Chapter 1: Background, Basic Concepts and Models
1.3 Models and Concepts
1.3.2 Induced Power Flow Model
Two Major Layouts in Radial Feeder Systems
As stated in Section 1.2, this thesis studies DG penetration for distribution systems dominated by voltage constraints, which is often decomposed by radial feeder systems. Figure 12 illustrates two different ways to lay out a radial distribution system. Each of the two configurations can be engineered to work in nearly any situation, but neither is always superior to the other in terms of reliability, cost, ease of protection, and service quality in all situations. Most planning engineers have a preference for one or the other. In fact, about of utilities have standardized on the large- trunk design as their recommended guideline while another prefer the multi-branch approach [37, 70, 104].
Figure 12. Two ways of routing a radial feeder to 108 service transformers. “multi-branch” (left) and “large trunk” (right) [70].
For convenience, the rest of the thesis uses the “large trunk” layout in deriving planning scheme for DG penetration. However, it shows, in the meanwhile, the results derived are not limited to this type of layout. Moreover, two assumptions are made to justify the development of the induced power flow model and other results:
Laterals on the feeder are negligible. All parameters of lateral level, such as voltage, current, and power flow, are aggregated to the primary distribution level;
Power Flow Model Induced from
Consider a practical feeder system (shown in Figure 13). Because feeder’s load size is much smaller than DG size, load density is treated with continuous functions, while DG density is treated with discrete functions. (For load, such as medium industry and commercial users, it can be treated the same way as DG.) This is more reasonable than previous studies, which uses continuous functions to model both DG and loads [6, 120, 125-128].
Figure 13. A practical feeder system penetrated with DG and its voltage-effective power flow.
Take load power density at location as and , measured in . The th of DG inserted at location is of capacity and , measured in . Hence, real and reactive power flows , , and are derived as:
Equation 11
∫
∫
Equation 12
∑
∑
Further assume that the feeder’s conductor is uniform and the unit resistance and impendence of the feeder is and , measured in .5
Based on Equation 7 and Equation 10, the voltage profile of the feeder can be calculated as:
Equation 13
∫ ∫
and
Equation 14
∫ ∫
where is the feeder’s primary voltage.
Tools and Implementation Environment
In this thesis, proposed methods and derived results are verified and examined mainly through two software tools. One is MATLAB R2012b, the other is DPlan.
DPlan is geographic based integrated analysis and optimization system for distribution network. It is developed by Instituto de Optimização Aplicada (IOA), Lisbon, Portugal, and is used in Europe. A graphical user interface of DPlan is shown in Figure 14. It runs power flow analysis in voltage and power loss analysis to evaluate and optimize performance for distribution grids.
5
Feeder’s conductor is treated as uniform based on Section 1.2.2, which presents most feeders are of “same” size. The results derived from the assumption, however, can be easily extended to the case where conductors are of difference sizes by changing the resistance and impedance in Equation 13 and Equation 14 as functions of locations on feeder, and .
Chapter 2: Mitigating Voltage Rise in
DG Penetration
Voltage rise is the bottleneck of DG penetration in distribution grids [4, 12, 57, 58]. This chapter gives a deeper view of how DG penetration causes voltage rise and how to prevent this problem in a planning scheme. Results of this chapter serves as tools that can be applied directly in practices. Fast examination of voltage profiles in DG penetration can prevent overvoltage, save ante-post engineering cost and accelerate the progress of DG penetration.
Section 2.1 introduces ways to analyze voltage profiles on feeder systems in an easy and fast manner. It revises the zero-point analysis, which has been conventionally used in determining the possibility of overvoltage occurrence, and points out its inaccuracy. This section further provides a graphical method that visualizes the voltage profile change during DG penetration. An Area
Criterion is proposed on this method as a revision of the zero-point analysis.
Section 2.2 discusses the permissible DG penetration in a distribution grid. Based on the early part of this thesis, it reveals that DG penetration should be defined on the feeder system level, instead of the whole distribution system level. Quantitative analysis is conducted and an analytical expression is derived to determine the DG penetration capacity for any given feeder system. Using this formula, distribution system planners can generate a DG penetration chart, which enables them to examine DG penetration feasibility on spot. In addition, DG penetration capacity is redefined according to the proposed formula.
Section 2.3 reveals six factors that causes voltage rise in DG penetration, including penetrating location, penetrating capacity, penetrating dispersion, feeder’s conductor, load profile and feeder’s primary voltage. Based on these factors, it further discusses methods used in practices to mitigate voltage rise. Two of these methods for voltage rise mitigation, demand response and reconfiguration, are highlighted in Section 2.4 by proposing their new implementation schemes.