatch problem. The large amount of CO_{2} emissions in the power industry is a major source of global warming effect. An efficient and economic approach to reduce CO_{2} emissions is to formulate the emission reduction problem as emission dispatch problem and combined with power system economic dispatch (ED). Because the traditional optimal power flow (OPF) model used by the economic dispatch is nonlinear and nonconvex, current nonlinear solvers are not able to find the global optimal solutions. In this paper, we use the convex optimal power flow model to formulate the combined economic and emission dispatch problem. The advantage of using convex power flow model is that global optimal solutions can be obtained by using mature industrial strength nonlinear solvers such as MOSEK. Numerical results of various IEEE power network test cases confirm the feasibility and advantage of convex combined economic and emission dispatch (CCEED).

Electricity generation from fossil fuel based power plants is one major source of greenhouse gas emissions, [_{2} emissions are from the global electricity supply sector. The current approaches to mitigate CO_{2} emissions include more efficient fossil fuel conversion, switching to low- carbon energy resources, decarbonisation of fuels and nuclear power, [_{2} reduction or capture approaches, [_{2} emissions. Reference [

For ease of illustration, the nonconvex AC optimal power flow model used in the economic dispatch problem is reformulated here as (1)-(11). The formulations in (1)-(11) are based on transmission line sending end power injection variables. The advantage of including voltage phase angle explicitly in the formulation (1)-(11) is that we can obtain voltage phase angle solutions directly by solving this model.

where

Apparently, the underlined assumptions for Equation (12) to be valid are (a)-(b).

Because the operation constraint for voltage magnitude (per unit value) is generally

Equation (6) is convexified by rotated cone expressed in (13).

The method used in (13) to make equation (6) convex is relaxation. In this case, we actually relax quadratic equality constraint to quadratic inequality constraint. The tightness of this relaxation can be guaranteed by implicitly include power loss component in the objective function. This has been proved by numerical results, [

where

To include the CO_{2} emission reduction target to the economic dispatch problem, we formulate the combined economic and emission dispatch by assigning weights to the cost and CO_{2} emission parts in the objective function as follows (15).

where _{2} emission. Obviously, when _{2} emission coefficient for fossil fuel power plant. It is calculated by Equation (16). The results of Equation (16) are listed in

Fuel Type | Emission Factor [tC/MWh] | Power Plant Efficiency | Emission Coefficient |
---|---|---|---|

Steam Coal | 0.9288 | 37% (Simple Cycle) | 2.5103 |

Fuel Oil | 0.7596 | 30% (Simple Cycle) | 2.532 |

Diesel Oil | 0.7272 | 30% (Simple Cycle) | 2.424 |

Natural Gas | 0.5508 | 50% (Combined Cycle) | 1.1016 |

cost [$] | CO_{2} Emission [tCO_{2}] | ||
---|---|---|---|

1 | 0 | 8078.84 | 2422.63 |

0.8 | 0.2 | 8095.65 | 2295.04 |

0.6 | 0.4 | 8171.71 | 2117.05 |

0.5 | 0.5 | 8253.02 | 2019.42 |

0.4 | 0.6 | 8431.85 | 1876.23 |

0.2 | 0.8 | 9607.23 | 1390.22 |

0 | 1 | 465485.22 | 1346.87 |

cost [$] | CO_{2} Emission [tCO_{2}] | ||
---|---|---|---|

1 | 0 | 41696.94 | 9139.32 |

0.8 | 0.2 | 41707.77 | 9040.54 |

0.6 | 0.4 | 41771.31 | 8901.59 |

0.5 | 0.5 | 41801.98 | 8859.66 |

0.4 | 0.6 | 41802.98 | 8858.86 |

0.2 | 0.8 | 41811.24 | 8855.75 |

0 | 1 | 460648.82 | 8845.95 |

The CCEED model is coded in the General Algebraic Modeling System (GAMS). MOSEK solver in GAMS is used to solve the CCEED model. Generator and IEEE test network parameters in MATPOWER [

It can be observed from Tables 2-4 that with the increase of weights _{2} emission term of the objective function in CEEED, the CO_{2} emission is decreasing. The cost of power production increase sharply when _{2} emissions without considering economic cost is not feasible in reality. As a good compromise, _{2} emissions.

cost [$] | CO_{2} Emission [tCO_{2}] | ||
---|---|---|---|

1 | 0 | 129619.53 | 37189.08 |

0.8 | 0.2 | 129672.93 | 36793.08 |

0.6 | 0.4 | 130094.74 | 35917.63 |

0.5 | 0.5 | 130630.21 | 35274.08 |

0.4 | 0.6 | 131444.34 | 34613.92 |

0.2 | 0.8 | 136241.22 | 32689.10 |

0 | 1 | 879402.23 | 31039.88 |

In this paper, we prove the feasibility of using convex optimal power flow model to solve the combined economic and emission dispatch problem. The original nonconvex optimal power flow model is approximated and relaxed by mathematical techniques. The underlined assumptions of these approximations are explained in detail. The CCEED problem is then formulated by assigning weights to the power generation cost minimization objective and CO_{2} emission minimization objective. The CCEED model is built in GAMS platform and solved by MOSEK. Numerical results from IEEE14, IEEE57 and IEEE118 test cases show that CCEED can be solved efficiently. By adjusting the weights for cost and CO_{2} emissions in the objective of CCEED, a compromise between power generation cost and CO_{2} reduction can be achieved. Instead of nonconvex model, our convex model can guarantee global optimal solutions. Though we demonstrate the usefulness of CCEED by reducing CO_{2} emissions here, the potential applications of CCEED can be extended to reducing other green-house gas emissions or air pollutants.

Zhao Yuan,Mohammad Reza Hesamzadeh, (2016) Applying Convex Optimal Power Flow to Combined Economic and Emission Dispatch. Journal of Geoscience and Environment Protection,04,9-14. doi: 10.4236/gep.2016.47002