Electric Springs- Part1

A mechanical spring is an elastic device that can be used to: i) provide mechanical support; ii) store mechanical energy; and iii) damp mechanical oscillations .When a mechanical spring is compressed or stretched, the force it exerts is proportional to its change in displacement. Potential energy is stored in the mechanical spring when the length of the spring deviates from its natural length. The principle of the mechanical springs has been described by Robert Hooke in 1678.The Hooke’s law states that the force of an ideal mechanical spring is:

                                           F= -kx                         (1)

where is the force vector, is the spring constant and is the displacement vector. The potential energy stored in the mechanical spring is

                                          P= 1/2kx*x                  (2)

Fig. 1.1 . An array of distributed mechanical springs (like those used in supporting

a mattress).

Mechanical springs have been widely deployed in many daily applications such as suspension springs for beds and vehicles. The common use of mechanical springs in an array form, such as the spring support for a mattress as shown in Fig. 1, is a highly reliable mechanical support structure because it remains effective even if a few mechanical springs fail to function. Despite its significance, the mechanical spring concept has not been extended to the electric field for over three centuries. In this paper, the practical realization of an electric spring is reported. The physics of an electric spring based on the Hooke’s law is first described. Then the operating modes, limitations, and practical implementation of the electric spring are explained. Finally, for the first time, the use of an electric spring for stabilizing the voltage of a power system fed by dynamically- changing wind energy is successfully demonstrated. It is discovered that electric spring has tremendous potential in mitigating stability problems of future power systems with substantial intermittent renewable energy sources.

BASIC PRINCIPLES AND REALIZATION OF ELECTRIC SPRINGS

2.1 Principles of Electric Spring

Analogous to a mechanical spring, an electric spring is an electric device that can be used to:

(1)   Provide electric voltage support

(2)   Store electric energy

(3)   Damp electric oscillations

Analogous to equation-1, the basic physical relationship of the electric spring is expressed as

where is the electric charge stored in a capacitor with capacitance C,v_a is the electric potential difference across the capacitor, and is the current flowing into the capacitor.

 Equation (3) shows that dynamic voltage regulation (i.e., voltage boosting and reduction) functions of the electric spring can be controlled by the charge stored in the capacitor. Equation (4) indicates that the charge (q) control can be realized by using a controlled current source. Therefore, an electric spring can be represented as a current-controlled voltage source [6]. An analogy of the mechanical spring and an electric spring under 3 conditions are illustrated in Fig. 2, in which an electric spring is connected in series with a dissipative electric load Z₁.The neutral position of an electric spring is a reference voltage at which the spring is designed to maintain. The series arrangement of the electric spring and Z₁ across the ac mains is used to maintain the ac mains voltage v_s to its nominal reference level(e.g., 220 V), which is considered as the neutral position .Similar to the mechanical spring that can develop mechanical force in either direction when the displacement is changed from the neutral position, an electric spring can provide voltage boosting and voltage reduction functions as illustrated in Fig. 2.

 

Fig. 2.1.1 Analogy of a mechanical spring and an electric spring

The electric spring voltage v_a can be generated practically by dynamically controlling the electric potential difference across a capacitor with a current source [Fig. 3(a)] under a closed loop control [Fig. 3(b)]. The charge control in (3) provides a means to generate an electric voltage in both directions to boost or reduce the mains voltage in a power system. This control makes the dynamic voltage support function of the electric spring feasible.

Fig.2.1.2 (a) An electric spring in form of a capacitor fed by a controlled current source. (b) Schematic of an electric spring with input-voltage control. (c) An electric spring in series with a dissipative load for energy storage, voltage support, and damping.

The energy storage capability of the electric spring can be seen from the potential electric energy stored in the capacitor:

 

so the capacitor serves as the energy storage element for the electric spring.

 Since an electric spring should provide a function for damping electric oscillations, it is necessary to connect the lossless electric spring in series with a dissipative electric load (such as a water heating system or a refrigerator or a combination of them) as shown in Fig. 3(c). The use of the series-connected electric load is two-folded. Firstly, it provides a mechanism to dissipate electric energy for damping purpose. Secondly, it will be shown in the analysis that the voltage across the electric load and the electric spring voltage can change in a special manner that the load power consumption of will follow the variation of the renewable power generation. This unique feature of the electric spring offers a new solution to supporting the mains voltage in future power systems with intermittent renewable energy source. The series connection with the load makes the electric spring behaves like a “voltage suspension,” analogous to the mechanical suspension spring for a mechanical load (such as a vehicle). 

Fig. 2.1.3. Schematic of the experimental setup with an electric spring connected in series with a resistive-inductive load Z₁

The electric system in Fig. 4 is used to illustrate the concept and the operating limits of an electric spring. This system consists of an unstable ac power supply generated by a wind power simulator supplemented by an ac power source. Due to the intermittent nature of wind, the power generated will be dynamically changing and the ac voltage of the bus bar will vary with wind power. In this system, an electric spring is installed in series with an electric load as previously explained. Together, the electric spring and form a “smart load.” The dissipative load is termed a “noncritical” load because it can be operated at an ac voltage supply with some degree of voltage fluctuation. Examples of “noncritical” loads include electric water heaters, refrigerators, and lighting systems. Generally, the electric load can be represented as an inductor in series with a resistor .Other electric load that requires a well-regulated mains voltage is termed a “critical” load.

The electric spring operation of (3) is essentially the dynamic control of an electric field in the capacitor. It can be realized with a simple closed-loop control using the nominal mains voltage as the reference. By varying the energy stored in electric field of the capacitor in a sinusoidal manner with the objective of keeping the rms value of equal to , an alternating mains frequency can be generated across the capacitor as the electric spring voltage . To ensure that this adjustable ac voltage source is lossless like an ideal mechanical spring, the vectors of and must be perpendicular. The current vector can either lead the voltage vector the by 90 (capacitive mode for voltage boosting) or lag by 90 (inductive mode for voltage reduction).

2.2 Practical Implementation and Characteristics of Electric Spring

In electrical engineering term, this electric spring is a special form of reactive power controller. In the last two decades ,power electronics based reactive power controllers (RPC) have been developed in power industry to control power flow in high voltage transmission lines and for dimming lighting systems . Their simplified control schematics are illustrated in Fig. 5(a) and 5(b), respectively.

Fig 2.2.1 Simplified control schematic of series reactive power compensator for output voltage support in transmission

 

 In these applications of series RPC, the input of the RPC is always and the output is regulated to a constant level (i.e., a traditional “output-feedback and output-voltage control” of is adopted). It is important to note that the electric spring differentiates itself from previous use of RPC with the adoption of an “input-feedback and input-voltage control”

 

Fig 2.2.3 Simplified control schematic of series reactive power compensator as an electric spring

By regulating the input voltage and letting the output voltage to fluctuate dynamically, such RPC would: i) provide the voltage support as an electric spring and ii) simultaneously shape the load power to follow the available power generated by renewable energy source. Such subtle change in the control strategy of a RPC from output control to input control offers new features and functions for power and voltage control. This new discovery provides the opportunity to apply the electric spring for balancing the instantaneous power of the load demand and the generated power for future smart grids with substantial renewable energy sources.