Due to the unique advantages in computational robustness and convergence, the linear approximation approach is and will remain to be an important method to solve the optimal power flow (OPF) problem, especially for industrial applications. The DC power flow method, which is currently used in the majority of power industries, is the representative. Many studies extend the DC power flow method by including voltage magnitude, reactive power, and losses. This study provides a detailed analysis and breakdown investigation of existing linear approximations of the OPF problem. The formulation and accuracy of existing linear approximations are compared. Taking advantage of the decoupled formulation of linear approximations, the property of power flow equations is illustrated from a new perspective. Why reactive power flow equations are hard to linearise is explained theoretically. The numerical performance of existing linear approximations is demonstrated in IEEE and Polish test systems. Evidence from the theoretical analysis and numerical studies shows that the accuracy of linear approximations could be substantially improved using a mathematical transformation of the non-linear voltage magnitude term. This finding provides a new research direction for solving the OPF problem using linear approximations.

The framework for virtual integration of laboratories enables co-simulation and joint experiments that include hardware and software resources hosted at geographically distributed laboratories. The underlying concept of such framework is geographically distributed real-time (RT) co-simulation. To this end, digital RT simulators are interfaced over long distances via shared communication network such as the Internet. This study proposes an architecture for a modular framework supporting virtual integration of laboratories that enable flexible integration of digital RT simulators across Europe. In addition, the framework includes an interface that enables access for third parties via a web browser. A co-simulation interface algorithm adopted in this study is based on representation of interface quantities in form of dynamic phasors. Time delay between RT digital simulators is compensated by means of phase shift that enables simulation fidelity for slow transients. The proposed architecture is realised for the integration of laboratories across Europe that are located at RWTH Aachen University in Germany, Politecnico di Torino in Italy and at European Commission Joint Research Centres in Petten, Netherland and in Ispra, Italy. The framework for virtual integration of laboratories presented in this study is applied for co-simulation of transmission and distribution systems.

Power swing blocking (PSB) is essential for distance relay to avoid unintended tripping of transmission lines. Conventional PSB techniques, which use local information, may not be able to distinguish power swing from fault for all system conditions. An accurate PSB algorithm is proposed in this study, which uses synchrophasor measurements to distinguish power swing from fault. During power swing, the impedance trajectory is predicted for next ten cycles to block the distance relay operation reliably. The prediction approach overcomes the latency issue with synchrophasor data in order to initiate the blocking decision for zone 1/zone 2 of distance relay well in advance. The proposed method is tested for two-area four-machine and ten-machine 39-bus systems under different conditions simulated in power systems computer-aided design/electro-magnetic transient design and control software and compared with conventional method. Execution time of the proposed method including latencies in data arrival are considered in the test results.

Multi-objective optimisation of capacity planning for a grid-connected Microgrid (MG) with multi-energy demands is developed in this study. The optimal multi-energy coordinated scheduling, in which uncertainties of renewable energy generation and electricity demand are described by uncertainty intervals, is considered within the capacity planning model. To solve the capacity planning problem while considering the optimal scheduling with uncertainties, a two-level optimisation approach is proposed by integrating interval mixed integer linear programming for scheduling into the multi-objective particle swarm optimisation for capacity planning. The multi-objective addresses the economic issue by minimising the worst-case optimal annual costs of device investments, operation and maintenance, and pollutant emission treatment, as well as the reliability concern by minimising the worst-case optimal annual costs of energy outage. Several MG cases studies are shown to demonstrate the proposed method.

Longitudinal current differential protection is often used as the main protection of ultra-high voltage (UHV)/extra-high voltage (EHV) transmission lines. It's sensitivity and selectivity will be severely influenced by the considerably increased distributed capacitive current with the increase of voltage level and transmission distance. In this study, a novel UHV/EHV transmission line protection is proposed based on longitudinal tapped impedance. For sound transmission line or transmission line with external faults, the calculated impedance is approximately equal to the capacitive reactance of the line. If internal faults occur on the line, the computed impedance of the faulty phase is approximately equal to the parallel value of the line capacitive reactance and the fault resistance. The proposed protection does not require the compensation of capacitive current and is not affected by load current and system impedance. This new protection principle has an improved selectivity and natural phase selection ability, and very high sensibility for high resistance faults. The correctness and effectiveness of the proposed protection have been verified by simulation tests.

In this study, the problem of optimal parameters in charge simulation method (CSM) is solved using the genetic algorithm (GA), particle swarm optimisation and differential evolution. The comparative study shows that the GA is more effective. A model based on a hybrid approach that combines CSM and the GA is proposed to calculate the electric field created by an overhead extra high voltage power line. The resulting field levels were compared with exposure values set by the ICNIRP and IRPA standards. The results show that these levels are less than the limit recommended by these standards. The simulation results of electric field intensity values are compared with those obtained from polarisation ellipse method. A good agreement has been reached.

Islanding detection is important for the protection of any distribution system supported by distributed energy resources. In this work, a number of islanding and non-islanding events are simulated to prioritise 16 different passive parameters on the basis of performance analysis. Among the parameters tested, the rate of change of frequency over reactive power (df/dq) attains the highest accuracy and consequently, a new passive technique is proposed that employs df/dq as discriminative feature. An extended study is carried out to further test the ability of the technique to differentiate the islanding from the non-islanding events of similar signatures, such as load variation, capacitor switching, faults and induction motor starting. The simulation results confirm that the technique is proficient enough to identify islanding from non-islanding events that cause minute disturbances in the power supply network.

Accurate fault locating minimises labour and outage time. Efforts to increase the accuracy of fault locating methods are on-going. In this study, a dynamic state estimation-based fault locating (EBFL) method is proposed. Best implementation requires GPS synchronised sample value measurements at both ends of the line. The dynamic state estimator operates on the sampled values using a detailed dynamic model of the line, which includes the fault location as a state. Specifically, the dynamic line model is represented as a multi-section transmission line model, inclusive of phase conductor type and size, shield wire(s) type and size, and tower ground impedances, integrated with the fault model. This study presents extensive numerical experiments demonstrating that the method has higher accuracy than traditional fault locating methods for different fault types, locations and impedances. Additionally, the method works for both two-terminal and three-terminal transmission lines.

This study addresses the distributed economic dispatch problem for DC microgrids when time-varying delays are present in communication networks. A novel distributed algorithm is proposed, and the proposed controller contains a distributed generation cost optimisation module and a voltage regulation module. The cost optimisation module is aimed to realise cost optimisation by driving the incremental cost rate of every distributed generator to be equal. In the voltage regulation module, a distributed synchronisation algorithm is used to restore the global average voltage. After the effect of the communication delay on the system stability is analysed, the robust stability criticality under load changes is obtained by using linear matrix inequality. The performance of the proposed scheme is validated through simulations and experimentally.

This study presents a probabilistic model to determine the optimal expansion of transmission network under uncertainties of demand, wind power generation, and energy price. The Benders decomposition approach and the point estimate method (PEM) are used to solve the developed mixed-integer optimisation problem and tackle the uncertainties, respectively. The proposed market-based expansion problem is a two-stage model in which the master problem optimises the investment cost, and the sub-problem (SP) includes the cost of energy not served, congestion cost and congestion rent. A new objective function is proposed to consider the congestion rent in the Benders algorithm. In the SP, a two-step optimisation process is then proposed to generate proper Benders cuts. The proposed model has been applied to the Garver's, and modified IEEE 24-bus and IEEE 118-bus test systems. Furthermore, to validate the accuracy of the proposed PEM, a Monte Carlo simulation method (MCSM) has been used and the results of PEM have been compared to the MCSM.

This study presents vacuum circuit breaker switching investigation on a grid connected photovoltaic power plants. The focal point of this research is to discuss potential overvoltages during various switching operations in terms of the medium-voltage insulation coordination procedure. Influence of the LC filters of solar converters on high-frequency transients was highlighted, with main focus on generation of arc re-strikes and pre-strikes during opening or closing of the vacuum circuit breaker. Scheduled and emergency switching operations were analysed by means of laboratory experiments and Power Systems Computer Aided Design (PSCAD) simulations. Alternative switching sequences were proposed for mitigation of transient overvoltages.

Recent studies have concluded that battery energy storage will soon be economically competitive if its cost continues to decline. The authors propose a two-stage look-ahead daily scheduling strategy for distributed energy storage located in distribution networks with a substantial photovoltaic (PV) penetration. They assume that the load serving entity operates this energy storage to harness simultaneously multiple streams of benefits: energy arbitrage, peak shaving, minimising deviations from the load forecast and regulation service. To determine the optimal capacity bid into the day-ahead regulation market and address the price, load, and solar forecast uncertainties, they propose a two-stage optimisation model that bids regulation capacity on the day ahead and determines the storage dispatch schedule in real time. At the day-ahead stage, the load serving entity reserves a portion of the storage capacity for regulation, while the remaining capacity is dispatched for energy arbitrage, peak shaving and minimising the deviations from the forecast. Result suggests that regulation services account for the majority of these benefits. The energy storage is dispatched for peak shaving and forecast-deviation minimisation from around noon to late evening. During the rest of day, storage is dispatched primarily for regulation services.

In power grids, directional relays are used in situations that direction of fault current is not fixed. Distribution networks including distributed generation (DG) resources and transmission networks are some of these situations. Directional relays as key elements of distance and over current relays provide selectivity for these protections to improve their performance and power systems stability. In this study, a directional algorithm is proposed, which is able to discriminate fault direction just by sign of imaginary part of post-fault current phasor. To evaluate the algorithm, plenty of simulations and experiments are carried out in different fault conditions. Moreover, impact of power flow direction at normal operation of the power system is considered in the evaluation of the algorithm. Also, its performance is compared with some other directional algorithms. The results confirm that the proposed algorithm is able to detect fault direction with high degree of accuracy. Moreover, simplicity of the algorithm represents its competence for practical implementation in transmission and distribution networks.

Unit commitment (UC) is an important decision-making tool in power system operations. As a critical input to UC, inaccurate day-ahead load forecasts could result in UC solutions of high operation cost, or even trigger involuntary load shedding and jeopardise system operational security in real time. Existing researches usually explore advanced forecasting techniques for reducing statistical load forecast errors and providing better inputs to UC, while load forecasting and UC are exclusively considered as two sequential tasks. This study intends to close the loop between the two tasks by effectively incorporating certain UC information back to load forecasting models, so that day-ahead load forecasts can be improved for deriving better UC solutions in terms of a more cost-effective real-time operation with respect to actual loads. Two approaches are investigated: (i) design asymmetric error penalty functions for individual forecasting models, based on asymmetric economic impacts of under- and over-predicted load forecasts on UC solutions; and (ii) build a combining forecast framework in which weights of individual independent forecasting algorithms are determined by their economic impacts on UC solutions. Numerical cases are analysed to illustrate the effect of the proposed load forecasting models.

This work addresses the problem of assessing to which extent a bidding zone delineation requires redispatching actions after the clearing of energy markets. Such issue arises in particular when policy makers review the organisation of electricity markets and question the design of uniform price zones. To avoid relying on arbitrarily-defined sensitive parameters, the authors propose a metrics based on information that is sufficient to perform nodal pricing for the whole region under consideration. The metrics is illustrated with a realistic model of the West-European power system considering two application cases, namely (i) selecting a clustering technique to define candidate bidding zones, and (ii) selecting candidate splitting and merging options for pre-existing bidding zones. Results show that the proposed index provides a consistent order of magnitude of the redispatching needs subsequent to market clearing, although it requires no specific user-defined parameters.

Precise knowledge of faults is very exigent to reduce the outage duration as most of the customer minute losses in distribution grids occur due to longer period of interruptions caused by faults. This study proposes a fault location technique combining advanced signal processing and machine learning tools for distribution grids. The proposed technique decomposes three-phase currents measured from sending end employing wavelet transform (WT) and collects useful features to fetch them as inputs of extreme learning machine (ELM). Satisfactory values of the selected statistical performance measures validate the efficacy of proposed fault location technique. Besides, the efficacy of support vector regression (SVR) and artificial neural network (ANN) are also tested employing the WT extracted features. The presented results show the superiority of ELM-WT technique over SVR-WT and ANN-WT techniques in terms of the selected performance measures and training times. Additionally, the proposed technique is independent of fault resistance, inception angle, the presence of measurement noise, thermal expansion/contraction of the distribution line and pre-fault loading condition. Furthermore, the hybrid method detects and classifies different types of faults before locating them with different machine learning tools.

Since failure of high- to medium-voltage (MV) transformers affect a large number of consumers, they are usually built with a redundancy to guarantee service restoration in the case of a single contingency. The redundancy can be provided by a backup transformer or by transferring the load to a neighbouring substation in case of failure. While a load transfer allows for more efficient use of transformers in normal operation, it also requires the MV network to be dimensioned with redundant transmission capability for the contingency case. In this study, the authors present their approach to determine if it is profitable in the long term to remove a backup transformer in intrinsically safe substations and handle resupply with load transfer to neighbouring substations instead. To this end, they compare the cost of the necessary network expansion to the costs of a backup transformer. They introduce an iterated local search algorithm for the calculation of emergency switching plans as well as expansion of the MV network. The methodology is applied to a large real MV network group, where reinforcing the network to allow a load transfer is cost efficient compared with the existing backup transformer in three of four substations.

Sweep frequency response analysis (SFRA) is a diagnostic technique which can identify faults within transformers. Though SFRA approaches are used to identify faults, their effectiveness in discriminating two same level faults at two different locations within transformer is not much analysed and reported. Experiments were carried out on a 1 kVA, single phase, 240 V/240 V laboratory transformers and on a 315 kVA, three phase, 11 kV/433 V, Dyn11, ONAN, distribution transformer, to analyse the usefulness of SFRA in inter turn short identification and discriminations. Faulty conditions were created artificially in transformers, by shorting the tappings provided in one of their windings, at different levels and locations. Open circuit self-impedance and transfer voltage transfer function approaches were experimented and transfer function plots representing winding impedance and voltage transfer ratios at various frequencies were developed for transformers, under normal and faulty conditions. Significant differences were identified at some frequencies while comparing normal case plots with faulty case plots. It was observed that the SFRA is effective in identifying shorts within transformer winding as well as, discriminating two same level shorts (i.e.) locating shorts. Statistical analysis using absolute difference and min–max ratio also confirmed the efficacy of these approaches.

Photovoltaic (PV) grid-connected inverter is the core component of PV generation system; quickly and accurately obtaining the parameters of inverter controller has great significance in analysis of transient characteristics of PV generation system. Parameter identification relies on disturbance signals and measurements selection, and the trajectory sensitivities of inverter controller parameters are calculated with different system outputs as the measurements, the disturbance signals include AC three-phase short-circuit fault and DC voltage reference jump, accordingly, a two-step identification method is proposed, the first step use a three-phase fault to identify all voltage loop parameters and the proportional coefficient of current loop, and the second step consider a DC voltage reference jump disturbance to identify the integral coefficient of current loop and the setting inductance value. The adaptive differential evolution is taken as the identification algorithm, which adopts adaptive strategies for algorithm parameters in order to speed up the convergence and enhances the balance between the global search and local mining. The simulation analysis validates the effectiveness of this method. In addition, the impact of the inductance error on the identification is discussed.

Before restructuring in the electricity industry, the primary decision-makers of the electricity market were deemed to be power generation and transmission companies, market regulation boards, and power industry regulators. In this traditional structure, consumers were interested in receiving electricity at flat rates while paying no attention to the problems of this industry. This attitude was the source of many problems, sometimes leading to collapse of power systems and widespread blackouts. Restructuring of the electricity industry however provided a multitude of solutions to these problems. The most important solution can be demand response (DR) programs. This study proposes an economic DR model for residential consumers in liberalised electricity markets to change their consumption pattern from times of high-energy prices to other times to maximise their utility functions. This economic model is developed based on constant elasticity of substitution utility function known as one of the most popular utility functions in microeconomics. Simulation results indicate that the proposed model is adaptable to any group of residential consumers with any disposition towards participation in DR programs and can be adjusted for any time period according to the preference given by the residential consumer.

With the rapid growth of distributed generation (DG) in distribution systems, DG penetration limit is becoming a more emergent issue. The short-term voltage fluctuation resulting from the DG power fluctuation of intermittent DG sources, e.g. photovoltaic (PV) and wind power, could trigger excessive actions of a transformer with on-load tap changer (OLTC) or a feeder step-voltage regulator (SVR). In addition, DG tripping from feeder will cause sudden large voltage step change. These facts limit the maximum allowable penetration of DG in distribution networks. This study proposes the constraint models of voltage fluctuation limit on OLTC/SVR resulting from DG power fluctuation and generator disconnection to assess their impacts on the DG penetration limit. A simple optimal power flow methodology is built according to the practical criteria and applied to the practical feeder systems, to demonstrate the huge advantages of the proposed constraint models in the assessment of DG penetration limit, which also validates that both factors have significant impacts on DG hosting capacity.

Load frequency control (LFC) for power systems with governor deadband (GDB) and generation rate constraint (GRC) non-linearities is discussed in this study, with the objective to add anti-windup schemes for any designed LFC controller, so that the stability and performance of the existing LFC controller can be retained when there are non-linearities. Effects of GDB and GRC on the performance of LFC controllers are first analysed via describing function method. Anti-windup schemes are then proposed to compensate the GDB and GRC non-linearities. For GDB, the error between the realistic and the ideal outputs of the generator is added to the output of LFC controller for rejection, and for GRC, the error between the realistic and the ideal outputs of the turbine is fed back to the observer of the LFC controller for estimation and elimination. Simulation results show that the compensation schemes are effective in overcoming the adverse effects of GDB and GRC.

In view of the incorrect operation of local protection caused by multiple distributed generations (DGs) and branches in distribution system, a regional protection scheme for distribution network based on logical information is proposed here. Moreover, a regional centralised protection system in parallel with and independent from the existing protection system is constructed. First, the problems in local current protection of lines with multiple DGs and branches are analysed. On this basis, protection regionalisation is conducted according to the configuration of circuit breakers. Also then, by combining the start-up information of existing over-current protection set-I, set-II, and set-III, the operation criterion of regional protection is formed. Simulation tests on the IEEE 33-node distribution system verify that, the proposed scheme could accurately locate in-zone fault and block out-of-zone fault, accelerate protection operation, and shorten the outage time. Besides, the proposed criterion is fault tolerant due to redundancy in the multi-source information used. With small amount of information transmission, the requirement on information synchronisation is low.

In this study, the main results of a new mitigation method to single-phase auto-reclosing switching in half-wavelength transmission lines are presented. Initially, the behaviour of single-phase reclosing on conventional lines was evaluated, then, the results obtained for half-wavelength lines are presented. Finally, the proposed solution for the manoeuvre to be successfully executed is described. The study proposes a very advantageous solution for the application of the single-phase switching in half-wavelength lines.

Probabilistic information about random variables describing equipment's reliability is not complete when there is a lack of statistical data about failure. The traditional reliability assessment cannot deal with the incomplete probabilistic information. Interval probability is an efficient method to address the incomplete probabilistic information. The interval value of reliability indices can reflect the degree of completeness of probabilistic information. In this study, the optimisation model of generating systems’ imprecise reliability assessment (IRA) is established and the efficient unit-adding algorithm is proposed to obtain the upper and lower bounds of reliability indices. The probability density and the expectation of reliability indices are also calculated by the Monte Carlo simulation method. In the process of IRA, massive calculations of the traditional reliability are needed, therefore the recursive convolution algorithm, which is based on the outage capacity table and has the merit of high-computation efficiency, is adopted. A case study on a revised IEEE-RTS79 system shows the rationality and equity of the presented method.

This study presents two-level static and dynamic responsive load scheduling strategies for optimal tradeoff between scheduling preferences of demand response provider (DRP), demand response provider agent (DRPA) and distribution system operator (DSO) using moving time horizon control for real-time scheduling. The first level comprises of DRP scheduling with the objective of minimizing the electricity bill payments. The second stage includes a rescheduling strategy aided by DSO scheduling preferences constrained by the economic preferences of consumers set up in the first level of the scheduling strategy. There are two strategies for the second level: namely, static residential demand response (S-RDR), and dynamic residential demand response (D-RDR), which differ by the time sequence of operation and interactions between DRPA and DRPs. In S-RDR, the interactions between the two are limited to single event-acknowledge policy wherein all the DRPs act to schedule their responsive loads in a day ahead fashion. However, in D-RDR, multiple/continuous iterations take place between DRPA and DRPs with the consideration of optimal performance with respect to real-time market prices. The proposed framework is simulated using IEEE 34 bus distribution system. The simulation results are presented and discussed to analyse and compare the performance of proposed scheduling strategies with tariff-based and centralized scheduling approaches.

In a smart grid environment, the utilities, which electric power distribution companies with different pricing strategies, are interested in demand side management (DSM) schemes to achieve reduction in peak demand. Utilities provide additional benefits and encourage the consumers to have direct interaction with the grid by actively participating in DSM programs. An intelligent residential load management system (IRLMS) is proposed for consumers to attain reduction in electricity bill and avail more incentive from the utility by responding to their DSM schemes. The IRLMS attempts to reduce the electricity bill and maintain the total load under maximum demand limit by scheduling the schedulable loads while considering the operating dynamics of non-schedulable loads. The IRLMS scheduler is built with two different techniques, namely priority-based scheduling algorithm and optimisation-based scheduling algorithm for different utility tariff methods such as flat rate tariff and real time pricing, respectively. The IRLMS model is implemented in MATLAB and the results illustrate significant benefits for both consumers and utility.

The low-frequency oscillation has become one of the most threatening problems of the electrical power system in the past few decades. The traditional Prony analysis method is seriously affected by noise and order estimation which cannot get the dominant oscillation sometime. A singular value decomposition-difference differential method is proposed for order estimation of Prony mode. A parameter optimisation method based on interior point method is also proposed eliminating the noise effects on dominant model parameters. The proposed method has a fairly good property in noise suppression and dominant oscillation mode tracking. The suitability of the proposed method had been demonstrated in the simulation and case study.

The performance of air-cooled units is significantly affected by meteorological conditions because they use the ambient air directly as the cooling medium. The purpose of this study is to determine the influence of air-cooled units on grid stability under extreme meteorological conditions. Based on the characteristics of air-cooled units, cooling air face velocity and temperature are two main meteorological factors taken into consideration. A dynamic model of the air-cooled units is developed. Since grid frequency is a representation of grid stability, the above model is then applied to a mathematical model to analyse the primary frequency regulation process of a grid. A coefficient to measure the primary frequency regulation ability (PFRA) is defined and the calculation of PFRA is put forward. To increase the reliability of the study, the performance of the grid under different meteorological conditions is also studied in frequency domain. Case studies under generator tripping and steep load rising conditions are studied. The corresponding PFRA and the maximum capacity proportion of air-cooled units are calculated. This study provides a constructive guide for the operation of air-cooled units under different meteorological conditions.

A distribution static compensator (DSTATCOM) is used for power quality improvement in the distribution system. In the conventional DSTATCOM, the dc voltage is kept constant and it is selected based on rated reactive load. Under light load or reduced load conditions, the compensator works perfectly even though the dc voltage is reduced from its rated value. Maintaining the dc voltage constant under reduced or light load conditions leads to unnecessary voltage stress across the switching devices. Therefore, in this study, a simple dynamic dc voltage regulation is proposed to reduce the voltage stress across switching devices under the reduced load conditions. The proposed algorithm optimises the value of dc voltage based on reactive load without compromising the performance of the DSTATCOM. To validate the proposed method, simulation and experimental studies were carried out on the three-phase two-level split-capacitor DSTATCOM for harmonic mitigation, reactive power compensation and load balancing.

This study proposes a decentralised droop control method for guaranteeing precise load sharing among distributed resources in an islanded microgrid. Distributed resources are usually fed through power electronic converters and the switching harmonics produced by them are eliminated by third-order output LCL filters. Output impedance is considered as a major factor for finding exact power-angle droop coefficient in droop design – neglecting this factor can affect the load sharing accuracy. Even though an acceptable active power sharing can be achieved with higher droop gains, increased droop gain may adversely affect the microgrid stability. Here, a modified angle droop control is proposed such that the dependence on the output inductance on the real power sharing is removed. Thus, the lower droop coefficients are sufficient for droop sharing and the system stability is not endangered. It has been assumed that the microgrid is converter-dominated, where a proportional-resonant controller has been utilised for converter switching control. This controller has an outer voltage loop and an inner current loop. A harmonic term has been added to the voltage loop to facilitate more accurate reactive power sharing. Simulation studies are conducted using PSCAD/EMTDC to validate the efficacy of the proposed controller.

As a significant demand response resource, air conditioning (AC) loads can respond to control signals quickly by on–off switches to provide fast regulation service. A uniform-time state bin aggregate model (UTIM) with higher accuracy is introduced and the corresponding modelling constraints are first presented. Then, based on the UTIM, a novel aggregate control model that takes into account both the external control signals and the time delay of the AC compressor is proposed to follow the dynamic collective behaviour of ACs, which will make the UTIM more practical and accurate. To relieve the communication burden and reduce the number of switching times, a generalised control method is also proposed to control ACs through the global signal. The simulation results show that considering the time delay of the compressor, the novel aggregate control model can track the collective performances of ACs more closely. In addition, the proposed control method needs fewer control signals and switch times.