Day-ahead coordinated operation of utility-scale electricity and natural gas networks considering demand response based virtual power plants

doi:10.1016/j.apenergy.2016.05.007

Applied Energy

Volume 176, 15 August 2016, Pages 183-195

https://doi.org/10.1016/j.apenergy.2016.05.007 Get rights and content

Highlights

•
A bi-level coordinated model to maximize profits for utility company is proposed.
•
Virtual power plant models using interruptible-load and coupon based DRs are proposed.
•
Profit increase of a utility company from VPP’s bidding depends on the type of VPP.
•
With VPP, the amount of LMP reduction depends on system size and utility scale.
•
DR based VPP may reduce gas network congestion at peak hours with reduced profits.

Abstract

The steady-state coordinated operation of electricity networks and natural gas networks to maximize profits is investigated under market paradigm considering demand response. The components in its gas supply networks are modeled and linearized under steady-state operating conditions where combined cycle gas turbine (CCGT) generators consume natural gas and offer to the electricity market. Interruptible-load based and coupon-based demand response virtual power plants are considered trading in the market like physical generators. A bi-level programming optimization model is formulated with its upper-level representing the coordinated operation to maximize profits and its lower-level simulating the day-ahead market clearing process. This bi-level problem is formulated as a mathematical program with equilibrium constraints, and is linearized as a mixed-integer programming problem. Case studies on a 6-bus power system with a 7-node natural gas system and an IEEE 118-bus power system with a 14-node gas system verify the effectiveness of the coordinated operation model. The impacts of demand response based virtual power plants on the interactions between the two networks are also analyzed.

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 ${NO}_{x}$ and ${SO}_{x}$ 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

$Max \sum_{i, t} π_{i, t} (G_{i, t}^{S} + G_{i, t}^{V}) - \sum_{i, t} (W_{i, t} (G_{i, t}^{S}) + κ_{i, t} G_{i, t}^{V})$ $Contraints in (3) – (13) and (20)$ $α_{i, t}^{ϕ} = λ_{t} + (ω_{i, t, \min}^{ϕ} - ω_{i, t, \min}^{ϕ}) + \sum_{i} [{GSF}_{l - i} (μ_{l, t}^{\min} - μ_{l, t}^{\max})], \forall i, \forall t$ $0 ⩽ ω_{i, t, \min}^{ϕ} ⊥ (G_{i, t}^{ϕ} - G_{i, \min}^{ϕ}) ⩾ 0, \forall i, \forall t$ $0 ⩽ ω_{i, t, \min}^{ϕ} ⊥ (G_{i, \max}^{ϕ} - G_{i, t}^{ϕ}) ⩾ 0, \forall i, \forall t$ $0 ⩽ μ_{l, t}^{\min} ⊥ \sum_{i} {GSF}_{l - i} \times (\sum_{ϕ} G_{i, t}^{ϕ} - D_{i, t}) + c_{l} ⩾ 0$ $0 ⩽ μ_{l, t}^{\max} ⊥ c_{l} - \sum_{i} {GSF}_{l - i} \times (\sum_{ϕ} G_{i, t}^{ϕ} - D_{i, t}) ⩾ 0$ $\forall ϕ \in \{S, V, O\}, \forall i, \forall t for (35), (36), (37)$

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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View full text

Day-ahead coordinated operation of utility-scale electricity and natural gas networks considering demand response based virtual power plants

Highlights

Abstract

Introduction

Section snippets

Literature review

Modeling assumptions

Virtual power plant from demand response

Formulation of an MPEC

Case study

Conclusions

Acknowledgment

Appl Energy

IEEE Trans Power Syst

Electric Power Syst Res

Appl Energy

Appl Energy

Appl Energy

Appl Energy

Energy Policy

Appl Energy

Appl Energy

Optimization models for the natural gas value chain

A market simulation program for the standard market design and generation/transmission planning

Market based transmission planning considering reliability and economic performances

A model to long-term, multiarea, multistage, and integrated expansion planning of electricity and natural gas systems

IEEE Trans Power Syst

Natural gas and electricity optimal power flow

2003 IEEE PES T&D Conf