Day-ahead coordinated operation of utility-scale electricity and natural gas networks considering demand response based virtual power plants
Introduction
Electricity generation comes from a mix of various primary energy resources such as coal, natural gas, nuclear energy, and renewables. Combined cycle gas turbines (CCGTs), which convert chemical energy to electric energy, are widely used due to their outstanding cost-effectiveness, low and emissions, and quick responses. According to the Annual Energy Outlook 2014 from US Energy Information Administration [1], the demand for natural gas in the power sector in 2013 is 232.22 billion cubic meters (Bcm). This amount is projected to rise to 266.21 Bcm by 2040 in the reference case in which the gas delivery price is assumed to be stable. Meanwhile, industry gas demand has been growing steadily throughout the decade. With CCGT units being the largest natural gas consumers outside the industry sector, electricity transmission systems and natural gas supply networks are more closely tied and are beginning to undergo new transformations.
The linkage of CCGT units between the electricity networks and natural gas networks in a utility company affect the supply and demand balance of both networks. On the gas network side, the fluctuations of industrial and residential demand may introduce volatility in the gas supply to CCGT units and consequently affect the daily scheduling. On the electricity network side, demand response (DR) programs aiming at reducing the electricity consumption at critical high load hours also affect the power output and the gas consumption of CCGTs, which are usually the marginal generating units at load peak hours. Hence, opportunities exist for the utility company to operate the integrated energy system in a coordinated way such that the overall scheduling is optimized.
In this paper, we consider a utility company that operates an integrated energy system that consists of a power plant and a gas network. The power plant consists of CCGT units and DR based virtual power plants. The gas network contains gas wells at the supply side and residential, industrial and CCGT units on its demand side. In a broader range, this company must strategically offer its generation at a price (or following a piece-wise price curve) to independent system operator (ISO) or a regional transmission operator (RTO) (see Fig. 1). The market operator clears the day-ahead market generation offers and load bids on a social welfare maximization basis. As for the money flow, this company pays for natural gas purchases and receives payments at the rate of locational marginal pricing (LMP) for each megawatt-hour generation output.
This paper focuses on the steady-state coordinated operation of the integrated energy system in an electricity market scheme, while taking into account the impacts of DR based virtual power plants. We formulate a bi-level optimization programming model that describes the utility company’s motivation to maximize its profit by participating in the electricity market at the upper-level and simulates the market clearing process performed by the system operator at the lower level.
At the electricity network side, the DR based virtual power plant (VPP) behaves in the same way as the CCGT units and offers to the market at an optimum price. The offering prices of other generators as well as the total load level are obtained from forecasting. We recast the lower-level problem as its Kuhn-Karash-Tucker (KKT) optimality condition, and plugged it into the upper-level problem to form a mathematical programming with equilibrium constraints (MPEC). This model is linearized with the non-linear terms replaced with primal and dual variables, and is re-formulated as a mixed-integer programming problem (MILP).
At the natural gas supply network side, gas wells, pipelines and compressors under steady-state operation are modeled. Weymouth equation [2] is adopted to describe the natural gas flow through the pipelines, while the compressor model is also represented by its compression ratio and its power consumption. Due to the fact that the Weymouth equation and the compressor flow equation are both non-linear, they would become extremely slow to solve with the integer variables from the electricity network model. Therefore, adequate linearization techniques are utilized to maintain the linearity of the model with satisfactory accuracy.
The rest of this paper is organized as follows. Section 2 reviews the steady-state operation of gas networks and electricity works. Section 3 lays out the bi-level day-ahead coordinated operation problem, presents the linearization of the natural gas network constraints, and discusses the assumptions and models. Section 4 describes a probability model for the coupon- based VPP and a deterministic model for the interruptible load VPP. Section 5 provides the mathematical solution to the MPEC model and the inclusion of VPP probability. Section 6 presents numerical studies of the model on a small test case and a larger one. Section 6 concludes the paper and outlines future research.
Section snippets
Literature review
Electric power systems have been under competitive market operation with transmission network modeled over a decade ago [3], [4]. In recent years, the study of gas network along with transmission network has gained interests among the power community [5], [6], [7]. In [5], a DC power flow model and a detailed gas network model are used for the expansion planning of combined gas and electricity network. [6] proposes a long-term co-optimization planning model of electricity and natural gas
Modeling assumptions
First, we define the scope of this problem. The day-ahead coordinated operation is a steady-state scheduling problem carried out on a 24-h time horizon with an hourly resolution. The choice of hourly resolution is to follow the electricity market offering rules, and is also sufficient to provide snapshots of steady-state natural gas networks.
Within this scope, we make the following assumptions:
- (1)
This model is to be used by a utility company to derive hourly offering curves and schedule generation
Virtual power plant from demand response
Virtual power plant (VPP), by definition, is an electric power generation system that can integrate several types of small to medium scale generations, such as micro combined heat and power (μCHP) systems, wind turbines, PV, and batteries. The inclusion of demand-side management further extends the scope of a virtual power plant. With a sophisticated central energy management system (EMS), those different sources are coordinated to provide reliable power generation like a conventional power
Formulation of an MPEC
By recasting the lower-level problem with its KKT optimality conditions (35), (36), (37), (38), (39), the bi-level optimization problem is transformed into an MPEC formulation. Non-linearlities
Case study
The proposed coordinated operation strategy is applied to two cases consisting of a six-bus electric system with a seven-node gas system and the IEEE 118-bus system with a 14-node gas system to illustrate its effectiveness. Assume 1 Mcm natural gas can generate 37.26 GJ energy in the case studies (equivalent to assume 1 cubic feet gas to generate 1 million British thermal unit energy). The coordinated scheduling is carried out on a 24-h time horizon with a 1-h interval, which is sufficient for
Conclusions
This paper presents a bi-level optimization model for day-ahead coordinated operation of an electricity a network and natural gas system. In this paper, the electricity market clearing process is modeled and incorporated into the coordinated operation model to formulate a MPEC model, wherein the non-linear components are linearized and the DR is modeled as a VPP in the electricity network.
The main conclusions from case studies are:
- 1.
The profit increase from VPP’s bidding in electricity market
Acknowledgment
The authors would like to acknowledge the support in part by the US NSF Grant ECCS-1001999 and the CURENT research center funded by NSF and DOE under the US NSF Grant EEC-1041877.
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