Nomenclature

	Active power error at node
	DC voltage error at node
	AC grid voltage at node
	Rate of change of active power reference at node
	Membership degree of a variable in fuzzy domain
	Degree of fulfillment of rule
	Minimization of a function
	Vector of individual chromosomes to be optimized
	Total DC power losses of the system
	Active power at node
	DC voltage at node
	Lower bound on all solutions of optimization
	Upper bound on all solutions of optimization
	Pre-defined power at a node

This chapter presents a novel control scheme for voltage and power control in high voltage multi-terminal DC (HV-MTDC) grids used for the grid connection of large offshore wind power plants. The proposed control scheme employs a computational intelligence technique in the form of a fuzzy controller for primary voltage control and genetic algorithms at the secondary control level. At the primary level, the fuzzy approach does not necessarily change the conventional structures proposed in the literature, but instead combines the best of several conventional strategies in a single “box” whilst at the same time eliminating their drawbacks. At the secondary level, the solution of the optimal HVDC grid load flow via genetic algorithms provides optimal set-points which are passed on to the primary level control. Time domain dynamic simulations on a three terminal HVDC grid benchmark are presented. It is demonstrated that the proposed method ensures optimal power dispatch in the HVDC grid ensuring robustness and flexibility in operation.

11.2 Conventional Control Schemes in HV-MTDC Grids

In HV-MTDC literature, two broad categories of control strategies have been proposed, viz. PI (proportional integral) based strategies—constant power, constant voltage—and droop (proportional control) strategies. All other strategies/modification schemes are related to one of these either singly or in combination. Such schemes include voltage margin, piecewise droop, dead/un-dead band droop, and numerous other schemes [1–13].

Constant voltage and power control, whilst very simple and straightforward in use, have a drawback of inherently assuming continuing normal operation of the grid [7]. Hence, they are incapable of online power compensation in the event of contingencies without applying communication resources. Power compensation during emergencies requires timeliness, for which reliability issues and the possible unavailability of communication channels or communication resources may prove a hindrance to the security of supply objective, not to mention possible damage to sensitive devices. However, they do have the advantage of reaching the desired set points without any deviation. That is, whenever a new power flow pattern is established and set points are sent to the respective converters, with PI strategies, the pre-determined power flow pattern will be reached (assuming the choice of other parameters is well conditioned).

In contrast, the droop control strategy similar to that employed in HVAC (High Voltage Alternating Current) grids allows for several capable terminals to contribute to power balancing during contingency, in order to keep the grid voltage within acceptable limits without the need for communication resources. This offers advantages in terms of security, robustness, stability, and safe operation. Nevertheless, droop strategies have a drawback of not reaching desired set points when a new power flow pattern is required. This is as a result of the inherent architectural structure of the droop controller.

As a result of the drawbacks attributed to these two broad categories, modifications have been proposed. Voltage margin is a modified form of constant voltage that whilst still a PI strategy, allows several converters to control the voltage in a coordinated manner in the event of an outage of the voltage priority control terminal [5, 14]. However, as the MTDC grid grows in size, there may be a need for a larger margin (which may not be feasible or realistic); this puts a limitation on the size of the grid, besides being not suitable in the event of cascaded outages where communication may have to be relied upon. Therefore, the droop strategy is still a better alternative notwithstanding its drawbacks.

Dead and un-dead band strategies have been proposed as acknowledged in [13, 15, 16]. The dead band approach combines the capabilities of voltage margin and droop voltage schemes, while the un-dead band scheme can be viewed as a combination of several droop characteristics (different gains in different regions). The principles of operation remain the same as that of the basic strategies. A huge drawback of both strategies are the sharp edges between transition points as acknowledged in [16]. Thus, smoothed nonlinear edges at transition points have been proposed. However, the drawbacks of conventional droop still presents.

Voltage and power deviations of the droop voltage strategy can be attributed to a number of factors. The voltage and power control blocks basically fight each other for control, leading to steady state deviations. Also, the fact that a voltage difference at terminals is required to establish a power flow contributes to the deviations. Converter losses, uneven DC line voltage drops, and topology all contribute to deviations. Deviations result to inaccurate power flows, poor loss profile, and inaccurate instantaneous power balancing [7, 9].

Some research effort has been dedicated to solving the problem of voltage and power deviations. Proposed methods include the influence of fixed droop constants analytically in power flow equations, exploiting the role of the Jacobian matrix of the traditional Newton–Raphson (N–R) method as reported in [7, 9]. According to [9], some percentage of deviation is still incurred. Besides, these methods require an elaborate mathematical framework that is tedious and not entirely clear.

This chapter proposes a new methodology with zero voltage and power deviation that does not include the influence of the droop constant in power flow equations, nor does it employ the traditional N–R method. Instead, an optimization problem is solved using genetic algorithms at the secondary level to calculate the optimal voltage references that minimize the losses and establish a pre-defined power flow pattern in the same way as N–R. These optimal voltage and power references are then passed on to a knowledge-based fuzzy-droop controller at the primary level that combines the capabilities of both constant power and droop voltage strategies.

Upon receiving the new set points, the fuzzy controller transitions the system to a constant power strategy for which set points will be reached and remains in this strategy until errors start to reduce. As errors starts to reduce below a given boundary, the strategy senses this and very smoothly transitions from constant power back to droop voltage control, and when steady state conditions are fulfilled, the system remains fully in droop mode. The MTDC stays in droop voltage control until new set points are received, irrespective of any contingency. The methodology is in retrospect a combination of the aforementioned broad strategies. This combination is made possible by fuzzy logic, which introduces inherent knowledge into the system control.

11.3 Principles of Fuzzy-Based Control

The objective of this section is to highlight the implementation of fuzzy logic and control as an intelligent technique and not to discuss the basics of fuzzy logic control. Readers are referred to [17] for a detailed treatment of the concept of fuzzy logic and control. Notwithstanding, a short overview is given.

Fuzzy logic and control is classified as one of the knowledge-based computational intelligence methods that mimic human behavior and actions. Fuzzy logic was formulated in 1965 by L. Zadeh who put forward the mathematical formulation as we know it today [18]. Fuzzy control can also be viewed as a natural language processing tool that allows for the use of human knowledge and experience about a system behavior, coded as rules, in order to take control actions without an explicit mathematical formulation of the system. Thus, fuzzy control is suitable for problems in which mathematical formulation is too expensive or for which a single control law is not applicable. A particular class of fuzzy systems is applicable to this work—rule-based fuzzy systems. Rule-based fuzzy systems are one of the most popular classes of fuzzy systems and most relevant to electrical power systems application. Rule based fuzzy system take the form:

IF antecedent proposition THEN consequent proposition

Both antecedents and consequents can combine variables with connectives such as “AND,” “OR,” and “NOT.” The form of the consequent determines the sub-class of rule-based systems. For this chapter, the linguistic model with special case of singleton consequents is utilized.

11.4 Implementation of the Knowledge-Based Power-Voltage Droop Control Strategy

As previously described, the broad categories of conventional strategies are in a way complementary to each other. When each broad category is used exclusively with and without modifications, several drawbacks exist, thus restricting practical use of these strategies. Therefore, the proposed strategy is capable of combining several complementary conventional strategies in such a way that it is easy to transition from one to the other very smoothly without causing instabilities. This combination eliminates the most important drawbacks of each while combining their advantages. In this chapter, the proposed strategy combines constant active power and droop voltage control strategies. The fuzzy controller acts as an autonomous supervisor in transitioning from one strategy to the other when the pre-defined conditions are fulfilled. A block diagram of the proposed control strategy is depicted in Figure 11.1. As can be seen, the droop gain is scheduled by the output of the fuzzy controller. The scheduling is performed online, based on local measurements as will be given in following sections. The main assumption for practical implementation is that the inner control loop of the converter where the fuzzy logic is applied is well tuned such that it is stable for the whole range of droop values. Also, we assume that the converters are connected to stiff grids with high short circuit ratios.

11.4.1 Control Scheme for Primary and Secondary Power-Voltage Control

A schematic diagram of the proposed primary and secondary control schemes is given in Figure 11.2. A three-terminal HVDC grid test system is utilized, connecting a far-from-shore wind power farm. An optimal power flow using genetic algorithms is solved at the secondary level. This defines the power and voltage set points for the given wind power generation and power dispatch at the onshore converters. Since the fuzzy controller schedules the gains such that the onshore converter is in constant power control when new power set points are ordered and achieved, droop gains do not affect the transition. As a result, the effect of the droop gain is not included in the optimal HVDC grid load flow. This simplifies the optimal load flow calculations.

The calculated optimal power and voltage set points, in combination with information obtained locally by the fuzzy controller, are used to determine if conditions are fulfilled for the transition from one strategy (constant power) to another (droop) and vice versa. By default, the system is designed to remain in droop strategy during normal operation. Hence, when set points are received, the transition occurs from the droop strategy to the constant active power strategy.

Hence, as soon as the the power set points are reached and the error gradually reduces to zero, the fuzzy controller smoothly transitions the system from constant active power back to droop control by increasing the droop gain. It completes the transition to droop and remains in droop until new set points are ordered. As long as new set points are not received (even if communication fails), the converter remains in droop strategy, ensuring that terminal voltages will be kept within bounds.

11.4.2 Input/Output Variables

Knowledge gained from system operation and desired control objectives determines the fuzzy supervisor inputs and outputs that would give sufficient information to take control actions on the main system. The distinct input variables for this strategy are: , , , with , the number of DC nodes in the DC grid, and the number of the offshore nodes. Furthermore, we define the following variables: and . Finally, is the AC grid voltage amplitude at the point of common coupling (PCC) of the onshore station i. The error variable that is used in the fuzzy rules is defined as . Finally, is the rate of change of the power reference set point.

A combination of , , , and determines the current and future state of the fuzzy controller. The signal in particular signals to the controller whether a reference change has occurred or not. Without this signal, the controller will always initiate a transition to constant power for any non-zero and . That is, even for a contingency scenario where both and signals are non-zero, the controller will try to switch over to constant power, which is quite the opposite of the control objectives. Thus, acts as a discriminatory signal to prevent controller from changing unless there is a reference change for which will be non-zero. acts to give information about fault scenarios during which we want priority to switch to droop mode to ensure voltage is kept within a tolerable range.

The output of the fuzzy controller is a singleton with gain bounded between the values 0 and 20 (VLOW or HIGH respectively) at the extremes. During the transitions, the gain (output of the fuzzy algorithm) varies smoothly between 0 and 20 as dictated by the sigmoidal MF of the error signal as shown in Figure 11.3.

11.4.2.1 Membership Functions and Linguistic Terms

There is no standard method for the choice of membership function (MF) type. The choice relies upon the developers intuition and expected performance, and is application-specific. There are several typical MFs to choose from, and more complicated MFs can be obtained from basic MFs. In very special circumstances depending on the application, there might be a need to develop customized MFs. Alternatively, different MFs can also be employed for different variables, again application specific. In this chapter, two major MFs, trapezoidal and sigmoidal, were employed to map variables from their natural domain onto the fuzzy domain [0, 1]. The simplest MFs, trapezoidal and triangular, can be employed at the development phase, and as experience is gained, more complicated MFs can be employed. Parameters of the MFs can be chosen based on intuition of the underlying dynamics, optimization based on expected performance, or other computational methods available.

In this chapter, the choice of parameters for the trapezoidal MF was straightforward. However, the sigmoidal MFs requires the solution of a system of nonlinear sigmoidal MF equations equal to the number of linguistic terms of the sigmoidal MF. Parameters of the sigmoidal MF are the unknowns of the equation. The sigmoidal MF is dictated by the equation:

11.1

where and are parameters of the sigmoidal curve.

The sigmoidal MF with two linguistic terms, “ZERO” and “PBIG,” were chosen for each of and , as shown in Figs. 11.3 and 11.4. PBIG implies “positive big,” and is just a term that is highly subjective. The sigmoidal MF was chosen for its smoothed curved surface. The trapezoidal MF was sufficient for AC grid voltage with two linguistic terms, “Faulty” and “OK,” following discretization of fault values, as shown in Figure 11.5.

11.4.4 Defuzzification and Output

Defuzzification takes the output of the inference engine from the fuzzy domain into the physical domain the system understands. The two most common defuzzification methods are the center of gravity (COG) method and the mean of max (MOM) method. In this chapter, COG with Mamdani inference was used for defuzzification for its ability to interpolate. In our case, only the extremes of 0 and 20 for droop gains were specified in the fuzzy design process. However, looking at the results in Section 11.6, it is clearly seen how interpolation occurred despite the use of discretized values. This was the intended purpose and is the rationale behind its choice. Equation (11.2) gives the general expression for the COG defuzzification method:

11.2

where is the number of elements, and is the membership grade of each element in the output fuzzy set. Since the singleton model was employed for this work, Equation (11.2) is adapted to:

11.3

Where is the number of rules, is the degree of fulfilment of each rule, and is the output singletons (0 and 20). Figure 11.6 shows a 3-D nonlinear surface plot that shows clearly the transition surface. Finally, Figure 11.7 presents a state machine that describes the operating steps of the proposed fuzzy logic based adaptive droop controller.

11.5 Optimization-Based Secondary Control Strategy

The Newton–Raphson (N–R) method is the traditional iterative procedure for solving power flow equations in power systems. Though very effective in terms of convergence, its flexibility to rapidly changing conditions involving a relatively large DC grid remains to be seen. The genetic algorithm (GA), though an optimization routine, offers flexibility irrespective of topology and size of grid and can be easily integrated with communication and measurement infrastructure, allowing it to adapt to changing situations—self-healing without any need to explicitly specify the power flow equations. Comparison of both GA and N–R show strikingly similar results, with negligible differences if any. The GA uses its operators—selection, crossover, mutation, and inheritance—to direct solutions toward convergence or a global optimum [19].

In this proposal, the GA is employed at the secondary control level to provide the unknown optimal voltage that minimizes losses and establishes a pre-defined power flow pattern in the DC grid from which the unknown power can be calculated—in essence, an optimal power flow (OPF). Optimal references are then passed on to the fuzzy-based strategy at the primary control level, responsible for taking the final action. With communication infrastructure (as typical with secondary control) the GA can be updated periodically to reflect current conditions in a dynamic way. The GA thus effectively replaces the N–R method despite being an optimization routine.

11.5.1 Fitness Function

As with most optimization algorithms, there is an objective function—or “fitness function”—that determines how good a solution is relative to the set tolerance. The objective of the OPF is to find a set of nodal voltages that minimizes the losses and establishes a power flow pattern in the network. The individual chromosomes are given in Equation (11.4):

11.4

where is the DC voltage reference of terminal and is the number of nodes in the DC grid. The nodal power at each terminal can be calculated from the voltage references by considering the topology and structure of the grid. All the information required to calculate the unknown power is in the “incidence matrix.”

The fitness function defines mathematically what is to be minimized and takes the form described by Equation (11.5). The fitness function (objective function) employed in this work is the total DC losses of the system given by the sum of DC nodal power.

11.5

where, is the total DC loss in the system, is the DC nodal power at node , and is the number of DC nodes in the grid. Equation (11.5) is thus expressed in terms of the chromosomes contained in Equation (11.4), that is, the nodal voltages.

11.5.2 Constraints

There are certain technical and physical/material limits that cannot be violated irrespective of any other conditions. In the present work, the consideration of the constraints is performed based on a static penalty scheme. Constraints can take the form of bound, linear, or nonlinear constraints, for both equality and inequality constraints.

Bounds constraints ensure that acceptable solutions are within a technically allowable range. With the current state-of-the-art of VSCs, the IGBT (insulated gate bipolar transistor) switches that make up the VSCs are still very sensitive devices. Over-voltages cause irreparable damage to switches; under-voltage in general lead to loss of controllability. Hence there must be a bound on the solution of GA. Bounds constraints take the form of Equation (11.6):

11.6

where is the lower bound and is the upper bound on all solutions. For this work, the bounds constraints on the references obtained are as described in Equation (11.7). A slight modification of Equation (11.7) was employed, as shown in Equation (11.8), where , and define allowable relaxations and are equal to 0.05 in this work:

11.7

11.8

Nonlinear equality constraints are especially important from an operational point of view. There are certain common instances that involve market, legal, or associated conditions, which stipulate that certain nodes in the DC grid get a fixed or pre-defined amount of power irrespective of changes in operating conditions, especially the amount of wind power (excluding any disruptive changes that may give priority to security instead of market or legal conditions). This is a nonlinear equality constraint, and these have the form described in Equation (11.9):

11.9

where is the nodal power of node .

11.10

where is the pre-defined power at a node.

11.6 Simulation Results

This section presents the time domain simulation results carried out with the proposed intelligent control strategy both at the primary and secondary levels. The results are meant to demonstrate the capabilities, robustness, and efficacy of the strategies. The strategy was implemented on the three terminal grid described in Figure 11.2. Several realistic scenarios were simulated. The proposed fuzzy logic based adaptive droop is installed at VSC 2 while VSC 3 applies constant voltage control operating as a slack DC bus.

11.6.1 Set Point Change

Prior to this simulation, the network is first initialized at equilibrium operating point. Wind power at VSC 1 is 1000 MW, VSC 2 is set at 300 MW (inversion). VSC 3 takes the difference after losses are accounted for.

At t = 1 s, the power set point of VSC2 changes from 300 MW to 500 MW (inversion). All the conditions were thus fulfilled for a transition from droop strategy to constant power mode dictated by a droop gain of zero. Figure 11.8 presents the transition from droop control (R = 20) to constant power (R = 0). At about t = 4 s when the steady state power and voltage error reduces to zero, the fuzzy supervisor gradually transitions back to droop mode (dictated by the droop gain) in a very smooth manner without sharp edges. A time delay block is added to the reference change in order to prevent oscillations as both power and voltage are dependent on each other.

11.6.2 Constantly Changing Reference Set Points

With the goal to test the efficacy and robustness of the proposed strategy, consequent reference changes were sent to the converter VSC2 every t = 10 s over a 50 s range just to ensure that the expected objective will be met regardless of the the way set points are provided and for different initial conditions. For this scenario, set points were changed from inversion to rectification to prove the efficacy of the strategy. As expected, the fuzzy supervisor met the objectives as designed regardless of the initial operating point and the change applied, ensuring a robust operation over the entire range. Figure 11.9 shows the superiority of the proposed strategy over the conventional droop only strategy as the fuzzy supervisor responded to every set point change as required. Finally, is worth observing the output of the fuzzy droop gain changing from 0 to 20.

11.6.3 Sudden Disconnection of Wind Farm for Undefined Period

During contingencies, it is important that the system remains in droop mode to keep voltages at all nodes controllable within acceptable bounds. In a DC grid, any change at all will cause a non-zero error to be measured at all nodes. Thus, the proposed strategy must be able to distinguish between a measured error due to a change in reference (or other conditions that facilitate a change to constant power mode) and an error due to contingencies, to make sure it does not act or transition to another strategy. Figure 11.10 shows the system response for sudden disconnection of a complete wind power plant.

Such sudden disconnection results in a deficiency of power in the DC grid, and an obvious response is a sag in voltage at all terminals. Since VSC 2 is in droop mode, it reacts to keep the grid voltage within acceptable bounds by injecting power from the adjacent AC grid. It is obvious from the subplot of droop gain that the system remained in droop, and terminal voltages barely rose from their set reference. With PI based strategies, the system voltage may well dip below the minimum threshold of 0.9 pu for stable operation.

11.6.4 Permanent Outage of VSC 3

This is a rather important scenario that must be considered in any realistic operation of the grid, that is, loss of any terminal. The response of a DC grid to loss of a terminal consuming power is voltage rise, as this surplus power charges the capacitance of the network. Notwithstanding, the rise must be kept in check to prevent instability. Any rise must not exceed the maximum voltage that a grid is designed to withstand (typically 1.2 pu). Figure 11.11 depicts this rise. As can be seen from the plot, despite the rise, the nodal voltages at all terminals are much below the threshold because the system remained in droop mode. For conventional PI strategies, a chopper may need to operate when voltage exceeds the threshold. This significantly adds to the total cost of a design.

11.7 Conclusion

This chapter presents a knowledge-based primary and an optimization-based secondary control scheme for offshore multi-terminal HVDC grids. The presented results reveal the superiority of adaptive fuzzy droop control to solve major drawbacks presented by conventional direct voltage and power control strategies. Based on the results, there were no observed deviations in the power or voltage with fuzzy control, which is a major drawback of power based droop. As a matter of fact, there is no need for secondary corrective actions.

In addition, fuzzy control is flexible, and can be applied as a “plug ‘n’ play” device to any VSC-HVDC converter without knowledge of inner controller proprietary information (interoperability). Moreover, its capabilities can be expanded off-line and on-line as more experience is gained.

The proposed strategy reveals the capabilities of a natural language processing tool to combine strategies that would not be possible with a single control law. Besides, the implementation of the proposed strategy requires very little knowledge or expertise of power systems, let alone HVDC grid operation. Topology, market conditions, configuration, size, and so on do not influence the proposed strategy in any way detrimental to the operation of the grid and can be extended to as many terminals as necessary.

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