POWER systems are undergoing a major transformation

Transcription

1 1 Generic Demand Model Considering te Impact of Prosumers for Future Grid Scenario Analysis Sariq Riaz, Student Member, IEEE, Hesamoddin Marzoogi, Member, IEEE, Gregor Verbič, Senior Member, IEEE, Arcie C. Capman, Member, IEEE, and David J. Hill, Life Fellow, IEEE arxiv:16.833v [mat.oc] 13 Sep 217 Abstract Te increasing uptake of residential PV-battery systems is bound to significantly cange demand patterns of future power systems and, consequently, teir dynamic performance. In tis paper, we propose a generic demand model tat captures te aggregated effect of a large population of price-responsive users equipped wit small-scale PV-battery systems, called prosumers, for market simulation in future grid scenario analysis. Te model is formulated as a bi-level program in wic te upper-level unit commitment problem minimizes te total generation cost, and te lower-level problem maximizes prosumers aggregate self-consumption. Unlike in te existing bi-level optimization frameworks tat focus on te interaction between te wolesale market and an aggregator, te coupling is troug te prosumers demand, not troug te electricity price. Tat renders te proposed model market structure agnostic, making it suitable for future grid studies were te market structure is potentially unknown. As a case study, we perform steady-state voltage stability analysis of a simplified model of te Australian National Electricity Market wit significant penetration of renewable generation. Te simulation results sow tat a ig prosumer penetration canges te demand profile in ways tat significantly improve te system loadability, wic confirms te suitability of te proposed model for future grid studies. Index Terms Demand response, aggregators, prosumers, PVbattery systems, generic demand model, future grids, scenario analysis, bi-level optimization. NOMENCLATURE B Set of buses. G Set of generators g. M Set of demand aggregators m. L Set of lines: L B B. R Set of regions r. H Set of time slots. x/x Minimum/maximum value of x. r g +/ Ramp-up/down rate of supplier g. τg u/d Minimum up/down time of supplier g. B i,j Susceptance of line between buses i and j. θ i, Voltage angle at bus i in. p i,j l, Power flow on line i-j: p i,j l, = B i,j(θ i, θ j, ). Sariq Riaz, Gregor Verbič, Arcie C. Capman, and David J. Hill are wit te Scool of Electrical and Information Engineering, Te University of Sydney, Sydney, New Sout Wales, Australia. s: sariq.riaz, gregor.verbic, arcie.capman, david.ill@sydney.edu.au. Hesamoddin Marzoogi is wit Scool of Engineering and Tecnology, Central Queensland University (CQ University), Brisbane, Australia. .marzoogi@cq.edu.au. Sariq Riaz is also wit te Department of Electrical Engineering, University of Engineering and Tecnology Laore, Laore, Pakistan. David J. Hill is also wit te Department of Electrical and Electronic Engineering, Te University of Hong Kong, Hong Kong. Power loss on line i-j. p g, Generated power of supplier g in. p m b, Battery storage power of aggregator m in. e m b, Battery storage state of carge of aggregator m in. p inf,m d, Inflexible demand of aggregator m in. p i,j l, p u,m d, Flexible demand of aggregator m in. d, Underlying prosumer demand of aggregator m in. p m pv, PV generation of aggregator m in. p res r, Required reserve in region r in te system in. s g, Binary decision variable on/off status of supplier g. u g, Binary start-up decision variable of supplier g. d g, Binary sut-down decision variable of supplier g. c fix/var c su/sd η b g Fix/variable cost of supplier g. g Start-up/sut-down cost of supplier g. Battery round-trip efficiency. λ Dual variable associated wit an equality constraint. µ Dual variable associated wit an inequality constraint. b Binary variable introduced to maintain complementary slackness. M Large positive number used in te MILP formulation of te lower-level KKT conditions. I. INTRODUCTION POWER systems are undergoing a major transformation driven by te increasing uptake of variable renewable energy sources (RES). At te demand side, te emergence of cost-effective beind-te-meter distributed energy resources, including on-site generation, energy storage, electric veicles, and flexible loads, and te advancement of sensor, computer, communication and energy management tecnologies are canging te way electricity consumers source and consume electric power. Indeed, recent studies suggest tat rooftop PVbattery systems will reac retail price parity from 22 in te USA grids and te Australian National Electricity Market (NEM) [1]. A recent forecast by Morgan Stanley as suggested tat te uptake can be even faster, by boldly predicting tat up to 2 million Australian ouseolds could install battery storage by 22 [2]. Tis as been confirmed by te Energy Networks Australia and te Australian Commonwealt Scientific and Industrial Researc Organisation (CSIRO) wo ave estimated te projected uptake of solar PV and battery storage in 2 to be 8 GW and 1 GW [3], wic will represent between 3% % of total demand, a scenario called Rise of te Prosumer [4]. Here, te prosumer tey refer to is a smallscale (residential, commercial and small industrial) electricity consumer wit on-site generation. A similar trend as been

2 2 observed in Europe as well []. Given tis, it is expected tat a large uptake of demand-side tecnologies will significantly cange demand patterns in future grids 1, wic will in turn affect teir dynamic performance. Existing future grid feasibility studies [6] [1] typically use conventional demand models, possibly using some euristics to account for te effect of emerging demand-side tecnologies, and te synergies tat may arise between tem. Tey also assume specific market arrangements by wic RES are integrated into grid operations. Te callenge associated wit future grid planning is tat te grid structure and te regulatory framework, including te market structure, cannot be simply assumed from te details of an existing one. Instead, several possible evolution pats need to be accounted for. Future grid planning tus requires a major departure from conventional power system planning, were only a andful of te most critical scenarios is analyzed. To account for a wide range of possible future evolutions, scenario analysis as been proposed in many industries, e.g. in finance and economics [11], and in energy [12] [14]. As opposed to power system planning were te aim is to find an optimal transmission and/or generation expansion plan, te aim in scenario analysis is to analyze possible evolution patways to inform policymaking. Given te uncertainty associated wit long-term projections, te focus of future grid scenario analysis is limited to te analysis of wat is tecnically possible, altoug it migt also consider an explicit costing [1]. Our work is part of te Future Grid Researc Program funded by te CSIRO, wose aim is to explore possible future patways for te evolution of te Australian grid out to 2 by looking beyond simple balancing. To tis end, a compreensive modeling framework for future grid scenario analysis as been proposed in [16], wic includes a market model, power flow analysis, and stability analysis. Te demand model, owever, assumes tat te users are price-takers, wic does not properly capture te aggregated effect of prosumers on te demand profile, as discussed later. A. Related Work Due to te influence of a demand profile on power systems performance and stability, recent studies ave attempted to integrate te aggregated impact of prosumers into te demand models [17] [22]. Te focus, owever, is usually on sceduling of particular emerging demand-side tecnologies, e.g. HVAC [17] [19], flexible loads [2], PV-battery systems [21], and plug-in electrical veicles (PEVs) [22]. Most of tese modeling approaces assume an existing market structure, wit te impact of prosumers incorporated by allowing demand and supply to interact in some limited or predefined ways. Specifically, tis is mainly done via tree different approaces: 1) Only te supply-side is modeled pysically wile prosumers are considered by a simplified representation of demand-side tecnologies. In [2], flexible loads effects 1 We interpret a future grid to mean te study of national grid type structures wit te above-mentioned transformational canges for te long-term out to 2. on reserve markets are analyzed by modeling prosumers wit a tank model; owever, te reserve market is greatly simplified. In [17], prosumers are represented by a priceelasticity matrix, wic is used to model canges in te aggregate demand in response to a cange in te electricity price, and are acquired from te analysis of istorical data. 2) Demand-side tecnologies are pysically modeled wile a simplified representation of supply-side is employed. For instance, in [21], te supply-side is represented by an electricity price profile. 3) Bot supply and demand sides can be modeled pysically and optimized jointly, as in [18], [22], wic can produce more realistic results. For example, te study in [22] integrates te aggregated carging management approaces for PEVs into te market clearing process, wit a simplified representation of te latter. Altoug te above models ave sown teir merits, tey are dependent on specific practical details suc as te electricity price or te implementation of a mecanism for demand response (DR) aggregation, wic limits teir usefulness for future grid scenario analysis were te detailed market structure is potentially unknown. Against tis backdrop, te paper proposes a principled metod for generic demand modeling including te aggregated effect of prosumers. Te model is formulated as a bi-level program in wic te upper-level unit commitment problem minimizes te total generation cost, and te lower-level problem maximizes te aggregate prosumers self-consumption. In more detail, te lower-level objective is motivated by te emerging situation in Australia, were rooftop PV owners are increasingly discouraged from sending power back to te grid due to very low PV feed-in-tariffs versus increasing retail electricity prices. In tis setting, an obvious cost-minimizing strategy is to install small-scale battery storage, to maximize self-consumption of local generated energy and offset energy used in peak pricing periods. Similar tariff settings appear likely to occur globally in te near future, as acknowledged in [23]. Moreover, self-consumption witin an aggregated block of prosumers is a good approximation of many likely beaviors and responses to oter future incentives and market structures, suc as (peak power-based) demand carges, capacity constrained connections, virtual net metering across connection points, transactive energy and local energy trading, and a (somewat irrational) desire for self-reliance. A key difference from existing bi-level optimization frameworks is tat in our formulation, te levels are coupled troug te prosumers demand, not troug te electricity price. In contrast, oter models, wic focus on te interaction between an aggregator and te prosumers [19] or te aggregator and te wolesale market [22], couple te levels troug prices. Tese approaces essentially define a market structure, tat is, a pricing rule to support an outcome. In contradistinction, our proposed model is market structure agnostic. Tat is, it implicitly assumes tat an efficient mecanism for demand response aggregation is adopted, wit prices determined by tat unspecified mecanism, wic support te outcomes computed by our optimization framework.

3 3 Te paper builds on our previous work [24], [2]. In [2], we ave assumed tat a prosumer aggregation represents a omogeneous group of loads; tat is, we ave assumed tat tey all beave in te same way and ave te same capacity, and are allowed to send power back to te grid. In te absence of an explicit transmission pricing, tis can create perverse outcomes, suc as power excange between aggregators located in different parts of te network. In te model proposed in tis paper, te aggregators are not allowed to send te power back to te grid, wic better models te assumption of self-consumption witin an aggregated block of prosumers. Te model proposed in [24] is similar to te model in tis paper, owever, te prosumer battery storage is modeled implicitly, wic requires a euristic searc to capture te prosumer beavior. Te remainder of te paper is organized as follows: Section II presents te proposed modeling framework. In Section III, te efficacy of te proposed framework is demonstrated on a simplified 14-generator network model of te NEM wit a significant RES penetration. Finally, Section IV concludes. II. GENERIC DEMAND MODEL CONSIDERING THE IMPACT OF PROSUMERS Generic demand models are essential for power system studies. Tey are commonly used to reflect te aggregated effect of numerous pysical loads [26], [27]. Conventional demand models only account for te accumulated effect of independent load canges and some relatively minor control actions, tat is, tey are by necessity simplified to not include all details of te loads. In te following, we explain te motivation beind tis work and te modeling assumptions. A. Researc Motivation and Modeling Assumptions Te main purpose of developing generic demand models is to provide accurate dispatc decisions for balancing and stability analysis of future grid scenarios. Given te uncertainty associated wit future grid studies, te modeling framework sould be market structure agnostic, and capable of easy integration of various types and penetrations of emerging demand-side tecnologies. To tis effect, we make te following assumptions: 1) Te loads are modeled as price anticipators. It is well understood tat price-taking load beavior, wic simply responds to a given price profile, can result in load syncronization, i.e. all users move teir consumption to a low-price period, resulting in an inefficient market outcome. In contrast, price anticipatory loads influence te electricity price by playing a game wit te wolesale market. Te game is captured by te proposed bi-level model. Specifically, te price-anticipating assumption implies tat te aggregate effect of te prosumers is to cange te market clearing prices and quantities, and, moreover, tat te prosumers ave a model of tis effect. Given tis, te prosumer aggregation bids follow an equilibrium strategy, wit an accurate expectation about te response of te market; tis is te standard reasoning beind a Cournot or Stackelberg game formulation corresponding to a bi-level optimization problem. Tis equilibrium strategy can be tougt of as being generated by te following iterative process: First, te market operator creates a price profile by clearing te market based on te predicted demand. Second, te prosumers (and oter price-anticipatory participants) respond by sifting teir consumption to ceaper time slots. Tis gives a new demand profile, and te market operator clears te market again, and te process repeats until convergence. Note tat te proposed model does not specify an iterative mecanism, but rater, it encodes te optimality conditions for any price profile for te prosumers in Karus-Kun-Tucker (KKT) conditions, and in tis way it captures te outcome resulting from te price-anticipatory prosumer beavior. In our previous work [16], [28], we modeled te loads as pricetakers, inspired by te smart ome concept [29], in wic te loads respond to te electricity price to minimize energy expenditure. Te study as sown tat wit large penetration of price-taking prosumers, te marginal benefit migt become negative wen secondary peaks are created due to te load syncronization (see Fig. 1 sowing te operational demand wit different penetrations of prosumers). Terefore, demand response aggregators (encefort simply called aggregators) ave started to emerge to fully exploit te demand-side flexibility. To tat effect, te model implicitly assumes an efficient mecanism for demand response aggregation (an interested reader migt refer to [3] for a discussion on practical implementation issues). However, specific implementation details, like price structure or te division of te profit earning by te aggregated collection of prosumers, are not of explicit interest in te proposed model. 2) Te demand model representing an aggregator consists of a large population of prosumers connected to an unconstrained distribution network wo collectively maximize self-consumption (made possible by an efficient internal trading and balancing mecanism). 3) Aggregators do not alter te underlying power consumption of te prosumers. Tat is, except for battery losses, te total power consumption before and after aggregation remains te same; owever, te grid power intake profile does cange, as a result of te prosumers using batteries to maximize self-consumption. 4) Prosumers ave smart meters equipped wit ome energy management (HEM) systems for sceduling of te PV-battery systems. Also, a communication infrastructure is assumed tat allows a two-way communication between te grid, te aggregator and te prosumers, facilitating energy trading between prosumers in te aggregation. Tese assumptions appear to be appropriate for scenarios arising in time frame of several decades into te future. B. Bi-level Optimization Framework In te model, we are specifically interested in te aggregated effect of a large prosumer population on te demand profile,

4 Power (GW) Power (GW) 4 12 Price takers No prosumers Low prosumers Hig prosumers G 1 G 2 G n 1 8 p G1 p G2 p Gn Market Price anticipators No prosumers Low prosumers Hig prosumers p d inf,m p b m Bus i p d flx,m p d u,m Aggregator m p pv m Time (ours) Fig. 2. Structure of te proposed modeling framework. Fig. 1. Operational demand wit different penetrations of price-taking (top) and price-anticipating prosumers (bottom). assuming tat te prosumers collectively maximize teir selfconsumption. Given tat te objective of te wolesale market is to minimize te generation cost, te problem exibits a bilevel structure. In game teory, suc ierarcical optimization problems are known as Stackelberg games. Tey can be formulated as bi-level matematical programs of te form [19]: minimize x,y subject to Φ (x, y) (x, y) Z y S = arg min{ω (x, y) : y C (x)} y were x R n, y R m, are decisions vectors, and Φ (x, y) : R n+m R and Ω (x, y) : R n+m R are te objective functions of te upper- and te lower-level problems, respectively. Z is te joint feasible region of te upper-level problem and C(x) te feasible region of te lower-level problem induced by x. In te existing market models tat adopt a ierarcical approac, te coupling variable y is te electricity price (e.g. [19], [22]). Tat is, te upper-level (te wolesale market in our case) determines te price scedule, wile te lower-level (te aggregator acting on bealf of te prosumers), optimizes its consumption based on tis price scedule. Fig. 2 sows te structure of te proposed modeling framework. Te demand model consists of two parts: (i) inflexible demand, p inf,m d, wit a fixed demand profile, representing large industrial loads and loads witout flexible resources; and (ii) flexible demand, d, comprising a large population of prosumers wo collectively maximize self-consumption. Note tat not every bus in te system as a load connected to it, ence te distinction between an aggregator m M and bus i B. Unlike in most existing studies, te interaction between te wolesale market and te aggregators in our model is troug te demand profile of te aggregator, d. Note tat in contradistinction to te price-taking assumption wen te electricity price is known in advance, now te collective action of te prosumers affects te wolesale market dispatc, wic is te salient feature of te proposed model. C. Upper-level Problem (Wolesale Market) To emulate te market outcome, te upper-level problem is cast as a unit commitment (UC) problem aiming to minimize te generation cost: minimize s,u,d,p,θ ( Hg G c fix g s g, +c su g u g, +c sd g d g, +c var g p g, ), (1) were s g,, u g,, d g, {, 1}, p g, R +, θ i, R are te decision variables of te problem. Te problem is subject to te following constraints: p g, = (p inf,m d, + d, ) + (p l, + p l, ), (2) g G i m M i l L i B i,j (θ i, θ j, ) p l, (3) p g s g, p g, p g s g,, (4) u g, d g, = s g, s g, 1, () (p g sync R gs g, p g, ) p res r,, (6) u g, + τ u g 1 d = g,+ 1, (7) d g, + τ d g 1 = g,+ 1, (8) rg p g, p g, 1 r g +, (9) { } arg min p flx d,pb,eb d, subject to (12)-(1), (1) H were (2) is te power balance equation at eac bus i in te system 2, wit G i, M i, L i representing respectively te sets of generators, aggregators and lines connected to bus i, and p inf,m d,, pflx,m d,, pi,j l, and pi,j l, representing respectively te inflexible and flexible demand of aggregator m, line power and line power loss (assumed to be 1% of te line flow) on eac line connected to bus i; (3) represents line power limits; (4) limits te dispatc level of a generating unit between its respective minimum and maximum limits; () links te status of a generator unit to te up and down binary decision variables; (6) ensures sufficient spinning reserves are available in reac region of te grid; (7) and (8) ensure minimum up and 2 Note tat te flexible demand of eac aggregator m, d,, couples te upper-level (wolesale market) problem wit eac of te m lower-level (aggregator) problems.

5 minimum down times of te generators; (9) are te generator ramping constraints; and (1) is te constraint resulting from te prosumer aggregation optimization problem, as explained in Section II-D. D. Lower-level Problem (Aggregators) Te prosumer aggregation is formulated in te lower-level problem. Te loads witin an aggregator s domain are assumed omogeneous, wic allows us to represent te total aggregator s demand wit a single load model. Te flexibility provided by te battery is only used to maximize self-consumption, wit grid supply readily available. Tis implies tat te endusers power consumption pattern is left unaltered, so tat teir comfort is not jeopardized. Te coupling between te upper-level (wolesale) and te lower-level (retail) problem in te proposed model is troug te power demand. Tis removes te need to define te market in terms of a pricing mecanism or rule, and it follows tat te electricity price is not explicitly sown in te optimization problem. Tis is wy it is called a generic model. Tis approac stands in contrast to oter existing bi-level formulations [19], [22], in wic te loads and wolesale market are coupled troug te electricity price. Te prices generated by any market depend inerently on te specific pricing mecanism adopted. However, in practice, several different pricing rules can implement a desired outcome, including te widely-used uniform price reverse auction or nodal pricing mecanisms. For example, te electricity price could comprise te dual variables associated wit te power balance constraint (2) and power flow constraints (3) of te upperlevel problem, plus retail/aggregator and network carges. Moreover, a range of different pricing rules result in different retail/aggregator and network carges, wit all supporting an efficient outcome. However, by instead coupling te upper- and lower-level problems via power demand, our proposed model avoids te need to specify a particular pricing rule, wic makes it market-structure agnostic (see also Assumptions 1 and 2 in Section II-A). Noneteless, it is fair to assume tat in any practical system, users will ave access to a price forecast 3 and oter bidders istorical beavior but tese are all market design-specific. In te absence of pricing rule details, te proposed optimization model does not require suc information. Specifically, te lower-level problem is formulated as follows for eac demand aggregator m M: minimize p flx d,pb,eb H d,, (11) were te decision variables of te problem are flexible demand p flx d, battery power p b, and battery capacity e b. Te 3 Note tat in a HEM problem [29], a HEM system is an agent acting on bealf of a prosumer, and te electricity price is known aead of time, resulting in a price-taking beavior. problem is subject to te following constraints: d, = p u,m d, pm pv, + p m b,, (12) e m b, = ηb m e m b, 1 + p m b,, (13) p m b pm b, p m b, (14) e m b e m b, e m b, (1) were (12) is te power balance equation; and (13)-(1) are te battery storage constraints. Power p u,m d, is te underlying power demand of te prosumers. Note tat according to te Assumption 3 in Section II-B, except for battery losses, te underlying power demand does not cange, owever te power intake from grid can. Finally, te KKT optimality conditions of te lower-level problem are added as te constraints to te upper-level problem, wic reduces te problem to a single mixed integer linear program tat can be solved using of-teself solvers. Note tat because te two levels interacts troug a power, not troug a price, unlike in [19], no linearization is required. III. CASE STUDIES To sowcase te efficacy of te model, we analyze steadystate voltage stability of a simplified model of te NEM wit scenarios reflecting different prosumer penetrations. A. Model of te Australian National Electricity Market (NEM) Te 14-generator IEEE test system sown in Fig. 3 was initially proposed in [31] as a test bed for small-signal analysis. Te system is loosely based on te NEM, te interconnection on te Australian eastern seaboard. Te network is stringy, wit large transmission distances and loads concentrated in a few load centers. It consists of 9 buses, 28 loads, and 14 generators. Te test system consists of four areas representing te states of Queensland, New Sout Wales, Victoria and Sout Australia, and 28 aggregators, one for eac load bus. Te generator tecnologies and modeling assumptions follow [24]. We consider two RES penetration rates. In te business as usual (BAU) scenario, te generation portfolio includes GW coal,.22 GW gas, and 2.33 GW ydro. In te ig-res scenario, 4 % of te total demand is covered by variable RES. Inspired by two recent Australian 1% renewables studies [6], [1], part of coal generation is replaced wit wind and utility PV using wind and solar traces from te AEMO s planning document [32], wic results in GW coal,.22 GW gas, 2.33 GW ydro, 21 GW wind, and 12 GW utility PV. Given te deterministic nature of te model, we assume 1 % reserves for eac region in te system to cater for demand and RES forecast errors. In market simulations, generators are assumed to bid according to teir sort-run marginal costs, wile RESs bid at zero cost. Simulations are performed using a rolling orizon approac wit ourly resolution assuming a perfect foresigt. Te optimization orizon is tree days wit a two-day overlap. Last, wind and solar generators are assumed to operate in a voltage control mode.

6 6 SESA Wind Farm Utility PV ADE NSA NNS NQ SWQ NCEN NVIC CAN SWNSW Fig. 3. Single-line diagram of te 14-generator model of te NEM wit te 16 zones tat define wind and solar traces [32]. B. Prosumer Scenarios We assume four different prosumer penetrations: zero, low, medium and ig. Wit no prosumer penetration, te demand is assumed inflexible. For te oter tree scenarios, we assume tat part of te demand is equipped wit small-scale (residential and small commercial) PV-battery systems. Te uptake of PV loosely follows a recent AEMO study [33]. Te PV capacities are respectively GW, 1 GW, and 2 GW for te low, medium and ig uptake of prosumers (te existing penetration in te NEM is GW). We consider tree different amounts of storage: zero, 2 kw, and 4 kw of storage for 1 kw of rooftop PV. 4 Hourly demand and PV traces are from te AEMO s planning document [32]. C. Dispatc Results Dispatc results for a typical summer week wit ig demand (12-1 January) for a few representative scenarios are sown in Figs. 4 and. Te figures sow, respectively, generation dispatc results (top row), combined flexible demand of all aggregators (middle row), and a combined battery carging profile of all aggregators (bottom row). Fig. 4 sows results for a medium prosumer penetration wit, respectively, zero, 2 and 4 ours of storage. Fig. sows results for 4 A typical ratio in te NEM today is 2 of storage [33], owever, in te future, tis will likely increase due to te anticipated cost reduction. MEL LV CQ SEQ different prosumer penetrations (zero, medium, ig) wit 4 of storage. Observe tat in all six cases peak demand occurs at mid-day due to a ig air-conditioning load. After te sunset, owever, te demand is still ig, so gas generation is needed to cover te gap. In te available generation mix, gas as te igest sort-run marginal cost, wic increases te electricity price in late afternoon/early evening. Te balancing results over te simulated year ave revealed tat te increased RES penetration in te renewable scenarios requires more energy from gas generation compared to te BAU scenario. Tis is due to RES intermittency, and te ramp limits of conventional coal-fired generation. An increased penetration of prosumers wit iger amounts of storage, owever, reduces te usage of gas due to a flatter demand profile. Observe in Fig. 4 ow an increasing amount of storage increases prosumers self-sufficiency. Witout storage, te load is supplied by PV during te day, and te rest is supplied from te grid. Wen storage is added to te system, batteries are carged wen electricity is ceap (mostly from rooftop PV during te day and from wind during te nigt) and discarged in late afternoon to offset te demand wen te electricity is most expensive. Note tat te plots in te bottom two rows sow a combined load profile of all aggregators in te system, wic explains wy storage is seemingly carged and discarged simultaneously. Observe ow ig amounts of storage (rigtmost columns in Figs. 4 and ) flatten te demand profile. During te day, te flexible demand is supplied by rooftop PV, wic reduces te operational demand, wile during te nigt, wit sufficient wind generation, batteries are carged, wic increases te operational demand. Tis as a significant beneficial effect on loadability and voltage stability, as discussed in te next section. D. Loadability and Voltage Stability Results Dispatc results from te market simulations are used to perform a load flow analysis, wic is ten used in te assessment of loadability and voltage stability. In te analysis, only scenarios wit 4 of storage were considered. Te prosumer scenarios are tus called, according to te respective penetration rates, zero (ZP), low (LP), medium (MP), and ig (HP). Note tat te market model only considers a simplified DC power flow wit te maximum angle limit set to 3. Tis can sometimes result in a non-convergent AC power flow in scenarios wit a ig RES penetration. Te number of non-convergent ours is, respectively, 17, 37, 12, and, in scenarios ZP, LP, MP, and HP. An increased penetration of prosumers tus improves voltage stability, as explained in more detail later. In loadability assessment, N-1 security is considered, so a contingency screening is performed first. We screened all credible N-1 contingencies to identify te most severe ones based on te maximum power transfer level [34]. Twenty most critical contingencies were selected for eac our of te simulated year. 1) Loadability calculation: To calculate system loadability (LDB), te load in te system is progressively increased using te results of te market dispatc as te base case. After eac

7 7 Hydro Brown Coal Black Coal WF Utility PV GT Op. Demand p d inf +p d u p inf Power (GW) u Rooftop-PV to Load Grid to Load Battery to Load p d Rooftop-PV to battery (Carg) Grid to Battery (Carg) Battery to load (Discarg) Time (ours) Fig. 4. Dispatc results for a typical summer week wit ig demand (12-1 January) for a medium prosumer penetration wit different amounts of storage: zero (left), 2 (middle) and 4 (rigt). Hydro Brown Coal Black Coal WF Utility PV GT Op. Demand p d inf +p d u p inf Power (GW) u Rooftop-PV to Load Grid to Load Battery to Load p d Rooftop-PV to battery (Carg) Grid to Battery (Carg) Battery to load (Discarg) Time (ours) Fig.. Dispatc results for a typical summer week wit ig demand (12-1 January) for different penetrations of prosumers wit 4 of storage: zero (left), medium (middle), ig (rigt). increase, load flow is calculated twice; first for te case after te last load increase witout a contingency, and ten again for eac of te preselected critical contingencies. Wen te load flow does not converge for a particular contingency, te last convergent load flow solution witout a contingency is considered te loadability margin. We considered two different load increase patterns, were load and generation are increased uniformly, in proportion to te base case: (i) NEM: only load and generation in te NEM are increased; (ii) SA/VIC: only load in VIC and generation in SA are increased. Te results are summarized in Table I. Comparing te BAU scenario and te renewable scenario wit conventional demand (ZP), it can be seen tat wit te increased RES penetration, te average loadability margin over te simulated year in te demand increase scenario NEM is decreased from 7.8 GW to 2. GW. Similarly, te average loadability margin in te demand increase scenario SA/VIC is reduced from 2.2 GW to.8 GW. Wit a ig RES penetration, conventional syncronous generation is replaced by inverter-based generation wit inferior reactive power support capability, wic results in a reduced reactive power margin in te system and ence lower stability margin. Wit an increased penetration of prosumers, te system loadability improves. Observe tat te average system loadability margin in bot load increase scenarios, NEM and SA/VIC, is increased from 2. GW and.8 GW for te renewable scenario wit no prosumers (ZP) to 7.1 GW and 1.7 GW for ig penetration of prosumers (HP), respectively, wic indicates a considerable improvement in te system loadability margin. Tis is explained by a demand reduction wen prosumer demand is supplied by rooftop PV. In te nigt ours, owever, even wit ig prosumer penetration, te loadibility can be reduced wen prosumers carge teir batteries, as observed in Figs. 4 and. Te situation is furter illustrated in Fig. 6 tat compares te loadability margin for For syncronous generation, a.8 power factor is assumed. For RES, we used te reactive power capability curve for te generic GE Type IV wind farm model [3], in wic te reactive power generation is significantly constrained close to te nominal active power generation. In practice, detailed planning studies are required before connection is granted, wic can result in an increased requirement for reactive power support.

8 Real(eigenvalue) (Neper/s) Loadability Margin (GW) 8 TABLE I LOADABILITY RESULTS 8 Loadability analysis BAU Low prosumer penetration Hig prosumer penetration Avg. LDB margin (GW) LDB Cases Scenarios BAU ZP LP MP HP NEM SA/VIC TABLE II MODAL ANALYSIS RESULTS Modal analysis BAU Low prosumer penetration Hig prosumer penetration Scenarios BAU ZP LP MP HP Avg. of minimum Real(eig) (Neper/s) Nodes wit igest participation factor in critical voltage modes Unstable ours te load increase scenario NEM and te results of te modal analysis, discussed next. 2) Modal analysis: Using te market dispatc results, modal analysis of te reduced V-Q sub-matrix of te power flow Jacobian is performed to assess voltage stability. Te smallest real part of te V-Q sub-matrix eigenvalues is used as a relative measure of te proximity to voltage instability. Furtermore, te associated eigenvectors provide information on te critical voltage modes and te weak points in te grid, tat is, te areas tat are most prone to voltage instability. Te results are summarized in Table II. Wit te increased RES penetration, te average of te minimum of te real part of all eigenvalues, encefort called te minimum eigenvalue, is reduced from 49. Np/s for te BAU scenario to 42.3 Np/s for te ZP scenario. Wit an increased prosumer penetration, te average of te minimum eigenvalue over te simulated year increases from 42.3 Np/s (ZP) to 48.8 Np/s (HP). Observe in Fig. 6 tat te results of te modal analysis confirm te results loadability analysis. Te general trend remains te same; iger RES penetration wit conventional demand reduces te minimum real value of an eigenvalue, wic implies a lower voltage stability margin. Anoter observation tat can be made from te modal analysis concerns te location of te weak points in te system, tat is, te buses wit te igest participation factor in te critical voltage modes. Tese clearly cange wit te increased RES penetration. In te BAU Scenario, te weakest points are typically buses wit large loads (e.g. 36 and 38, representing Melbourne). Wit te increased RES penetration and no prosumers (ZP), owever, te weakest part of te system become buses located close to RESs (e.g. and 41, representing, respectively a large wind farm in SA and a large solar PV farm in QLD). Furter, we observed tat te voltage stability margin in te system improves significantly wen tere are more syncronous generators in te grid, due to teir superior reactive power support capability compared to RES. Te participation factor analysis of te renewable scenarios revealed tat SA and QLD are te most voltage constrained regions were te penetration of WFs and utility PVs is iger compared to Time (ours) Fig. 6. Comparison of te loadability and modal analysis results for a typical summer week wit ig demand (12-1 January) for te load increase scenario NEM for BAU, and low and ig prosumer penetration. oter regions in te NEM, wic can be, to a large extent, mitigated wit a sufficiently large penetration of prosumers. Tis clearly illustrates tat RESs and prosumers cange power system stability in ways tat ave not been experienced before, wic requires a furter in-dept analysis. IV. CONCLUSION Te emergence of demand side tecnologies, in particular rooftop PV, battery storage and energy management systems is canging te way electricity consumers source and consume electric power, wic requires new demand models for te long-term analysis of future grids. In tis paper, we propose a generic demand model tat captures te aggregate effect of a large number of prosumers on te load profile tat can be used in market simulation. Te model uses a bi-level optimization framework, in wic te upper level employs a unit commitment problem to minimize generation cost, and te lower level problem maximizes collective prosumers selfconsumption. To tat effect, te model implicitly assumes an efficient mecanism for demand response aggregation, for example peer-to-peer energy trading or any oter form of transactive energy. Given tat any efficient mecanism for demand response aggregation tat aims to minimize generation cost will utilize self-generation first, te self-consuming assumption appears reasonable at te level of abstraction assumed in long-term future grid scenario analysis. Moreover, te model is generic in tat it does not depend on specific practical implementation details tat will vary in te long-run. To sowcase te efficacy of te proposed model, we study te impact of prosumers on te performance, loadability and voltage stability of te Australian NEM wit a ig RES penetration. Te results sow tat an increased prosumer penetration flattens te demand profile, wic increases loadability and voltage stability, except in situations wit a low underlying demand and an excess of RES generation, were te aggregate demand migt increase due to battery carging. Te analysis also revealed tat wit a ig RES penetration, te weakest points in te network move from large load

9 9 centers to areas wit ig RES penetration. Also, loadability and voltage stability are igly dependent on te amount of syncronous generation due to teir superior reactive power capability compared to RES, wic requires furter analysis. Our future work will focus on designing market mecanisms for large scale aggregation of distributed energy resources to enable te participation of prosumers in power system operation. APPENDIX MILP FORMULATION OF THE LOWER-LEVEL KKT OPTIMALITY CONDITIONS For te sake of completeness, we provide te complete optimization problem below. Te upper-level problem (1)-(9) remains te same. Te price-anticipatory prosumer beavior is captured in constraint (1), defined as te solution to te lowerlevel prosumer aggregation problem. To be able to incorporate it in te upper-level problem, we first need to convert it into a set of MILP constraints. We do tat by using te optimality (KKT) conditions of te underlying optimization problem. Te KKT conditions follow from te associated Lagrangian: L(x, λ, µ) = f(x) + λ g(x) + µ (x), (16) were x = {p flx d, p b, e b } is te decision vector of te lowerlevel problem; f(x) is te objective function (11); g(x) is te vector of equality constraints (17)-(18); (x) is te vector of inequality constraints (19)-(23); λ = {λ m,p, λ m,e } is te vector of Lagrange multipliers associated wit te equality constraints, and µ = {µ flx,m, µ m,p, µ m,p, µ m,e, µm,e } is te vector of Lagrange multipliers associated wit te inequality constraints. Te KKT optimality conditions consist of: primal feasibility (17)-(23) wit te associated Lagrange multipliers given in parenteses: d, + pm pv, p m b, p u,m d, =, (λm,p ) (17) e m b, ηb m e m b, 1 p m b, =, (λ m,e ) (18) d,, (µ flx,m ) (19) p m b pm b,, (µ m,p ) (2) dual feasibility: p m b, p m b, (µ m,p ) (21) e m b em b,, (µ m,e ) (22) e m b, e m b, (µ m,e ) (23) µ flx,m stationarity (2)-(27):, µ m,p, µ m,p, µ m,e, µm,e, (24) L d, = 1 + λ m,p µ flx,m =, (2) L p m b, L e m b, = λ m,p = λ m,e λ m,e µ m,p + µ m,p =, (26) ηb m λ m,e +1 µm,e + µ m,e =, (27) complementary slackness (28)-(32): d, µflx,m =, (28) ( p m + b pm b,)µ m,p =, (29) ( p m b, + p m b )µ m,p =, (3) ( e m b + e m b,)µ m,e =, (31) ( e m b, + e m b )µ m,e =. (32) Complementary slackness conditions (28)-(32) are bilinear, owever tey can be linearized by introducing one binary variable b and a sufficiently large and positive constant M resulting in two constraints per complementarity slackness condition (42)-(1). Given tat te KKT conditions are sufficient and necessary for optimality, te bi-level constraint (1) can be replaced wit mixed integer linear constraints (33)-(1): d, + pm pv, p m b, p u,m d, =, (33) e m b, ηb m e m b, 1 p m b, =, (34) 1 µ flx,m + λ m,p =, (3) λ m,p µ m,p + µ m,p λ m,e =, (36) µ m,e + µ m,e + λ m,e ηb m λ m,e 1 =, (37) p m b pm b,, (38) p m b, p m b, (39) e m b e m b,, (4) e m b, e m b, (41) d, µ flx,m M flx b flx,m, (42) M flx (1 b flx,m ), (43) p m b, M p b m,p, (44) µ m,p M p (1 b m,p ), (4) p m b, M p b m,p, (46) µ m,p M p (1 b m,p ), (47) e m b, M e b m,e, (48) µ m,e M e (1 b m,e ), (49) e m b, M e b m,e, () µ m,e M e (1 b m,e ), (1) wic adds te following additional decision variables to te upper-level problem (1)-(9): b flx,m, b m,p, b m,p, b m,e, bm,e {, 1},, λ m,e R,, em b,, µ flx,m, µ m,p, µ m,p, µ m,e, µm,e R +. p m b,, λ m,p d, Te resulting optimization problem is an MILP tat can be solved efficiently wit off-te-self solvers. REFERENCES [1] EPRI, Te Integrated Grid Realizing te Full Value of Central and Distributed Energy Resources, Tec. Rep., 214. [2] Morgan Stanley, Australia Utilities Asia Insigt: Solar & Batteries, Tec. Rep., 216.

10 1 [3] Energy Networks Australia and CSIRO, Electricity Network Transformation Roadmap: Key Concepts Report, Tec. Rep. December, 216. [4] CSIRO, Future Grid Forum: Cange and Coice for Australian Electricity System, Tec. Rep., 213. [] B. Kampman, M. Afman, and J. Blommerde, Te potential of energy citizens in te European Union, CE Delft, Tec. Rep., 216. [6] M. Wrigt and P. Hearps, Zero Carbon Australia Stationary Energy Plan, Te University of Melbourne Energy Researc Institute, Tec. Rep., 21. [7] B. Elliston, I. MacGill, and M. Diesendorf, Least Cost 1% Renewable Electricity Scenarios in te Australian National Electricity Market, Energy Policy, vol. 9, pp , Aug [8] C. Budiscak, and et al., Cost-Minimized Combinations of Wind Power, Solar Power and Electrocemical Storage, Powering te Grid up to 99.9% of te Time, Journal of Power Sources, vol. 22, pp. 6 74, Mar [9] I. G. Mason, S. C. Page, and A. G. Williamson, A 1% renewable electricity generation system for New Zealand utilising ydro, wind, geotermal and biomass resources, Energy Policy, vol. 38, pp , Aug. 21. [1] Australian Energy Market Operator (AEMO), 1 per cent renewable study - modelling outcomes, Tec. Rep., 213. [11] L. Faey and R. M. Randall, Learning From te Future. Wiley, [12] J. Foster, C. Froome, C. Greig, O. Hoeg-Guldberg, P. Meredit, L. Molyneaus, T. Saa, L. Wagner, and B. Ball, Delivering a competitive Australian power system Part 2: Te callenges, te scenarios, Tec. Rep. Oct, 213. [13] G. Sancis, e-higway2: Europe s future secure and sustainable electricity infrastructure. Project results. Tec. Rep., 21. [14] M. Hand, S. Baldwin, E. DeMeo, J. Reilly, T. Mai, D. Arent, G. Porro, M. Mesek, and D. Sandor, Renewable Electricity Futures Study), National Renewable Energy Laboratory (NREL), Tec. Rep., 212. [1] B. Elliston, J. Riesz, and I. MacGill, Wat cost for more renewables? Te incremental cost of renewable generation An Australian National Electricity Market case study, Renewable Energy, vol. 9, pp , 216. [16] H. Marzoogi, D. J. Hill, and G. Verbič, Performance and stability assessment of future grid scenarios for te Australian NEM, in 214 Australasian Universities Power Engineering Conference (AUPEC), Sep 214. [17] F. Ramos, C. Cañizares, and K. Battacarya, Effect of price responsive demand on te operation of microgrids, in 18t International Conference on te Power Systems Computation (PSCC 214), Aug 214. [18] K. Bruninx, D. Patteeuw, E. Delarue, L. Helsen, and W. D aeseleer, Sort-term demand response of flexible electric eating systems: Te need for integrated simulations, in 1t International Conference on te European Energy Market (EEM 212), May 212. [19] M. Zugno, J. Miguel Morales, P. Pinson, and H. Madsen, A bilevel model for electricity retailers participation in a demand response market environment, Energy Economics, vol. 36, pp , 213. [2] S. Matieu, Q. Louveaux, D. Ernst, and B. Cornelusse, A quantitative analysis of te effect of flexible loads on reserve markets, in 18t International Conference on te Power Systems Computation (PSCC 214), Aug 214. [21] O. Mégel, J. L. Matieu, and G. Andersson, Sceduling distributed energy storage units to provide multiple services under forecast error, International Journal of Electrical Power & Energy Systems, vol. 72, pp. 48 7, 21. [22] M. Gonzalez Vaya, and G. Andersson, Optimal bidding strategy of a plug-in electric veicle aggregator in day-aead electricity markets under uncertainty, IEEE Transactions on Power Systems, vol. 3, no., pp , Sep 21. [23] S. Teske, T. Brown, E. Tröster, P.-P. Scierorn, and T. Ackermann, PowE[R] 23 - A European Grid for 3/4 Renewable Energy by 23, Greenpeace Germany, Tec. Rep., 214. [24] H. Marzoogi, G. Verbič, and D. J. Hill, Aggregated demand response modelling for future grid scenarios, Sustainable Energy, Grids and Networks, vol., pp , 216. [2] S. Riaz, H. Marzoogi, G. Verbič, A. C. Capman, and D. J. Hill, Impact study of prosumers on loadability and voltage stability of future grids, in 216 IEEE International Conference on Power System Tecnology (POWERCON), 216. [26] P. Kundur, Power System Stability and Control. EPRI Power System Engineering Series, McGraw-Hill, [27] T. Van Cutsem, and C. Vournas, Voltage Stability of Electric Power Systems, ser. Kluwer international series in engineering and computer science. Springer, [28] H. Marzoogi, D. J. Hill, and G. Verbič, Aggregated Effect of Price- Taking Users Equipped wit Emerging Demand-Side Tecnologies on Performance of Future Grids, in 216 IEEE International Conference on Power System Tecnology (POWERCON), 216. [29] H. Tiscer, and G. Verbič, Towards a Smart Home Energy Management System-A Dynamic Programming Approac, in Innovative Smart Grid Tecnologies Asia, 211. [3] A. C. Capman, G. Verbič, and D. J. Hill, Algoritmic and strategic aspects to integrating demand-side aggregation and energy management metods, IEEE Transactions on Smart Grid, vol. 7, no. 6, pp , Nov 216. [31] M. Gibbard, and D. Vowles, Simplified 14-generator model of te SE Australian power system, Te University of Adelaide, Tec. Rep., 21. [32] Australian Energy Market Operator (AEMO), 212 NTNDP Assumptions and Inputs, Tec. Rep., 212. [33], Emerging Tecnologies Information Paper, National Electricity Forecasting Report, Tec. Rep., 21. [34] E. Vaaedi, C. Fucs, W. Xu, Y. Mansour, H. Hamadanizade, and G. K. Morison, Voltage stability contingency screening and ranking, IEEE Transactions on Power Systems, vol. 14, no. 1, pp , Feb [3] K. Clark, N. W. Miller, and J. J. Sancez-Gasca, Modeling of GE Wind Turbine Generators for Grid Studies, Tec. Rep., 213. Sariq Riaz (S 14) received te B.Sc. and M.Sc. degrees in electrical engineering from te University of Engineering and Tecnology Laore, Laore, Pakistan in 29 and 212, respectively. He is currently pursuing te P.D. degree from Te University of Sydney, Sydney, Australia. His expertise is in power system operation, demand response, and electricity markets. His current researc interests include integration of renewable generation, storage and prosumers into electricity markets, demand response and operation of concentrated solar termal plants. Hesamoddin Marzoogi (S 13-M 16) graduated wit Bacelor and Masters degrees in electrical engineering (power) bot wit first class onors from Siraz University, Iran in 29 and 211, respectively. He was awarded is PD degree in electrical engineering (power) at Te University of Sydney in 216. He is now a researc associate at Te Central Queensland University (CQUniversity), Australia, and an academic visitor at Te University of Mancester, UK. Hesamoddin s researc interests are in stability analysis and control of power systems wit ig penetration of renewable energy sources, distributed generation and energy storage, planning of future grids, and applications of intelligent systems in power engineering. Gregor Verbič (S 98-M3-SM 1) received te B.Sc., M.Sc., and P.D. degrees in electrical engineering from te University of Ljubljana, Ljubljana, Slovenia, in 199, 2, and 23, respectively. In 2, e was a NATO-NSERC Postdoctoral Fellow wit te University of Waterloo, Waterloo, ON, Canada. Since 21, e as been wit te Scool of Electrical and Information Engineering, Te University of Sydney, Sydney, NSW, Australia. His expertise is in power system operation, stability and control, and electricity markets. His current researc interests include integration of renewable energies into power systems and markets, optimization and control of distributed energy resources, demand response, and energy management in residential buildings. He was a recipient of te IEEE Power and Energy Society Prize Paper Award in 26. He is an Associate Editor of te IEEE Transactions on Smart Grid.

11 Tecnology, Teran, Iran. He is currently working toward te P.D. degree at Te University of Sydney. His researc interests include power system stability and control, integration of renewable energy sources into power systems, and smart grid tecnologies. David J. J. Hill Hill (S 72-M 76-SM 91-F 93-LF 14) (S'72 M'76 SM'91 F'93 LF'14) re- receivedtetep.d. degree in in electrical engineering from te University of Newcastle, Australia, in He He olds olds te te Cair of ofelectrical Engineering in te Department of Electrical and Electronic Engineering at te Universityof Hong of Hong Kong. Kong. He is also He aispart-time also a part-time Professor Professor Electrical of Electrical Engineering Engineering at Te University at Te University of Sydney, of Australia. Sydney, During Australia. 2 21, During 221, e was an e Australian was an Researc AustralianCouncil Researc Federation Council Fellow Federation te Fellow Australian at te National Australian University. National Since University. 1994, e Since as 1994, eld various e as eld positions various at positions te University at te of University Sydney, of Australia, Sydney, including Australia, te including Cair of teelectrical Cair ofengineering Electrical Engineering until 22until and again 22 and during again during along witalong an ARC wit Professorial an ARC Professorial Fellowsip. He Fellowsip. as also eld He as academic also eld and academic substantialand visiting substantial positions visiting at tepositions universities at te of Melbourne, universities of California Melbourne, (Berkeley), California Newcastle (Berkeley), (Australia), Newcastle Lund (Australia), (Sweden), Lund Munic, (Sweden), Hong Munic, Kong (City Hong andkong Polytecnic). (City andhis Polytecnic). general researc His general interests researc are ininterests control systems, control complex systems, networks, complex power networks, systemspower and stability systems analysis. and stability His work analysis. now are in His mainly work onis control now mainly and planning on control of future and planning energy networks of futureand energy basicnetworks stability and control basic stability questions andfor control dynamic questions networks. for dynamic networks. Prof. Hillisisa a Fellowof of te te Society Society for Industrial for Industrial and Applied and Applied Matematics, Matematics, te Australian te Australian Academy Academy of Science, of Science, and te Australian and te Australian Academy Academy of Tecno- of Tecnological Sciences Sciences and Engineering. and Engineering. He is also He is a Foreign also a Foreign Member Member of te of Royal te Royal Swedis Swedis Academy Academy of Engineering of Engineering Sciences. Sciences. In 2, e was a Nort Atlantic Treaty Organization-Natural Sciences and Engineering Researc Council of Canada Post-Doctoral Fellow wit te University of Waterloo, Waterloo, ON, Canada. 11 Since 21, e as been wit te Scool of Electrical and Information Engineering, University of Sydney, Sydney, NSW, Australia. His expertise is in power system operation, stability Arcie and control, C. Capman and electricity (M 14) markets. receivedhis tecurrent B.A. researc interests include degree integration mat of renewable and political energies science, intoand power te B.Econ. systems and markets, optimization(hons.) and control degree of distributed from te University energy resources, of Queensland, demand response, and energy management Brisbane, inqld, residential Australia, buildings. in 23 and 24, respectively, of te IEEE and Power te P.D. anddegree EnergyinSociety computer Prize science Paper Dr. Verbič was a recipient Award in 26. He is an associate from teeditor University of te IEEE of Soutampton, TRANSACTIONS Soutampton, ON SMART GRID. U.K., in 29. He is currently a Researc Fellow in Smart Grids wit te Scool of Electrical and Information Engineering, Centre for Future Energy Networks, Te University of Sydney, Sydney, NSW, Australia. Jin Ma (M'6) He as received expertise te B.S. is inand game-teoretic M.S. degree and reinforcement learning from tecniques Zejiangfor University, optimization Hangzou, and control Cina, in inlarge 1997 distributed systems. His researc and 2, focuses respectively, on integrating and te renewables P.D. degree into legacy from power networks, using distributed Tsingua energy University, and load Beijing, sceduling Cina, metods, in 24, and allon in designing tariffs and market electrical mecanisms engineering. tat support efficient use of existing infrastructure and new controllable From 24 devices. to 213, e was a Faculty Member of Nort Cina Electric Power University. Since September, 213, e as been wit te Scool of Electrical and Information Engineering, University of Sydney. His major researc interests are load modeling, nonlinear control system, dynamic power system, and power system economics. Dr. Ma is a registered Cartered Engineer in te U.K. He is te member of CIGRE W.G. C4.6 Modeling and aggregation of loads in flexible power networks and te corresponding member of CIGRE Joint Workgroup C4-C6/ CIRED Modeling and dynamic performance of inverter based generation in power system transmission and distribution studies.