Data-driven robust stochastic optimization for power systems operations

Xiaoqing Bai , ... Rujie Zhu , in Uncertainties in Modern Power Systems, 2021

2.1.4 The compressed-air-assisted wind turbine system

The CAAWTS is adopted to improve the consumptive ability of the power grid from distributed generation (DG). It provides an adaptive structure to reduce the deviation between wind energy and load. From an energy point of view, the storage system serves as a buffer between the mechanical power of the wind power and the electric power to the load. A more detailed discussion about CAAWTS can be found in Ref. [19]. We have derived the relationship between the power of CAAWTS and the pressure, the volume, the moment, the angle, and the angular velocity. As a result, the relationship between power and energy can be obtained, and a dynamic mathematical model of CAAWTS is established as follows.

(4.34) 0 P D G i t P w i n d i t + P v p i t P v c i t

(4.35) P v p i t = κ E i t + β

(4.36) E i t + 1 = η e E i t + η V c P v c i t Δ t P v p i t Δ t / η V p

(4.37) E m i n t E i t E m a x t

(4.38) E 0 φ E i φ , T

(4.39) P v p , m i n t P v p i t P v p , m a x t

(4.40) P v c , m i n t P v c i t P v c , m a x t

(4.41) P v p i t P v c i t = 0

Eq. (4.34) indicates the relationship between wind power, energy storage, and distributed generations. It is noticed that Eq. (4.41) is a complementary constraint, which can be expressed as follows using a Big-M method [4]:

(4.42) { P v p i t M ( 1 d v p i ) P v c i t M ( 1 d v c i ) d i = d v p i + d v c i 0 d i 1

where ( d v p i , d v c i ) are binary variables to indicate the status of energy storage. If energy is stored, then (1,0); if energy is released, then (0,1).

Thus, an optimization network reconfiguration (ONR) model is Eqs. (4.10)–(4.24), (4.31)–(4.40), and (4.42). Noted that CAAWTS in this model, namely hard strategy, is not enough to eliminate the uncertainty of DG because its capacity is only a kilowatt-level generally, but the capacity of a distribution network is mostly a megawatt-level. Therefore, it is necessary to consider the uncertainty of wind power in ONR, where the RO method is used to eliminate uncertainty further, namely soft strategy.

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Design of floating offshore wind turbines

M. Collu , M. Borg , in Offshore Wind Farms, 2016

11.2.1.2 Maximum inclination angle

While FOWT systems can experience relatively large inclination angles (in roll and/or pitch), onshore and fixed-to-seabed offshore wind turbines do not experience such angles. As a consequence, there is very little experience in estimating the performance of wind turbines at large inclination angles, and relatively few data have been presented in literature.

Taking also into account the fact that many of the sub-systems of an offshore wind turbine (bearings, gearbox, generator, etc.) have been designed to operate close to the upright condition, it is necessary to impose a maximum roll/pitch inclination angle.

The exact value of this maximum inclination angle is still open to discussion, but according to the literature a good starting value is 10   degree. It is important to remember that this is the total angle of inclination, the sum of the static and the dynamic angles of oscillations, due, respectively, to the average value (mainly due to the wind) and the oscillation amplitude (mainly due to waves) of the inclining moments. In terms of the design, this requirement can be translated into a floating support structure minimum rotational stiffness (Section 11.2.2).

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Floating Wave Driven Wind Turbines and Island Supplies

W.M. Somerville , in Alternative Energy Systems, 1984

Autonomous Control for Small Isolated Power Networks

Two wind turbine systems are in operation on Fair Isle 2–3 and Lundy 4 , described in detail elsewhere, which can operate giving normal voltage and frequency under the overall control of a load management system. In each case the demand on the system is classified into essential and non-essential services. Essential services include lighting, power for entertainment and food preservation (freezers). Non-essential services include water heating, space heating and cooking, as alternative means for providing these services are available. Essential services are assured for two periods each day if there is not sufficient wind energy to meet demand by diesel generator plant.

The maximum demand for essential services lies between 30 and 40% of the wind turbines noted capacity. Power generated by the wind turbine, which is surplus to essential services demand, is automatically distributed first to heat domestic water and subsequently to block storage heaters.

This arrangement falls short of the consumers' expectation as part of the output is subject to availability. Public acceptance was obtained on Fair Isle by an operating tariff structure which favoured the use of non-essential service loads on an 'as available' basis for space heating using heat storage appliances. A facility was provided to householders indicating in broad terms the energy available from the wind turbine generator and a preferred tariff on essential services encouraged use of power from the wind turbine generator in preference to diesel generated power. Indication of the source and tariff applicable for essential services was provided in each household.

The participation of the islanders in controlling the use of essential service power to avoid diesel generation at the highest tariff has been enthusiastic and has resulted in a marked reduction of diesel fuel consumption whilst the energy consumption has more than doubled. The real cost of providing electrical power on the island has fallen to about one-third and the average cost per unit to the consumers is now comparable to mainland charges.

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Matlab and Simulink Implementations

Silvio Simani , Saverio Farsoni , in Fault Diagnosis and Sustainable Control of Wind Turbines, 2018

6.3.4 Fault Diagnosis Module Implementation

The problem of the residual generator design for the FDI of the wind turbine systems is implemented as described in this section.

The wind turbine system is assumed to be modeled by the description provided in Section 2. The main signals used in the simulation blocks described by the variables u ( k ) and y ( k ) represent the controlled inputs and the system outputs, respectively. As remarked in Chapter 3, the model–reality mismatch in fault-free conditions can be represented by the difference y ( k ) y ˆ ( k ) . In fact, it takes into account measurement errors, parameter variations, and disturbances. The reconstruction of the measurement y ( k ) , i.e., y ˆ ( k ) , is obtained from an identified model, as described in Chapter 3. According to the description provided in Chapters 2 and 3, in practice, the signals u ( k ) and y ( k ) are acquired by measurement sensors, which are inevitably affected by errors.

On the other hand, if the sensor dynamics are neglected, also faults affect the measurement process, which are modeled as highlighted in Fig. 6.28, where the faults f u ( k ) and f y ( k ) are additive signals affecting the measurements u ( k ) and y ( k ) .

Figure 6.28

Figure 6.28. The residual generation block for FDI.

Regarding the FDI task, this monograph recalled both the data-driven and model-based approaches described in Chapter 3 that are exploited for residual generators from the redundant input and output signals u ( k ) and y ( k ) . In this way, Fig. 6.28 shows that proper residual signals are computed as the different between the actual y ( k ) and its reconstruction y ˆ ( k ) , as represented in Fig. 6.29.

Figure 6.29

Figure 6.29. The residual generation module for FDI.

After the residual generation task, its evaluation is performed for detecting any fault occurrence, and for isolating the faulty actuator or sensor signals.

A direct geometric threshold comparison is recalled in Chapter 3 to perform the fault detection stage. However, a detection delay can be present due to the fault modes. The fault detection logic is performed according to the test described in Chapter 3 and implemented by the Simulink® block outlined in Fig. 6.30.

Figure 6.30

Figure 6.30. The residual evaluation block for FDI.

Actually, the residual r ( k ) is modeled as a stochastic variable, whose mean and variance values are estimated by means of the constant blocks shown in Fig. 6.30. These functions evaluate the mean and variance values of the fault-free residual signals. Note that these parameters could be exactly computed from the r ( k ) statistics, usually unknown.

A robustness and reliability degree is introduced for distinguishing the normal and the faulty behaviors, which is represented by the tolerance parameter δ (normally δ 2 ) remarked in Chapter 3. As shown by the results achieved in Chapter 5, the technique relying on the Monte Carlo tool is used here in order not to obtain conservative results. In particular, extensive simulations lead to the optimal value of δ that minimizes the false alarm probability and maximizes the true detection rate. This topic was addressed in Chapter 5.

Another important issue concerns the fault isolation task, and it is achieved using a bank of residual generators properly designed, which is based on the Generalized Observer Scheme (GOS). This task can be easily solved as recalled in Chapter 3, since different faults can affect different input or output measurements. In this way, when the outputs are fault-free, the input fault f u ( k ) , possibly affecting one of the inputs u ( k ) , is diagnosed with the bank of estimators depicted in Fig. 6.31.

Figure 6.31

Figure 6.31. Simulink scheme for the isolation of the system faults.

In general, the number of residual generators coincides with the number of faults to be diagnosed. Fig. 6.31 shows that the ith residual generator is fed by all but the ith input measurement (or even more input signals, if necessary) and all output measurements. The generated residual signal is thus sensitive to all but the ith fault f u ( k ) . These residual generators were described in Chapter 3. In particular, the ith estimator that does not depend on the ith input measurement is obtained using y ( k ) and all but the ith input measurement u i ( k ) ( i = 1 , , r ).

In the same way, when the input variables are fault-free, a fault f y ( t ) affecting the output measurement is diagnosed with another output estimator bank. The fault isolation scheme is based on a residual evaluation logic whose implementation is depicted in Fig. 6.32.

Figure 6.32

Figure 6.32. Simulink® scheme for the evaluation of the residuals generated by the estimator banks.

With reference to the scheme of Fig. 6.31, when a counter block has the value of "1", it means that the residual is affected by the fault, whilst "0" indicates that the corresponding residual does not depend on the particular fault.

Finally, as remarked in Chapter 3, according to the scheme of Fig. 6.31, note that multiple faults are isolable, as only the ith output signal feeding the residual generator is affected by the fault on y i . On the other hand, multiple faults on the inputs u i are not isolable as the residuals depend on the faults affecting different inputs.

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Model predictive control of power converters, motor drives, and microgrids

Zhenbin Zhang , ... Jose Rodriguez , in Control of Power Electronic Converters and Systems, 2021

4.4.2 Direct model predictive current control

For PMSG WTSs, DMPCC is applied for GSC and MSC. The DMPCC is illustrated in Section 4.2; only DMPCC for GSC is presented in this section. In the analogy to DMPCC for MSC, instead of using the grid-side instantaneous power as tracking targets, the grid-side current performances are of higher level priority for direct model predictive current control. The inner loop itself can be designed in the αβ frame, and the grid-side cost function is defined as

(4.25) J DMPC g ( u g ) = ( i g α i g [ k + 1 ] α ( u g ) ) 2 + ( i g β i g [ k + 1 ] β ( u g ) ) 2 .

The predicted current vector i g [ k + 1 ] α β ( u g ) ( u m U 8 ) can be obtained by Eq. (4.20). The current references are generated/set by a proper outer control loop (here a PI controller for the DC-link control is used to generate the d-axis current reference and the q-axis current is set to be zero for unity power factor control. These two references are then transferred into αβ frame). In the analogy, due to the currents both in α- and β-axis are equally important to the system, again no extra weightings are required for these targets.

After evaluating and minimizing the costs obtained from (4.25) for u m U 8 for the two-level MSC, an optimal voltage vector of G g will be obtained and assigned to the machine-side converter. An overview of the predictive current control method for both the grid- and machine-side control is shown in Fig. 4.11.

Figure 4.11. Control structure of direct model predictive current control for three-level NPC back-to-back power converter PMSG wind turbine system.

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Options for Remote Locations

Galen J. Suppes , Truman S. Storvick , in Sustainable Power Technologies and Infrastructure, 2016

Cost of Wind Turbine Systems

For large commercial wind turbine systems (1500  kW) the National Renewable Energy Laboratory's 2013 Cost of Wind Energy Review [1] identified installed capital costs from $1450 to $3000 per kW ($1730 best estimate) and capacity factors of 25–50% (38% best estimate) for wind turbine systems. For the installed costs, average breakdown is 32% for the turbine, 18% for support structure, and 10% for electrical infrastructure. The levelized cost of electricity based on 200 year operational life was about 6.6   ¢/kWh.

Comparative data on small scale wind turbine systems is not readily available. A survey of prices versus capacity for advertized systems is summarized in Figure 9.1 and is compared to the commercial benchmark prices of $1730 per kW installed and 32% of that for just the wind turbine. The conclusion is that commercial price statistics for 1500   kW systems have applicability to residential systems of 0.5–6   kW. This is reflective of the impact of two separate economies of scale.

Figure 9.1. Trends in cost of wind turbine power systems as available from internet marketing. Costs generally do not include installation and conversion from DC to AC.

Commercial wind farms have economies of scale related to the large size of the units which is common in engineering. The residential system has economies of scale related to large-scale production of identical units. In addition, smaller residential systems can benefit for the lower degree of specialization both in skilled labor and equipment needed for installation. None of the systems in Figure 9.1 included shipping and installation, and most did not include a DC to AC converter. The conclusion is that on the topic of residential and small community wind turbines, installed cost of $1530 per kW is a good benchmark to which costs of such systems can be compared.

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Design and implementation of a power supervisory of a controlled greenhouse in the north of Tunisia

Rim Ben Ali , ... Abdelkader Mami , in Recent Advances in Renewable Energy Technologies, 2021

5.4.1 Description of the power supervisory

Energy management of the WTS requires an appropriate strategy to control its generated power to avoid energy losses, especially that produced during a period of low consumption. The combination of several renewable energy system, which are available in many areas with a fixed required power can be more efficient than a standalone source of energy. Meanwhile, it is necessary to manage the produced energy, while using a BBS for the storage of excess energy [28]. The scheme of the proposed HPS is shown in Fig. 10.8. In this configuration, the proposed HPS consists of the following subsystems:

Figure 10.8. The proposed hybrid power system.

PMSG, Permanent magnetic synchronous generator.

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WTS based on a PMSG generator.

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AC/DC converter (rectifier).

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Supervisory control.

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Resistance used to dissipate excess energy.

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BSS linked to the HPS without a DC/DC converter to reach a higher required voltage with a minimum of controllable parameters.

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Environmental impacts of renewable energy

Rosnazri Ali , ... Syed Idris Syed Hassan , in Electric Renewable Energy Systems, 2016

21.5.3.2 Noise

Noise produced by the wind turbine system may disturb surrounding residents especially at night where conditions are tranquil. There are two sources of noise produced by wind turbines, which are mechanical and aerodynamic noise. Mechanical noise comes from turbines' internal gear, generator, and other auxiliary components but is not affected by the size of turbine blades. Proper insulation during manufacturing and installation could reduce this noise level. In contrast, the aerodynamic noise comes from blades passing through the air and is proportional to the blades' swept area, wind speed, and speed of rotation. For example, a bigger size wind turbine is noisier than a smaller one. To mitigate the effect of noise, there should be a minimum distance between the residents and the wind farms; this practice varies between countries and regions.

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Comparison of objective functions on the sizing of hybrid PV and wind energy systems with and without energy storage systems

Loiy Al-Ghussain , Onur Taylan , in Hybrid Energy System Models, 2021

7.3.2.2 Wind turbines with zinc-bromine battery (Scenario 6)

Scenario 6 investigates the feasibility of WTS with ZBB, and Table 7.12 shows the optimized results of this scenario. The integration of ZBB increased the RES fraction in all the optimization scenarios when compared to WTS without any ESS in Scenario 5, where ZBB assisted in reallocating the excess energy. So, ZBB enhanced the matching between the energy generation from WTS and the demand. Notice in Table 7.12 that the WTS capacity in Scenario 6A increased almost four times compared to Scenario 5A, where Scenario 6A required the huge capacity of the ZBB, which enabled more energy to be stored to satisfy the optimization objective which is maximizing the RES fraction in Scenarios A. Moreover, the RES fraction increased by 0.5% in Scenario 6B when compared to the one in Scenario 5B where the contribution of ZBB was smaller as a result of the losses in the energy stored in the battery due to the rated DoD and the round trip-efficiency of the ZBB. Furthermore, notice in Scenario 6C that the integration of ZBB with the same WTS capacity increased the RES fraction and DSF by about 8.2% and 14%, respectively, while maintaining its economic feasibility.

Table 7.12. Optimal WTS and ZBB capacities using the three optimization scenarios in METU NCC.

Parameter Scenario A Scenario B Scenario C
WTS capacity (MW) 1792 2 2
ZBB (kWh) 46,635 113.3 6322.7
R F (%) 99.9 45.0 53.2
DSF (%) 99.9 27.5 41.5
E C (USD/kWh) 45.56 0.1476 0.1750
NPV (M USD)   3362 2.07 1.58
PBP (years) 39.3 5.5 6.8
A CO2 (tons) 2,647,349 2955 2955

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Stochastic-based energy management of hybrid AC/DC microgrid

Hamed Pashaei-Didani , ... Sayyad Nojavan , in Risk-based Energy Management, 2020

11.3.10 Power generation of renewable energy sources in the DC subgrid

Power generation of PV and WT systems in the DC subgrid are depicted in Figs. 11.17 and 11.18, respectively. As wind speed and solar irradiation is the same in the location of the hybrid AC/DC MG, generated power by the RESs follows same pattern. It should be noted that the operational requirements of WTs and PVs are considered the same in AC and DC subgrids although they differ in system capacities. The maximum power generation of WTs in DC subgrids is equal to 0.27   MW. In addition, the highest level of generated power by the PV systems in the DC subgrid is equal to 0.15   MW.

Figure 11.17. Generated power by the wind turbines in the DC subgrid.

Figure 11.18. Generated power by the photovoltaics in the DC subgrid.

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