Analytic Research Foundations for the Next-Generation Electric Grid (2016) / Chapter Skim
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1 Physical Structure of the Existing Grid and Current Trends
1 Physical Structure of the Existing Grid and Current Trends
Pages 7-31
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From page 7... ...
Economies of scale resulted in most electric energy being supplied by large power plants. Control of the electric grid was centralized through exclusive franchises given to utilities, which in turn had an obligation to serve all existing and future customers.
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From page 8... ...
. So by the 1890s, ac transmission lines operating at tens of kilovolts (kV)
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From page 9... ...
SOURCE: NERC. This information from the North American Electric Reliability Corporation's website is the property of the North American Electric Reliability Corporation and is available at http://www.nerc.com/docs/oc/rs/NERC%20Balancing%20and%20Frequency%20Control%20040520111.pdf.
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From page 10... ...
The first is reliability. By interconnecting hundreds or thousands of large generators in a network of high-voltage transmission lines, the failure of a single generator or transmission line is usually inconsequential.
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Being an ac system, the voltages and currents would actually be varying at close to 60 Hz. But the displayed average power consumed by the load
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From page 12... ...
= P + jQ (5) where the magnitude of S is known as the apparent power, P as the real power, and Q as the reactive power.
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From page 13... ...
The concept of reactive power is quite useful for power system analysis and it is treated in a manner analogous to the real power. It is easy to show that resistors always consume real power, inductors always consume reactive power, and capacitors always generate reactive power.
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From page 14... ...
In order to model the interconnected power network, appropriate models need to be developed for the transmission lines, transformers, generators, and loads. The analysis of a balanced three-phase system can be greatly simplified by using a technique known as per-phase analysis, in which the system is treated as an equivalent single-phase system.
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From page 15... ...
analysis, in which the system values are normalized using base values that depend on a systemwide power base and voltage bases that differ by the turns ratios of the ideal transformers. PU analysis can be used with either single-phase systems or, as presented here, three-phase systems.
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From page 16... ...
bus, in which the voltage magnitude and angle at the generator's bus is specified, and the power flow algorithm determines the generator's real and reactive power output. Power flow equation derivation starts with applying KCL at each bus so that the net current injection into the bus must equal the current going into the network.
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From page 17... ...
. For PV buses the reactive power balance equations are not included since the voltage magnitude at these buses is specified; the reactive power outputs of the PV generators are dependent variables.
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From page 18... ...
The only changes were to the power-flow-dependent variables, including the PQ bus voltage magnitudes, the PV generator reactive power outputs, and the slack bus real and reactive outputs. A single contingency, such as opening the line between buses 2 and 3, also changes the flows throughout the system, albeit with the largest changes usually closest to the contingency.
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From page 19... ...
(11) where g is a vector of algebraic constraints including the real and reactive power balance equations, y is the solution variable vector such as the PQ bus voltage magnitudes and angles, and u is the input parameter vector such as the load real and reactive power values.
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From page 20... ...
. The transmission lines that join two areas are known as tie lines, and the algebraic sum of the real power flow on the tie lines for an area is known as its net interchange, with the usual sign convention that power flow out of an area is defined as positive.
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From page 21... ...
Examples of limits include keeping the transmission line and transformer flows below a specified MVA value and keeping the bus voltage magnitudes within a PU range (e.g., between 0.95 and 1.05 PU)
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From page 22... ...
≤ hmax umin ≤ u ≤ umax The key equality constraints are the power balance equations from the power flow shown in equations (11) , while the key inequality constraints are the need to operate with the branch flows, bus voltage magnitudes, and generator reactive powers within their limits.
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From page 23... ...
A discussion of the currently used algorithms for solving power flow -- CA, OPF, and SE -- is contained in Chapter 4. Day-Ahead Planning and Unit Commitment In order to operate in the steady state, a power system must have sufficient generation available to at least match the total load plus losses.
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From page 24... ...
As illustrated in Figure 1.5, ramping of generation to meet the changing load has long been a part of power system operations. However, with the growth in solar PV generation, ramping is becoming more of an issue as the net load rapidly decreases in the morning as the sun rises and falls in the evening as it sets.
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From page 25... ...
. Traditionally, transient stability solutions involved just a few seconds of simulation looking at "first swing" instability, though now they can run for dozens of seconds, looking at the longer-term behavior of quantities such as frequency and bus voltage magnitudes.
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From page 26... ...
1.19 FIGURE 1.20 Seven-bus system generator torque angles for a bus fault. SOURCE: Courtesy of PowerWorld Corporation.
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From page 27... ...
In addition to generator torque angles, quantities of interest during a transient stability study include the generator speeds, the bus voltage magnitudes, and the bus frequencies. As a large case example, Figure 1.21 shows the generator speeds for an 18,000-bus case with a contingency modeling the opening of two large generators.
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From page 28... ...
In referring back to Figure 1.4, the time scales of transient stability and voltage stability fall between the quasi-steady-state power flow and the faster switching surges, harmonics, and subsynchronous resonance. Like power flow, the assumption is that speed of light effects in the transmission network can be ignored, though this assumption is certainly less valid given that it can take 10 msec for light to transit a 2,000-mile grid, so the coupled algebraic power balance equations assumed in equation (15)
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From page 29... ...
An advantage of this approach is that a portion of a system can be solved in parallel since there is a natural decoupling due to the transmission line propagation delays. However, because of the small time constants, this approach requires large amounts of hardware for studies of even small systems.
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From page 30... ...
Hence the distribution system is now an equal partner with the rest of the grid, with its challenges equally in need of the fundamental research in mathematical and computational sciences being considered in this report. ORGANIZATION OF THE REPORT Chapter 1, "Physical Structure of the Existing Grid and Current Trends," Chapter 2, "Organizations and Markets in the Electric Power Industry," and Chapter 3, "Existing Analytic Methods and Tools," lay out the current structure of the power grid, the economic markets involved in ultra-short-term decision making to long-term planning, and the analytic techniques that are currently used to study the behavior of the grid.
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From page 31... ...
:1387-1401. NERC (North American Electric Reliability Corporation)
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