Expansion of Power System Corridors Using Tier-1 Technique for Reactive Power Compensation

Electrical energy efficiency is of prime importance to industrial and commercial companies operating in today’s competitive markets. Optimum use of power system components is one main concern that needs to be balanced with energy efficiency, for both economic and environmental reasons. Electricity plays a fundamental role in the economic development of any country. Every country seeks to ensure supply of electricity that is affordable, reliable and secure in order to sustain modern ways of living. The availability of electricity greatly facilitates industrialization. This is because, electricity is a convenient way to transport energy in which they are also converted into transmission, distribution, and consumption [1]. Investigations are done in this paper to see how capacitors distributed along the transmission lines can expand the transmission line corridor by the release of embedded transmission capacity.

During the past two decades, the increase in electrical energy demand has presented higher requirements from the power industry. In interconnected power systems, it has become important to fully utilize the existing transmission facilities in preference to building new power plants and transmission lines that are costly to implement and involving long construction times. This necessitated the need for alternative technology through the use of solid state electronic devices with fast response characteristics [2]. The requirement was fuelled by worldwide restructuring of electric utilities, increased environmental and efficiency regulations and difficulty in getting permit and right of ways for the construction of overhead power transmission lines. Different approaches such as reactive power compensation and phase shifting have been applied to increase the capacity, stability and security of the power system. This need in conjunction with the development of semiconductor thyristor switch opened the door for the development of flexible alternating current transmission system (FACTS) controllers [3]. FACTS controllers make it possible to control the voltage magnitude of a bus, active and reactive power flows through transmission line of a system. The MOV has been designed to withstand the energy from external faults; faults appearing outside the series compensated circuit, without by-passing the DCC. The DCC module may be by-passed for any internal fault, (faults in the same circuit where the DCC is located). Each DCC is connected and disconnected from the line by means of two isolating disconnectors and one by-pass disconnector. The by-pass switch is of Sf 6 type, with a spring operating mechanism.
The CLDE consists of a current limiting reactor, a resistor and a varistor in parallel with the reactor. The purpose of the resistor is to add damping to the capacitor discharge current, and thus quickly reduce the voltage across the capacitor after a by-pass operation. The varistor help to avoid fundamental frequency losses in the damping resistor during steady state operation.
The FPD scheme is based on a hermetically sealed and very fast high power switch, which replaces conventional spark gaps. The FPD works in combination with the MOV, and allows by-passing in a very controlled way in order to reduce the energy dissipated in the MOV.

The Mathematical Model of Tier-1 Compensation
Electrical power is transmitted through the transmission line from the sending-end of the line to the receiving-end of the line. This can be analyzed through parameterization and modeling of the transmission line with passive components such as resistors, capacitors and inductors. The quantities of these parameters depend mostly on the line conductors and the physical or geometrical configuration of the lines. These conductors will have certain characteristics such as resistance and reactance both in series (from sending to receiving-ends of the line) and shunts (from the line to ground) associated with them.

Basic principle of power in transmission
Loads are more often expressed in terms of real (watts/KW) and reactive (vars/Kvars) power. It is convenient to deal with transmission line equations for the sending and receiving-end complex power and voltages [8,9].
For a two-bus system shown in Figure 2, the sending and receivingend voltages are represented by the bus voltages while the sending end voltage leads the receiving end voltage by an angle, δ. This angle is called the torque angle. The complex power leaving the receiving end and entering the sending-end of the transmission line can be expressed as Similarly, At , δ β = the maximum power delivered at the load will be; If, , But the resistance R of a transmission line is very small compared to its reactance, so that; Where = + Z R jX and . θ δ = Therefore the receiving-end power (P j ) becomes; For a very small value of δ, cos δ=1 thus; ∆V is called the magnitude of voltage drop across the transmission line. Therefore;

Reactive Power compensation of transmission lines
Equations (8) through (11) indicate that the active and reactive power/current flow can be regulated by controlling the voltages, phase angles and line impedances of the transmission system. It has been shown above that the active power flow will reach the maximum when angle δ is 90 0 .

Series Compensation of A Transmission Line:
A series-connected capacitor adds a voltage in opposition to the transmission line voltage drop, therefore reducing the series line impedance. Figure 3 show a simplified model of a transmission system with series compensation. The voltage magnitude of the sending-end is assumed equal as |V|, and the phase angle between them is δ. The transmission line is assumed lossless and represented by the reactance X L . A control capacitor is series-connected in the transmission line with voltage addition V inj .

The Degree Of Series Compensation (Ks):
The degree of series compensation or percentage compensation (K s ) is used to analyze a transmission line with the required addition of series capacitor. It is defined as the fraction of X c , which refers to the total capacitive reactance of series compensators and X L , which refers to the total inductive reactance of the line, as defined in equation 12; Therefore, the capacitance, C as a portion of the line react   The overall series reactance, X of the transmission line is; Thus the active power transmitted becomes; ( ) The reactive power supplied by the capacitor is calculated as; From the above equation, it can be seen that transmitted active power increases with Ks [10].

Effective line reactance with and without dcc device
Where X eff is the effective reactance of the line.

The power flow equation becomes
Inserting a single series capacitor device on the line as in Figure 4 changes the ABCD parameters and the effective reactance of the line becomes ( Figure 5) As the power flow equation changes to; The ABCD parameters are halved because the DCC is place at exactly midpoint ( Figure 6) to the length of the line hence one DCC device is used.
Inserting several series capacitor devices on the line will change the ABCD parameters hence the more the capacitors on the line are distributed, the better the performance. Figure 6 shows a transmission line with multiple series capacitor devices and equation 21 changes to; The ABCD constants are divided by four ( Figure 6) when the DCC is placed at quarter of the line hence three Capacitors are used and placed at every quarter of the line.

Power flow including dcc in matrix forms
From equation (21), the transfer admittance matrix of the DCC is given by [11]; Equation (23) holds for inductive operation while for capacitive operation, the sign are reversed. The active and reactive power equations at bus j are as in equations (25) and (26)  ( ) In Newton-Raphson solutions, these equations are linearized with respect to the series reactance. For the condition shown in Figure 3 where series reactance regulates the amount of active power flowing from bus i to j at a value P, [11] the set of linearized power equation is,

Bus j Bus i ABCD Constants
Where, ∆ c X ij P is the active power flow mismatch for the series reactance calculated; ∆ c X is the incremental change in series reactance; and is the calculated power given by equation (25). The state variable X c of the DCC controller is updated at the end of each iterative step according to equation (30);

The Standard IEEE 14 Bus Test Systems (Revalidation)
One of the international load flow test systems is the IEEE-14 bus system. Load flow analysis is carried out in IEEE 14 bus test system. Figure 7 show the standard IEEE 14 bus network simulated in Powerworld platform. The run mode of Power world simulator enable the simulation of the existing IEEE 14 bus test system model using N-R iterative method to obtain the bus voltages, phase angles, line losses, real and reactive power flows. The system topology consists of 14 buses, 20 transmission lines or branches, 2 online generators, 3 online synchronous compensators used only for reactive power support, and 11 loads totaling 259 MW and 78.7 Mvar.
The simulated result of the test system in Power world shown in Table 1 gives a very close result when compared with the MATLAB results of Table 2. It was therefore confirmed that the result obtained when DCC is applied on the IEEE 14 bus network using only Power world simulation software due to its flexibility and simplicity.
Using codes written in MATLAB and system information exported from Power world simulator, the standard IEEE 14 bus network is revalidated and reconfirmed.

Simulation result
The revalidated Standard IEEE 14 bus network shows that the total real and reactive power loss of the system are 15.31 MW and 36.77 Mvar respectively with the systems maximum current rating totaling 2948.91 Amps. As a result, the system's maximum MVA loading becomes 696.604 MVA. These results confirmed and agreed with the standard performance of the standard IEEE 14 bus system as shown in Tables 1 and 2 (Power world simulator tool) and Table 2 (MATLAB simulator tool). All bus voltages were also confirmed to fall within the recommended limit (0.9 ≤ V ≤ 1.1 p.u).  To illustrate that an already saturated network can be expanded by the use of capacitors distributed along the lines at strategic places, an existing load of a selected Company in Nigeria was used -the General Steel Mills (GSM), Asaba. The Company's total maximum active and reactive power demand are 17.80 MW and 25.71 Mvar respectively [12]. These loads were added to bus 6 of the standard IEEE 14 bus system which modified the revalidated results of the system. The active and reactive power losses increased from the normal operating performance of the 14 bus standard network to 59.85 MW and 226.84 Mvar respectively. The system's maximum amperage was 5658.287 Amps as all the bus voltages dropped below 0.9 p.u except the slack bus-bus 1 ( Table 4). The MVA maximum loading also increased to 1062.225 MVA (Overloading). For these reasons, it is enough to say       that the modified IEEE 14 bus system got overloaded and cannot accept this extra load (Table 5).

Case 2: Application of tier-1 compensation to the modified standard IEEE 14 bus network
The distributed capacitor technology applied on the transmission lines were used in this case to know how much the lines can be freed of their carriage even when the loads were operating. This was verified by placing capacitors on all the lines (interline action) with degree of compensation Ks allowed to operate by 0.7 or 70% of the original line reactance value ( Table 6). The bus and line results were compared, from which the total active power loss reduced from 59.85 to 17.79 MW (70.28% reduction) while the total reactive power loss reduced from 226.84 to 59.17 Mvar (73.92% reduction). By this margin, the system's MVA loading was released from 1062.225 to 744.193 MVA (29.94% released) (Figure 8). This is resulted from the reduction in system's current from 5658.287 to 3212.958 Amps (43.94% reduction) with all lines still operating within their normal limits. Bus voltages were also restored appreciably (Table 7). The percentage reduction in MVA loading and savings determines how much the systems corridors have been expanded by the release of the embedded system capacity on which the system can be available for extra loadings (

Conclusion
The use of DCC creates more loops in the transmission system by providing more active power routes without having to build new generating stations, new transmission stations or dealing with rightof-way issues. Application of the tier-1 compensation was able to accommodate the added load in the existing 14 bus system by releasing the system up to 29.94% MVAof its overloading which remarkably reduced the system's active losses by 70.28% and reactive losses by 73.92%. Recommendations are made to simultaneously apply also the teir-2 and 3 to the network in other to ensure maximum restoration of the power (up to 100% restoration). This efficient control method can salvage the power system from total collapse and as well serves as a quick way to respond to consumers power satisfaction quest.