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Dynamic Modeling and Interaction of Hybrid Natural Gas and Electricity Supply System in Microgrid X. Xu, Student Member, IEEE, Hongjie Jia, Member, IEEE, H.-D. Chiang, Fellow, IEEE, D. C. Yu, Member, IEEE, and D. Wang, Member, IEEE
Abstract—Natural gas (NG) network and electric network are becoming tightly integrated by microturbines in the microgrid. Interactions between these two networks are not well captured by the traditional microturbine (MT) models. To address this issue, two improved models for single-shaft MT and split-shaft MT are proposed in this paper. In addition, dynamic models of the hybrid natural gas and electricity system (HGES) are developed for the analysis of their interactions. Dynamic behaviors of natural gas in pipes are described by partial differential equations (PDEs), while the electric network is described by differential algebraic equations (DAEs). So the overall network is a typical two-time scale dynamic system. Numerical studies indicate that the two-time scale algorithm is faster and can capture the interactions between the two networks. The results also show the HGES with a single-shaft MT is a weakly coupled system in which disturbances in the two networks mainly influence the dc link voltage of the MT, while the split-shaft MT is a strongly coupled system where the impact of an event will affect both networks. Index Terms—Dynamic modeling, hybrid natural gas and electricity system (HGES), interaction, microgrid, microturbine (MT), natural gas network.
I. INTRODUCTION
C
LIMATE change and energy security are among the central factors that will shape energy systems world-wide [1]. A new trend in energy systems is to create an integrated energy system (IES), by overlapping the fields of energy, control, chemical, material, and environment, management. IES is a multi-function energy system with characteristics of multiple energy inputs, multiple outputs, multiple operation states, and multiple transfer conditions [2]. Microgrid, which can combine diverse sources, is becoming an integrated part of the energy web [3], [4]. As one of the most successful commercial ap-
Manuscript received October 01, 2013; revised March 08, 2014 and June 05, 2014; accepted July 11, 2014. This work was supported in part by the National Science Foundation of China (No. 51377117), the National High-tech R&D Program of China (863 Program with No.2014AA051901), and China Postdoctoral Science foundation funded project (2013M540207). Paper no. TPWRS-012522013. (Corresponding author: Hongjie Jia). X. Xu, H. Jia, and D. Wang are with the Key Laboratory of Smart Grid of Ministry of Education, School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China (e-mail:
[email protected]; hjjia@tju. edu.cn;
[email protected]). H.-D. Chiang is with the School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853 USA (e-mail:
[email protected]). D. C. Yu is with the University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2014.2343021
plications for microgrids, combined heating, and power (CHP) system [5], is a typical IES. In a CHP system, microturbine fueled by natural gas, is a key component. It couples natural gas network and electric network. When many CHP units are applied, interactions between natural gas and electric system will be very complex and should be carefully studied, especially for companies like PG&E and Edison that provide both natural gas and electricity to customers. Also, for microgrids owned by universities or industrial parks who can build their own energy networks, dynamic simulation is significant for the hybrid energy system planning. Since a large portion of electricity is generated by gas-powered units in the US, to optimize the operation of hybrid natural gas and electricity system (HGES) draws more and more concern. A detailed analysis of the interactions between the natural gas network and the electric network is presented in [7]–[12], including the impact of natural gas price fluctuations [7] and pipeline faults [8] on the power system security, unit commitment [9] and risk assessment [10], [11]. Brazilian researchers analyzed the interaction between the natural gas infrastructure and the hydropower system, considering only a steady state natural gas network and a DC power flow model [12]. A multi-time period optimization method was proposed to reduce operating cost, based on the Great Britain gas and electricity network [13]. The interactions among energy networks of a few units were analyzed based on energy hub in [14]. As illustrated in [15], it is not accurate to analyze the HGES using only steady state model. However, the published studies are mostly focused on steady state or quasi-steady states. Few discussions have been given to HGES’s dynamic interactions. To study the interaction mechanism of HGES, dynamic characteristics of the two systems should be considered. Gas-powered generator units, which are coupling points of the two networks, play a significant role in the interaction chain. Thus, a suitable dynamic model of the gas turbine is necessary. In a microgrid, micro-turbine (MT) is the most widely used gas turbine. Dynamic characteristic of MT was analyzed in [16] and a gas turbine (GAST) model was proposed in [17]. In [18], the MT model characteristic under different load conditions was analyzed. Both grid-connected mode and island mode were discussed. A prime mover model of the grid-connected gas-powered units was presented in [19]. Due to other gas loads variation, gas network upstream compressor faults and slow response time, the natural gas network pressure is in a dynamic state most of the time. As illustrated in [20], electric generators are more susceptible to pressure drops than other natural gas loads However, all the above methods are not designed to analyze the im-
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Fig. 1. Structure of the hybrid natural gas and electrical supply system.
pact of natural gas fluctuation on power system and the influence of a gas generator on a natural gas system. Moreover, in order to follow the load variation in the electrical system, MT gas consumption change faster and more frequently, compared with other gas loads Thus, establishing suitable MT models and HGES model that can capture characteristics of the two networks are important. This paper aims to find such models and use the models to analyze the dynamic interactions between the two networks. Main works of this paper are as follows: 1) two improved MT models are proposed to analyze the interaction between the natural gas network and the electric network by adding valve opening controller model to control the MT gas inlet pressure; 2) Based on the improved MT models, an HGES model is presented. It has DAE and PDE components. In this paper, it is denoted as the DAE-PDE model; 3) A two-time scale algorithm is developed to solve the DAE-PDE problem; 4) The interactions between the two networks are investigated by the HGES analysis. The results demonstrate that the HGES model and the two-time scale algorithm developed in this paper are effective in capturing the interactions. With the proposed model and numerical algorithm, it became possible to simulate dynamic behavior of the HGES. For successful planning and operation of hybrid gas and electricity network, dynamic simulation will assist engineers in making reasonable decisions for a reliable configuration of the HGES in addition to operators’ experience. The study also shows that the Single-shaft MT (SIMT) HGES is a weakly coupled system which can prevent the interactions between the two networks, while the SPlit-shaft MT (SPMT) HGES is a strongly coupled system which can easily propagate the fault from one network to the other one and distribute the fault impact among two networks. II. HYBRID NATURAL GAS AND ELECTRICITY SYSTEM (HGES) MODEL The proposed HGES model can be illustrated in Fig. 1. The system includes natural gas supply system, MT, electrical system (utility) and electrical, heating and natural gas loads. The utility for electricity is considered as an infinite bus, and the utility for gas is considered as a constant pressure gas well. A. Improved MT Model Two common types of MTs are available based on the positions of the turbine and generator. They are the Rowen’s model (SIMT system) described in [19] and a prime mover model
(SPMT system) described in [21]. As shown in the dashed box in Fig. 2 and Fig. 3, it can be found that the valve and fuel supply systems in the two MT models are considered as first order inertial links. These models neglect dynamics of natural gas system outside the MT and consider the natural gas network as a constant pressure gas supply system. However, there exist two problems in the traditional models. On the one hand, MT output power regulation will cause pressure variation to the gas network, but traditional MT models only provide gas volume consumed by the MT, which is not an appropriate boundary condition1 for natural gas network simulation [23]. On the other hand, natural gas network pressure can be influenced by the gas well or other gas loads, which will also affect the MT output. Traditional MT models do not have an item that is connected to the natural gas network. Thus, two improved MT models are proposed to reflect the interaction between the two networks. In the improved models, a valve controller is added into the original fuel supply system. The valve controller controls the valve opening to adjust the inlet pressure of the MT, which will change the gas flow injected into the MT. 1) SIMT: For the SIMT model, the subsystem in the dashed box in Fig. 2 is replaced by the system in Fig. 4. The MT inlet pressure is also the outlet pressure of the pipeline connected with the MT, and is used as the boundary condition of the pipeline model. The PI regulator that is used to control the fuel injected into the combustor. Natural gas network will influence the MT electric output through the gas flow variation caused by the gas pressure fluctuation. In the model, the inlet pressure of the MT is a boundary condition of the natural gas system: (1) The MT controls the inlet flow by regulating with the valve. The gas source pressure and the regular gas load pressure are also boundary conditions of the NG network. The natural gas flow going through network including the MT inlet flow will be influenced when are changed. Therefore, the improved model can reflect both the impact of the natural gas load change on the MT and the impact of the MT output on the natural gas network. 2) SPMT: In Fig. 3, the fuel supply system of the split-shaft model is described by a steady state transformation. The impact of the NG pressure is also neglected. In the improved model, the fuel supply system is replaced by the system in Fig. 4 and connected to the combustor model, so that the impact of NG pressure fluctuation can be reflected to the MT and vice versa. B. Natural Gas System The equations expressing mass and momentum conservation laws and describing one-dimensional compressible flow within a gas pipeline (see Fig. 5) can be expressed as follows [23]: (2) (3) 1The solution of PDEs is generally not unique, additional conditions must be specified on the boundary of the region where the solution is defined.
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Fig. 2. Rowen’s model [19] (for details, see the Appendix).
Fig. 3. SPMT prime mover model [21] (for details, see the Appendix).
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Fig. 4. Proposed Natural gas network and MT fuel supply sub-system in the Rowen’s model.
Fig. 7. Proposed two-time scale simulation algorithm. Fig. 5. Control volume in a general pipeline [24].
pressure and mass conservation. In Fig. 6, the mass flows at node 2 should satisfy (5) (5) where , , and represent the mass flow in the pipelines connected to the node 2. In addition to the mass conservation, the gas well pressure at node 1 is also considered a boundary condition: Fig. 6. Structure of the natural gas network.
(6)
where is the speed of sound, represents the isentropic process, is the cross-sectional area of the pipe, is the pipe diameter, is the mass flow, is the Fanning friction coefficient, is the acceleration of gravity, and is the angle between the horizon and the direction . The steady state pipeline model is normally used at the initial stage of the simulation to obtain the initial values for transient analysis. The steady state model can be obtained by ignoring dynamics of the pipeline model, as depicted in (4) (4) where and are the upstream and downstream pressure, is the pipeline volume flow, and the properties of the pipeline and the fluid are represented by [23]. The natural gas supply system of HGES can be simplified to Fig. 6. During normal operation, the inlet pressure of MT is around 0.4 MPa [25]. MT is usually connected to a low pressure pipeline and receives natural gas from the low pressure network. Therefore, a low pressure pipeline model is chosen to simulate the natural gas network, including dynamic model and boundary conditions. 1) Boundary Condition: In the natural gas system, the boundary conditions are given by the gas well pressure, loads
2) Dynamic Model of Natural Gas Supply System: Define , , , the pipeline network dynamic system can be represented as (7) The boundary conditions (5), (6), and pressed by
can be ex(8)
C. Dynamic Model of Electrical System Model The electrical system and gas turbines model can be described by the following DAEs [6]: (9) are state variables of the equipment, e.g., generators, where controls, loads at buses, are algebraic variables (usually the magnitudes and phase angles of the complex node voltages). D. Load It is assumed that all heat loads are supplied by the MT. Heat loads in a CHP system are supplied by the fuel gas of the MT.
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Because the MT efficiency changes little in the normal operation and the time constant of the heating system is large, the impact of heat loads on the system are reflected by affecting the natural gas consumption of the MT. III. TWO-TIME SCALE METHOD The HGES is a complex multi-time scale dynamic system composed of interconnected electric and pipeline components. A two-time scale method will be presented to simulate this system. The HGES consists of power system, natural gas system and the MT. The MT couples the two independent systems. Hence, the two systems become a cascade system. Combining (7), (8), and (9), a typical dynamic model of HGES can be expressed by (10) , , and are where state variables of the MT, are algebraic variables of the MT. Traditionally, the natural gas supply system and electric power system are usually treated as two independent systems. The impact of pipeline dynamics is usually neglected or treated as algebraic constraints when analyzing the influence of gas turbine system on the electric network [26]. The dynamic characteristic of a gas turbine is ignored when the impact of gas-powered units on power system is analyzed. As mentioned above, the output power of a gas turbine will affect the gas pressure while the gas pressure fluctuation of the NG network will also affect the output power of gas turbine. Thus, the impact of the natural gas network on power networks should not be neglected. In microgrids, the HGES is widely used, such as CHP. Due to the fast dynamics, the power system (DAE) has to be simulated in a short time step. Considering time and space dependent characteristics of the gas network models (PDE system), the pipelines are usually simulated based on the finite difference scheme [24], which separates the pipeline into subsections. In order to get a consistent numerical scheme, the time step and space step should satisfy a link (c is the isothermal speed of sound (m/s)) [27]. The gas system time step is decided based on the gas system response time characteristics. If the HGES is considered in one time scale, the time step has to be very small, which is not needed for gas system. Also, the space step has to be very small. Then the pipelines will be divided into many small subsections, which will make the system dimension too big for the solver and cause convergence and precision problems to the simulation. Therefore, this paper propose a two time-scale method to handle the PDE-DAE system time domain problem by converting the original model into one DAE system based on their time scale: (11) where and
are slow dynamic state variables, are fast dynamic state variables. For
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the SIMT, includes state variables of the speed governor, the temperature control system, the fuel control system and the gas turbine. represents state variables of permanent magnet synchronous motor (PMSM) and the control system of the converters. For the SPMT, includes state variables of the speed governor, the temperature control system, the fuel control system and the gas turbine. represents the generator state variables. Based on the singular perturbation theory, this two-time scale method can be expressed as the general form: (12) where is a small non-negative scalar. 1) Slow System: The slow system, ignoring the fast dynamics, is formally obtained by setting in (12): (13) The algebraic equation contains the fast dynamics which satisfy the set . 2) Fast System: In order to solve , we define the fast time scale . In the new time-scale, (12) is transformed into (14) is obtained According to [28], the fast system by formally setting in (14). In the fast system, variable is frozen. Consequently, (14) can be treated as a family of boundary layer systems (BLS): (15) is frozen and considered constant values. where Since power system dynamics are much faster than NG network dynamics, are understood to change instantaneously with variations of the states. The proposed two-time scale method (see Fig. 7) is composed of the following steps: Step 1) Solve the electric network to obtain the power flow solution and use it as an initial guess of power system states and calculate the gas powered unit consumption. Step 2) Compute steady state values of the NG network , based on the gas consumption of the gas-powered unit . Present an initial guess of the MT inlet pressure . Step 3) Divide state variables into two groups based on their time scale and obtain initial states of the whole system . Step 4) Solve (15) to obtain and , with the variable steps until simulation time . Step 5) Solve (13) to update the slow variables and , and .
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TABLE II INITIAL STATES OF THE HGES
Fig. 8. Matlab/Simulink implementation of an HGES with a SIMT.
Fig. 9. Matlab/Simulink implementation of an HGES with a SPMT.
TABLE I PIPELINE NETWORK DATA
Step 6) Exchange data between the fast solvers and slow solvers, and return to Step 4, until . IV. NUMERICAL STUDIES In this paper, we focus on simulating an HGES system with MT and NG supply system in MATLAB/Simulink. Both SIMT and SPMT are studied, as shown in Figs. 8 and 9. Based on the two MT models, the interaction between the NG and electric network is investigated in the studied HGES model. The NG network topology parameters are estimated based on the NG network supplying gas to the CHP experimental platform under construction at Tianjin University (TU) in China. The pressure of gas well in the NG network shown in Fig. 6 is assumed to be 5kPa based on the gas utility pressure connected to Tianjin University. The TU natural gas system (node 1) that supply NG to the microturbine (node 3) at TU smart grid laboratory and the regular gas load (node 3) at the restaurant besides the laboratory. The pipeline data is shown in the Table I. The altitude and temperature difference in the small-scale low pressure network are ignored in this paper. Considering the slow variation speed of temperature compared with gas and electricity, the environment temperature assumed to be constant at 15 in the whole
simulation process.2 The NG is composed of 90% methane and 10% ethane and the lower heating value (LHV) is used in the fuel consumption computation.3 The power is converted into the volume flow of the NG by dividing the LHV. Considering the complexity of the start-up process, the MT speed is assumed to be between 95%–107% of the rated value, the start-up process of the HGES is neglected. Besides, MTs in this paper are operated in PQ control mode. in the both SIMT and SPMT are set equal to zero in the whole simulation process. The initial states of HGES are obtained based on the power flow and the steady state natural gas flow computation, as shown in Table II. For the two-time scale method, the simulation step size are chosen as and , respectively, and . A. Comparisons Between the Improved MT Model and the Original MT Model In order to ensure the accuracy of the improved models, electric characteristics of the original models and the improved models were compared when the electric network was not impacted by the natural gas network. The electric power variation of the HGES with the SIMT and the SPMT are shown in Figs. 10–12. Due to the harmonics caused by electronic devices (the rectifier and the inverter) in the SIMT as shown in Fig. 8, there are some noises in Figs. 10, 11, 16, and 18. The results show that the improved model can be used to replace the original model in the normal state without the impact of natural gas network.4 In the next cases, we will show the interactions between the two networks based on the improved models. B. Impact of the Electrical Load Changes on the Natural Gas Supply Network Some existing MT models can obtain the NG gas consumption of the MT, but only the volume of the gas are given which is not suitable for NG network simulation [23]. The inlet pressure 2The gas in the pipeline is in close contact with the wall of the pipelines and the gas temperature in the pipelines can be approximated by the temperature in the external environment considering the heat transfer between the gas and its surroundings. The thermal system will be taken into consideration for the long term analysis in future work. 3The reason for this assumption is that natural gas is mixtures of different types of alkanes. The composition of alkanes depends on gas wells. Methane is the main component of the natural gas (87.0%–97%) and ethane is the second higher amount of components. Thus, the natural gas is approximated as mixtures of 90% methane and 10% ethane. 4Due to the initialization process difference, the green line and the red line are not completely overlap.
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Fig. 13. Pressure variation of pipeline connected to the SIMT. Fig. 10. DC link voltage of the two SIMT models.
Fig. 11. Active output power of the two SIMT models.
Fig. 14. Pressure variation of pipeline connected to the SPMT.
used for the two MT, there are some pressure differences between Figs. 13 and 14. C. Impact of the Natural Gas Load Variation on the Electric Network
Fig. 12. Active output power of the two SPMT models.
of the MT can be obtained by the improved models. The electric power variation of the HGES with the SIMT and the SPMT are shown in Figs. 11 and 12. As depicted in Figs. 13 and 14, the electric output variation of the MTs have obvious effects on the NG network. Therefore, the proposed MT models are important for capturing the interaction between the two networks. Because different models (both prime mover and electric generator) are
The impact of the NG network on the electric network has also seldom been discussed in traditional MT models. In this case, we will show how an NG load variation affects the electric network through the two improved MT models. 1) SIMT: At 55 s, the regular NG load is increased by decreasing the pipeline outlet pressure, and the MT inlet pressure drops, as shown in Fig. 15. As illustrated in Fig. 16, the power fluctuation range had no obvious variation, but (MT’s rotational speed) and (DC link voltage of the SIMT) change evidently. The NG pressure disturbance was isolated from the electric network by the converter system. It shows that the HGES with the SIMT is a weakly coupled system. Also, it can be observed from Figs. 17 and 18 that the fluctuation range of and is larger when the inlet pressure increases at 55 s compared with when the inlet pressure decreases at 95 s, although the amplitude of the pressure rise is smaller than the amplitude of the pressure drop. This is because the machine side controller is used to control the DC link voltage. The machine side commanded voltage reference goes below its
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Fig. 15. Node pressure of the NG network connected to the SIMT.
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Fig. 18. DC link voltage variation for the SIMT.
Fig. 16. Active power variation of the SIMT.
Fig. 19. Machine side converter voltage reference command.
Fig. 15 and the rotational speed of the SIMT changes much faster than the SPMT as shown in Figs. 17 and 21. Also, the output power fluctuation range has an evident variation compared with normal operation states, as shown in Fig. 22. The fluctuations in the HGES with SPMT shows that the NG pressure variation is transferred to the electric network easily and the two networks are strongly coupled in this system. Because the energy is easily transferred the NG pressure fluctuation amplitude in this system is smaller the one in the HGES with SIMT, as illustrated in Figs. 15 and 20. Fig. 17. Speed variation of the SIMT.
lower bound at 95 s as shown in Fig. 19. The controller at 95 s is not as effective as the one at 55 s. Thus, has bigger disturbance at 95 s, although the gas pressure variation is smaller. 2) SPMT: The regular gas load increases at 55 s and decreases at 95 s. It can be observed that the pressure fluctuation process in the SPMT inlet as shown in Fig. 20 was shorter and smaller than the SIMT inlet pressure fluctuation process in
V. CONCLUSION This paper investigates the dynamic interaction between the natural gas (NG) network and the electric network in a microgrid. To address this issue, two improved models for the Single-shaft micro turbine (SIMT) and the Split-shaft micro turbine (SPMT) are developed to capture the interactions between the two networks. Transient behaviors of the NG network were also considered in the proposed models. In addition, a two-time scale method was proposed to simulate the interaction between the natural gas and electric networks based on improved MT
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TABLE III SINGLE-SHAFT MT PARAMETERS
Fig. 20. Node pressure of natural gas network connected to the SPMT.
Fig. 21. Speed variation of the SPMT generator.
Fig. 22. Active power variation of the SPMT.
TABLE IV SPLIT-SHAFT MT PARAMETERS
as decoupled networks for small disturbances. On the contrary, the SPMT based HGES is a strongly coupled system and the disturbance in one network will easily impact the other network. As a consequence, the dynamic energy transfer between the two networks after the disturbance will reduce the impact of disturbances on the disturbed system. The model and numerical method developed in this paper can also be used to analyze the interactions between natural gas network and renewable energy sources, such as solar and wind. This will facilitate the study on the interaction mechanism, stability, and coordination control of the hybrid energy system in the microgrid. Although the proposed two time-scale method in this paper is developed based on the HGES in a microgrid, it can also be used to analyze the large-scale integrated model for assessing the dynamic impact of interdependency of electricity and natural gas networks on power system dynamic performance if the following factors are added into the proposed method: 1) more complex pipeline model for temporal-spatial temperature variation in large areas; 2) altitude difference of nodes in natural gas network considering pipeline structure and altitude difference in different area; 3) compressor dynamics that are commonly used in higher pressure gas network. APPENDIX
models. The modeling and performance analysis of the HGES was tested in MATLAB. Based on this study, it can be concluded that the SIMT based HGES is a weakly coupled system and the energy transfer from the disturbed system to the other is mainly absorbed by the DC link of the SIMT. Therefore, the SIMT based HGES can be seen
Table III shows the single-shaft MT parameters, and Table IV lists the split-shaft MT parameters. REFERENCES [1] F. Birol, World Energy Outlook 2010. International Energy Agency, 2010.
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IEEE TRANSACTIONS ON POWER SYSTEMS
[2] H. Jin, H. Hong, and B. Wang et al., “A new principle of synthetic cascade utilization of chemical energy and physical energy,” Sci. ChinaSer. E, vol. 48, no. 2, pp. 163–179, 2005. [3] R. H. Lasseter, A. Akhil, C. Marnay, J. Stephens, J. Dagle, R. Guttromson, A. Meliopoulous, R. Yinger, and J. Eto, “The CERTS microgrid concept,” White paper for Transmission Reliability Program, Office of Power Technologies, U.S. Department of Energy, Apr. 2002. [4] E. Santacana, G. Rackliffe, and L. Tang et al., “Getting smart,” IEEE Power Energy Mag., vol. 8, no. 2, pp. 41–48, 2010. [5] C. Marnay and G. Venkataramanan et al., “Optimal technology selection and operation of microgrids in commercial-building microgrids,” IEEE Trans. Power Syst., vol. 23, no. 3, pp. 975–982, Aug. 2008. [6] P. Kundur, Power System Stability and Control. New York, NY, USA: McGraw-Hill, 1994. [7] S. Mohammad, F. U. Yong, and W. Thomas, “Impact of natural gas infrastructure on electric power systems,” Proc. IEEE, vol. 93, no. 5, pp. 1042–1056, May 2005. [8] L. Tao, M. Eremia, and S. Mohammad, “Inter-dependency of natural gas network and power system security,” IEEE Trans. Power Syst., vol. 23, no. 4, pp. 1817–1824, Nov. 2008. [9] C. Sahin, L. Zuyi, and S. Mohammad et al., “Impact of natural gas system on risk-constrained midterm hydrothermal scheduling,” IEEE Trans. Power Syst., vol. 26, no. 2, pp. 520–531, May 2011. [10] C. Sahin, S. Mohammad, and I. Erkmen, “Generation risk assessment in volatile conditions with wind, hydro, natural gas units,” Appl. Energy, vol. 96, no. 8, pp. 4–11, 2012. [11] B. Marti, “Integrated analysis of energy and transportation systems,” Master’s thesis, ETH Zurich, Zurich, Switzerland, 2006. [12] C. R. Cintra, C. L. T. Borges, and D. M. Falcao, “A simplified operation planning model considering natural gas network and reservoir constraints,” in Proc. 2010 IEEE PES Transmission and Distribution Conf. Expo., New Orleans, LA, USA, pp. 1–7. [13] C. Modassar, J. Nick, and S. Goran, “Multi-time period combined gas and electricity network optimization,” Elect. Power Syst. Res., vol. 78, no. 7, pp. 1265–1279, 2008. [14] M. Geidl and G. Andersson, “Optimal power flow of multiple energy carriers,” IEEE Trans. Power Syst., vol. 22, no. 1, pp. 145–155, Feb. 2007. [15] L. Cong, M. Shahidehpour, and J. Wang, “Coordinated scheduling of electricity and natural gas infrastructures with a transient model for natural gas flow,” Chaos: Interdiscipl. J. Nonlin. Sci., vol. 21, no. 2, 2011, 025102. [16] D. N. Gaonkar, R. N. Patel, and G. N. Pillai, “Dynamic model of microturbine generation system for grid connected/islanding operation,” in Proc. IEEE Int. Conf. Industrial Technology, Mumbai, India, pp. 305–310. [17] M. Nagpal, A. Moshref, G. K. Morison, and P. Kundur, “Experience with testing and modeling of gas turbines,” in Proc. IEEE PES Winter Meeting, Columbus, OH, USA, pp. 652–656. [18] A. K. Saha, S. Chowdhury, S. P. Chowdhury, and P. A. Crossley, “Modeling and performance analysis of a microturbine as a distributed energy resource,” IEEE Trans. Energy Convers., vol. 24, no. 2, pp. 529–538, Jun. 2009. [19] W. I. Rowen, “Simplified mathematical representations of heavy-duty gas turbines,” J. Eng. Power, vol. 105, no. 4, pp. 865–869, 1983. [20] North American Electric Reliability Council, Reliability Assessment 2001–2011: The Reliability of Bulk Electric Systems in North America, 2002. [21] L. Ma, “The Research on the operation characteristic of CCHP and MicroGrid composed of CCHP,” Ph.D. dissertation, Dept. Elect. Eng. & Autom., Tianjin Univ., Tianjin, China, 2008. [22] M. Y. El-Sharkh et al., “Dynamic behavior of PEM fuel cell and microturbine power plants,” J. Power Sources, vol. 164, pp. 315–321, 2007. [23] E. Shashi Menon, Gas Pipeline Hydraulics. Boca Raton, FL, USA: CRC Press, 2005. [24] M. Behbahani-Nejad and A. Bagheri, “The accuracy and efficiency of a MATLAB-Simulink library for transient flow simulation of gas pipelines and networks,” J. Petroleum Sci. Eng., vol. 70, pp. 256–265, 2010. [25] C. Soare, Microturbines: Applications for Distributed Energy Systems. Oxford, U.K.: Butterworth-Heinemann, 2007. [26] D. N. Gaonkar and S. Nayak, “Modelling and performance analysis of microturbine based distributed generation system, a review,” in Proc. IEEE Int. Conf. Energy Tech, Case Western Univ. USA, 2011, pp. 1–6. [27] A. Herrán-González, J. M. De La Cruz, B. De Andrés-Toro, and J. L. Risco-Martín, “Modeling and simulation of a gas distribution pipeline network,” Appl. Math. Model., vol. 33, no. 3, pp. 1584–1600, 2009.
[28] L. F. C. Alberto and H. D. Chiang, “Controlling unstable equilibrium point theory for stability assessment of two-time scale power system models,” in Proc. 2008 IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, 2008, pp. 1–9. [29] S. K. Yee, J. V. Milanovic, and F. Michael Hughes, “Overview and comparative analysis of gas turbine models for system stability studies,” IEEE Trans. Power Syst., vol. 23, no. 1, pp. 108–118, Feb. 2008. X. Xu (S’13) received the B.Sc. degree in electrical engineering and automation from Tianjin University, Tianjin, China. He is currently pursuing the Ph.D. degree in the Electrical Engineering Department, Tianjin University. His research interests include modeling and optimization of hybrid energy system.
Hongjie Jia (M’04) received the Ph.D. degree in electrical engineering from Tianjin University, Tianjin, China, in 2001. He became an Associate Professor at Tianjin University in 2002, and was promoted as Professor in 2006. His research interests include power stability analysis and control, distribution network planning and automation, and smart grids.
H.-D. Chiang (F’97) received the Ph.D. degree in electrical engineering and computer sciences from the University of California at Berkeley, CA, USA, in 1986. He is currently a Professor of electrical and computer engineering at Cornell University, Ithaca, NY, USA. His research and development interests include theoretical developments and practical applications of nonlinear system theory, computation, and application to electrical circuits, signals, systems, and medical images.
D. C. Yu (M’84) received the Ph.D. degree in electrical engineering from University of Oklahoma, Norman, OK, USA, in 1983. Currently, he is a full Professor in the Department of Electrical Engineering and Computer Science at the University of Wisconsin-Milwaukee (on leave), Milwaukee, WI, USA, as well as an oversea professor in the School of Electrical Engineering at the Chongqing University in China. His research interests include distribution system analysis and microgrid analysis.
D. Wang (M’11) received the Ph.D. degree in power system and its automation from Tianjin University, Tianjin, China, in 2009. Now he is a postdoctoral fellow at Tianjin University. His research currently focuses on smart grid technology implementation in power system ancillary service design, demand-side management, and large-scale renewable resources integration.
