Dynamic stability of wind farm multi-machine power system

Abstract

Since it is difficult to store electrical energy, production, and consumption must be in equilibrium under constant voltage and frequency. The producers, the receivers, and the electrical networks that connect them, have mechanical and electrical inertias which disturb this balance. Faced with a variation in power, the electrical system, after oscillations, returns to a stable state. In some cases, the oscillatory regime may diverge. Studies are being carried out to remedy this problem and ensure the stability of the electricity network. This manuscript focuses on FACTS regulation which helps electrical systems, subjected to strong disturbances, to maintain their stability. Magnetic Energy Storage Superconductor (SMES) contains a short-circuited superconducting coil on itself, which injects or absorbs active and reactive power into the system, thereby improving the stability of electrical systems.

Keywords

SMES dynamic stability multi machine power systems short circuit

Introduction

Few direct electrical energy systems are used in energy storage like SMES (Superconducting Magnetic Energy Storage). This latter is used for flexible AC transmission systems (Facts) or uninterruptible power supplies (UPS) (Tixador et al., 2005). Superconducting magnetic energy storage is a system that stores energy in magnetic form by passing a current through a superconductor (Sutanto and Cheng, 2009). The storage of superconducting magnetic energy (SMES) is considered as a means of charge compensation of the storage device. It is capable of simultaneously providing or absorbing active and reactive power. It is also used for network stabilization. The applications of such a system have been developed by many researchers (Dechanupaprittha et al., 2005).

The remaining of the paper is organized as follows: Section “Description and basic principle of SMES” and Section “Description and basic principle of SSSC” configure the description and the basic principle of SMES and SSSC respectively. In Section “Description of the systems studied,” a detailed description of the studied power systems is presented. Section “Integration of the wind farm into the electricity system” is designed to the integration of the wind farm into the electricity system, and the analysis of the results is interpreted in Section “Simulation Results.” Section “Conclusion” closes the paper.

Description and basic principle of SMES

SMESs consist of a superconducting coil maintained at a very low temperature by a cryostat containing liquid helium or liquid nitrogen. In order to reduce energy losses, a switch is used when the coil is stopped (Mohd et al,. 2010). The operational superconducting coil, charged from the power supply, is connected to the grid via a power conversion system consisting of a rectifier and an inverter. As soon as it is charged, current is conducted through the superconducting coil with virtually no loss (Sathans and Swarup, 2011). The energy stored in the coil is given by equation (1) below:

E_{smes} = \frac{{LI}_{smes}^{2}}{2}

(1)

L: Inductance of the superconducting coil

I: Current through the coil (Jin et al., 2007).

By assuming that the SMES discharges with constant power P₀ following a time ts, energy in the coil E(t) with t < ts is given by equation (2) below:

E (t) = E_{smes} - P_{ot}

(2)

The constituents of SMES are displayed in Figure 1 underneath.

Figure 1.

Constituents of a SMES system.

The SMES is modeled by a transfer function of the first order with a time constant T_sm = 0.03 seconds and gain K_SMES = 10,000 given in Figure 2 (Vijaya et al., 2010).

Figure 2.

Control schemes of SMES.

Description and basic principle of SSSC

As a result of the development of power electronics, Flexible AC Transmission System Controllers (FACTS) are used in power systems. The unique property of FACTS to control the state of the network in a very fast time is beneficial for improving the stability of the system. The Serial Synchronous Static Compensator (SSSC) is an important member of the FACTS family, installed in series in transmission lines (Allaoui et al., 2002, 2006, 2007; Bouhamida et al., 2009; Denaï and Allaoui, 2002; Sidhartha, 2010).

Its basic principle is illustrated using the simple two-bus system according to the current and voltage phasor diagram shown in Figure 3.

Figure 3.

Simple two-bus power system and phasor diagram.

The active power flow among two buses is given in equation (3):

P_{12} = \frac{U_{1} U_{2}}{X_{L}} \sin δ

(3)

Where:

P ₁₂: active power flow between the two buses (Bus 1 and Bus 2)

U ₁: magnitude of voltage at Bus 1

U2: magnitude of voltage at Bus 2

δ: phase angle difference between two buses

X _L: transmission line reactance

The SSSC accomplishes the role of controlled voltage source when it is coupled in series to the transmission line. Figure 4 presents a single line diagram and a phasor diagram of a transmission line connected to series compensated controllable voltage source.

Figure 4.

Two-bus systems with the controllable voltage source.

The active power flow between two buses of the compensated transmission line injected by the quadrature voltage U_q (Sidhartha and Padhy, 2007) is definite in equation (4):

P_{12} = \frac{U_{1} U_{2}}{X_{L}} \sin δ + \frac{U_{1} U_{q}}{W X_{L}} \cos (\frac{δ}{2})

(4)

The single-line block diagram of control system of SSSC is shown in Figure 5.

Figure 5.

Single line diagram of the control system of SSSC.

The control system includes:

A phase locked loop (PLL): It is synchronized with the direct module of current I. The direct axis (Vd or Id) and quadrature (Vq or Iq) components of the three-phase alternating voltages and currents are calculated by the output of the PLL.

Measuring systems: Used to measure the direct voltage Vdc, and the components V1q and V2q of the direct alternating voltages V1 and V2.

AC and DC voltage regulators: They calculate the two components of the converter voltage (Vdcnv and Vqcnv) to acquire the desired direct voltage (Vdcref) and the injected voltage (Vqref) (Voraphonpiput et al., 2008).

Description of the systems studied

The system consists of an infinite machine bus power supply system subjected to a three-phase short-circuit lasting 150 ms, located 100 km from the generator (Shahraki, 2003) as shown in Figure 6.

Figure 6.

Simplified diagram of monomachine power system.

The system consists of two coupled units, each having a rated power of 900 MVA and a voltage of 20 kV. The parameters per unit of the generator on the basis of MVA and kV are given below (Eskandar,2003) as shown in Figure 7.

Figure 7.

Simplified diagram of multimachine power system.

Integration of the wind farm into the electricity system

Previously, the stability of the wind farm integrated in an electrical system (Figure 8) was maintained by correctly selecting the proportional gain of the speed controller and the power factor (Deepa and Rizwana, 2013). The security of the electrical system is considered to be the ability of the system to withstand disturbances without interruption (Ayodele et al., 2013).

Figure 8.

Simplified diagram of wind farm integration.

Simulation results

The simulation results give various characteristic parameters for different power system configurations (an infinite machine bus, a two-zone power system of four machines and a wind farm). The system is subject to several fault cases such as the three-phase short-circuit lasting 1 second, the power supply system under load variation, the first 967 MW load connected at t = 5 seconds and disconnected at t = 8 seconds, the second 500 MW load connected at t = 20 seconds and disconnected at t = 24 seconds, connection and disconnection of a 9 MW wind farm integrated into the electrical system. These results show that many oscillations appear in the different configurations for all the types of faults mentioned above. Figure 9 shows the appearance of many oscillations when the electrical system is subjected to a short circuit (blue color curve). By using the SSSC, the power system returns to its stability faster and the oscillations are damped.

Figure 9.

Three phase short circuit of mono-machine power system.

In Figure 10, we have applied the variation of two loads at different times of simulation. The graph shows the efficiency of SMESs in damping oscillations and ensuring the stability of the power system.

Figure 10.

Load variation power system.

Figure 11 shows the consequences of integrating the wind farm into the electrical system and the importance of SMEs in dampening the oscillations caused by this integration.

Figure 11.

Wind farm integration results.

A three-phase short circuit was applied at time t = 5 seconds as shown in Figure 12. Oscillations immediately appear in the power system. The red curve illustrates the importance of using the SMES to damp these oscillations and to ensure the stability of the power supply system.

Figure 12.

SMEs effect on three phase short circuit.

Conclusion

In this article, we programmed a dynamic stability study by simulating different electrical system configurations. For this, we simulated many disturbances. The simulation results revealed that the uncontrolled system loses its stability, and an increase in the machine rotor speeds is perceived, which results in the loss of synchronism and consequently the loss of stability of the power system. The power system returns to its stability quickly and the oscillations dampen, when the power system is equipped with SSSC and SMES.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Seddiki Zahira

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