Mechanical accumulator of electrical energy. The use of energy storage devices. General information about energy storage

Mechanical storage (MH), or mechanical energy accumulator, is a device for storing and storing kinetic or potential energy with its subsequent release for useful work.

As for any type of energy storage device (EE), the characteristic modes of operation of the MN are charge (accumulation) and discharge (energy return). Storage energy serves as an intermediate mode of MN. In the charging mode, mechanical energy is supplied to the MN from an external source, and the specific technical implementation of the energy source is determined by the type of MN. When the MN is discharged, the main part of the energy stored by it is transferred to the consumer. Some part of the accumulated energy is spent on compensation for losses occurring in the discharge mode, and in most types of magnetic circuitry - and in storage modes.

Since in a number of storage installations the charge time D3 can be much greater than the discharge time (r3 "g), a significant excess of the average discharge rate is possible. RP over average power P3 charge MN. Thus, it is permissible to accumulate energy in the MP using relatively low-power sources.

The main types of MN are subdivided into static, dynamic and combined devices.

Static MN store potential energy by elastic change in the shape or volume of the working fluid, or when it moves against the direction of gravity in the gravitational field. Solid, liquid or gaseous working fluid of these MN has a static state in the energy storage mode, and the charge and discharge of NEs are accompanied by the movement of the working fluid.

Dynamic MN accumulate kinetic energy mainly in rotating masses of solids. Conditionally - storage devices of accelerators of charged elementary particles, in which the kinetic energy of electrons or protons, cyclically moving along closed trajectories, is stored can also be attributed to dynamic MPs.

Combined MN store both kinetic and potential energy. An example of a combined MH is a super flywheel made of a high-strength fibrous material with a relatively low modulus of elasticity. When a given MI rotates, the potential energy of elastic deformation is stored in it along with the kinetic energy. When extracting the accumulated energy from such a MN, the use of both of its types is achieved.

In terms of the level of specific accumulated energy per unit mass or volume of the accumulating element, dynamic inertial MN are significantly superior to some other types of NEs (for example, inductive and capacitive storage). Therefore, MN are of great practical interest for various applications in various branches of technology and scientific research.

Certain types of MP have found by now large-scale application in the electric power industry, for example, guide - Roof storage installations of power plants. Charging - The discharge cycle of their work reaches tens of hours.

For inertial MPs, short-term discharge modes are characteristic. The extraction of energy from the MP is accompanied by a decrease in the angular velocity of the flywheel to the permissible level. In some cases, braking can occur up to a complete stop of the flywheel. Possible "shock" discharges, characterized by a one-time or cyclic withdrawal of stored energy, and due to the large angular momentum and short discharge time of the MN, the decrease in the angular velocity of its rotor is relatively small, although the power supplied can reach sufficiently high values. In this MN mode, special requirements are imposed on ensuring the strength of the shaft. Under the influence of the torque, dangerous shear stresses arise in the shaft, h. the kinetic energy of the rotor is converted into the potential energy of elastic deformations of the torsion of the shaft. To overcome the above difficulties, elastic or friction clutches are provided in individual MH designs.

Static MNs preserve the stored energy, being in a stationary state. The carriers of potential energy in them are elastically deformed solids or compressed gases under excessive pressure, as well as masses raised to a height relative to the earth's surface. Typical examples of static MN are: stretched or compressed springs, rubbers; gas-cylinder accumulators and pneumatic accumulators; impact devices of various piles, for example, for driving piles, using the energy of the masses in a raised state; reservoirs of pumped storage power plants, tanks of water-pressure installations. Here are the main energy ratios and characteristic parameters of some typical devices.

Consider an MN with elastic elements.

We believe solid state the system is linear, then the elastic storage element has constant stiffness (or elasticity) N= Const. Force acting on him F\u003d Nx proportional to linear deformation x. Elementary work perfect when charged with MH dW\u003d Fdx. Total stored energy

W = J Fdx \u003d J Nxdx \u003d NAh2 / 2-FaAh / 2, Oo

WhereAh - the resulting deformation, limited, for example, Admissible tension ar material; Fn = NAh - the applied force.

Let's estimate the specific energy Wya \u003d Wj M, per unit mass M \u003d yV\u003d ySh spring or rod volume V and section S, whose material has a density y and works to break within the limits of Hooke's law a \u003d xfE, moreover X* \u003d xfh- relative deformation, E-module of elasticity (Young), G ^ Gp. Introducing da \u003d Edx„ we can write DW\u003d Fhdx* \u003d Fhdo/ E and dWya \u003d dW/ ySh \u003d Fda/ ySE, whence at C \u003d F/ S find

Wya \u003d] (aljE) da \u003d a2J (2jE).ABOUT

For steel we will accept springs with „\u003d 8 108 N / m "E \u003d 2 , 1-1011 N / m2, y \u003d 7800 kg / m3, then Wya ^200 J/ kg. AnaA logical calculation for technical rubber gives ^ beats ^ 350 J / kg, however, due to the hysteresis nature of the dependence F= F(X) In the charge-discharge cycle, the resulting losses and heating lead to TO gradual aging (destruction) of rubber, instability and deterioration of its elastic properties.

Gas storage the system is in a mechanically non-equilibrium state with respect to the environment: when the temperatures of the system and the environment are equal (T \u003d T0C) system pressure p\u003e p0, c, therefore the system can do work. The reserve of elastic energy compressed in a cylinder with a volume V gas is

W \u003d P (vdp \u003d v (p2-pi) .. (4.1)

According to (4.1), per unit mass M of any compressed gas, there is a specific energy

Wya \u003d W / M \u003d V (p2-Pl) IM \u003d Aply. (4.2)

Based on (4.2) at K \u003d 1m3, the value W- WysM numerically equal to pressure drop Ap \u003d p1-p1. For example, if A /? \u003d 250 105 Pa (initial pressure p! \u003d 105 Pa), then IL \u003d 25-106 J regardless of the chemical composition of the gas. The maximum value of Wya during expansion of compressed gas to zero pressure at a given temperature according to the Mendeleev - Clapeyron equation PV- MvRyT is

Wya\u003d WlM \u003d RyTI ", (4.3)

Where c \u003d M / Mts - molar mass (kg / kmol); Ry & ~ 8.314 kJ / (kmol K) - universal gas constant at Тх273 К; /? "105Pa; Mm is the number of kilomoles in a gas of mass M.

It can be seen from (4.3) that the use of light gases in ML is most effective. For the lightest gas, hydrogen (μ \u003d 2 kg / kmol) at T \u003d 300 K, the specific energy is ~ 1250 kJ / kg (or 1250 J / g). In (4.3), the pressure is not explicitly included, since Wya is determined by (4.2) by the ratio of the excess gas pressure to its density. The latter with increasing pressure and Г \u003d const increases linearly (in the isothermal process PV= Const). It should be noted that the high pressures that are reasonable for the effective application of the MN under consideration cause, for strength reasons, a significant mass of gas cylinders, taking into account which the value of Wya of the installation as a whole can decrease by almost an order of magnitude compared to fVya from (4.2), (4.3). Evaluation of the strength of the cylinders can be carried out using the Design Relationships § 4.5.7.

Consider gravitational energy storage devices.

The gravistatic energy of gravity of the Earth (at the level of ory) is estimated by a rather high indicator "beats \u003d 61.6 MJ / kg, which characterizes the work necessary for the uniform movement of a body with a mass of Mx \u003d Kg from the earth's surface into outer space (for comparison, we indicate that this value PVya is approximately twice the chemical energy of 1 kg of kerosene). M to the height h \u003d x2 - xl stored potential energy

W \u003d jgMdx \u003d gMh , (4.4)

Where M \u003d const, g \u003d 9.8l m / s2. According to (4.4), the specific energy Wya\u003d Wj M\u003d gh depends only on the height h. The stored energy is released when the load falls and the corresponding useful work is performed as a result of the transformation of potential energy into kinetic one. The highest specific kinetic energy in nature when falling can be developed by meteorites, for which Wya ^ 60 MJ / kg (excluding the energy consumption for friction in the atmosphere).

Direct use of gravistatic forces generated by natural masses is practically impossible. However, by pumping water into raised artificial reservoirs or from underground reservoirs to the surface, a sufficiently large amount of potential energy can be accumulated for large-scale applications in electric power systems. If the level difference h \u003d 200 m, then, based on the mass of water M \u003d 103 kg, the stored energy according to (4.4) is equal to I\u003e "\u003d 1962 kJ, specific energy Wya\u003d WjM= 1.962 kJ / kg.

Consider inertial kinetic MN.

In principle, kinetic energy can be stored for any movement of the mass. For uniform translational motion of a body with a mass M with speed v kinetic energy W\u003d Mv2 / 2. Specific energy Wya\u003d W/ M \u003d v2 j2 depends (quadratically) only on the linear velocity of the body. A body moving with the first cosmic speed km / s has a specific

Energy Wyax32 MJ / kg.

For a variety of energy and transport applications, MNs of rotary motion are rational - inertial MNs (flywheels). The stored kinetic energy W \u003d J & / ~ is determined by the square of the angular velocity Q \u003d 2nn (P - speed) and moment of inertia J flywheel relative to the axis of rotation. If the flywheel has a radius r and mass M = yV (V-volume, at - material density), t °

J ^ Mr2 / 2 \u003d yVr2j2 and W \u003d n2Mr2n2 \u003d n2yVr2n2. The corresponding specific energy (per unit M or V) is FV/ M\u003d n* r2n2 , J / kg and lV0ya\u003d W/ V\u003d n2yr2n2 , J / m3. The values \u200b\u200bof Q and n for a given size r are limited by the linear peripheral speed v \u003d Q.r \u003d 2mr, associated with the permissible breaking stress of the material ar. It is known that the voltage a in a disk or cylindrical rotor MH depends on v2. Depending on the geometric shape of the metal flywheels, they are characterized by permissible maximum speeds at the periphery of approximately 200 to 500 m / s.

Stored energy, in particular for a slender rim flywheel, W\u003d Mv /2 (Mis the mass of the rotating ring). Specific energy Wya\u003d W/ M \u003d v2 /2 does not depend on the size of the ring and is determined by the ratio of the parameters Op / y of its material (see Sec. 4.5.1, where it is shown that v2 \u003d opjY). It should be noted that a similar pattern for Wya ~ avjу also takes place in inductive energy storage devices (see Ch. 2), although they differ significantly from MN in physical nature. In the general case, in the manufacture of MN storage elements, it is necessary to use materials with increased values \u200b\u200bof Gp / y\u003e 105 J / kg. The most suitable materials are high-strength alloy steels, titanium alloys, as well as light aluminum alloys (duralumin type) and magnesium alloys (electron type). Using metallic materials, it is possible to obtain the specific energy MN up to Wm \u003d 200-300 to J / kg.

Designed for the creation of flywheels with especially high specific energies (super flywheels), fine-fiber materials can theoretically provide the following levels of the Wya index: glass filaments - 650 kJ / kg, quartz filaments - 5000 kJ / kg, carbon fibers (with a diamond structure) -15000 kJ / kg ... The filaments (or tapes made from them) and adhesive resins form a composite structure, the strength of which is lower than that of the original fibers. Taking into account the fastening elements in real super - flywheels, the values \u200b\u200bof Zhud are practically achieved, which are less than the indicated ones, but still relatively higher than in other Varieties of MN. Super flywheels allow peripheral speeds up to v "1000 m / s. The technical implementation of such devices requires special conditions. For example, It is necessary to install a flywheel in an evacuated casing, since the indicated values v correspond to supersonic velocities in the air (Mach number Ma\u003e 1), which in the general case can cause a number of unacceptable effects: the appearance of compaction shocks in air and shock waves, a sharp increase in aerodynamic drag and temperature.

Multilayer fiber super flywheels have a fairly high reliability and are safer in operation than solid flywheels. Under unacceptable loads caused by inertial forces, only the most stressed outer layers of the fiber composite structure of the super flywheel are destroyed, while the destruction of a massive flywheel is accompanied by the scattering of its torn parts.

The combination of the properties of static and dynamic MN takes place in various devices. The simplest of these is the oscillating pendulum. The cyclic process of mutual transformation of potential energy into kinetic energy can be maintained for a rather long time if the losses in the pendulum mechanism are compensated.

Let us consider illustrative examples of MNs that store kinetic and potential energies at the same time when charged. They demonstrate the fundamental possibilities of joint practical use of both types of accumulated mechanical energy. In fig. 4.1, and the weight is shown M, revolving around the center ABOUT on an absolutely rigid string of length /, deviated from the vertical position by an angle cp. Linear Velocity v corresponds to the rotational motion of M along a circle of radius g. Potential energy of the load Wn\u003d gMh due to its rise to a height h as a result of rejection. The kinetic energy of the load is 1FK \u003d 0.5 Mv2 . A force F \u003d F „+ Fr. acts on the load. Its inertial component is equal to FK \u003d Mv lr\u003e the value of the gravitational component F T \u003d gM. Since F „/ Fr \u003d r2 / rg \u003d tg (D, insofar as Wn/ Wk \u003d 2h/ rtg^>. If Uchest ^! that A \u003d / (l - coscp) and r \u003d / sincp, then / y / r \u003d (1 - coscp) / sinср. Thus, W„L lFK \u003d 2coscp / (l + cos (p), and in the case of cp-\u003e 0 we obtain Wn / WK-\u003e 1. Consequently, at small angles cp, the stored energy fV \u003d JVK + Wn can be distributed at equal frequencies (W The value of Wn can be increased , if you fix the load on an elastic suspension (bar or string).

Another example of joint accumulation W„ and Wk a rotating fine-rim flywheel serves as (Figure 4.1, b), which had elasticity (rigidity) N. The tension in the rim ^ p \u003d NAI is proportional to the elastic elongation A / \u003d 2n (r - r0) caused by inertial forces AFr \u003d AMv2 / r, distributed Nymi along the rim circumference with radius r. Equilibrium of a rim element with a mass of 2DM \u003d 2 (A // 2l;) A (p is determined by the relation 2A / v \u003d 2A / 7 (() sinAcp ^ Ai ^ Acp, whence 0.5 Mv2 \u003d 2K2 (r - r0 ) N. Therefore, the kinetic energy of the rim lVK \u003d 2n2 (r - r0 ) N. Since the stored potential energy)