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Challenges in Simulation and Design of µµµµGrids

A. P. Sakis Meliopoulos School of Electrical and Computer Engineering

Georgia Institute of Technology Atlanta, GA 30332-0250

Abstract: This paper discusses a number of issues associated with simulation and design of µGrids, i.e. distribution systems with distributed energy sources. Basically, such a system has sources with or without energy storage. The sources interface with the system via inverters. The overall system operates under non-balanced conditions. Since energy sources may be three phase or single phase, customers can be three phase of single phase, and the system design may involve three-wire, four-wire and five-wire circuits, the simulation and design of the system poses a number of challenges. In this paper we try to address the design issues by proper analysis software by which many problems can be studied prior to actual system experimentation. Introduction The concept of the µGrid was introduced by the DoE as a distribution system with distributed energy sources (microturbines, fuel cells, photovoltaics, etc.). The µGrid may be connected to a 35kV or 25kV or 13.8kV distribution system. It includes the step-down transformers and the 480V/208V system. The 480V or 208V system (secondary distribution system) may be radial or networked. Therefore the topology of the µGrid comprises the step down transformers, the 480V or 208V circuits – radial or networked, the electric loads and micro-sources (Distributed Energy Sources) that may be distributed along the 480V or the 208V system. A pictorial view of the single line diagram of a radial system is illustrated in Figure 1. A pictorial view of the single line diagram of a networked system is illustrated in Figure 2. The design of this system may include three-wire, four-wire and or five-wire circuits in accordance to the National Electrical Code (NEC). The operation of this system in general will be characterized with unbalance and by the fact that most of the distributed resources are inertialess (because they are interfaced to the system via inverters and typically without

available storage). At the present time we know very little about the performance of such a system. Research projects are underway to quantify the performance of such systems and to utilize the benefits of the µGrid.

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MicroGrid - Conceptual A µGrid may operate in non-autonomous manner, if it is interconnected to the main power grid or autonomous, if it is isolated from the power grid. A desirable future is to have energy sources that include protection and control in such a way that they can be used in a “plug and play” manner. µGrids have the

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potential of providing additional benefits, such as improved power quality and reliability and cogeneration options. However, the operation, control and protection of the µGrid is a challenging problem. Especially challenging is the problem of operation and control of an autonomous micro grid. A partial list of challenging simulation and design issues is given below: Safety Protection Unbalance/Asymmetry Plug and Play Operation of DERs Voltage Profile Control Power Quality Stray Voltages and Currents Electromagnetic Compatibility Issues Non-autonomous/Autonomous Operation A subset of above issues is discussed in the context of requirements for modeling and analysis of associated problems. Safety A µGrid is subject to the same safety concerns as any utility system. Any faults on the utility side may generate substantially high ground potential rise at the energy source location, even if the source may operate at low voltage (208 or 480 volts). This means that distributed energy sources must be grounded with the same rules and standards as conventional systems to achieve the same level of safety. Analysis and design tools for safety assessment should explicitly model the grounding and bonding of the µGrid circuits. Power Quality A µGrid is subject to the same voltage distortion, sags, swells, outages and imbalances from a variety of events such as lightning, switching, power faults, feeder energization, inrush currents, motor starts, load imbalance, harmonics, resonance, etc. The power quality can be measured with voltage sags and swells, unbalance in the phases and harmonics. We discuss these issues and conclude with the observation that traditional power system analysis methods are not suitable to analyze these events in a µGrid.

Voltage Sags and Swells: The level of the voltage swells and sags depends on grounding system design.

This fact had been recognized long time ago. For example, an IEEE committee has drafted the nomogram of Figure 3 using an approximate model based on sequence parameters representation of the power system. This nomogram provides the percent voltage (voltage swell) on the unfaulted phases for a single line to ground fault at the same location as a function of the zero sequence resistance (R0), zero sequence reactance (X0) and positive sequence reactance (X1). Note that the zero sequence components depend on the design of the grounding system and the voltage swells depend on the zero sequence impedance. A power system model based on explicit representation of neutrals, ground wires and groundings provides the exact voltage swells and voltage sags for any fault at any location and for any design system in terms of neutral size, grounding design, etc. As an example, Figure 4 illustrates the voltage swells and sags along a circuit during a single line to ground fault. Note that the two unfaulted phases experience a different level of voltage sags and swells due to the asymmetry of the system. Note that the model reveals that the level of voltage swells and sags is dependent of grounding system arrangements and impedances. The data shown in Figure 3 do not capture this dependency.

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Figure 4. Distribution of Voltage Swells and

Sags for a Specific Fault Condition and Circuit Design

Asymmetry/Unbalance: µGrids are not symmetric and they are loaded with many single phase loads. Both factors generate unbalanced conditions that can be accentuated with the interaction of dynamic loads such as induction motors. These unbalances can be controlled by appropriate grounding of circuits, use of transformers, placing neutral in symmetric locations with multi-grounds, increasing the size of the neutrals, use of zig-zag transformers, decreasing the impedance of the grounds, etc. Again, to model these effects, the analysis tool must model the system with its three phases, the neutral conductors, the ground conductors and the groundings. As an example, Figure 5 illustrates an example system that consists of a small section of a typical µGrid with two induction motor loads. One induction motor is directly connected to the distribution system via a cable circuit and the other is connected to the distribution system via a delta-wye connected transformer, solidly grounded on the wye side. This induction motor operates near balanced conditions. The other induction motor, however, is experiencing a rather substantial unbalance as it is shown in Figure 6 leading to an uneven loading of the three phases.

Figure 5. Example Distribution System for Unbalance Studies

Figure 6. Typical Results of Unbalance and Effects on Induction Motors Harmonic Resonance A similar issue arises from resonance in the system. As an example Figure 7 illustrates the resonance analysis of a simplified µGrid. One can observe the multiple resonance conditions even for this very simple system. For accurate description of the resonance frequencies and their Q, the model of the µGrid should again be three-phase with explicit modeling of all factors affecting this analysis, i.e. configuration of capacitor banks, grounding of capacitor banks, transformers, power lines, etc.

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System Asymmetry and Imbalance Example

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Stray Voltages and Currents A µGrid, by virtue of its imbalance, is subject to stray voltages and currents. The µGrid can be designed with a “common neutral”, i.e. a neutral that is grounded in more than two locations. In this case, the unbalance current will split between the neutral and the ground conductors and earth, thus generating stray voltages and currents. Most of the times, stray voltages and currents are harmless. However, the µGrid is very close to the end user and therefore the exposure to humans is quite high. Analysis of the problem requires explicit modeling of the grounding system and grounding conductors together with the phase conductors and neutrals. This is a challenging analysis problem that is not addressed by conventional analysis methods. Electromagnetic Compatibility Issues µGrids are very close to end users who use more and more sensitive electronic devices that may be

susceptible to E/M fields. For example, electromagnetic fields may cause flickering of CRT displays, interfere with the operation of pacemakers, affect the current distribution in other circuits causing local overheating, etc. These issues can be addressed as pure engineering problems. Of course there is the related issue of health effects from E/M fields that is quite controversial. The IEEE has taken the position of “prudent avoidance” of electromagnetic fields. Any electric current carrying circuit will generate a magnetic and electric field around it. The design and arrangement of circuits does affect the level of E/M fields. The concept of the µGrid offers an opportunity to rethink these issues and provide good engineering practices. Analysis methods that are capable of accurately addressing these issues are needed. Such a model has been developed and few examples are provided below. Specifically, a simplified set of µGrid circuits is illustrated in Figure 8. The system consists of two identical 208 V (line to Line) circuits. One circuit is enclosed in aluminum conduit and the other in steel conduit of same nominal diameter. Figures 9 and 10 illustrate the magnetic field around each one of the circuits at the same distance from the center of the circuit. Note that the magnetic field around the circuit enclosed in steel conduit is much lower (peak value of 76 miligauss) than the magnetic field around the circuit enclosed in the aluminum conduit (peak value of 365 miligauss). The availability of these analysis methods will provide the proper tools to investigate electromagnetic compatibility issues.

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Proposed Model to Meet Challenge The described problems and other challenges that the analysis and design of mGrids is facing can be met with new approaches for electric power system modeling and simulation. Such an effort is underway. This section describes the approach. The results and examples shown in previous sections have been generated with the method to be described here. The proposed method has the capability to perform steady state (frequency domain) analysis and well as time domain analysis. These two analysis methods are based on a quadratized model of all power system components (with explicit representation of neutrals, ground conductors and grounds) and use Newton’s

method to obtain the network solution. A brief description of the method (both frequency domain and time domain) is presented first. The description is concise and with minimal mathematics. The reader is referred to references 6 and 7 for additional details. Time Domain Analysis Any power system device is described with a set of algebraic-differential-integral equations. These equations are obtained directly from the physical construction of the device. It is always possible to cast these equations in the form of a set of differential equations in terms of the device terminal currents, terminal voltages, additional (internal) state variables and a set of device independent controls, if present. In general, these equations form a consistent set of equations, i.e. the number of equations equals the number of state variables. The device equations may contain linear and nonlinear terms. It is always possible to quadratize these equations, i.e. to convert them into a set of quadratic equations by introducing a series of intermediate variables and expressing the nonlinear components in terms of a series of quadratic terms. The resulting equations are integrated using a suitable numerical integration method. Assuming an integration time step h, the result of the integration is given with a second order equation. We refer to these equations as the algebraic companion form (ACF). Note that this procedure is quite similar to the procedure of the EMTP (Electromagnetic Transients Program) except that the resistive companion form of devices has been replaced with the algebraic companion form. The network solution is obtained by application of Kirchoff’s current law at each node of the system, in the same way as in the EMTP program. The difference is that since we are now using the ACF (Algebraic Companion Form), the resulting network equations are a set of equations of maximum order 2 (quadratic equations). These equations are solved using Newton’s method. Since the equations are quadratic, Newton’s method is very efficient.

Frequency Domain Analysis The frequency domain analysis is also based on the quadratized equations of a device. Assuming that the

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device operates under steady state (single frequency) conditions, the differential quadratized device equations are transformed into a set of quadratized equations in complex variables. The solution method proceeds in the same manner as the time domain solution. Specifically, application of Kirchoff’s current law at each node of the system, results in elimination of the currents and a set of network equations which are at maximum of order 2 (quadratic) in terms of a set of complex state variables. The set of equations is consistent, i.e the number of equations is equal to the number of state variables. These equations are solved using Newton’s method, which is very well suitable for quadratic equations. Summary and Conclusions This paper has presented a summary of challenging analysis and design issues associated with µGrids. The examples illustrate the need for analysis methods that meet the following requirements:

1. Three phase analysis 2. Explicit modeling of grounding and bonding

of the system, i.e. modeling of 3-wire, 4-wire and 5-wire systems, and

3. Methods for the calculation of electromagnetic fields around the circuits of a mGrid

Traditional power system analysis methods cannot provide tools that meet the challenges of the µGrid. New methods and analysis software are needed.

References 1. Beides, H., Meliopoulos, A. P. and Zhang, F.

"Modeling and Analysis of Power System Under Periodic Steady State Controls", IEEE 35th Midwest Symposium on Circuit and Systems

2. IEEE Std 141-1986, IEEE Recommended Practice for Electric Power Distribution for Industrial Plants.

3. IEEE Std 1159-1995, IEEE Recommended Practice for Monitoring Electric Power Quality.

4. IEEE Std 1250-1995, IEEE Guide for Service to Equipment Sensitive to Momentary Voltage Disturbances.

5. ANSI/IEEE Std 519-1981, IEEE Guide for Harmonic Control and Reactive Compensation of Static Power Converters.

6. A. P. Sakis Meliopoulos and George J. Cokkinides, ‘A Virtual Environment for Protective Relaying Evaluation and Testing’, Proceedings of the 34st Annual Hawaii International Conference on System Sciences, p. 44 (pp. 1-6), Wailea, Maui, Hawaii, January 3-6, 2001.

7. E. Solodovnik, George J. Cokkinides, Roger Dougal and A. P. Sakis Meliopoulos, “Nonlinear Power System Component Modeling Using Symbolically Assisted Computations”, Proceedings of the 2001 IEEE/PES Summer Meeting, Vancouver, BC, CN, July 15-19, 2001.

ACKNOWLEDGEMENTS The work reported in this paper has been partially supported by the ONR Grant No. N00014-96-1-0926 and NSF/PSERC/CERTS project E21-F96. This support is gratefully acknowledged. Biographies A. P. Sakis Meliopoulos (M ’76, SM ’83, F ’93) was born in Katerini, Greece, in 1949. He received the M.E. and EE diploma from the National Technical University of Athens, Greece, in 1972 and the M.S.E.E. and PH.D. degrees from the Georgia Institute of Technology in 1974 and 1976, respectively. In 1971, he worked for Western Electric in Atlanta, Georgia. In 1976 he joined the Faculty of Electrical Engineering, Georgia Institute of Technology, where he is presently a professor. He is active in teaching and research in the general modeling, analysis, and control of power systems. He has made significant contributions to power system grounding, harmonics, and reliability assessment of power systems. He is the author of the books, Power Systems Grounding and Transients, Marcel Dekker, June 1988, Lightning and Overvoltage Protection, Section 27, Standard Handbook for Electrical Engineers, McGraw Hill, 1993, and the monograph, Numerical Solution Methods of Algebraic Equations, EPRI monograph series. Dr. Meliopoulos is a member of the Hellenic Society of Professional Engineering and the Sigma Xi.

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