POWER FLOW LIMITS AND SYSTEM CONSIDERATIONS

Generally, this section considers methods to improve the thermal capacity, and therefore the rating, of under-ground cable systems. However, transmission circuits may be limited by factors external to the cable circuit being considered. Specifically, system considerations may not allow a cable circuit to be fully loaded to its thermal capacity. This section describes these factors.

3.3.1 Thermal, Stability, and Surge Impedance Loading Limits

Transmission circuits, in general, may be constrained based upon one of three limits—thermal, stability, and surge impedance loading—each of which is summarized in the sections that follow.

Thermal Limits

All transmission cables are limited by thermal consider-ations. “Weak link” analysis applies to underground cable ratings where the section of cable that has the worst thermal conditions limits the overall circuit capacity. The causes of these thermal limits will be dis-cussed in more detail in Section 3.4.5. Sections of the

route that result in the cable having a higher operating temperature for a given load condition will limit the overall line capacity. These limits may result from greater soil thermal resistivity, deeper burial depth, higher ambient soil temperature, or possibly mutual heating from multiple cables in the same trench or other external heat sources. Conceivably, conditions along a few meters of cable may limit the rating for several kilo-meters of an underground line.

Cables also have much higher charging current per unit length as compared to overhead lines, and the charging current must pass through the conductor. Although the cable charging current is 90° out of phase from the cur-rent for real power transfer, it significantly reduces the amount of real power that may flow through the cable conductor for some underground lines. The cable charg-ing current per unit length is given by Equation 3.3-1.

3.3-1

Where:

f is the power frequency.

C is the capacitance in Farads per meter.

E₀ is the line-to-ground voltage.

ε is the dielectric constant.

The natural log term contains the insulation and con-ductor shield diameters.

In determining the allowable real power transfer for a cable circuit, the square of the capacitive current (leads the real current by 90°) is subtracted from the square of the maximum allowable current (e.g., the normal rating or “ampacity”), as described in Equation 3.3-2.

3.3-2

Cable circuits are always limited by thermal constraints, which is generally consistent with overhead lines that are less than 80 km (50 miles) in length. Although eco-nomic considerations constrain the lengths for under-ground cables, the maximum length ac cable circuits between shunt compensation reactors are technically limited by the charging current. The charging current increases proportionally with length and represents actual amperes that flow through the cable.

Figure 3.3-1 shows the magnitude of the charging cur-rent for cable circuits with the charging from one end and from both ends of the line.

]

As the length of the underground line is increased, a point is reached where the total charging current equals the cable ampacity. This occurs at what is called the

“critical length” of the cables, where no real power may be transferred without overloading the cable circuit. The critical length can be calculated from Equation 3.3-3.

3.3-3

Where:

INormal is equal to the normal ampacity.

ICharging is equal to the charging current per meter.

It is obvious that the maximum feasible line length must be significantly less than the critical length in order to transmit reasonable amounts of real power. However, the concept of critical line length quantifies the absolute maximum lengths between shunt compensation that can be achieved for different types of underground cables.

Table 3.3-1 shows critical line lengths based on typical insulation thicknesses and parameters.

In real situations, economic considerations, rather than the critical length considerations, limit the construction length for most land cables. However, charging current limitations have been a significant factor for long sub-marine cable circuits. In these cases, owners sometimes consider using HVDC cables where there are only

resis-tive losses to consider and the cost of the HVDC valves and convertor stations is more easily justified relative to the cable cost. In some other cases, shunt compensation reactors were installed on intermediate islands.

Note that reactive compensation can mitigate cable charging current effects on the system to which the cables are connected, but the charging current still flows in the cables, potentially limiting the real power transfer.

It is common practice to install shunt reactors at one or both ends of relatively long underground transmission lines to mitigate the effects of cable-generated charging current on the power system. The amount of shunt com-pensation depends upon the ability of the power system to “absorb” the reactive MVARs generated by the cables during light load conditions. The amount of leading reactive MVARs that generation units can absorb is generally less that the amount of lagging MVARs that they can generate. During normal and peak load condi-tions, the leading MVARs generated by the cable capac-itance are typically offset by lagging power factor loads.

Consequently, high-voltage load-switching devices (i.e., circuit switchers) are typically used to disconnect shunt compensation reactors during periods of relatively high load. The reactors are then connected to the power sys-tem during periods of light load. The reduction of trans-mission system losses is another consideration in sizing shunt compensation reactors for underground

transmis-Figure 3.3-1 Charging current magnitude profile.

[Meters]

Length Critical

arg ing Ch

Normal

I

= I

Table 3.3-1 Critical Lengths for Underground Cable Circuits with Typical Insulation Thicknesses^a

a. Assuming 3158 kcmil (1600 mm²) segmental copper con-ductor.

Voltage Kraft Paper

Laminated Paper

Polypropy-lene

Cross-Linked

Polyethyl-ene

Ethylene-

Propylene-Rubber Critical Lengths, miles (km) 69 kV 63 (101) n.a.^b

b. Laminated paper-polypropylene is not generally used for voltages below 161 kV.

163 (262) 120 (193) 115 kV 48 (77) n.a.^b 130 (209) 82 (132) 138 kV 45 (72) n.a.^b 120 (193) 70 (113) 161 kV 42 (67) 52 (84) 114 (183) n.a.^c

c. The relatively high dielectric constant and dissipation factor for EPR insulation limit the application of these cables to 138 kV or below.

230 kV 30 (48) 36 (58) 81 (130) n.a.^c 345 kV-400

kV 20 (32) 29 (47) 53 (85) n.a.^c

500 kV n.a.^d

d. At this voltage, with conventional Kraft paper insula-tion, the dielectric losses are so great that the ampacity is zero.

23 (37) 47 (76) n.a.^c

sion lines. Typically, the shunt reactors are chosen so that the lagging MVARs created by the shunt reactors are between 60% and 100% of the leading MVARs gen-erated by the cable capacitance. In most cases, a series of load flow cases must be performed for light and heavy load conditions to determine the optimum amount and location for cable system shunt compensation.

Voltage Profile and Stability Limits

Some overhead lines may have voltage regulation prob-lems (i.e., excessive voltage drop) when transmitting power to lagging power factor loads. As the line length increases, the voltage on the line tends to drop. This can cause problems in transferring power from the sending end to the receiving end of a line.

The relatively high capacitance of cable circuits may have adverse effects on the voltage profile in the vicinity of underground transmission lines. Since a capacitive current flowing through an inductance causes a voltage rise across the inductor, the charging current created by the capacitance of a cable circuit can cause high system voltage by two related phenomena. The first and most common situation is for the cable charging current to cause voltage rises across the inductive impedances external to the cable circuits. This situation, which is worst during light load conditions, is illustrated in Fig-ure 3.3-2.

In this circuit, the reactances, XL and XT, represent inductive impedances of transmission lines and trans-former impedances between the generator and the cable circuit. Since the voltages at the load must be held near rated voltage, the system voltages rise significantly above the rated voltage as the cable charging current flows through the inductive impedances, XL and XT, to the generation units. During light load conditions (assumed in Figure 3.3-2), this voltage rise may cause voltages above the maximum rated voltage that most power system components are designed for (105%) with-out shunt compensation.

Cable circuits are not generally associated with voltage stability problems because of their capacitive nature—

they are generally shorter as compared to overhead lines, are naturally compensated, and generate voltage-supporting vars.

Surge Impedance Loading (SIL) Limits

Surge impedance loading (SIL) limits involve a greater than allowable phase shift in power frequency from one end of a transmission system to the other. As a result, the two ends of the system cannot remain synchronous, resulting in instability and outages. This system stability consideration is generally an issue on overhead trans-mission lines that are 80-320 km (50-200 miles) in length.

The positive sequence surge impedance, ZS, of a trans-mission line is defined by Equation 3.3-4

3.3-4

where, L and C are the positive sequence series induc-tance and shunt capaciinduc-tance, respectively.

Cables have lower series inductances and much higher shunt capacitances compared to overhead lines. Conse-quentially, cables have very low surge impedance relative to overhead lines. Typical surge impedances for over-head and underground lines are 375 ohms and 30 ohms, respectively.

The SIL limit, based on the line-to-line voltage (V_LL), is defined by Equation 3.3-5

3.3-5

SIL power transfer limits are rarely a problem for underground transmission lines because of their low surge impedance and relatively short lengths.

Figure 3.3-2 Voltage rise due to cable charging current.

C Ohms Z_S = L

MVA Limit

SIL

2

S LL

Z

=V

3.3.2 Load Flow Considerations

Low cable system series impedances, and the resulting unequal distribution of load flow between overhead and underground lines, are important considerations when evaluating the uprating potential on underground cable circuits.

The reactive loading of various transmission lines in a power system is controlled by the magnitude of the volt-ages across the system and can be adjusted by generator excitation and transformer taps. The flow of real power over the lines is a function of the relative voltage angles around the system and the interconnecting impedances.

Unfortunately, the distribution of real power flow is not as easily controlled as reactive power flow because the circuit impedances are fixed in most cases, and it is not economical to control power flows by changing angles at the generation units. Therefore, where transmission line loadings are not approximately equal to the thermal capacities of the circuits, the power transfer cannot be increased once a circuit is loaded to its thermal limit even though the other circuits may be lightly loaded.

Because underground cables have much lower series impedances than overhead lines, a higher portion of power will flow over the underground lines compared to overhead lines in the same area. Figure 3.3-3 shows an extreme situation where an underground cable is con-nected electrically in parallel with an overhead line.

The sending and receiving end phasor voltages are the same for both overhead and underground circuits. Then the power flow between the two buses along the cable and line is defined by Equations 3.3-6 and 3.3-7.

3.3-6

3.3-7

Since the series impedance of cables is typically 25-30%

of length compared to those for overhead lines, the power flow along the cable circuit is greater, perhaps exceeding the ampacity of the cable circuit or resulting in underutilization of the overhead line. While the above example is extreme, cables may be put in parallel with overhead lines indirectly in a conventional power sys-tem. Is some cases, relatively expensive phase shifting transformer must be placed in series with underground cables to more evenly distribute power flows with over-head lines in the same area.

3.3.3 Uprating Hybrid (Underground and Overhead) Circuits

Hybrid transmission circuits contain sections of both overhead lines and underground cables. The reasons for these types of installations are numerous (rights-of-way congestion, available ROW, water crossings, tunnels, air-ports, etc.), but the issues with uprating these types of circuits are complicated by considering all of the equip-ment along the circuit. Overhead lines are typically operating at only 30-40% of their rated capacity, and in hybrid circuits usually have a normal rating that is 40-60% greater than the connected underground sections.

As a result, the cable section is usually studied first from the standpoint of increasing a circuit’s capacity since the circuit will be limited by the section with the lowest rat-ing – often the cable.

From the standpoint of typical design limits, an over-head line usually can obtain 1 ampere of capacity for each kcmil (2 amperes per square millimeter), while a cable will generally have half that capacity. Also, over-head lines do not suffer from mutual heating effects among phases or circuits, but this is a significant consid-eration where cables are installed in the same trench.

Therefore, additional overhead conductors added to increase capacity cannot be equally matched by the same number of underground conductors, since the bur-ied cables will experience a net de-rating from mutual heating.

While overhead lines typically have greater ampacity for normal operating conditions, the large thermal time constant of buried transmission cables – typically 50-150 hours – compared with overhead lines (5-15 min-utes) means that for short-duration emergencies, cables typically have a higher emergency rating. Also, because of the relatively short time constant of overhead lines, the load cycle on the overhead line does not have a sig-nificant impact on the normal or emergency capacity.

However, with buried cables, the long thermal time con-stant has a big impact on ratings. This is factored into daily ratings by considering a 24-hour loss factor (essen-Figure 3.3-3 Simplified power system network with

parallel overhead and underground circuits.

(

)

tially, the daily load factor of the losses). This is dis-cussed in greater detail in Section 3.4.