Control under Autonomous Mode

Microgrids are expected to operate in grid-forming mode upon islanding and subsequent isolation from the main grid. The inverter in this mode is controlled to form the grid by establishing the rated voltage and frequency in the local grid. The control objective is to regulate the amplitude and frequency of the voltage at the inverter output and provide the active and reactive power demand of the loads on the microgrid. The grid-forming inverters are generally powered from storage battery. However, in recent times, inverters of various RE sources are also entrusted with the responsibility of grid formation, yet with adequate transient power support provided by fast responding storage systems like super capacitors and battery. Accomplishing grid formation with PV inverters is relatively easier than that with the inverters of wind electric systems. Grid-forming converters are to be enabled with black start capability, as this mode of operation starts instantaneously with islanding.

Voltage and Frequency Regulation in Grid-Forming Mode

The grid-forming power converters are controlled in any frame of reference like SRF-dq or stationary reference frame-сф, depending on the computing power available. Various methods are available to generate the reference signal for the grid-forming controller, like look-up-table, local oscillators, etc. The control scheme for a grid-forming converter is presented in Figure 2.56, wherein the reference voltage, Vrated, and the reference frequency, wrateii, are pre-fed into the controller and these represent the voltage and frequency to be established at PCC. The outer loop regulates the voltage at PCC by maintaining the charge balance of the filter capacitor, C„. The holdup time in

equation 2.9, when applied in grid-forming applications to design Ca, has to consider the source power variation as well as the load dynamics. The variation in the voltage at PCC, VL, is an indication of mismatch between the current delivered by the inverter and that demanded by the load. The inner loop regulates the current so as to maintain the voltage across CB as V*rated. The dynamic control equation for voltage regulation is,

where /inv and I, are the inverter current and the load current, respectively. The dynamics of the voltage control loop in dq reference frame can be expressed as,

where Vu and V4 are the d and q axes components of the voltage at PCC, w is the frequency at PCC, /invd and /invq are the d and q axes components of the inverter current, iLd and ilq are the d and q axes components of the load current, respectively.

Grid-forming mode control will make the inverter interact with the loads in the microgrid in the absence of the main grid as well as any local synchronous generation. So, black start capability is essential in this mode; in other words, there must be a reliable source to initiate the formation of the microgrid from a complete shutdown. Additionally, the grid-forming asset is expected to dispatch a required amount of power to the microgrid loads. The voltage generated by the grid-forming inverter will serve as the reference for the rest of the grid-feeding inverters of the microgrid. Deferrable loads, diesel generators and high-power density storages like super capacitors in conjunction with the battery can improve the transient power support within the microgrid which eventually improves the grid reliability in autonomous mode.

Black Start Capability

Black start can be defined as the capability of the microgrid to boot up without any external power support. Auxiliary battery powered systems can provide black start in a microgrid. The black start requirement of a microgrid can be classified based on the operating condition; namely, whether it is a cold start (a first time start up) or a re-connection (after a fault or an intentional shut down). The “grid former” is expected to ensure short start-up time so that fast reconnection of loads is possible. The asset which takes the responsibility of grid formation should also be rated to handle large in-rush currents during the re-connection of typical loads.

Sometimes, diesel generators are assigned the responsibility of black start so that the inverters in the microgrid can synchronize to it. However, the black start time required by a diesel generator is high (typically 10-20 s), so it hardly fits the definition of uninterrupted power supply. Moreover, diesel generators do not find a place in 100% RE microgrids. So, a battery-powered inverter has to play the role of grid former or master generator in such systems; it provides faster post-fault reconnection unlike the diesel generator. Yet, it is ideal in autonomous RE microgrids to assign one of the RE generators to be the grid former and either a battery or super capacitor can be assigned as the standby. The RE fed master generator will have a hybrid inverter capable of moving into grid-forming mode in case of islanding. The mode change is possible as long as the RE source has energy to maintain a stiff DC-link at the inverter input; else, the standby battery will replace the RE generator.

There is, however, an interesting question as to which RE generator should be given the responsibility of grid formation. There are two contradicting approaches: The first being to optimize the power rating of the master generator in order to reconnect as many loads as fast as possible, and the second to focus on the maximum utilization of the RE source through MPPT. The voltage regulation required in the grid-forming mode often will not support MPPT, and as a consequence choosing a large inverter for grid tying will not guarantee higher utilization of RE. If a larger number of inverters are used to form the grid (using an appropriate parallel operation algorithm during the mode change from grid-tied to grid-forming), then rapid reconnection of a large number of loads can be possible; this approach can also reduce the power loss due to off-MPPT operation.

Further, the stochastic nature of RE power will create an additional issue of inter- mittency in the grid-forming operation. This can however be addressed by addition of dynamic energy storage systems like super capacitors which can impart transient stability against RE variability.

Grid Forming with Wind Driven Generators

Wind electric generators will have a major share of distributed generation in microgrids. Variable speed wind electric generators like permanent magnet synchronous generators (PMSG) and doubly fed induction generators (DFIG) have proven capability to extract more from wind energy than fixed speed squirrel cage induction generators (SCIG). Of late, the wind electric generators are in demand to operate in autonomous mode on autonomous microgrid. The following sections address the microgrid interfacing and control of PMSG and DFIG in autonomous mode or gridforming mode of operation.

Crid-Forming Control of PMSC

The PMSG is preferred to SCIG and DFIG in stand-alone wind energy systems because of the self-excitation characteristic. Figure 2.57 presents the grid forming

Grid-forming control of wind driven PMSG system

FIGURE 2.58 Grid-forming control of wind driven PMSG system.

scheme of wind driven PMSG in autonomous mode, where the load side inverter is controlled to establish the grid at PCC. However, the power variance due to intermit- tency in wind speed and its implications on the AC voltage regulation are very severe which demand complex control of the inverter. The load side inverter control of the PMSG system for grid formation is presented in Figure 2.58.

This PMSG system has only one controllable converter, which is the load side inverter. So, the grid formation control targets the output voltage and frequency of the load side inverter using SRF controllers explained in Section The control scheme of Figure 2.58 follows the SRF control voltage equations from 2.30 to 2.34, and targets delivery of the active and reactive powers of equations 2.37 and 2.38 to the loads. The voltage regulation is obtained through the outer loop of the reactive power controller, wherein the rated load voltage is provided as a reference and compared with the measured voltage at PCC. The rated frequency is used to obtain the sine reference for the PWM block of the load side inverter of Figure 2.58. This control does not account for unbalance in the load, power intermittency due to wind speed variations and MPPT operation of the wind turbine (WT). Therefore, alternative schemes are suggested here to address the aforesaid issues by adding a battery in the DC link and an additional DC-DC converter after the rectifier.

MPPT Operation of WT

The main advantage of a variable speed wind electric generator is that the average aerodynamic efficiency of WT is relatively high, as the latter is made to operate at or near its maximum efficiency point by allowing the shaft speed to vary over a wide range in proportion to wind speed variation. This scenario is explained below.

The power input to the electric generator, or the mechanical power output of the wind turbine, can be expressed in Watts as,

where CP is the power coefficient which is a function of the tip speed ratio, X, and blade pitch angle, (h p is air density in kg/m- A is the blade swept area in m2 and v,„ is the wind velocity in m/s. X is the ratio of blade tip speed (which is the product of angular speed of the turbine, and blade length, R) to v„. When the wind electric generator operates in varying wind speed, X will vary if the variations in r and v„, are disproportionate; then the Cp variation will be hyperbolic and its maximum value, CPmax, will correspond to optimum tip speed ratio, Я ,, for a given ().

Therefore, the mechanical power extracted by the WT when operates at CPmm is,

and the corresponding shaft speed is,

In order to ensure maximum power point tracking in a wind electric generator, the shaft speed is forced to vary continuously such that X is kept constant at 2opt against any variation in v„,; this is called the TSR-MPPT method. An optimum torque MPPT (OT-MPPT) algorithm can be further developed continuing on the same concept as follows. The mechanical torque delivered by the WT can be obtained from equation 2.72 as,

If the turbine shaft speed is maintained at cOj-op„ then the optimum value of torque to be obtained from WT can be identified and subsequently used as the reference in the control loop. By use of equations 2.73-2.75 can be rewritten as,

Computing 7^nopt from equation 2.76 with the sensed shaft speed, the reference for the MPPT control loop can be obtained.

MPPT is not possible in stand-alone mode of operation, unless the demand matches the maximum power available; therefore, energy storage is integrated into the stand-alone WT driven PMSG system for harnessing maximum power. And the stored energy can be used to compensate the power deficit during intermittent dips in wind speed. Such a scheme of WT driven PMSG is presented in Figure 2.59.

The MPPT converter in Figure 2.59 is a DC-DC converter which is controlled to extract maximum power from the WT-PMSG. The MPPT control loop senses the shaft speed and ensures that the sum of the power delivered by the load side converter and the power delivered to battery is as demanded by the shaft speed such that A,opt is maintained in the WT. In addition to the storage, deferrable loads can

WT driven PMSG in autonomous mode with MPPT control and battery backup

FIGURE 2.59 WT driven PMSG in autonomous mode with MPPT control and battery backup.

be identified on the AC bus in order to ensure MPPT even when the battery is full. Deferrable loads are loads which can wait until power is available in excess of the regular load demand, which means these need not be dispatched on a fixed schedule. The presence of energy storage and deferrable loads will increase RE utilization and make the microgrid operation more flexible. The control schemes for TSR-MPPT and OT-MPPT are presented in Figure 2.60.

A separate DC-DC. converter establishes battery charge control and supports MPPT operation of WT by constituting itself as a controllable load. The combined load on WT comprises the regular load on the AC bus, the battery and the deferrable load. At any instant one or more of these three loads are regulated to maintain the shaft speed of equation 2.74. Despite the varying demand on the AC bus, the battery

charge controller is operated to adjust the charging current to fill the gap between the total generation and demand. Such matching of generation to demand is essential to ensure the operation of WT at its Aopt and CP at its maximum value. Upon the battery reaching its maximum capacity - with the requirement to sustain the match between total generation and total demand - the deferrable loads are operated.

The grid-forming control of grid side converter of PMSG in autonomous mode is presented in Figure 2.61. SRF controller is used to accomplish voltage and frequency regulation. The voltage and frequency references represent the respective rated values. In Figure 2.61, imparting the value of reference frequency, ft>’rated, will provide the value of 0 needed for abc to dq transformation and will ensure the inverter output voltage will have this frequency. The DC link voltage regulation will provide the active power reference of the inverter as discussed in Section 2.4.1.З.1. The load voltage at PCC is measured and its d-axis component, Vd is regulated with an outer PI regulator to obtain the current reference //. Vdrated in Figure 2.61 represents the c/-axis component of the required AC bus voltage which is added along with the PI compensated filter drop and the cross coupling factor to obtain the d-axis reference voltage Vd for the inverter as per equations 2.30-2.34. Similarly, in the reactive power loop, the amount of i’ to be delivered along with the cross-coupling factor amounts to be the g-axis reference voltage for the inverter V These reference voltages will accomplish the required AC bus voltage through PWM switching of the load side inverter. In addition, the maximum value for the DC link voltage, VDCnm, can be declared and any increase beyond this value is an indication of excess power available in the system, and then the deferrable load can be operated for power balance.

Crid-Forming Control of DFIC

The DFIG is the cost-effective choice of generator in large variable speed WT systems as the power electronics carries only the slip fraction of the rated power.

Grid-forming control of load side converter of DFIG

FIGURE 2.61 Grid-forming control of load side converter of DFIG.

But its range of operating speed is also limited, by the slip, unlike in PMSG. Its inherent double feeding feature provides the opportunity to integrate energy storage into its rotor circuit and it is controlled to accomplish different operating conditions of the generator. However, the stand-alone operation of DFIG demands yet more sophisticated control as the stator voltage and frequency regulation has to be obtained through a rotor side converter. Several control methods are available for grid-forming operation of DFIG including direct voltage control, field-oriented control, direct power control, etc.

Concept of voltage and frequency regulation in DFIG: The steady state equivalent of a slip ring induction machine operating in stand-alone mode and supplying a load of R + jX is presented in Figure 2.62.

Here Vr is the rotor voltage, E represents the air-gap voltage, a is the turns across ratio the stator and rotor, /, is the stator current, /,. represent the rotor current referred from stator, Vs is the stator terminal voltage, Rr is the rotor resistance referred to stator, Xr is the rotor reactance referred to stator, Rs and Xs are stator resistance and reactance respectively, Rm and Xm are shunt resistance and magnetizing reactance respectively, s is the slip. The KVL equation of the rotor side circuit results,

The air gap voltage E in terms of stator voltage and the stator drop be expressed as,

The rotor current due to the applied rotor voltage is,

On substituting equations 2.78 and 2.79 in equation 2.77 and simplifying to result the stator voltage is,

Equation 2.80 conveys that in stand-alone mode of DFIG, the stator voltage magnitude varies with variations in slip, the rotor voltage and the load on the stator. Thus, whenever the load or the slip varies, the control should counteract by varying the rotor voltage such that the stator voltage is maintained at its rated value.

Similarly, the stator frequency of DFIG when working in stand-alone mode varies due to the generation-load mismatch on the system. When the power available from the generator is more than the load connected on the stator, then the shaft speed increases and while the power generated is less than the load the shaft speed decreases. During this speed transition, if the shaft speed is greater than the synchronous speed, then the mode of operation is called super-synchronous while a lower shaft speed than synchronous speed results a sub-synchronous operation. Such speed variations cause the magnetic field of the machine to rotate at speeds other than the synchronous speed, thus deviating the stator frequency from its rated value. In standalone DFIG, if a constant stator frequency is to be established and sustained then the air gap magnetic field needs to be rotating at synchronous speed.

The relationship between the stator and rotor frequency in induction machines can be written as,

where cor is the rotor frequency in rad/s, cos is the stator frequency rad/s, m is the mechanical angular speed, and P is the number of poles. In equation 2.81, if com varies due to change in load or change in the wind speed, then the frequency injected at rotor circuit should be varied so as to maintain cos, at its rated value. So, the desired rotor frequency to be injected can be obtained from equation 2.81. Such a variable frequency variable voltage can be obtained through an inverter in the rotor circuit, which can be powered by a battery source or by a DC grid in case of a hybrid microgrid of Figure 2.6 dealt in Section

With reference to Figure 2.16, DFIG can be made to work as generator in both super-synchronous and sub-synchronous modes of operation. In sub-synchronous generation, the active power flows into the rotor circuit, whereas the active power is delivered by the rotor circuit in super- synchronous generation. Therefore, the converter provided in the rotor circuit has to support bidirectional power flow, simultaneously injecting a voltage with appropriate magnitude and frequency.

The rotor in any induction machine has induced voltage at slip times the stator frequency which creates its own magnetic field rotating at the rotor frequency. Since the wind turbine is rotating the DFIG rotor shaft, the speed of rotation of the rotor magnetic field is together decided by the injected rotor frequency and the mechanical rotation of the rotor shaft. This rotor magnetic flux linking with the stator windings and the rate of change of that flux linkage will decide the magnitude and frequency of the stator voltage.

The sub- and super-synchronous generation by DFIG will have its rotor shaft speed below and above the synchronous speed respectively. This will respectively result in positive and negative values of wr as per equation 2.81. The change in polarity of wr indicates the change of phase sequence of the three phase voltages. This phase sequence reversal is necessary to facilitate the reversal of power in the rotor circuit while the operation moves across sub- and super-synchronous modes.

A variety of stand-alone DFIG controllers are reported in research literatures and are broadly classified as (i) sensorless controllers and (ii) controllers with rotor position encoder. The stator voltage magnitude at a given speed and load will be proportional to the rotor current and its frequency. Once the rotor current frequency is decided based on Equation 2.81, then the magnitude of rotor current is varied until the reference amplitude of the stator voltage is generated.

Stator voltage and frequency control with speed encoder: The block diagram of simple stator voltage and frequency control to form a microgrid with DFIG is presented in Figure 2.63. This scheme includes a speed encoder and utilizes the position information in the control loop to establish the frequency relationship of equation 2.81. The reference angle of the rotor current ir is obtained by subtracting the angle corresponding to the

Grid-forming control of DFIG with speed sensor

FIGURE 2.63 Grid-forming control of DFIG with speed sensor.

rotational speed, 0m, from the angle corresponding to the reference stator frequency, 0S, as,

where со* is the reference stator frequency. The reference space vector magnitude of stator voltage, lv/1, is applied and the actual stator voltage, lvtl, is calculated using the orthogonal components in the stationary reference frame. The load changes contribute to the error between these two voltages, and so the compensated error serves as the reference rotor current magnitude, l/rl*. This is fused with the angle information (0*) of equation 2.82 to complete the rotor reference current vector calculations. This current vector is further transformed as three phase current references, irab*, and is used in a hysteresis current controller to make the actual rotor current to follow this. Conversely, these rotor reference currents can also be used with SRF current controllers, instead of the hysteresis controller, as described in Section Capacitor, Cf, at the stator terminals can serve as the filter as well as provide reactive power support for the stand-alone loads.

Stator voltage and frequency control without speed encoder: The angle of the reference rotor current if obtained without a speed encoder represents a sensorless DFIG system. вг* can be obtained by the principle of phased locked loops (PLL) adapted in grid-connected systems for synchronization. The PLL is used for the synchronization of the induced stator voltage vector with the arbitrarily assigned reference voltage vector. A small modification in the control loops along with a PLL can establish the stator voltage exactly in synchronism with the phase angle of the reference frequency. Such a sensorless grid-forming control of DFIG is presented in Figure 2.64, wherein the stator voltage is sensed and converted with SRF as dq quantities with the angle information obtained through integration of the reference stator frequency cof. The d- and q-axis voltages are used to obtain the magnitude of the stator voltage vector, lyj and its angle 0S as follows:

Two PI controllers are used to compensate the error in the voltage and the angle control loops. The reference for the voltage loop will be the magnitude of the rated stator voltage vector, lv/l. The compensated voltage error will result the rotor current magnitude to be injected.

The angle reference, 0 ", is maintained as zero for the grid-forming control. This will ensure that the reference voltage vector aligns with the d-axis of the SRF. Such an alignment will result V equal to zero and Vds= lv/l. Finally, the angle loop error after compensation will yield the reference rotor frequency, cof, and its integration will provide the angle of the rotor reference current, 0r‘.

Sensorless grid-forming control of DFIG

FIGURE 2.64 Sensorless grid-forming control of DFIG.

This angle, when fused with the rotor current magnitude information I/,.I* from the voltage loop, gives the reference rotor current vector. Further transformation of this current vector into three phase current reference, irabc*, will complete the calculations. Subsequently, a hysteresis current controller is employed to make the actual rotor current to follow the reference current, imbc

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