A two-stage approach for combined heat and power economic emission dispatch: Combining multi-objective optimization with integrated decision making

Abstract

To address the problem of combined heat and power economic emission dispatch (CHPEED), a two-stage approach is proposed by combining multi-objective optimization (MOO) with integrated decision making (IDM). First, a practical CHPEED model is built by taking into account power transmission losses and the valve-point loading effects. To solve this model, a two-stage methodology is thereafter proposed.The first stage of this approach relies on the use of a powerful multi-objective evolutionary algorithm, called θ-dominance based evolutionary algorithm (θ-DEA), to find multiple Pareto-optimal solutions of the model. Through fuzzy c-means (FCM) clustering, the second stage separates the obtained Pareto-optimal solutions into different clusters and thereupon identifies the best compromise solutions (BCSs) by assessing the relative projections of the solutions belonging to the same cluster using grey relation projection (GRP). The novelty of this work is in the incorporation of an IDM technique FCM-GRP into CHPEED to automatically determine the BCSs that represent decision makers' different, even conflicting, preferences. The simulation results on three test cases with varied complexity levels verify the effectiveness and superiority of the proposed approach. (Yang Li). 2 multi-objective optimization; integrated decision making; valve-point loading effects; θ-dominance based evolutionary algorithm; grey relational projection; integrated energy system. NOMENCLATURE Acronyms CHP combined heat and power CHPED CHP economic dispatch CHPEED CHP economic emission dispatch MOEAs multi-objective evolutionary algorithms MOPSO multi-objective particle swarm optimization EFA enhanced firefly algorithm MOO multi-objective optimization

Improving operational flexibility of integrated energy system with uncertain renewable generations considering thermal inertia of buildings

“…2. According to the operating principle of the extraction unit, the output model is as follows [23]:…”

“…where max i P and min i P are the maximum and minimum electric power of thermal power unit i, respectively. Ramp rate constraint: When studying system scheduling, the ramp rate limit of each unit is one of the constraints which can't be neglected [23]. The ramp rate constraint is…”

Indicator & crowding distance-based evolutionary algorithm for combined heat and power economic emission dispatch

“…In addition, as an environmentally friendly system, cogeneration units can reduce greenhouse gas emissions by 13% to 18% [6]in comparison with the conventional generating units. Combined Heat and Power Economic Dispatch (CHPED) is to optimize the distribution of heat load and power load commands to reduce fuel costs [7]. However, with the increasing prominence of social environmental problems, economic optimization alone cannot meet the needs of social energy conservation and environmental protection.…”

“…The Multi-objective Line-up Competition Algorithm (MLCA) is submitted to solve the problem by extracting compromise solutions from Pareto optimal solutions using fuzzy decision [24]. A two-stage algorithm is presented to provide different solutions according to different decision makers [7]. In a word, the algorithms mentioned in the above literature are the Pareto-based evolutionary algorithms, while the effectiveness of the algorithms depends on the shape and distribution of the Pareto Front (PF) of the problem.…”

“…Step (7). Replace: Make the offspring individuals become the new parent individuals, which means replace parent population P with offspring population S; increment the counter: M = M + 1.…”