2014 IEEE 28-th Convention of Electrical and Electronics Engineers in Israel
Using synchronverters for power grid stabilization Eitan Brown (
[email protected])
George Weiss (
[email protected])
School of Electrical Engineering Tel Aviv University, Israel
School of Electrical Engineering Tel Aviv University, Israel
Abstract—We demonstrate how adding synchronverters to a power grid can help stabilize the system. By using fast communication between two synchronverters in separate areas, we can create virtual friction between their virtual rotors. We show by simulations that this virtual friction is an effective way to suppress inter-area oscillations.
I. I NTRODUCTION Synchronous generators (SG) have the following useful property: once synchronized, they stay synchronized even without any control, unless strong disturbances destroy the synchronism. This is one of the features that have enabled the development of the AC electricity grid at the end of the XIX century. Today, the stability of networks of synchronous generators that are coupled with various types of loads and other types of power sources (such as renewables) and are operated with the help of multiple control loops, is an area of high interest and intense research, see for instance Alipoor et al [1], Blaabjerg et al [3], Guerrero et al [7], Kundur [10], Ulbig et al [14]. This is partly due to the proliferation of power sources that are not synchronous generators, which threatens the stability of the power grid. These power sources use inverters to deliver power to the grid. Most inverters are designed to deliver maximum power from the source and they do not contribute to grid stability, quite the contrary: they introduce disturbances due to the intermittent nature of the power source and they increase the sensitivity of then grid to other disturbances such as faults. An inverter which behaves like a synchronous generator can simplify the modelling of the overall system and the overall system behaviour during sudden disturbances or faults will be as stable as it would be without the inverter or even better. Such inverters, sometimes called synchronverters, have been proposed in Beck and Hesse [2], Driesen [5], Visscher and de Haan [15], Zhong et al [20], [19]. (Actually, the control algorithms proposed in these papers are different and the term synchronverter refers to inverters controlled as in [20].) The grid operator can relate to synchronverters in the same way as to classical generators, which makes the transition to the massive penetration of renewable and other distributed energy sources easier and smoother. In this paper we explore a new application of synchronverters, namely, their ability to dampen inter-area oscillations via virtual friction between synchronverters in different locations. This research was supported by grant no. 800/14 from the Israel Science Foundation.
Fig. 1. The simple power network (without synchronverters) exhibiting interarea oscillations. The model includes steam turbines as prime movers for the two synchronous generators. The oscillations are triggered by closing the switch connecting an additional load of 60MW.
This can be achieved by adding a friction torque to the virtual torque of each synchronverter, which is equivalent to viscous friction being present between the virtual rotating axes of the different synchronverters. This stabilizing effect will come in addition to the frequency droop, which is like a viscous friction acting locally (against an imaginary axis rotating at the nominal grid frequency). We explore virtual friction by simulation experiments: we look at a simple grid composed of two synchronous machines of 1 GW nominal power, each using a steam turbine and a governor with an IEEE type 1 synchronous machine voltage regulator and exciter, see Figure 1. These generators operate at 22 KV and are connected to a 22/130 KV transformer. Each generator has a local load of 300 MW and both generators are connected via a 220 KM line with 0.05 Ω/Km resistence and 1.4 mH/Km inductance. The capacitance of the line was neglected to improve the simulation run time (but it would not change significantly the results, according to our tests). In the middle of the line there is a substation composed of a 130/22 KV transformer and a small load of 55 MW. A small load of 60 MW located near one of the generators is switched on after 10 seconds. This sudden change causes power oscillations between the generators until a new equilibrium is reached. Our system vaguely resembles the one used in the simulation package SimPower (the example called power PSS). Inter-area oscillations are caused by the electro-mechanical nature of the generators. They constitute a well known problem, see for instance Kundur [10], Klein et al [8], Pal and Chaudhury [11] and Yang and Feliachi [17], and the usual solution is to regulate the field voltage with a controller called Power System Stabilizer (PSS). This requires additional hardware and each type of PSS has its own pros and cons.
Our solution proposes to use the inverters already present in the power grid to dampen the inter-area oscillations. For this (and also for other reasons), the inverters should be controlled in such a way that they are synchronverters. II. T HE EQUATIONS
OF A SYNCHRONVERTER
The mathematical model of a synchronous machine can be found for instance in [6], [16], [10], [9], [20]. For the synchronverter model we consider that the rotor is round (nonsalient) and, for the sake of simplicity, that the machine has one pair of poles per phase, the rotor current i f is constant (or equivalently, the rotor is a permanent magnet) and the machine is “perfectly built”, meaning that in each stator winding, the flux caused by the rotor is a sinusoidal function of the rotor angle θ (with shifts of ±2π /3 between the phases of course). The stator windings are connected in star and there are no damper windings. We will quickly derive the equations that we need for our study, following the notation and sign conventions in [20]. The mechanical part of the machine is governed by J θ¨ = Tm − Te − D p (θ˙ − ωr ), where J is the moment of inertia of all the parts rotating with the rotor, Tm is the mechanical torque, Te is the electromagnetic toque, D p is the droop constant (damping factor) and ωr is the reference angular velocity (ωr = 100π for a 50Hz grid). We have D E fθ , Te = M f i f i, sin (2.1)
where i is the vector of (instantaneous) stator currents and i f is the field (or rotor) current. The electrical part of the synchronous machine is governed by fθ, (2.2) e = θ˙ M i sin f f
Ls i˙+ Rs i = e − v,
between synchronverters which may incur costs, however, communication systems have improved and have become very cost efficient. This additional torque will be added to the total torque acting on the imaginary rotor of the synchronverter. To make this more precise, consider for simplicity a small grid with only two synchronverters with rotor angles θ1 and θ2 . Newton’s law of rotational motion for the first generator is J θ¨1 = Tm1 − Te1 − D p1(θ˙1 − ωr ) − D pv(θ˙1 − θ˙2 ). Here D p1 > 0 is the droop constant of the first synchronverter, while D pv > 0 is the virtual friction coefficient that helps damping unwanted inter-area oscillations. A similar equation is imposed for the other synchronverter. In the nominal operation mode the virtual friction torque is zero. When there is a sudden load change and the system starts to go off balance then the virtual rotors of the synchronverters slightly rotate against each other and the virtual friction torque starts working to counteract this. Notice that the rotor of a real synchronous generator stores the kinetic energy 21 J[θ˙ ]2 , proportional to its moment of inertia J. The importance of inertia in power systems is discussed for instance in [14]. Inverters have no moving mechanical part, so they cannot store kinetic energy. To imitate the effect of the kinetic energy, a synchronverter needs large capacitors on its DC bus or (a better but more expensive solution) storage batteries. Another important advantage the synchronverter has is that it does not need an additional PLL unit to synchronize with the grid. Instead, the synchronverter acts itself as a PLL, as proposed in Zhong et al [19]. The full scheme of the synchronverter revels more advantages such as a simple mechanism for controlling the active power (with reference signal Pset ) and the reactive power (with reference signal Qset ), as seen in Figure 2, taken from [20]. The initial synchronization mechanism (used when starting the converter) is not shown in this figure, but it can be found in [19].
where e is the vector of induced electromotive forces and v is the vector of stator terminal voltages. The real power and reactive power are, respectively, D E fθ , P = θ˙ M f i f i, sin f θi. Q = −θ˙ M f i f hi, cos
(2.3)
An actual synchronous machine also has mechanical controls for Tm , which comes from a steam turbine (or another prime mover). This mechanical control loop, called frequency droop, is very slow (it is low-pass filtered with a time constant of the order of one minute) and this very low bandwidth greatly contributes to the unwanted oscillations in the power grid. The synchronverter’s fast frequency droop is an essential improvement over conventional generators and it helps to dampen unwanted oscillations of the active power. If there are several generation areas where each has a synchronverter present, an additional torque can be introduced that acts as if there were viscous friction between the imaginary rotors of the synchronverters. This will require fast communication
Fig. 2.
The basic algorithm running in the processor of a synchronverter
III. S HORT
REVIEW ON INTER - AREA OSCILLATIONS IN GENERAL AND IN OUR TEST SYSTEM
In this section, we will describe in brief the different oscillations in a power grid. Oscillations may be associated with a
single generator, due to its dynamics vaguely resembling the dynamics of a damped pendulum (the swing equation). The frequency range of these damped oscillations is approximately 0.7 to 2 Hz. Inter-area oscillations involve groups of generators which oscillate one against the other, when the physical link between them is weak (i.e., it has relatively high impedance), see the explanations in [8]. These oscillations are much more complex since they involve several non-linear systems. The oscillation frequencies range from 0.1 Hz to 0.8 Hz. A key feature is that the power variations in one (group of) generators will be opposite to the power variations in the other (group of) generators.
power. If we look at the formula for the active power in sinusoidal steady state, VE · sin(δ ) , X (E is the effective induced voltage in the stator) we see that P depends on the voltages V and E, however, since the variations of V are small, P is mainly changed via δ (which changes as a result of changes in the active torque of the prime mover). Power System Stabilizers (PSS) use the connection between P and E to dampen inter-area oscillations as well as local oscillations, see for instance Kundur [10], Zea [18]. The general structure of a PSS shown below is taken from [18]: P=
Fig. 4.
Fig. 3.
Power oscillations in the system from Figure 1
In Figure 3 we see that in our model, the powers from the two generators oscillate (with damping) against each other and the frequency is 0.625 Hz, which is well in the range of interarea oscillation and below the range of local oscillations. The system was stable before the load jump and no power was transferred from one generator to the other. After the load jump the phase difference between the generators is negative due to power going from generator 2 to generator 1, where an increase in load has occured. The oscillations lasts for more than 20 seconds and even after 10 seconds they reach an amplitude of 10 MW which can cause heating in the lines and transformers. IV. S HORT
REVIEW ON
PSS
We have demonstrated the efficiency of various PSS by adding them to our simulation model from Figure 1. We have used 3 types of PSS available in the Matlab Simpower library. The first is called Multi Band PSS (MB PSS) and it works on the rotor speed deviation and handles 3 bands of frequencies (low, intermediate and high) adjusted in advance. The second is a generic PSS that works on the rotor speed deviation multiplied with a constant gain and filtered, as shown in Figure 4. The last PSS is almost like the second, but works on the difference between electrical and mechanical power instead of rotor speed deviation.
SOLUTION
The excitation control system in a conventional SG controls the rotor current i f and its main purpose is to make sure that the generator maintains a terminal voltage close to the nominal voltage. The reactive power of a generator is tightly connected to the terminal voltage: in sinusoidal steay state, Q=
General model of a PSS
V2
VE · cos(δ ) − , X X
which means that changing the phase difference between the generator and the grid will hardly change Q but changing the generator voltage will be meaningful. The excitation control system provides the direct current to the field winding which in turn determines the voltage of the generator and the reactive
Fig. 5. Comparison of power oscillations using three types of PSS, as well as no PSS, in the system from Figure 1
We can see that the various PSS perform well, but have certain disadvantages. MB PSS is the best of those tested here but it requires very precise design based on an accurate model of the system. The second PSS (also called d ω PSS) takes a long time to reach the new equilibrium point, even after 20 seconds it is far from settled. The third type of PSS
(also called Pm − Pe PSS) causes large and very low frequency power oscillations. All three PSS also have the disadvantage of not maintaining constant voltage, since after all they work by changing the field current and hence E. Constant voltage is important for transformers and certain loads. V. P OWER GRID
BEHAVIOUR WITH THE SYNCHRONVERTER
We will now study the performance of our virtual friction scheme. Two synchronverters were added into the small grid from Figure 1, one to each generator, via transformers since inverters don’t work at high voltages due to limitations of the electronic switches. Each synchronverter was designed to give 45 MW maximum power and we have operated them at 35 MW each. This means that the synchronverters have supplied roughly 10% of the power.
VI. P OWER GRID
BEHAVIOUR WITH A CONVENTIONAL INVERTER
We will not go into the many types of inverter control strategies available today. We want to choose an inverter with an advanced controller to compare with ours. The paper Pogaku, Prodanovic and Green [12] presents an inverter control technique with frequency droop and advanced load sharing capabilities. We have connected two such inverters to our system simulation, after adjusting them as we did with the synchronverters. We found that the resulting system behaves similarly to the one containing synchronverters without virtual friction. This means that synchronverters have the advantages of other advanced inverters, and this is probably due to the fast frequency droop, as opposed to the very slow droop of a real generator.
Fig. 6. The network from Figure 1 after adding synchronverters next to each generator
The first simulation was without any virtual friction between the synchronverters, so that only the frequency droop contributes to stabilizing the system. We can see in Figure 7 that even in this mode of operation, the synchronverters improve the response of the system. We have also simulated this system with a virtual friction torque between the two synchronverters. The improvement can easily be seen: the oscillations disappear completely about 10 seconds after the event (extra load) that has caused them.
Fig. 7.
System with two synchronverters
Fig. 8.
Comparison of system behaviour with inverter and synchronverter
VII. C ONCLUSION
AND FUTURE WORK
We have shown that an inverter that mimics a synchronous generator can have both the advantages of being an inverter and of being like a synchronous machine. It can actually outperform a synchronous machine (from the point of view of system stability) because the frequency droop can act much faster, and we can create virtual friction between synchronverters, which help to dampen inter-area oscillations. Moreover, this way of dampening the inter-area oscillations has almost no effect on the voltage. We have created a grid simulation containing two large synchronous generators and two much smaller synchronverters connected next to the large generators. A line with relatively high impedance links the two generators, and there are various loads. We have compared the oscillations triggered by a sudden load change, when using the damping scheme via PSS, compared to virtual friction acting on the synchronverters. The results for damping the power oscillations are similar (the virtual friction perform somewhet better) while for voltage oscillations, the virtual friction definitely outperforms the PSS.
Active power of generator 1
8
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MB PSS dw PSS Pm − Pe PSS Synchronverter With Virtual Friction
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Generetor 1 active power
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x 10
3.6 3.5
5 4.5
Synchronverter With Virtual Friction MB PSS dω PSS Pm − Pe PSS
3.4
4
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Fig. 9.
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Comparison of system power flow with synchronverter or PSS
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Fig. 11. Comparison of system power flow with synchronverter or PSS, with the switched load increased to 150 MW (from 60 MW) and the substation load increased to 150 MW (from 55MW).
Voltage of generator 1 1.02
Voltage of generator 1 1.1
MB PSS dω PSS Pm − Pe PSS
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0.98 Synchronverter With Virtual Friction MB PSS dω PSS P − P PSS
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Fig. 10.
Comparison of system voltage profile with synchronverter or PSS
R EFERENCES [1] J. Alipoor, Y. Miura and T. Ise, Distributed generation grid integration using virtual synchronous generator with adoptive virtual inertia, IEEE Energy Conversion Congress and Exposition, Denver, Colorado, 2013, pp. 4546-4552. [2] H.P. Beck and R. Hesse, m Virtual synchronous machine, IEEE Electrical Power and Utilization , Barcelona, Spain, 2007. [3] F. Blaabjerg, R. Teodorescu, M. Liserre and A.V. Timbus, Overview of control and grid synchronization for distributed power generation systems, IEEE Trans. on Industrial Electronics, vol. 53, 2006, pp. 13981409. [4] F. D¨orfler and F. Bullo, Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators, SIAM J. Control and Optim., vol. 50, 2012, pp. 1616-1642. [5] J. Driesen and K. Visscher, Virtual synchronous generators, IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy, Pittsburgh, PA, 2008, pp. 1-3. [6] A.E. Fitzgerald, C. Kingsley and S.D. Umans, Electric Machinery, McGraw-Hill, New York, 2003. [7] J.M. Guerrero, J.C. Vasquez, J. Matas, M. Castilla, and L.G. de Vicuna, Control strategy for flexible microgrid based on parallel line-interactive UPS systems, IEEE Trans. on Industrial Electronics, vol. 56, 2009, pp. 726-736. [8] M. Klein, G.J. Rogers and P. Kundur A fundamental study of inter-area oscillations in power systems, IEEE Trans. on Power Systems, vol. 6, 1991, pp. 914-921. [9] D.P. Kothari and I.J. Nagrath, Electric Machines (third edition), Tata McGraw-Hill, New Delhi, 2004. [10] P. Kundur, Power System Stability and Control, McGraw-Hill, New York, 1994. [11] B. Pal and B. Chaudhuri, Robust Control in Power Systems, Springer Verlag, New York, 2005.
10
15 Time [Sec]
20
25
30
Fig. 12. Comparison of system voltage profile with synchronverter or PSS, under the same conditions as in Figure 11.
[12] N. Pogaku, M. Prodanovic and T.C. Green, Modeling, analysis and testing of autonomous operation of an inverter-based microgrid, IEEE Trans. on Power Electronics, vol. 22, 2007, pp. 613-623. [13] J. Strand, Energy efficiency and renewable energy supply for the G-7 Countries, with emphasis on Germany, International Monetary Fund, Munich, Germany, 2007. [14] A. Ulbig, T.S. Borsche and G. Andersson, Impact of low rotational inertia on power system stability and operation, IFAC World Congress 2014, Cape Town, South Africa, August 2014. [15] K. Visscher and S.W.H. de Haan, Virtual synchronous machines (VSG’S) for frequency stabilization in future grids with a significant share of decentralized generation, CIRED Seminar SmartGrids for Distribution, Frankfurt, Germany, 2008, paper no 0118. [16] J.H. Walker, Large Synchronous Machines: Design, Manufacture and Operation, Oxford University Press, Oxford, 1981. [17] X. Yang and A. Feliachi, Stabilization of inter-area oscillation modes through excitation systems, IEEE Trans. Power Systems, vol. 9, 1994, pp. 494-502. [18] A.A. Zea, Power system stabilizers of the synchronous generetor, tuning and performence evaluation, thesis, Chalmers University of Technology, Goteborg, Sweden, 2013. [19] Q.-C. Zhong, P.-L. Nguyen, Z. Ma and W. Sheng, Self-synchronized synchronverters: Inverters without a dedicated synchronization units, IEEE Trans. Power Electronics, vol. 29, 2014, pp. 617-630. [20] Q.-C. Zhong and G. Weiss, Synchronverters: Inverters that mimic synchronous generators, IEEE Trans. Industr. Electronics, vol. 58, 2011, pp. 1259-1267.
