Combined heat and power dispatch promotes interactions and synergies between electric power systems and district heating systems. However, nonlinear and nonconvex heating flow imposes significant challenges on finding qualified solutions efficiently. Most existing methods rely on constant flow assumptions to derive a linear heating flow model, sacrificing optimality for computational simplicity. This paper proposes a novel convex combined heat and power dispatch model based on model simplification and constraint relaxation, which improves solution quality and avoids assumptions on operating regimes of district heating systems. To alleviate mathematical complexity introduced by the commonly used node method, a simplified thermal dynamic model is proposed to capture temperature changes in networked pipelines. Conic and polyhedral relaxations are then applied to convexify the original problems with bilinear and quadratic equality constraints. Furthermore, an adaptive solution algorithm is proposed to successively reduce relaxation gaps based on dynamic bivariate partitioning, improving solution optimality with desirable computational efficiency. The proposed method is verified on a 33-bus electric power system integrated with a 30-node district heating system and compared to nonlinear programming solvers and constant-flow-based solutions.
Uncertainty in distributed renewable generation threatens the security of power distribution systems. The concept of the dispatchable region was developed to assess the ability of power systems to accommodate renewable generation at a given operating point. Although DC and linearized AC power flow equations are typically used to model dispatchable regions for transmission systems, these equations are rarely suitable for distribution networks. To achieve a suitable trade-off between accuracy and efficiency, this paper proposes a dispatchable region formulation for distribution networks using ti…
The problem of heat and electricity pricing in combined heat and power systems regarding the time scales of electricity and heat, as well as thermal energy quality, is studied. Based on the asynchronous coordinated dispatch of the combined heat and power system, an energy-grade double pricing mechanism is proposed. Under the pricing mechanism, the resulting merchandise surplus of the heat system operator at each heat dispatch interval can be decomposed into interpretable parts and its revenue adequacy can be guaranteed for all heat dispatch intervals. And the electric power system operator's r…
Combined heat and power systems facilitate efficient interactions between individual energy sectors for higher renewable energy accommodation. However, the feasibility of operational strategies is difficult to guarantee due to the presence of substantial uncertainties pertinent to renewable energy and multi-energy loads. This paper proposes a novel efficient robust dispatch model of combined heat and power systems based on extensions of disturbance invariant sets. The approach has high computational efficiency and provides flexible and robust strategies with an adjustable level of conservative…
In combined heat and power systems, varying mass flow can better make use of the heating system inertia to increase the flexibility of electric power systems. This is challenging, however, due to integer variables and bilinear constraints in existing optimal dispatch models. In this paper, we incorporate an improved heat pipeline model to eliminate complexity from integer variables without compromise on accuracy. Subsequently, the resulting optimal dispatch model with bilinear constraints is solved by the proposed modified Generalized Benders Decomposition method, which decomposes the optimal …
We analyze pricing mechanisms in electricity markets with AC power flow equations that define a nonconvex feasible set for the economic dispatch problem. Specifically, we consider two possible pricing schemes. The first among these prices are derived from Lagrange multipliers that satisfy Karush-Kuhn-Tucker conditions for local optimality of the nonconvex market clearing problem. The second is derived from optimal dual multipliers of the convex semidefinite programming (SDP) based relaxation of the market clearing problem. Relationships between these prices, their revenue adequacy and market e…
Heat and power have become the most indispensable resources. However, the traditional ways of generating power and heat are inefficient and cause high pollution; a CHP (Combined Heat and Power) unit can solve these problems well. In recent years, more attention has been paid to energy conservation and environmental protection, and Combined Heat and Power Economic Emission Dispatch (CHPEED) has become an important multi-objective optimization problem. In this paper, an Indicator & crowding Distance-based Evolutionary Algorithm (IDBEA) is put forward for handling this non-convex and non-linear p…
A Water Mass Method and Its Application to Integrated Heat and Electricity Dispatch Considering Thermal Dynamics
Department of Electrical Engineering, State Key Laboratory of Electricity Systems, Tsinghua University（清华大学电机工程与应用电子技术系，电力系统国家重点实验室）；Shenzhen Environmental Science and New Energy Technology Engineering Laboratory, Tsinghua-Berkeley Shenzhen Institute (TBSI), Tsinghua University（清华大学深圳国际研究生院（TBSI），深圳环境科学与新能源技术工程实验室）
The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness about the consequences of modeling simplifications in these problems. The inaccurate representation of Kirchhoff's voltage law under the premise of a DC power flow is an example. Under a non-linear AC model, however, the LTHDP becomes intractable, and the literature lacks an accurate evaluation method of different modeling alternatives. In this paper, we ex…
Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual inertia and damping provided by inverters are essential to synchronism and frequency stability of future power grids. This paper numerically addresses the problem of dispatch of virtual inertia and damping (DID) among inverters in the transmission network. The DID problem is first formulated as a nonlinear program (NLP) by the Radua collocation method which is flexible to handle various types of disturbances and bounds constraints. Since the NLP of DID is highly non-convex, semi-definite programming (SDP) re…
Carnegie Mellon University（卡内基梅隆大学）；SYSU-CMU Joint Institute of Engineering, Guandong, China（中山大学-卡内基梅隆大学联合工程学院）；Energy Science, Technology and Policy, CIT interdisciplinary, Carnegie Mellon University, Pittsburgh, PA, US（卡内基梅隆大学跨学科科学、技术与政策中心）；SYSU-CMU Shunde International Joint Research Institute, Guandong, China（中山大学-卡内基梅隆大学顺德国际联合研究院）
The development of miniaturized nuclear power (NP) units and the improvement of the carbon trading market provide a new way to realize the low-carbon operation of integrated energy systems (IES). In this study, NP units and carbon trading mechanisms are introduced into the IES to build a new low-carbon scheduling model. In view of the decrease in system operation flexibility caused by the introduction of NP unit, on the one hand, the heating renovation of the NP unit is carried out to make it a cogeneration unit, to expand its operating range and improve its operating flexibility; on the other…
The problem of heat system pricing is considered. A direct extension of locational marginal prices (LMP) in electricity markets to heat systems may lead to revenue inadequate issues. The underlying reason for such a problem is that, unlike electric power, heat has different grades and cannot be considered as homogenized commodity. Accordingly, an energy-grade double pricing rule is proposed in this paper. Heat energy and grade prices are explained as the shadow prices related to the nodal heat balance constraints and temperature requirements constraints at the optimal solution. The resulting m…
District energy systems can not only reduce energy consumption but also set energy supply dispatching schemes according to demand. In this paper, the combined cooling heating and power economic emission dispatch (CCHPEED) model is established with the objective of economic cost, primary energy consumption, and pollutant emissions, as well as three decision-making strategies, are proposed to meet the demand for energy supply. Besides, a generalized differential evolution with the best compromise solution processing mechanism (BCS-GDE) is proposed to solve the model, also, the best compromise so…
The dynamic response of power grids to small events or persistent stochastic disturbances influences their stable operation. Low-frequency inter-area oscillations are of particular concern due to insufficient damping. This paper studies the effect of the operating point on the linear time-invariant dynamics of power networks. A pertinent metric based on the frequency response of grid dynamics is proposed to quantify power system's stability against inter-area oscillations. We further put forth an optimal power flow formulation to yield a grid dispatch that optimizes this novel stability metric…
