The Protectorate is a relatively neglected topic in seventeenth century English history, especially compared to the vast literature on the causes of the civil war and the Glorious Revoltion of 1688/9.

The most thorough chronological study of the Protectorate are the four volumes written between Samuel Gardiner and his student Charles Firth. They are Gardiner, History of the Commonwealth and Protectorate, Volumes 3 and 4. Firth's are The Last Years of the Protectorate Volume 1 and 2. Gardiner had intended to cover the whole of the Protectorate but unfortuneatly died before he could finish the last two volumes.

Of the more recent short surveys, the best two are Hutton, British Republic, 2nd edition (2000), and Barnard, English Republic, 2nd edition (1997). Hutton is the preferable of the two, mainly because he is a more enjoyable writer. Barry Coward's biography of Cromwell is alright, but his more recent The Cromwellian Protectorate is better suited to your question. Lastly, Little and Smith's Parliaments and Politics during the Cromwellian Protectorate is the most recent (and thorough) monograph in the literature.

So, first of all, Cromwell's position as Lord Protector takes its name and function from a position that already existed in English tradition. When a minor inherited the thrown, a Lord Protector was appointed to oversee the workings of government on their behalf. The most recent examples to Englishmen in 1653 were Lord Somerset and Lord Northumberland, both Lord Protectors for Edward VI (Loach, Edward VI; Woodford, Perceptions of a Monarchy Without a King, p. 14). While there are some disagreements about the theoretical limitations of Cromwell's power, in practice he was a monarch with an advisory council and a parliament (Hutton, British Republic). He adminstered the assizes & quarter sessions, initiated policy with advice from his council, (Woolrych, "The Cromwellian Protectorate: A Military Dictatorship?" History Volume 75 (1990) pp. 207-231), made proclamations, could pardon persons convicted of felony (Gardiner, History of the Commonwealth, 4:10, 264), kept a "court" in the monarchical sense, and was able to negotiate foreign policy (Roberts, Swedish Diplomats at Cromwell's Court, introduction). All of these had been major components of early Stuart monarchy.

There were some limitations on Cromwell's power, though whether some of these were a concious choice by Cromwell, or whether they were actually impossible is an ongoing debate. Cromwell refused royal title and hereditary succession (Richard Cromwell is a whole other issue), he refused to dissolve a parliament against it's will (James I in 1614 and Charles I in 1629 & 1640 being the major examples). Cromwell, at his swearing in ceremony (a republican reflection of the coronation) swore to uphold the laws and customs of England, Ireland and Scotland, an act which Barnard and Woolrych take quite seriously. Cromwell did have an advisory council, and like the Monarchs, most members had close familial or personal ties to Cromwell (Coward, Cromwellian Protectorate, p. 31). The Council of State was intended to play a major role in the governance of the realm, though how effective it was in asserting itself independently of Cromwell is debatable. In the end, between the three tiers of government (Protector, Council & Parliament), Cromwell had the largest concentration of power, and was able to exert his influence over the other branches. The major difference between how he exerted influence compared to Charles and James was that Cromwell's authority was derived from his personal charisma and ability to manipulate/influence people, and the large military force he commanded. Cromwell went out of his way to ensure that the army was appeased, as it had a direct connection to his ability to maintain stability in England (Hutton, pp. 58-60).